QVF format specification (v1)

Status: Normative. This document specifies the QVF v1 container format and its producer/consumer contract. The machine-readable contract is the JSON Schema qvf_manifest.schema.json (shipped alongside this file); where prose and schema disagree, the schema wins. This is a self-contained copy of the specification maintained by the vibe-qc project, distributed under Apache-2.0 so that any code can implement a conforming producer or consumer.

QVF (.qvf, “Quantum Visualization Format”) is a ZIP-based container for quantum-chemistry visualization and analysis data. It keeps one calculation’s structure, scalar fields, spectra, bands, trajectories, wavefunctions, provenance, and viewer hints in a single random-access file, instead of scattering them across Cube, XYZ, Molden, XSF, log, and program-specific sidecar files. It is also a document format for the steps before a calculation: the species of a reaction scheme with their chemical identity (§ 5.1), the scheme that relates them (§ 5.14), the jobs to run on them (§ 5.9) and a picture of the whole (§ 5.15) travel in one file that the calculation’s results later join.

The format is intended for the whole quantum-chemistry ecosystem. A QVF producer may be any quantum-chemistry code. A QVF consumer may be a structure viewer, a band plotter, a spectrum tool, a validator, a notebook script, or a GPU viewer.

QVF v1 is deliberately not a restart format. It does not encode integral caches, SCF internal state, engine-internal grids, or every possible wavefunction representation. The optional wavefunction.gto section is a visualization-oriented, Molden-like molecular-orbital carrier, not a universal restart record.

The keywords MUST, MUST NOT, REQUIRED, SHOULD, SHOULD NOT, and MAY are used as in RFC 2119.

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1. Design goals

1. One shareable artifact. A calculation’s visualization data travels as one .qvf file.

2. Random access. A consumer reads only the members it needs.

3. Typed payloads. Every member declares format, dtype, shape, and a sha256 checksum where applicable.

4. Stable common vocabulary. Common data types use canonical section kinds.

5. Partial support. A consumer can support a subset of kinds and still open the file. Unsupported vendor sections are reported, not misinterpreted.

6. Producer neutrality. source.program can name any code; core kinds are not producer-specific.

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2. Archive model

A QVF file is a ZIP archive. The only mandatory member is manifest.json at the archive root. Every other member is named from the manifest — member paths are part of the manifest contract, not hard-coded by the container.

A typical archive:

example.qvf
├── manifest.json          (REQUIRED — the only member read by name)
├── structure/
│   └── structure.json
├── wavefunction/
│   ├── basis.json
│   ├── mo_metadata.json
│   └── mo_coefficients.dat
├── volumes/
│   ├── density.dat
│   └── density_grid.json
├── spectra/
│   └── ir.json
└── citations/
    └── references.bib

Path layout is not semantic. Consumers MUST follow the path fields in manifest.json and MUST NOT assume ZIP entry order or directory names. Producers SHOULD use stable, readable directory names for debuggability.

2.1 Byte-level container requirements

• The archive MUST be a valid ZIP (PKZIP APPNOTE, deflate/store methods).

• manifest.json MUST be present at the archive root (path exactly manifest.json, no leading directory). In an archive updated in place, which holds more than one entry of that name, the manifest is the entry whose central-directory record comes last (§ 2.3).

• Producers SHOULD store manifest.json uncompressed (STORE method) so a consumer can read the table of contents cheaply; other members SHOULD be DEFLATE-compressed. Neither is mandatory — a consumer decompresses via the ZIP method recorded in the central directory regardless.

• Producers SHOULD write manifest.json last (or ensure its recorded checksums match the already-written member bytes). Because each member’s sha256 is embedded in the manifest, all member bytes must be finalized before the manifest is serialized.

• Member paths — every path in the manifest and every ZIP entry name — MUST be relative and use / as the only separator: a path MUST NOT contain a backslash (\) or a NUL character, MUST NOT begin with / or with a drive-letter prefix (^[A-Za-z]:), and MUST NOT contain any .. path segment. (Schema: ZipPath expresses the leading-/, NUL, and .. rules; validators enforce all of them, § 6.)

• Each ZIP entry name MUST occur only once in the archive, with one exception: an archive updated in place holds its superseded manifest.json entries until it is repacked (§ 2.3). The ZIP format permits duplicate names and readers disagree on which entry wins, so an archive that duplicates any other name is ambiguous; a consumer SHOULD refuse to open it.

• Every ZIP entry other than the current manifest.json and directory entries (names ending in /) SHOULD be referenced by a member path. An unreferenced (“orphan”) entry, a superseded manifest.json included, does not make the archive invalid — it is the expected by-product of updating an archive in place (§ 2.3) — and consumers never read it, because members are reached only through the manifest (§ 2). Validators report it as a warning (§ 6).

• A consumer SHOULD enforce resource caps before decompressing or parsing anything — per-member and total uncompressed size, compression ratio, and JSON size and nesting depth — to guard against zip-bomb and parser-exhaustion inputs. The sizes are recorded in the ZIP central directory, so they can be checked without decompressing; a reader MUST NOT inflate an entry past the uncompressed size recorded for it. § 6.1 lists the reference values; the reference tools cap each member at 8 GiB (1 gigavoxel of float64).

2.2 Endianness

All binary members are stored in little-endian byte order. QVF v1 dtype names (§ 4.2) do not carry a byte-order mark. Producers on big-endian platforms MUST byte-swap to little-endian before writing.

The optional root field byte_order (§ 3.1) states this explicitly. Its only valid value in v1 is "little", and it documents what every v1 archive already is: an archive without the field is little-endian too, and a consumer MUST NOT read its absence as an unknown byte order. Any other value is invalid — the JSON Schema rejects it, so a validator reports E_SCHEMA (§ 6) — and a consumer SHOULD refuse an archive that carries one rather than guess how to read its binary members. Producers MAY write the field; the reference writers write it in every archive.

The tag belongs in the dtype names themselves (<f8 rather than float64), where it would describe each binary member. That changes the dtype vocabulary every consumer validates, so it cannot happen within v1; it is recorded as a candidate for the next major version (V2-01 in docs/format_review.md), and byte_order is the v1 declaration until then.

2.3 Updating an archive in place

A producer may change an existing archive without rewriting it: a runner that executes a pending job.spec archive and writes its results back (§ 5.9), a program that saves live checkpoints of a running calculation (§ 3.2), a tool that adds an analysis to a finished archive. The ZIP format allows this by appending. This section fixes how a QVF archive is appended to, so that every consumer reads an updated archive the same way.

An update:

1. MAY append new ZIP entries. The producer leaves the bytes of the existing entries where they are, writes the new entries after the last of them (where the old central directory began), and then writes a new central directory that lists every entry of the archive, old and new, in the order of their data.

2. MUST write a new manifest.json as the last entry of the archive, after every member it references; like any manifest it SHOULD be stored uncompressed (§ 2.1). The new manifest is complete: it lists every section of the updated archive, and its member specs reference the entries the update appended as well as the earlier entries it keeps, whose bytes, sha256 and size (§ 4.2) are unchanged.

3. MUST NOT give a new entry the name of an existing entry, other than manifest.json. A member whose content changes is written under a new path, and the new manifest references that path.

The previous manifest.json, and every entry the new manifest no longer references (a replaced member, the members of a removed section), are superseded. They stay in the archive as orphans (§ 2.1): a consumer MUST ignore them, and a validator reports each one as the warning W_ORPHAN_MEMBER. They still count towards the total-size cap of § 6.1.

A consumer that reads manifest.json by name MUST use the entry whose central-directory record comes last when the archive holds more than one entry of that name. This is the one exception to the rule that entry names are unique (§ 2.1): a validator reports E_ZIP_DUPLICATE_ENTRY for any duplicated name except manifest.json, and for a duplicated manifest.json it reports W_ORPHAN_MEMBER for each superseded copy. Because an update writes its manifest last, a reader that walks the local headers in data order instead of reading the central directory also meets the current manifest last.

Repacking writes the archive anew from its current manifest: every entry the manifest references, then the manifest, and nothing else. It removes every orphan and every superseded manifest and changes no member’s bytes, so the sha256 and size values of the manifest stay valid. The reference toolkit provides it as the repack operation (informative).

The updated manifest records what changed:

• metadata.modified_utc (§ 3.5) SHOULD be set to the time of the update; metadata.created_utc and metadata.uuid MAY be kept, because the archive is the same archive, changed.

• provenance.run_status (§ 3.2) follows the calculation’s lifecycle: a pending archive becomes running while a runner writes checkpoints, and converged or failed when it settles.

• Each program run an update records is a run.record section (§ 5.8). When an archive carries several, their sequence fields order them: an update adds its run record with the next sequence and keeps the earlier ones unchanged.

• A job.spec section is kept verbatim (§ 5.9), so a settled archive still records what was asked.

Appending overwrites the old central directory, so an update interrupted before it writes the new one leaves an archive that cannot be opened. A producer that must not lose the previous state writes the updated archive to a copy and renames it over the original (informative).

2.4 File identification

A QVF archive is identified to operating systems, file managers and web servers by the names below. Every program that reads or writes QVF files SHOULD declare them exactly as given, so that the desktop associates .qvf files with one type whichever program installed it last.

Identifier	Value
File name extension	.qvf (lowercase when written; matched case-insensitively)
Media type	application/vnd.vibe-qc.qvf+zip
macOS Uniform Type Identifier	com.vibe-qc.qvf, conforming to public.zip-archive and public.content
Type description	QVF quantum-chemistry archive

The media type is in the IANA vendor tree with the registered +zip structured-syntax suffix (RFC 6838, RFC 6839): a generic ZIP tool may open the archive, and a program that knows the type reads it as QVF. It is the type a web server sends for a .qvf file and the one a desktop entry or file association names. A QVF archive has no magic number of its own beyond the ZIP signature, and the manifest is written last (§ 2.1), so content sniffing cannot tell it from other ZIP files; programs identify it by the extension, or by finding manifest.json with a qvf_version.

registry.json carries the same values under file_type, and spec/file-type/ carries the declarations ready to copy (informative):

• qvf-uti.plist — the macOS type declaration, the dictionary that goes into an application’s UTImportedTypeDeclarations (or UTExportedTypeDeclarations) array in Info.plist, with the type’s description, conformance, the extension and the media type. One program of a family of applications exports the type and the others import it; the declarations are identical, so macOS resolves the type the same way whichever of them is installed.

• qvf-mime.xml — the freedesktop.org shared-mime-info definition, a subclass of application/zip matched by the glob *.qvf, for Linux desktops (installed into $XDG_DATA_HOME/mime/packages/ or /usr/share/mime/packages/ and activated with update-mime-database).

On Windows, the file association’s Content Type value is the media type.

A picture of the archive, for a file manager’s thumbnail or a quick-look preview, is the thumbnail member of its first preview section (§ 5.15).

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3. The manifest

3.1 Root object

{
  "qvf_version": 1,
  "schema_uri": "https://vibe-qc.org/spec/qvf/1/manifest.schema.json",
  "byte_order": "little",
  "source": {
    "program": "my-code",
    "version": "1.2.3",
    "calculation": "h2o_rhf_sto3g"
  },
  "sections": [ /* … */ ]
}

Root field	Required	Meaning
qvf_version	yes	Integer format version. v1 = 1.
source	yes	{program, version, calculation}, all strings; program and version non-empty.
sections	yes	Array of section objects (§ 4).
schema_uri	no	Canonical URI of the JSON Schema. Informational.
byte_order	no	Byte order of every binary member. The only valid value is "little", which every v1 archive is whether it declares it or not (§ 2.2).
provenance	no	Calculation-level metadata (§ 3.2).
metadata	no	Descriptive metadata of the archive itself: title, authors, licence, identifiers, time stamps (§ 3.5).
viewer_defaults	no	Viewer hints: auto_open, camera bookmarks, the initial camera, a crossfade and per-section hint objects (§ 3.4). The keys auto_open, bookmarks, camera and crossfade are reserved, so no section may use one as its id (§ 4.1).
thermochemistry	no	Root thermochemistry block (§ 3.3).
dipole_moment	no	Root dipole block (§ 3.3).
constraints	no	Root geometry-constraint block (§ 3.3).
energies	no	Root energies block: the energy of the primary result, its components, and energies by method (§ 3.6).
extensions	no	Extension governance block (§ 7).

Producers MUST emit qvf_version: 1. A consumer that only understands v1 MUST refuse to open a file whose qvf_version is an unrecognized major version — with the one historical exception below.

Historical note — archives stamped qvf_version: 2. vibe-qc v0.10.0 – v0.15.x stamped qvf_version: 2 on archives containing a periodic reaction.path. That bump was a mistake: the only difference from v1 is a single optional member (lattice on reaction.path, § 5.5), which is the additive case that the versioning policy says must not bump the version. The bump was withdrawn by a governance ruling on 2026-07-10 (see GOVERNANCE.md § Version history).

Such archives are v1-compatible. Consumers SHOULD accept qvf_version: 2 and treat it as 1. Producers MUST NOT emit it. A periodic reaction path is detected by the presence of the lattice member, never by the manifest version.

A validator treats such an archive as qvf_version: 1 for every check, the JSON Schema check included, and reports the warning W_VERSION_WITHDRAWN (§ 6): the archive is valid, and the warning records that its producer wrote a version producers must not write. A tool that updates such an archive in place (§ 2.3) writes qvf_version: 1 and the v1 schema_uri into its new manifest. Every other value of qvf_version is the error E_VERSION.

3.2 provenance

Optional and open (additionalProperties: true): a key that is not in the table below is allowed, and a consumer ignores one it does not know. A producer emits only what it knows. The recognised fields are typed by the schema’s root provenance property:

Field	Type	Unit	Meaning
method	string	—	Method of the calculation, e.g. "rhf". Beyond SCF it names the SCF method whose energy scf_energy is (§ 3.6).
functional	string	—	Exchange–correlation functional of a DFT method.
basis	string	—	Basis-set name.
charge	integer	e	Net charge.
multiplicity	integer	—	Spin multiplicity 2S+1.
n_electrons	integer ≥ 0	—	Number of electrons the calculation treats explicitly, the same quantity as basis.n_electrons (§ 5.3): the total electron count minus the core electrons an ECP replaces.
n_scf_iterations	integer ≥ 0	—	Number of SCF iterations.
scf_converged	boolean	—	Whether the SCF converged.
scf_energy	{value, units}	units is a unit name (§ 4.3), conventionally hartree	Energy of the SCF method that method names.
fermi_energy	{value, units}	units is a unit name, conventionally ev	Fermi energy.
wall_seconds	number ≥ 0	s	Wall-clock time of the calculation.
dimensionality	integer, 0–3	—	Echo of the structure’s periodic-axis count (§ 5.1): informational here, and never a substitute for reading pbc.
run_status	enum	—	The archive’s place in a calculation’s lifecycle; see below.
checkpoint	object	—	Informative bookkeeping of a running snapshot, with a monotonic seq; see below. The schema does not type it.
software	array of software objects	—	The programs and libraries that produced the results; see below.
git_commit	string, 7–64 hexadecimal characters	—	The producer’s own source revision: a git commit hash, abbreviated or full (40 characters for SHA-1, 64 for SHA-256). Git prints lowercase.
n_threads	integer ≥ 1	—	Threads the calculation ran with, per process.
n_mpi_ranks	integer ≥ 1	—	MPI ranks (processes); 1 for a serial run.
n_gpus	integer ≥ 0	—	GPUs the calculation used; 0 for none.
started_utc	string	UTC	When the calculation started, in the form below.
finished_utc	string	UTC	When the calculation finished, in the same form.
hostname	string	—	Deprecated; see below.

scf_energy and fermi_energy carry the unit names of § 4.3; the legacy spellings Eh, eV and Hartree are accepted there but deprecated. started_utc and finished_utc take the form of the time stamps of the root metadata block (§ 3.5): an ISO 8601 date and time in UTC, YYYY-MM-DDThh:mm:ssZ, optionally with a fractional second, the trailing Z required. A validator checks the form (§ 6), not the truth or the order of the two. n_threads, n_mpi_ranks and n_gpus record what the run used; the resources a job.spec asks for are hints (§ 5.9), and the two need not agree. A pending archive has not run, so these fields and the time stamps, when it carries them, describe the step that prepared it.

Agreement with the sections. provenance.n_electrons, when present, MUST agree with basis.n_electrons of a wavefunction.gto section (§ 5.3) that states one.

software is an array of objects, one per program or library, each $defs/ProvenanceSoftware (strict: only the fields below and vendor keys beginning x_). The root source names the QVF producer (§ 3.1) and run.record.program the code that ran (§ 5.8); software lists every component that shaped the numbers, such as an integral library or an exchange–correlation library.

Field	Type	Required	Meaning
name	string, non-empty	yes	Name of the program or library, e.g. "integral-lib".
version	string	no	Version, as the component reports it.
url	string	no	Where the component is published, e.g. its home page. A public address only: machine names and internal addresses are private operational detail, like hostname below.

"provenance": {
  "method": "rks", "functional": "pbe",
  "software": [{"name": "my-code", "version": "1.2.3"},
               {"name": "integral-lib", "version": "2.9.0",
                "url": "https://example.org/integral-lib"}],
  "git_commit": "9f2b6c1d4e7a",
  "n_threads": 8, "n_mpi_ranks": 4, "n_gpus": 0,
  "started_utc": "2026-10-07T12:00:00Z", "finished_utc": "2026-10-07T12:07:31Z",
  "wall_seconds": 451.0
}

One provenance field has normative lifecycle semantics:

• run_status — one of "pending", "running", "converged", "failed"; the archive’s place in a calculation’s lifecycle. pending describes a job that has not yet run — typically a container carrying a structure (§ 5.1) plus a job.spec (§ 5.9) and no result sections. running marks a live mid-run checkpoint snapshot (such snapshots may also carry an informative checkpoint bookkeeping object with a monotonic seq). converged and failed mark a settled terminal archive; a terminal archive whose producer embeds its own input/log also carries a run.record (§ 5.8). An absent run_status means “not stated” — a consumer MUST NOT infer a status, and in particular MUST NOT treat absence as converged. An archive moves from one status to the next by being updated in place (§ 2.3) or written anew. An archive that carries several job.spec sections (a job set, § 5.9) states the status of the set: pending until one of its jobs starts, running from then until every job has settled, then converged when every job converged and failed when at least one failed; the status of each job is the run_status of the run.record that names it (§ 5.8).

One provenance field is deprecated:

• hostname — the name of the machine the calculation ran on. Producers SHOULD NOT emit it. Consumers MUST ignore it for any purpose other than display and MUST NOT rely on it. It may be removed in a future major version. Archives are meant to be shared, and machine names are private operational detail rather than part of a calculation’s result. The field stays listed so that archives which already carry it remain interpretable; its presence never makes an archive invalid. See also “Sharing and sanitisation” in § 5.8.

3.3 Root metadata blocks

These describe the calculation as a whole (not binary payloads), so they live at the manifest root rather than as sections.

• thermochemistry — zpve_eh, enthalpy_eh, entropy_cal_mol_k, gibbs_free_energy_eh (Hartree / cal·mol⁻¹·K⁻¹), temperature_k, pressure_atm. All optional.

• dipole_moment — total_debye, vector_debye (3-vector, Debye), origin: either a conventional name ("center_of_mass", "center_of_nuclear_charge", "origin") or an explicit 3-vector in bohr. This block stays the canonical place for a bare dipole. A properties.electric section (§ 5.13) may restate it beside the higher multipoles, and the two statements MUST then agree.

• constraints — frozen_atoms (0-based indices), distance_constraints (each {atoms: [i, j], target_angstrom}).

• energies — the energies of the calculation, specified in § 3.6.

3.4 viewer_defaults

An optional root object carrying hints for consumers that render the archive: which sections to show first, camera bookmarks and the initial camera, a cross-fade between two volumes, and how to draw each section. Hints are suggestions, not data. A consumer MAY ignore any hint, MUST ignore a hint it does not understand, and MUST NOT refuse to open a file because a hint is malformed: it ignores that hint and opens the file as if the hint were absent. A consumer that validates the manifest against the schema before opening therefore does not refuse a file over a finding in viewer_defaults. Producers SHOULD emit hints in the shapes and the lowercase spellings given here.

Member	Value
auto_open	Array of section ids to show first. The first structure section it lists is the archive’s first structure (§ 4.1).
bookmarks	Ordered camera bookmarks ($defs/Bookmark): a name, an optional description and a camera ($defs/Camera) with position, focal_point and view_up in Å and exactly one of view_angle (perspective, degrees) or parallel_scale (orthographic). The list order is the playback order.
camera	The camera a consumer starts with, an object in the shape of a bookmark’s camera ($defs/Camera); below.
crossfade	Two volume sections to cross-fade between and where the blend starts, {a, b, blend}; below.
any other key	A section id; the value is that section’s hint object (§ 3.4.1). A key that names no section is ignored.

auto_open, bookmarks, camera and crossfade are reserved: a section MUST NOT use one as its id, because its hint object could not be told apart from the reserved member. A validator reports a section that does (§ 6).

camera. The view a consumer opens the archive with: position, focal_point and view_up, Cartesian 3-vectors in Å, and exactly one of view_angle (perspective, in degrees, between 0 and 180 exclusive) and parallel_scale (orthographic, in Å, positive), the shape of $defs/Camera. A consumer that cannot use the camera, because it is not such an object or because the consumer draws no 3-D scene, ignores it. A consumer MAY open an archive without a camera hint at the camera of its first bookmark.

crossfade. An object that asks a consumer to show two volume sections (volume.*, § 5.2) blended into each other, for example two orbitals or two densities on one grid:

Key	Required	Type	Meaning
a	yes	string	id of the first volume section.
b	yes	string	id of the second volume section.
blend	no	number, 0 to 1	Where the blend starts: 0 shows a alone, 1 shows b alone. Default 0.5.

A consumer ignores a crossfade that is not an object or lacks a or b, and one whose a or b does not name a section it can draw. It reads a blend that is absent, not a finite number, or outside 0 to 1 as 0.5 and still applies the pair.

camera, crossfade and the per-section key energy_window (§ 3.4.1) are specified here only, like render and transfer_function: the schema reserves camera and crossfade but does not check their values, a validator MAY report a value that does not match this section as a warning, and it MUST NOT fail an archive because of one.

3.4.1 Section hint object

A section hint object ($defs/ViewerHint) suggests how one section is drawn. It is defined independently of where it is stored: v1 keys it by section id directly inside viewer_defaults, and the keys below keep their meaning wherever a later version places the object. Every key is optional. The object is open, so a consumer ignores keys it does not know.

Key	Type	Meaning
isovalue	number	Contour level, in the section’s data units (§ 4.3).
colormap	string	Name of the colour map to draw with. Names are not standardised; a consumer uses its default for a name it does not know.
opacity	number, 0 to 1	Opacity of the drawn surface; in volume mode, the peak of the consumer’s default opacity ramp.
replication	three integers ≥ 1	Cells to draw along each lattice vector of a periodic structure.
render	string	How a scalar-field section is first drawn: "isosurface" (the default) or "volume".
transfer_function	object	The function a scalar-field section is drawn with as a volume.
energy_window	[min, max]	The energy range a bands or dos.* section is first plotted over, in eV relative to the Fermi level.

A scalar-field section is one a consumer draws from a 3-D grid: volume.* and basis.ao. The schema types the first four keys, so a malformed value of one of them fails schema conformance (§ 6). render, transfer_function and energy_window are specified here only: a validator MAY report one that does not match this section as a warning, and MUST NOT fail an archive because of it.

render. "isosurface" contours the field at isovalue; "volume" draws the field itself through a transfer function. A consumer MAY accept other capitalisations and surrounding whitespace, and treats any value it does not recognise as "isosurface". A consumer that cannot draw the section as a volume (it has no volume renderer, does not draw that kind as one, or the field has no finite samples) ignores render and draws the section as it otherwise would. In volume mode isovalue is unused. Without a transfer_function the consumer builds its own default function for the kind, with colormap as the palette and opacity as the peak of its opacity ramp; with one, the function’s opacity nodes decide the opacity and opacity is not applied.

transfer_function. A JSON object, used whenever the section is drawn as a volume, whether render or the user chose that mode:

Key	Required	Shape	Meaning
range	yes	[low, high]	Two finite numbers, high > low, in the section’s data units (§ 4.3). The window the function is defined over; samples outside it take the value at the nearer end.
color	yes	array of [x, r, g, b]	Colour nodes, at least one: x in data units, r, g, b from 0 to 1.
opacity	yes	array of [x, a]	Opacity nodes, at least one: x in data units, a from 0 to 1.
preset	no	string	Name of the opacity ramp the nodes were derived from, for a consumer’s editor. Names are not standardised; the nodes, not the name, define the function.
colormap	no	string	"custom": the color nodes are the palette. Absent or any other value: the palette follows the section’s colormap hint (or the consumer’s default), and the value names the colour map the nodes were sampled from; a consumer that cannot resolve that palette MAY draw the nodes as given.

Between nodes, colour and opacity vary linearly with x; beyond the outermost node they keep its value, and a node position outside range clamps to the nearer end. A consumer drops a node that is not an array of the right length, has a non-finite member, or has a colour or opacity outside 0 to 1, and sorts the remaining nodes by x. It ignores the whole function, drawing with its default as if none were given, when range is not two finite numbers with high > low or when no colour node or no opacity node remains. Other keys are ignored. A producer that wants its colour nodes drawn as given sets colormap to "custom".

A spin density that opens as a volume, with a diverging palette and both lobes visible (spin is the section’s id):

"viewer_defaults": {
  "spin": {
    "render": "volume",
    "transfer_function": {
      "range": [-0.02, 0.02],
      "color": [[-0.02, 0.23, 0.30, 0.75], [0.0, 0.95, 0.95, 0.95], [0.02, 0.71, 0.02, 0.15]],
      "opacity": [[-0.02, 0.5], [-0.002, 0.0], [0.002, 0.0], [0.02, 0.5]],
      "colormap": "custom"
    }
  }
}

energy_window. The energy range a consumer first plots a bands section or a dos.* section (§ 5.6) over, so that a producer can open an all-electron spectrum, whose core states lie hundreds of eV below the Fermi level, on its valence region. The value is [min, max]: two finite numbers, max > min, in eV relative to the Fermi level (the band energies minus kpath.fermi, and the DOS energy grid as stored, which is referenced to it). A consumer MAY also accept the objects {"min": …, "max": …} and {"emin": …, "emax": …}, which a producer SHOULD NOT write. It ignores any other value, a non-finite number or a window with max ≤ min, and plots as if no window were given. A consumer that draws a bands and a dos.* section on one energy axis may apply the window of either. The user’s own choice of range overrides it, like any hint.

A periodic archive that opens at a saved view, with its band structure and DOS on the valence region and two densities half cross-faded (bands, dos, rho_a and rho_b are section ids):

"viewer_defaults": {
  "camera": {"position": [0.0, -12.0, 4.0], "focal_point": [0.0, 0.0, 0.0],
             "view_up": [0.0, 0.0, 1.0], "view_angle": 30.0},
  "crossfade": {"a": "rho_a", "b": "rho_b", "blend": 0.5},
  "bands": {"energy_window": [-15.0, 10.0]},
  "dos": {"energy_window": [-15.0, 10.0]}
}

3.5 Root metadata

An optional root object ($defs/Metadata) that describes the archive itself, so that it can be cited, found, and traced: what it is, who made it, under which licence it may be used, and which identifiers name it and its sources. The blocks of § 3.2 and § 3.3 describe the calculation; this one describes the archive. Every field is optional. None of them changes how the rest of the archive is read, and a consumer MAY ignore the block. The block is strict: a key not listed below is an error unless it begins with x_, which a producer may use for its own additions.

"metadata": {
  "title": "Water: RHF/STO-3G density and orbitals",
  "created_utc": "2026-10-07T12:00:00Z",
  "uuid": "3f2504e0-4f89-41d3-9a0c-0305e82c3301",
  "authors": [{"name": "A. Researcher", "orcid": "0000-0002-1825-0097"}],
  "license": "CC-BY-4.0",
  "keywords": ["water", "electron density"]
}

Field	Type	Meaning
title	string	Short human-readable title.
description	string	Free-text description of the contents.
created_utc	string	When the archive was first written: an ISO 8601 date and time in UTC, YYYY-MM-DDThh:mm:ssZ, optionally with a fractional second (…:00.25Z). The trailing Z is required.
modified_utc	string	When the archive was last changed, in the same form. Absent means not changed since created_utc.
uuid	string	Identifier of this archive: an RFC 4122 UUID in lowercase hexadecimal 8-4-4-4-12 form, with a version digit from 1 to 8 and the RFC 4122 variant (the first digit of the fourth group is 8, 9, a, or b).
authors	array of author objects	People or groups responsible for the contents, in citation order.
license	string	Licence of the contents. An SPDX identifier or expression (e.g. "CC-BY-4.0") is RECOMMENDED.
doi	string	DOI under which the archive is published, without a resolver prefix (e.g. "10.5281/zenodo.1234567").
keywords	array of strings	Subject keywords for search and cataloguing.
derived_from	array of strings	Archives or publications this archive was derived from, each a uuid or a DOI.
tags	array of strings	Free labels for a user’s own organisation of archives; unlike keywords, not meant for publication.

An author object ($defs/MetadataAuthor, strict like the block):

Field	Required	Meaning
name	yes	Name as it should be cited.
orcid	no	ORCID iD, e.g. "0000-0002-1825-0097".
affiliation	no	Institution.
email	no	Contact address.

email and affiliation are personal data. Archives are meant to be shared, so a producer SHOULD NOT emit either by default, but only when the person concerned asks for it; a tool that sanitises an archive for sharing treats them like the personal content of a run.record (“Sharing and sanitisation”, § 5.8).

Identity and time. A producer SHOULD set created_utc and uuid in every archive it writes, generating a random (version 4) uuid for each one; the reference writers do so by default and let the caller turn it off, for example to keep test vectors reproducible. An archive that its producer updates in place (§ 2.3), such as a job.spec archive that moves from pending to converged (§ 3.2), MAY keep its uuid and then SHOULD set modified_utc. A tool that writes a new archive from an existing one (a converter, a sanitiser, a subset) SHOULD give the new archive its own uuid and list the source’s uuid or DOI in derived_from. A validator checks the form of the two time stamps and of uuid (§ 6), not their truth.

3.6 Root energies

An optional root object ($defs/Energies) stating the energies of the calculation: the energy of the archive’s primary result, a decomposition of it into components, and the energies of the same system by further methods, for example the SCF reference and the correlated energy of an MP2 calculation. Every energy is a {value, units} object ($defs/ValueWithUnits), and producers SHOULD write hartree. The object is strict: it carries only the fields below and vendor keys beginning x_.

Field	Type	Required	Meaning
total	{value, units}	yes	Energy of the archive’s primary result: the calculation its result sections (wavefunction.gto, forces, hessian, …) belong to.
method	string	no	Method of the primary result, e.g. "rhf", "rks" or "mp2".
components	object ($defs/EnergyComponents)	no	Named contributions to total; table below.
by_method	array of objects ($defs/EnergyByMethod)	no	The energy of the same system by each further method: method (string, required), total ({value, units}, required) and components (as above, optional). Strict, like the block itself.
units_note	string	no	Free-text note on the units, for people; it declares nothing.

components ($defs/EnergyComponents, strict) names each contribution by one of the keys below; every key is optional and its value is a {value, units} object. A key beginning x_ names a further, producer-defined component and is a {value, units} object as well.

Component	Meaning
nuclear_repulsion	Nuclear–nuclear repulsion energy.
electronic	Electronic energy: everything but nuclear_repulsion.
one_electron	One-electron energy: kinetic energy plus electron–nuclear attraction.
two_electron	Two-electron energy: Coulomb plus exchange (Hartree–Fock), or Coulomb plus exchange–correlation (Kohn–Sham).
exchange_correlation	Exchange–correlation energy of a density functional.
exchange	Exchange energy: Hartree–Fock exchange, or the exchange part of exchange_correlation.
correlation	Correlation energy: a correlated energy minus its reference energy, or the correlation part of exchange_correlation.
dispersion	Dispersion correction, e.g. DFT-D3.
solvation	Contribution of a solvent model.
zpve	Zero-point vibrational energy.
thermal	Thermal correction to the energy at thermochemistry.temperature_k (§ 3.3), excluding zpve.
embedding	Interaction with an embedding environment, e.g. QM/MM or an embedding potential.

Components may overlap (exchange_correlation contains exchange and correlation) and need not be exhaustive, so a consumer MUST NOT add them up to obtain total.

Consistency with the other root blocks. Where the manifest states one energy twice, the two statements MUST agree within 1e-8 hartree:

• provenance.scf_energy (§ 3.2) is the energy of the method that provenance.method names. Every energy that energies states for that same method — each by_method entry whose method is that name, and total when energies.method is that name — MUST agree with it. Method names are compared case-insensitively in ASCII, so "RHF" and "rhf" are one method. For a calculation beyond SCF, provenance.method accordingly names the SCF method whose energy scf_energy is, and energies.method the method of the final result. An energy of energies whose method is not named, or is another method, is not compared.

• components.zpve MUST agree with thermochemistry.zpve_eh (§ 3.3).

A validator converts both values to hartree before comparing them (1 hartree = 27.211386245988 eV = 627.5094740631 kcal/mol = 2625.4996394799 kJ/mol, CODATA 2018), reports a disagreement as E_ROOT_INCONSISTENT (§ 6), and skips a comparison when it does not recognise a unit. The unit strings it recognises, case-insensitively, are hartree (and its older spellings Eh and Ha), ev, kcal_per_mol and kj_per_mol.

An MP2 calculation on an RHF reference:

"provenance": {"method": "rhf", "scf_energy": {"value": -74.9629, "units": "hartree"}},
"energies": {
  "total": {"value": -75.0124, "units": "hartree"},
  "method": "mp2",
  "components": {"correlation": {"value": -0.0495, "units": "hartree"}},
  "by_method": [
    {"method": "rhf", "total": {"value": -74.9629, "units": "hartree"}},
    {"method": "mp2", "total": {"value": -75.0124, "units": "hartree"}}
  ]
}

The rhf entry restates provenance.scf_energy and must agree with it. The MP2 total and the mp2 entry are not compared with it, because their method is not the one provenance.method names.

---

4. Sections and members

4.1 Section object

{
  "id": "vol_dens_0",
  "kind": "volume.density",
  "label": "Electron density",
  "members": { /* role -> member spec */ }
}

Field	Required	Meaning
id	yes	Unique within the archive. ^[A-Za-z0-9_.-]+$. MUST NOT be auto_open, bookmarks, camera or crossfade (reserved viewer_defaults keys, § 3.1, § 3.4).
kind	yes	Canonical kind (§ 5) or x_<vendor>.*.
members	yes	Map from member role to a JSON or binary member spec.
label	no	Human-readable display label.
component	no	Component hint (e.g. for volume.orbital).
critical	no	If true, a consumer that does not support kind MUST refuse to open the archive. Default false (§ 7.4).
schema_uri	no	URI of a JSON Schema for a vendor section’s members.
structure_ref	no	Id of the structure section (§ 5.1) this section describes.
run_ref	no	Id of the run.record section (§ 5.8) of the program run that produced this section.
group	no	Free-text label that groups related sections for display, e.g. "step 2: frequencies".

Some kinds add kind-specific peer fields on the section object (e.g. volume.difference carries operand_a/operand_b; reaction.waypoints carries trajectory_ref). These are documented per kind in § 5.

Section references and grouping. Any section, of any kind including a vendor kind, MAY carry structure_ref, run_ref, and group. They make an archive that holds several structures or several steps of a calculation unambiguous: a consumer learns which geometry a volume, wavefunction, or spectrum belongs to and which program run produced it, instead of guessing from section order or ids. structure_ref MUST name a section of kind structure, and run_ref a section of kind run.record, in the same archive; a validator reports one that does not (§ 6). A section without them makes no statement, and a consumer keeps its usual behaviour, for example using the archive’s only structure, or the first structure of an archive with several (below). group carries no meaning beyond grouping: sections with equal group values belong together, and a consumer MAY present them together, for instance as one node of a tree.

Section ids carry no meaning. An id names a section so that other sections and viewer_defaults can refer to it; nothing else may be read into it. structure is a conventional id that the reference writers use by default, not a role: an archive may hold structures with any ids, such as structure_m1 and structure_m2 for the species of a scheme, and none named structure. A consumer MUST find sections by their kind and by the references of § 4.1 and § 5, and MUST NOT depend on a conventional id.

The first structure. A consumer that shows one structure at a time, or needs one structure for an operation that names none, uses the first structure: the first structure section that viewer_defaults.auto_open lists (§ 3.4), else the first section of kind structure in sections order. It SHOULD also offer the archive’s other structures, for example by showing a structure when its section is selected. A producer that wants a particular structure shown first lists it in auto_open. The rule chooses what to show and changes no reference: a section without structure_ref in an archive with several structures still makes no statement about which one it describes. A standalone bonds section is the one exception: its atom indices need a structure, and without structure_ref they address the first structure (§ 5.1).

The kind-specific references stay as they are: operand_a and operand_b of volume.difference (§ 5.2), trajectory_ref of reaction.waypoints (§ 5.5), and the structure_ref inside the basis payload of wavefunction.gto (§ 5.3) and wavefunction.bloch (§ 5.3.1). When a section carries a structure_ref and one of its payloads carries one too, the section’s takes precedence: a consumer reads the payload’s atom indices, such as the shell center indices of a basis, against the atoms of the structure that the section names. Producers SHOULD keep the two equal.

4.2 Member specs

JSON member:

{ "path": "structure/structure.json", "format": "json", "sha256": "<64 hex>",
  "size": 1834 }

Binary member:

{
  "path": "volumes/density.dat",
  "format": "binary",
  "dtype": "float32",
  "shape": [80, 80, 80],
  "sha256": "<64 hex>",
  "size": 2048000
}

• format is "json" or "binary".

• sha256 is the lowercase hex sha256 of the exact bytes stored for that member (the uncompressed payload). Consumers MUST verify it before use.

• size (optional, on every member spec: JSON, binary and opaque) is the uncompressed byte count of the stored member, an integer ≥ 0. It MUST equal the uncompressed size that the ZIP central directory records for the member’s entry, so for a binary member with a dtype it is itemsize(dtype) × ∏(shape). Producers SHOULD write it; the reference writers write it for every member. A validator checks it against the central directory before reading the member, and reports a disagreement as E_BINARY_SIZE (§ 6). A consumer that relies on size — to allocate a buffer before inflating, or to size-gate rendering (§ 5.8) — MUST first check that it equals the size the central directory records, and treat a member whose size disagrees as invalid. Archives written before size existed omit it and remain valid.

• JSON members MUST parse as UTF-8 JSON.

• Binary members are raw, C-contiguous, little-endian arrays. dtype is one of: int8, int16, int32, int64, uint8, uint16, uint32, uint64, float32, float64. The stored byte length MUST equal itemsize(dtype) × ∏(shape).

• A small set of opaque binary members carry no dtype/shape: citations.references (UTF-8 BibTeX bytes), the run.record members input / log (UTF-8 text) and attachment.* (arbitrary bytes, § 5.8), the preview members thumbnail and image (§ 5.15), and any member of a vendor section (§ 7.3) that its producer writes without them. Consumers skip the byte-length check for these and decode per the owning kind’s contract.

• media_type (optional, on every member spec) is the IANA media type of the member’s bytes, such as image/png, text/plain or application/json: a type and a subtype, without parameters (RFC 6838). It describes the bytes and changes nothing in how they are read: a JSON member is UTF-8 JSON and a binary member with a dtype is a little-endian array whatever its media_type says. A kind may require it, as preview does (§ 5.15); elsewhere it is a hint for programs that hand a member to another program, most usefully on opaque members.

4.3 Units and numeric conventions

Producers convert to these units at write time. Consumers MUST treat on-disk units as the contract (they may convert for display).

Field	Unit / convention
structure.atoms[].position	Ångström
structure.lattice_vectors	Ångström, row vectors
trajectory.lattice	Ångström, row vectors (the structure convention); see Lattice conventions below
reaction.path.lattice	bohr, column matrix (columns = a, b, c); see Lattice conventions below
volume.*.grid.origin	bohr
volume.*.grid.voxel_vectors	bohr per grid step
volume.density.data	e / bohr³ (electron density)
volume.orbital.data	orbital amplitude on a bohr grid
volume.potential.data	hartree / e (atomic units of potential)
volume.rdg.data	dimensionless, s(r) = |∇ρ| / (2(3π²)^⅓ ρ^⅔)
volume.transition_density.data	e / bohr³ (the transition density of one excitation, § 5.2)
volume.laplacian.data	e / bohr⁵ (∇²ρ); the vocabulary has no unit name for it, so grid.units.data is not declared
volume.vector.data, volume.complex.data, volume.series.data	the unit of the sampled field, declared as grid.units.data when the vocabulary names it; vector components are Cartesian, in the frame of origin
volume.series axis.values	axis.units; dimensionless when absent
periodic volume.*.grid axis a	voxel_vectors[a] × (shape[a] − 1) (includes_endpoint true, the default) or voxel_vectors[a] × shape[a] (false) equals lattice vector a of the grid’s structure, in bohr (§ 5.2)
trajectory.coords, reaction.path.coords	Ångström
trajectory.metadata.energies, trajectory.energies, reaction.path.energies, reaction.path.waypoints[].energy_eh	Hartree
trajectory.velocities, reaction.path.velocities	Å / fs
trajectory.gradient, reaction.path.gradient	hartree / bohr; the energy gradient, so the forces are its negative (§ 5.5)
trajectory.times, reaction.path.times, metadata.timestep_fs	fs
trajectory.cell_volumes	ų
trajectory.temperatures	kelvin
bands.eigenvalues, bands.kpath.fermi, fermi_energy_ev	eV
spectra.ir.frequencies / intensities	cm⁻¹ / km·mol⁻¹
spectra.uvvis.frequencies / energies_ev	eV
vibrations.metadata.frequencies	cm⁻¹
wavefunction.gto.basis.shells[].exponents	bohr⁻²
wavefunction.gto.mo_metadata.energies	Hartree
wavefunction.gto.basis.ecp[].projectors[]	exponents bohr⁻²; coefficients hartree · bohr^(2 − n) for the radial power n, so U(r) is in hartree (§ 5.3)
wavefunction.gto.overlap	dimensionless; AOs as Appendix A.1 defines them
wavefunction.gto.density_matrix, density_matrix_alpha, density_matrix_beta	electrons: tr(P · S) is the electron count (§ 5.3)
wavefunction.bloch.energies	hartree (§ 5.3.1)
wavefunction.bloch.kpoints.kpoints	fractional reciprocal-lattice coordinates, k = k₁b₁ + k₂b₂ + k₃b₃ with a_i · b_j = 2π δ_ij (§ 5.3.1)
dos.*.energies	eV (referenced to E_F at 0.0)
fermi_surface.energies	eV (signed: E(k) − E_F)
fermi_surface.mesh.lattice_vectors / reciprocal_lattice	Ångström, row vectors / Å⁻¹, row vectors, 2π included
phonon_bands.frequencies, phonon_dos.frequencies	cm⁻¹
equation_of_state.volumes / energies	ų / eV
equation_of_state.fit.V0 / E0 / B0	ų / eV / GPa
forces.gradient	hartree / bohr; the energy gradient ∂E/∂R, so the forces are its negative (§ 5.10)
forces.stress	hartree / bohr³
hessian.matrix	hartree / bohr²; hartree / (bohr² · amu) when meta.mass_weighted is true (§ 5.11)
excited_states excitation_energy / total_energy	{value, units} objects; producers SHOULD write ev / hartree (§ 5.12)
excited_states oscillator_strength	dimensionless
excited_states rotatory_strength_cgs	10⁻⁴⁰ esu²·cm² (the “10⁻⁴⁰ cgs” unit), signed
excited_states transition_dipole / transition_magnetic_dipole	atomic units: e·bohr / e·ħ/mₑ (= 2 μ_B)
root energies	{value, units} objects; producers SHOULD write hartree (§ 3.6)
properties.electric.dipole	debye (§ 5.13)
properties.electric.quadrupole / .octupole	debye · Å / debye · Ų; origin, when a vector, in bohr (§ 5.13)
properties.electric.polarizability / .hyperpolarizability	atomic units, e² a₀² / E_h and e³ a₀³ / E_h² (§ 5.13)
properties.elastic.stiffness, moduli	GPa; compliance in GPa⁻¹; poisson_ratio dimensionless (§ 5.13)
properties.dielectric.electronic / .ionic / .static	dimensionless (relative permittivity) (§ 5.13)
properties.dielectric.born_charges / .piezoelectric	e / C · m⁻² (§ 5.13)

When adding fields, prefer unit-bearing names (energy_eh, energy_ev, frequency_cm) or a {value, units} object.

Unit names

A unit is named by one of the unit names below, a controlled vocabulary. The JSON Schema carries the same list in the same order as $defs/UnitName, and the two are kept identical. Names are case-sensitive. The list names units; it changes none: every unit of the table above keeps its meaning.

Unit name	Quantity	Definition or note
angstrom	length	1 Å = 10⁻¹⁰ m
bohr	length	a₀ = 0.529177210903 Å (CODATA 2018)
hartree	energy	E_h = 27.211386245988 eV (CODATA 2018)
ev	energy	1 eV = 1.602176634 × 10⁻¹⁹ J (exact)
kcal_per_mol	molar energy	thermochemical kcal·mol⁻¹, 4.184 kJ·mol⁻¹ (exact); E_h N_A = 627.5094740631 kcal·mol⁻¹
kj_per_mol	molar energy	kJ·mol⁻¹; E_h N_A = 2625.4996394799 kJ·mol⁻¹ (CODATA 2018)
cm-1	wavenumber	1 cm⁻¹ = 100 m⁻¹; as an energy E = h c ν̃, with E_h / (h c) = 219474.6313632 cm⁻¹ (CODATA 2018)
nm	length (wavelength)	1 nm = 10⁻⁹ m; as a photon energy E = h c / λ, with h c = 1239.841984332 eV·nm (exact)
debye	electric dipole moment	1 D = 10⁻²¹ / c C·m ≈ 3.335641 × 10⁻³⁰ C·m
mhz	frequency	1 MHz = 10⁶ s⁻¹
hz	frequency	1 Hz = 1 s⁻¹
ppm	dimensionless ratio	10⁻⁶; chemical shifts and shieldings
km_per_mol	IR intensity	km·mol⁻¹, the integrated molar absorption coefficient
a3	volume	1 ų = 10⁻³⁰ m³
bohr3	volume	a₀³
gpa	pressure	1 GPa = 10⁹ Pa
fs	time	1 fs = 10⁻¹⁵ s
ps	time	1 ps = 10⁻¹² s
kelvin	temperature	the SI kelvin
atm	pressure	standard atmosphere, 101 325 Pa (exact)
e	electric charge	elementary charge, 1.602176634 × 10⁻¹⁹ C (exact)
amu	mass	unified atomic mass unit (dalton), 1.66053906660 × 10⁻²⁷ kg (CODATA 2018)
radian	plane angle	the SI radian
degree	plane angle	π / 180 rad
dimensionless	—	a pure number, such as a normalized intensity

Legacy spellings. Archives written before this vocabulary carry three other spellings in the units of a {value, units} object (scf_energy, fermi_energy, § 3.2). They remain valid there, and only there, and are deprecated: producers SHOULD write the unit name, and consumers MUST read a legacy spelling as the unit name it stands for. The schema lists them as $defs/LegacyUnitName.

Legacy spelling	Unit name
Eh	hartree
eV	ev
Hartree	hartree

Declared units

A payload can say which unit its values are in. The units object of the volume grid (§ 5.2), of the trajectory, reaction-path and scan metadata (§ 5.5), of the kpath, DOS meta, Fermi-surface mesh, qpath and phonon meta payloads (§ 5.6), of the QTAIM payload (§ 5.7) and the meta.units object of the excited_states payload (§ 5.12) maps a key to a unit name. The key is the name of a field of the payload (for excited_states, of a state), or the role of a binary member of the same section, such as coords or eigenvalues. A one-dimensional spectrum declares the units of its axes in x_units and y_units, and the unit of its line width in broadening.units (§ 5.4). The axis of a volume.series declares the unit of its values in units, a single unit name (§ 5.2).

• Producers MAY declare units. A declaration is not a conversion: the values are stored in the declared unit.

• Consumers MUST honour a declared unit: they read the values in it, and convert from it when they need another.

• Where the table above fixes the unit of a field or member, a declaration only restates it, and a declared unit that contradicts it is an error: a grid units.origin other than bohr, a trajectory units.coords other than angstrom, or a trajectory units.lattice other than angstrom (a reaction path’s is bohr). The payload definitions encode these fixed units, so a validator that runs the JSON Schema check reports the contradiction as E_PAYLOAD_SCHEMA (§ 6).

• Where a payload leaves the unit open (a spectrum’s x axis, QTAIM positions, the scan axes), a declaration chooses it, within the quantity the field holds: a position takes a length.

• A declared unit is a unit name. So is the units of a {value, units} object, except that it may also be a legacy spelling. A validator reports any other string in these places as the warning W_UNIT_UNKNOWN (§ 6). The schema types these strings as well, so a validator that runs the JSON Schema check also reports E_SCHEMA or E_PAYLOAD_SCHEMA for an unknown unit, and the archive does not validate there.

The older unit-bearing keys (unit of a scan axis, reaction_coordinate_unit, energy_unit, coordinate_a_unit and the like) stay free text in v1, because archives already carry spellings outside the vocabulary, such as "rad". Producers SHOULD use unit names in them as well. When a scan’s units.energies and energy_unit, or a units entry and an axis unit, are both present they MUST name the same unit.

Lattice conventions

QVF v1 carries the same physical object, a periodic cell, in three members that follow two conventions, which differ in layout and in unit. structure.lattice_vectors and trajectory.lattice use the structure convention (rows, Å); reaction.path.lattice uses the reaction-path convention (columns, bohr). Both conventions are normative and frozen for the whole of v1; neither will change within it. This subsection is the one place that states both, and the member descriptions in § 5.1 and § 5.5 refer to it.

	structure.lattice_vectors	trajectory.lattice	reaction.path.lattice
Convention	structure	structure	reaction path
Where	JSON payload of a structure section (§ 5.1)	binary member lattice of a trajectory section (§ 5.5)	binary member lattice of a reaction.path section (§ 5.5)
Shape	[3, 3]	[3, 3] (fixed cell) or [n_frames, 3, 3] (one cell per frame)	[3, 3] (fixed cell) or [n_frames, 3, 3] (one cell per frame)
Layout	rows: row i is the lattice vector of axis i, paired with pbc[i]	rows: row i of each [3, 3] matrix is the lattice vector of axis i, paired with metadata.pbc[i]	columns: column j of each [3, 3] matrix is lattice vector j (a, b, c)
Unit	Ångström	Ångström	bohr
Storage	JSON numbers	float64, little-endian, C order (element [i][j] at offset 3i + j)	float64, little-endian, C order (element [i][j] at offset 3i + j)
Periodicity is signalled by	pbc	metadata.pbc, REQUIRED with the member	presence of the member

A [3, 3] slice of trajectory.lattice is laid out and scaled exactly as structure.lattice_vectors: the frame-0 cell of a trajectory equals the lattice_vectors of its structure, element for element, with no conversion. The two conventions differ deliberately: reaction.path.lattice predates the structure-convention carriers and stays columns in bohr for the whole of v1, and trajectory.lattice, added later, adopts the structure convention so that new carriers converge on one layout.

Write R for a matrix in the structure convention (structure.lattice_vectors or one [3, 3] slice of trajectory.lattice; Å, rows) and L for one [3, 3] slice of reaction.path.lattice (bohr, columns), and f = 1.8897261246 bohr per Å (the reciprocal of 1 bohr = 0.529177210903 Å, CODATA 2018, rounded to ten decimals). Then

L[i][j] = f · R[j][i]        i.e.  L = f · Rᵀ     (structure → reaction.path)
R[i][j] = L[j][i] / f        i.e.  R = Lᵀ / f     (reaction.path → structure)

so the columns of L are the rows of R scaled by f. For a per-frame [n_frames, 3, 3] member, apply the conversion to each frame’s slice.

Worked example. A hexagonal cell with a = 2.46 Å and a 15.875 Å normal (the 2-D graphene slab of the conformance corpus). As structure.lattice_vectors (Å, rows):

[[2.46, 0.0,    0.0   ],     // a
 [1.23, 2.1304, 0.0   ],     // b
 [0.0,  0.0,    15.875]]     // c

and as the equivalent reaction.path.lattice (bohr, columns, 4 decimals):

[[ 4.6487,  2.3244,  0.0000 ],      column 0 = a = (4.6487, 0.0000,  0.0000)
 [ 0.0000,  4.0259,  0.0000 ],      column 1 = b = (2.3244, 4.0259,  0.0000)
 [ 0.0000,  0.0000, 29.9994 ]]      column 2 = c = (0.0000, 0.0000, 29.9994)

The second matrix is the transpose of the first times f: row a of the Å matrix, (2.46, 0, 0), becomes column 0 of the bohr matrix, (4.6487, 0, 0)ᵀ, and row b, (1.23, 2.1304, 0), becomes column 1, (2.3244, 4.0259, 0)ᵀ. Reading the bohr matrix by rows would give a = (4.6487, 2.3244, 0) and b = (0, 4.0259, 0), which is a different cell. For an axis-aligned cubic or orthorhombic cell the matrix is diagonal and the transpose is invisible, leaving only the unit factor, so a diagonal test case does not show that the two conventions agree.

A consumer MUST NOT assume the convention of one member for another: it MUST read structure.lattice_vectors and trajectory.lattice as rows in Å and reaction.path.lattice as columns in bohr, and convert explicitly when it combines a reaction path with either of the others (for example to overlay a path on the cell of its structure). A producer that writes several MUST write each in its own convention. A validator reads each member in its own convention and never mixes them: it checks the shape of each lattice against the frames of its own section (§ 6), and never compares one carrier with another.

Note (informative). New carriers of a cell adopt the structure convention. Unifying reaction.path.lattice with it is a v2 ledger item (V2-05).

---

5. Canonical section kinds

Every kind below is a oneOf branch in the schema. A section’s kind selects its required member set. The table lists each kind and its required members; subsections give the payload shapes that matter for interoperability.

Kind	Required members (roles)
structure	structure (JSON, $defs/StructurePayload); optional bonds (JSON); optional section fields for biomolecules and for the chemical identity of the species (§ 5.1)
bonds	bonds (JSON)
bond_orders	bond_orders (JSON)
volume.density / .orbital / .spin / .elf / .generic / .potential / .rdg / .laplacian	grid (JSON, $defs/VolumeGridPayload) + data (3-D float32/64 binary)
volume.vector	grid (JSON, $defs/VolumeGridPayload) + data (float32/64 [nx, ny, nz, 3], $defs/Volume4DVectorBinary)
volume.complex	grid (JSON, $defs/VolumeGridPayload) + data (float32/64 [nx, ny, nz, 2], last axis [re, im], $defs/Volume4DComplexBinary)
volume.series	grid (JSON, $defs/VolumeGridPayload) + data (float32/64 [n, nx, ny, nz]) + axis (JSON, $defs/VolumeSeriesAxisPayload)
volume.difference	grid (JSON, $defs/VolumeGridPayload) + data; optional section fields operand_a, operand_b, description
volume.transition_density	grid (JSON, $defs/VolumeGridPayload) + data; optional section fields excited_states_ref, state_index
wavefunction.gto	basis (JSON, $defs/BasisPayload) + mo_metadata (JSON, $defs/MoMetadataPayload) + mo_coefficients or (mo_coefficients_alpha + mo_coefficients_beta) (float64 binary); optional overlap and density_matrix or (density_matrix_alpha + density_matrix_beta) (float64 [n_ao, n_ao], $defs/WavefunctionAoMatrix)
wavefunction.bloch (provisional)	basis (JSON, $defs/BasisPayload) + kpoints (JSON, $defs/BlochKpointsPayload) + mo_metadata (JSON, $defs/BlochMoMetadataPayload) + mo_coefficients (float64 [n_k, n_spin, n_mo, n_ao, 2]) + energies + occupations (float64 [n_k, n_spin, n_mo])
basis.ao	grid (JSON, $defs/VolumeGridPayload) + data; section field ao_metadata
atom_properties	≥1 of the scalar roles mulliken_charge, loewdin_charge, hirshfeld_charge, iao_charge, spin_population, cm5_charge, chelpg_charge, resp_charge, esp_charge, nbo_charge, mbis_charge, bader_charge, ddec_charge, valence, bonded_valence, fukui_plus, fukui_minus, fukui_zero, dual_descriptor, atomic_energy_eh, atomic_volume_bohr3, nmr_shielding_iso_ppm (float64 [n_atoms] binary, $defs/AtomChargeBinary) and the vector roles magnetic_moment, force_eh_bohr (float64 [n_atoms, 3] binary, $defs/AtomVectorBinary); optional custom.<name> roles (either shape), each described by the meta member (JSON, $defs/AtomPropertiesMetaPayload)
trajectory	metadata (JSON, $defs/TrajectoryMetadataPayload) + coords ([n_frames, n_atoms, 3]; float64, or float32 with metadata.precision); optional lattice (float64 [3, 3] or [n_frames, 3, 3], rows, Å), velocities, gradient (float64 [n_frames, n_atoms, 3]), times, energies, cell_volumes, temperatures (float64 [n_frames]) (§ 5.5)
reaction.path	metadata (JSON, $defs/ReactionPathMetadataPayload) + coords; optional lattice (periodic marker; columns, bohr), velocities, gradient, times, energies (as for trajectory), frame_volumes (4-D) + volume_grid (JSON, $defs/VolumeGridPayload)
reaction.waypoints	waypoints (JSON, $defs/ReactionWaypointsPayload); section field trajectory_ref (REQUIRED)
reaction.scheme	scheme (JSON, $defs/ReactionSchemePayload) (§ 5.14)
scan.surface	metadata (JSON, $defs/ScanSurfaceMetadataPayload) + axis_a + axis_b + energies; optional geometries
vibrations	metadata (JSON, $defs/VibrationsMetadataPayload) + displacements (float64 [n_modes, n_atoms, 3]); optional section field hessian_ref
spectra.ir / .raman / .uvvis / .ecd / .vcd / .nmr / .epr / .generic	spectrum (JSON)
bands	kpath (JSON, $defs/KpathPayload) + eigenvalues (float64 [n_spin, n_k, n_bands]); optional projections, occupations
dos.total	energies + dos (binary); optional section fields (§ 5.6)
dos.projected	energies + projections (binary); optional section fields, including channels (§ 5.6)
dos.coop / dos.cohp	energies + projections + integrated + meta (JSON, $defs/DosMetaPayload)
structure.symmetry	data (JSON)
scf_history	iterations (JSON)
citations	references (binary BibTeX)
run.record	≥1 of input, log (opaque UTF-8 binary); optional files (JSON, $defs/RunRecordFilesPayload) + attachment.* (opaque binary); section field program (REQUIRED); optional section fields job_ref, run_status (§ 5.8)
job.spec	spec (JSON, $defs/JobSpecPayload)
fermi_surface	mesh (JSON, $defs/FermiMeshPayload) + energies (4-D float32/64)
phonon_bands	qpath (JSON, $defs/QpathPayload) + frequencies (binary); optional eigenvectors (float64 [n_q, n_modes, n_atoms, 3] or [n_q, n_modes, n_atoms, 3, 2])
phonon_dos	meta (JSON, $defs/PhononMetaPayload) + frequencies + dos (binary); optional projected (float64 [n_channels, n_points])
equation_of_state	volumes + energies (binary) + fit (JSON, $defs/EosFitPayload)
topology.qtaim	critical_points (JSON)
forces	gradient (float64 [n_atoms, 3]); optional stress (float64 [3, 3]) + meta (JSON, $defs/ForcesMetaPayload)
hessian	matrix (float64 [3N, 3N]); optional meta (JSON, $defs/HessianMetaPayload)
excited_states	states (JSON, $defs/ExcitedStatesPayload); optional section field wavefunction_ref
properties.electric	properties (JSON, $defs/ElectricPropertiesPayload)
properties.elastic	properties (JSON, $defs/ElasticPropertiesPayload)
properties.dielectric	properties (JSON, $defs/DielectricPropertiesPayload)
preview	thumbnail (opaque binary, image/png or image/jpeg); optional image (opaque binary, image/svg+xml, image/png or image/jpeg); both with media_type (§ 5.15)
x_<vendor>.*	any mix of valid JSON/binary members

Payload definitions. A JSON member whose section kind and role have a payload definition, the $defs entry of the JSON Schema named in the table above and in the subsections below, MUST conform to it, and a validator checks that it does (§ 6). A payload definition describes an archive member, not manifest content, so nothing in the manifest refers to it. Each payload table below names the strictness level of its definition:

• strict — the payload carries only the keys its table lists. Any other key is an error, except a key that begins with x_: a producer may use such keys for its own additions, and a consumer that does not understand one ignores it.

• typed-open — the keys its table lists are typed, and any other key is accepted; a consumer that does not understand one ignores it.

5.1 structure and bonds

structure.json — schema’d as $defs/StructurePayload:

{
  "atoms": [
    {"symbol": "O", "position": [0.0, 0.0, 0.1173], "atomic_number": 8},
    {"symbol": "H", "position": [0.0, 0.7572, -0.4692], "atomic_number": 1}
  ],
  "pbc": [false, false, false],
  "lattice_vectors": null
}

Each atom carries symbol, position (Cartesian Å, never fractional), and atomic_number; producers may add further per-atom fields.

Periodicity

pbc is an array of three booleans and is the normative carrier of periodicity: axis i is periodic iff pbc[i]. It is REQUIRED whenever lattice_vectors is a non-null array. When absent the structure is a molecule, exactly as if [false, false, false] had been written.

All eight patterns are legal. The periodic axes need NOT be the leading ones: a slab whose surface normal lies along y is [true, false, true], and a producer MUST NOT be required to permute its lattice to satisfy a consumer.

lattice_vectors is a [3,3] array of row vectors in Å — row i is the lattice vector of axis i, paired with pbc[i]. It is REQUIRED (non-null) when any pbc[i] is true, and SHOULD be null or absent otherwise. trajectory.lattice (§ 5.5) uses the same layout and unit; the other lattice carrier in v1, reaction.path.lattice, uses a different layout and unit; see Lattice conventions in § 4.3.

For every axis i where pbc[i] is false, row i is non-physical bookkeeping. Producers keep the matrix full-rank 3×3 so that integral codes and symmetry finders always see a 3-D lattice, but such a row spans no periodicity and encodes no geometry. A consumer MUST NOT draw it as a cell edge, replicate the structure along it, or read it as a vacuum extent. This is not a hypothetical: a synthesized 30-bohr normal and a real 30-bohr vacuum gap are numerically identical in lattice_vectors, so pbc is the only signal that tells them apart. Any heuristic of the form “is this row long and orthogonal? then it is vacuum” silently renders 2-D slabs inside empty boxes.

dimensionality (0–3) is OPTIONAL and derived, with the invariant

dimensionality == the number of true entries in pbc

A producer that emits it MUST satisfy that invariant; a validator MUST reject a payload that violates it. It is a convenience scalar and carries no axis identity: a consumer MUST take per-axis periodicity from pbc, and MUST NOT infer which axes are periodic from dimensionality.

dimensionality lives in the payload, alongside the pbc it is derived from — not on the section object. An earlier revision of this section placed it on the section object; a consumer MUST NOT read it from there. Archives that carry it in the old position remain fully interpretable, because pbc is what a consumer reads.

Note (informative). Some producers — vibe-qc among them — order their lattice so the periodic axes come first, emitting pbc as [true] * dim + [false] * (3 - dim). A consumer reading a pre-conformance archive that has dimensionality but no pbc may assume that ordering as a fallback. This is a legacy accommodation, not part of the contract, and it is unnecessary for any archive conforming to this section, where pbc is always present when it matters.

Connectivity

Explicit connectivity is a separate bonds section ({"pairs": [{"i": 0, "j": 1, "order": 1.0}, …]}), or the optional bonds member of the structure section itself. If neither is present, a viewer may infer bonds from covalent radii. The payload, of a bonds section and of a structure section’s optional bonds member alike, is $defs/BondsPayload (§ 5.7).

The atom indices of a bonds member of a structure section address that structure’s atoms. A standalone bonds section names its structure with the generic section field structure_ref (§ 4.1):

• Present: the bonds belong to the structure section it names, and their indices address its atoms. A validator reports a structure_ref that does not name a structure section (E_REF_UNRESOLVED), and an atom index i or j that is not below the atom count of that structure (E_MEMBER_MALFORMED, § 6).

• Absent: the bonds belong to the archive’s first structure (§ 4.1), in an archive with one structure that structure, as before this field was specified.

A producer that writes several structure sections SHOULD set structure_ref on every standalone bonds section, or, simpler, write each structure’s bonds as that section’s own bonds member.

{"id": "bonds_product", "kind": "bonds", "structure_ref": "structure_product",
 "members": {"bonds": {"path": "bonds_product/connectivity.json", "format": "json",
                       "sha256": "…"}}}

Biomolecule metadata

The structure section object (peer to id/kind/members, not inside the payload) MAY carry optional biomolecule metadata for cartoon/ribbon rendering. All four fields are OPTIONAL and independent; a structure carrying none of them is a valid plain structure, and a consumer that does not understand them MUST ignore them.

Field	Type	Schema
chains	array of chain-id strings, in presentation order	—
residues	array of {name, seq, chain, atom_indices}	$defs/BiomoleculeResidue
secondary_structure	array of {type, chain, start_seq, end_seq}, type in helix/sheet/coil, ranges inclusive	$defs/BiomoleculeSecondaryStructure
b_factors	array of number, one per atom, parallel to the payload’s atoms order	—

atom_indices are 0-based into the structure member payload’s atoms array. residues are listed in chain order — the order a ribbon is drawn in — not sorted by seq: insertion codes and non-monotonic numbering are both legal, and sorting would silently reorder them. seq is not a global key: PDB residue numbers are four columns wide and wrap at 9999, so a solvated system reuses them.

Precedence. Many consumers can derive residues, chains, and secondary structure themselves — from the per-atom fields below, and from CA geometry. Where a producer supplies these fields, a consumer MUST prefer the supplied values over its own inference. A producer knows what geometry cannot reveal: an α- from a π- from a 3-10 helix, a β-bridge from a sheet.

A payload’s atoms MAY additionally carry the per-atom biomolecular fields atom_name (PDB cols 13-16, e.g. "CA"), residue_name (cols 18-20), residue_seq (cols 23-26), chain_id (col 22) and b_factor (cols 61-66). Where both carriers are present, the per-atom b_factor wins over the section-level b_factors array: it cannot desynchronize from its own atom. A consumer MUST ignore a b_factors array whose length differs from the atom count rather than applying a partial mapping.

These fields were added under v1: an optional member is the additive case and does not bump qvf_version (see GOVERNANCE.md).

Chemical identity

The structure section object MAY also say which chemical species the structure is: its net charge and spin multiplicity, a name, and line notations. Like the biomolecule metadata they are peers of id and members, so a consumer reads them from the manifest without opening a member, and a program that lists the molecules of an archive, or searches archives for one, needs nothing else. All are OPTIONAL and independent.

Field	Type	Meaning
charge	integer	Net charge of the species, in units of the elementary charge.
multiplicity	integer ≥ 1	Spin multiplicity 2S+1 of the species.
name	string, non-empty	Name of the species, e.g. "ethanol" or "Grubbs II".
smiles	string, no whitespace	SMILES of the species.
inchi	string beginning InChI=	InChI of the species, standard (InChI=1S/…) or not.
inchikey	string, AAAAAAAAAAAAAA-BBBBBBBBBB-C	InChIKey of the species: 14 and 10 uppercase letters and one more, joined by hyphens.

The generic section field label (§ 4.1) is the short label a scheme or a viewer shows for the species, such as its compound number ("1", "3a"); name is its chemical name.

The fields describe the species whose atoms the structure payload holds: all of them, hydrogens included, with the stated charge. The line notations name the species as a whole and imply no atom order, so a consumer MUST NOT map a SMILES atom to a payload atom by position. A producer writes only identifiers that it derived from these atoms or knows to describe them; when it writes several they name the same species. The validators cannot compare a SMILES or an InChI with the atoms and do not try.

A field that is absent states nothing: in particular a structure without charge is not declared neutral. A consumer that needs the charge or the multiplicity of such a structure takes it from provenance (§ 3.2) when the archive has exactly one structure section, and otherwise from its own default. The charge and multiplicity of a calculation are those of its job.spec (§ 5.9), which is authoritative for the job and may differ on purpose, for a vertical ionization for example.

Two rules relate the fields to the rest of the archive, and a validator checks both (§ 6):

• Electron count. When charge is present the species has N = Σ Z − charge electrons, Σ Z being the sum of the payload’s atomic_number values: N MUST NOT be negative, and when multiplicity is present too, the unpaired electrons, multiplicity − 1, MUST NOT exceed N and MUST have the parity of N. A violation is E_CHARGE_MULTIPLICITY.

• Agreement with provenance. In an archive with exactly one structure section, its charge and multiplicity MUST equal provenance.charge and provenance.multiplicity where both are present: there they state the same thing twice. A disagreement is E_ROOT_INCONSISTENT.

A methane molecule labelled as compound 2 of a scheme:

{
  "id": "structure_methane", "kind": "structure", "label": "2",
  "name": "methane", "charge": 0, "multiplicity": 1,
  "smiles": "C", "inchi": "InChI=1S/CH4/h1H4",
  "inchikey": "VNWKTOKETHGBQD-UHFFFAOYSA-N",
  "members": {"structure": {"path": "structure_methane/structure.json",
                            "format": "json", "sha256": "…"}}
}

These fields were added under v1, like the biomolecule metadata. An archive that holds several molecules, such as the species of a reaction scheme (§ 5.14), gives each its own structure section and identity, and every reader then knows which molecule is which and what its charge and spin are.

5.2 volume.*

A volume section samples a field on a regular grid. Every volume kind has a JSON grid member (the payload below) and a binary data member, float32 by default and float64 by opt-in. The kind fixes what data holds and its shape; the grid always describes the three spatial axes of data.

Kind	data shape	Holds	Unit of data
volume.density	[nx, ny, nz]	electron density	e / bohr³
volume.orbital	[nx, ny, nz]	orbital amplitude	amplitude on a bohr grid
volume.spin	[nx, ny, nz]	spin density	—
volume.elf	[nx, ny, nz]	electron localization function	—
volume.difference	[nx, ny, nz]	difference of two fields (below)	that of the operands
volume.potential	[nx, ny, nz]	electrostatic potential	hartree / e
volume.rdg	[nx, ny, nz]	reduced density gradient	dimensionless
volume.generic	[nx, ny, nz]	any other scalar field, named by the section label	—
volume.laplacian	[nx, ny, nz]	Laplacian of the electron density, ∇²ρ	e / bohr⁵
volume.vector	[nx, ny, nz, 3]	a Cartesian vector field (below)	—
volume.complex	[nx, ny, nz, 2]	a complex scalar field (below)	—
volume.series	[n, nx, ny, nz]	n scalar fields on one grid, with an axis member (below)	—

The units are those of § 4.3. A dash means that § 4.3 fixes none: the unit is that of the field, and a producer declares it as grid.units.data when the vocabulary of § 4.3 names it.

The grid shape is the [nx, ny, nz] of this table: the shape of a 3-D data member, the leading three extents of a volume.vector or volume.complex member, and the trailing three of a volume.series member.

The grid payload

// the CHGCAR-style grid of the conformance archive volume_periodic.qvf
// (a hexagonal cell; voxel vectors shown to 4 decimals)
{
  "origin": [0.0, 0.0, 0.0],
  "voxel_vectors": [[0.7748, 0.0, 0.0], [-0.3874, 0.6710, 0.0], [0.0, 0.0, 0.7913]],
  "shape": [6, 6, 8],
  "periodic": [true, true, true],
  "includes_endpoint": false,
  "structure_ref": "structure"
}

The grid payload is schema’d as $defs/VolumeGridPayload (strict). The same definition governs the grid member of basis.ao (§ 5.7) and the volume_grid member of reaction.path (§ 5.5).

Field	Type	Required	Meaning	Unit
origin	3 numbers	yes	Cartesian position of grid point (0, 0, 0).	bohr
voxel_vectors	3 × 3 numbers	yes	The step vectors v_0, v_1, v_2: row a is the displacement between neighbouring points along data axis a. Non-orthogonal grids use non-zero off-diagonal components.	bohr per step
shape	3 integers ≥ 1	yes	Number of points [nx, ny, nz] along the three spatial data axes; MUST equal the spatial extents of the data member (table above; for volume_grid, the trailing three dimensions of frame_volumes).	—
units	object	no	Declared units (§ 4.3, Declared units), keyed by a field of this payload or a member role of the section; data declares the unit of the values. origin and voxel_vectors are bohr when declared.	—
periodic	3 booleans	no	periodic[a] true: the field repeats with lattice vector a of the grid’s structure along data axis a. Absent means [false, false, false], a finite box.	—
includes_endpoint	boolean	no	Whether the points along a periodic axis include the endpoint of the period (below). Absent means true. It has no effect on an axis that is not periodic.	—
structure_ref	string	no	id of the structure section whose cell the grid samples. The section-level structure_ref (§ 4.1) takes precedence when both are present.	—

Point positions. For data index (i, j, k), with 0 ≤ i < shape[0], 0 ≤ j < shape[1] and 0 ≤ k < shape[2], the point position is

r(i, j, k) = origin + i·v_0 + j·v_1 + k·v_2

This is point-centred data: the grid has exactly shape points, at these positions, whatever the other fields say. For the 4-D kinds the extra axis is not a spatial axis: the point of data[i][j][k][c] (vector, complex) and of data[s][i][j][k] (series) is r(i, j, k).

Periodic grids. The grid’s structure is the structure section the section-level structure_ref names, else the one the grid’s structure_ref names; when neither is given, it is the archive’s structure section if the archive has exactly one. Along an axis a with periodic[a] true, the field is periodic with the lattice vector L_a of that structure, which is row a of its lattice_vectors converted to bohr (L_a = f · R[a], § 4.3, Lattice conventions), and the grid samples exactly one period. includes_endpoint says how:

• includes_endpoint: true (the default; the convention of cube files): the points span the closed period. The last plane is the image of the first, so shape[a] − 1 steps span one period: v_a · (shape[a] − 1) = L_a, and plane shape[a] − 1 repeats plane 0. The grid holds shape[a] − 1 distinct planes per period.

• includes_endpoint: false (the convention of VASP CHGCAR files): the points span the period exclusive of its endpoint, so shape[a] steps span one period: v_a · shape[a] = L_a. Index shape[a] would be plane 0 of the next cell; every plane is distinct.

A consumer that tiles a periodic grid along axis a (replicates it to draw a supercell), or that wraps an index or interpolates across the cell boundary, MUST drop the duplicated plane when includes_endpoint is true: the period in index space is shape[a] − 1, and plane shape[a] − 1 is not repeated before plane 0 of the next cell. When includes_endpoint is false the period is shape[a] and no plane is dropped. A producer MUST write the includes_endpoint value that matches its points, and SHOULD write structure_ref when the archive has more than one structure.

Worked example. One axis of a cell with L = 4.0 bohr, sampled by four points in each convention:

includes_endpoint: false  (CHGCAR style)   v = L / 4 = 1.0 bohr
  index         0      1      2      3   | 4 = index 0 of the next cell
  position     0.0    1.0    2.0    3.0  | 4.0
  distinct planes per period: 4
  tiled:       f0 f1 f2 f3 | f0 f1 f2 f3 | f0 …

includes_endpoint: true   (cube style)     v = L / 3 = 1.3333 bohr
  index         0       1       2       3
  position     0.0   1.3333  2.6667   4.0     index 3 is index 0 shifted by L
  distinct planes per period: 3
  tiled:       f0 f1 f2 | f0 f1 f2 | f0 …     plane 3 dropped

A consumer that tiles the cube-style grid without dropping plane 3 draws f0 f1 f2 f3 f0 … with f3 = f0: a doubled plane at every cell boundary, and a period of four steps where the cell has three, so the field drifts by one step per cell. A consumer that drops the last plane of the CHGCAR-style grid loses a quarter of the period. Producers of both conventions exist, and the numbers alone do not say which one an archive holds; includes_endpoint does. The conformance archive volume_periodic.qvf holds one periodic density in both conventions.

A validator checks, for every grid payload whose periodic[a] is true and whose structure resolves, that the structure’s pbc[a] is true and that v_a · (shape[a] − 1) (when includes_endpoint is true) or v_a · shape[a] (when it is false) equals L_a within a relative tolerance of 10⁻⁶, |span − L_a| ≤ 10⁻⁶ |L_a|, comparing the vectors component by component rather than their lengths (§ 6). An axis that periodic does not mark is not checked, so a grid may sample a box that is finite along an axis the structure is periodic in, such as the vacuum direction of a slab. A grid structure_ref that names no structure section is an unresolved reference.

volume.difference may add operand_a and operand_b (section ids); if one is present both MUST be. Sign convention: data = operand_a − operand_b.

volume.transition_density holds the transition density of one electronic excitation, ρ₀ₙ(r): the one-particle transition density between the reference state 0 and the excited state n, summed over spin, in e / bohr³. It integrates to zero, and its first moment ∫ r ρ₀ₙ(r) d³r is the transition dipole up to its sign. Its overall sign is arbitrary, as is the phase of the excited state. The density of the excited state minus that of the reference state is a difference density and is written as volume.difference. Two optional section fields (peers of members) name the state:

Field	Type	Meaning
excited_states_ref	string	id of the excited_states section (§ 5.12) the state belongs to.
state_index	integer ≥ 1	The index of the state in that section. Requires excited_states_ref.

A validator checks that excited_states_ref names an excited_states section and that state_index is the index of one of its states (§ 6).

volume.laplacian

data[i][j][k] is ∇²ρ at r(i, j, k) in e / bohr⁵: negative where the density concentrates charge and positive where it depletes it, the map QTAIM reads valence-shell charge concentrations from. The vocabulary of § 4.3 has no unit name for e / bohr⁵, so a producer does not declare grid.units.data for it (§ 9).

volume.vector and volume.complex

A volume.vector section holds a Cartesian vector at every grid point, such as the gradient of a density, an electric field or a current density: data[i][j][k][c] is component c (0 = x, 1 = y, 2 = z) of the vector at r(i, j, k), in the Cartesian frame of origin. The member is $defs/Volume4DVectorBinary, whose trailing extent is 3. Its unit is that of the field; a producer declares it as grid.units.data when the vocabulary of § 4.3 names it. The section field component is not used.

A volume.complex section holds a complex scalar field, such as a complex molecular orbital or a Bloch function at one k-point: data[i][j][k][0] is the real part and data[i][j][k][1] the imaginary part at r(i, j, k), the [re, im] layout of complex phonon eigenvectors (§ 5.6). The member is $defs/Volume4DComplexBinary, whose trailing extent is 2.

volume.series

A volume.series section holds n scalar fields on one grid, such as the density along a trajectory, a time-dependent density or the densities of several electronic states: data[s], the slab s, is the field at the axis value axis.values[s]. The members are grid, data ($defs/Volume4DBinary, [n, nx, ny, nz]) and axis, a JSON member that says what indexes the slabs.

Payload axis ($defs/VolumeSeriesAxisPayload, strict):

Field	Type	Required	Meaning	Unit
kind	"time", "frame", "state" or "custom"	yes	What indexes the slabs: a time; a frame of the trajectory or reaction path that trajectory_ref names; an electronic state; anything else, which labels describe.	—
values	array of numbers	yes	The axis value of each slab, in slab order: n entries. For kind: "frame" they are 0-based frame indices into the coords of the section trajectory_ref names, which need not be consecutive (a series may sample every other frame), and the schema requires non-negative integers.	units
units	unit name	no	Unit of values (§ 4.3). Absent means the values are pure numbers (dimensionless), as frame and state indices are; a time axis SHOULD declare its unit (fs or ps).	—
labels	array of strings	no	Display label of each slab, n entries, e.g. "S1".	—
trajectory_ref	string	no	id of the trajectory or reaction.path section whose frames the slabs belong to.	—

A validator checks that data has rank 4, that values and, when present, labels have one entry per slab (n, the leading extent of data), and that trajectory_ref names a trajectory or reaction.path section (§ 6).

volume.series is the general form of the per-frame volumes that a reaction.path carries as frame_volumes and volume_grid (§ 5.5); a producer SHOULD write new per-frame volumes as a volume.series.

5.3 wavefunction.gto

Carries an atom-centered Gaussian basis and MO coefficient matrices for molecular wavefunctions and the Γ-point (k = 0) crystalline orbitals of periodic systems. Crystalline orbitals at other k-points, or at several, are carried by wavefunction.bloch (§ 5.3.1), which shares the basis payload defined here. See Appendix A for the AO-ordering and primitive-normalization contract — this is the single most error-prone part of implementing a producer, and getting it wrong silently corrupts every rendered orbital. A producer that also writes the AO overlap member makes the contract checkable: validators compare its diagonal with Appendix A.1.

{
  "kind": "wavefunction.gto",
  "members": {
    "basis":       {"path": "wavefunction/basis.json", "format": "json", "sha256": "…"},
    "mo_metadata": {"path": "wavefunction/mo_metadata.json", "format": "json", "sha256": "…"},
    "mo_coefficients": {
      "path": "wavefunction/mo_coefficients.dat", "format": "binary",
      "dtype": "float64", "shape": [41, 41], "sha256": "…"
    }
  }
}

mo_coefficients shape is [n_mo, n_ao] (rows are MOs). Unrestricted wavefunctions replace it with mo_coefficients_alpha + mo_coefficients_beta. Complex coefficients add a trailing axis of length 2, and a two-component wavefunction doubles the AO axis (Spin and complex coefficients below).

Role	Format	Required	Meaning
basis	JSON, $defs/BasisPayload	yes	The basis set (below).
mo_metadata	JSON, $defs/MoMetadataPayload	yes	Orbital energies, occupations and labels (below).
mo_coefficients	float64 [n_mo, n_ao], or [n_mo, n_ao, 2] when complex	yes, single set	The MO coefficients, one row per MO, columns in the AO order of basis.
mo_coefficients_alpha, mo_coefficients_beta	as mo_coefficients	yes, unrestricted	The α and the β coefficients, replacing mo_coefficients.
overlap	float64 [n_ao, n_ao]	no, SHOULD	The AO overlap matrix (AO overlap and density matrices below).
density_matrix	float64 [n_ao, n_ao]	no; only with mo_coefficients	The spin-summed one-particle density matrix.
density_matrix_alpha, density_matrix_beta	float64 [n_ao, n_ao]	no; both or neither, only with the α and β coefficients	The α and the β one-particle density matrices.

n_ao is the number of AOs of the basis payload: the sum over its shells of 2l+1 (spherical) or (l+1)(l+2)/2 (Cartesian).

basis payload — schema’d as $defs/BasisPayload (strict). The AO order is the concatenation of the shells in array order, each in the in-shell order of Appendix A.2.

Field	Type	Required	Meaning	Unit
structure_ref	string	yes	Id of the structure section whose atoms the shell center indices refer to. A structure_ref on the section object takes precedence over this one (§ 4.1).	—
shells	array of shells (below)	yes	The contracted shells, in AO order.	—
pure	boolean	no	Angular type of every shell without its own pure: true = spherical harmonics, false = Cartesian. Absent means true.	—
n_ao	integer ≥ 0	no	Number of AOs: the sum over the shells of 2l+1 (spherical) or (l+1)(l+2)/2 (Cartesian); equals the AO dimension of the coefficient members (half of it for generalized).	—
ecp	array of ECP entries (below)	no	Effective core potentials, at most one per atom.	—
n_electrons	integer ≥ 0	no	Number of electrons the wavefunction describes: Σ Z − Σ n_core_electrons − charge, the sum of the atomic numbers of the structure, minus the core electrons the ecp entries replace, minus the total charge.	electrons

Each shell ($defs/BasisShell, strict):

Field	Type	Required	Meaning	Unit
center	integer ≥ 0	yes	0-based index into the atoms of the structure_ref section.	—
l	integer, 0–7	yes	Shell angular momentum.	—
exponents	≥ 1 numbers, each > 0	yes	Primitive exponents.	bohr⁻²
coefficients	≥ 1 numbers	yes	Contraction coefficients on N_i-normalized primitives (Appendix A.1), one per exponent.	—
pure	boolean	no	Overrides the payload-level pure for this shell.	—

exponents and coefficients MUST have the same length. JSON Schema cannot express that rule, so the schema does not check it.

n_electrons, when present, MUST equal the sum of the mo_metadata occupations over both spin channels, within 1e-6, unless occupation_semantics is transition_weight; and when root provenance.n_electrons (§ 3.2) is present as well, the two MUST be equal.

Effective core potentials

An ecp entry ($defs/BasisEcpCentre, strict) replaces the n_core_electrons innermost electrons of one atom by a potential. The wavefunction describes the other Z − n_core_electrons electrons of that atom, which is why n_electrons subtracts the core counts. A consumer that computes a property from the wavefunction, such as the electrostatic potential, a population or an electron count, gives an ECP atom the effective nuclear charge Z − n_core_electrons.

Field	Type	Required	Meaning	Unit
center	integer ≥ 0	yes	The atom, a 0-based index as for a shell’s center. No two entries name the same atom.	—
n_core_electrons	integer ≥ 0	yes	Number of electrons the potential replaces on this atom.	electrons
label	string	no	Name of the potential, e.g. "def2-ECP".	—
projectors	array of radial functions (below)	no	The local part and the semi-local channels. Absent, the potential is named by label and its core count only, and cannot be evaluated.	—

Each radial function ($defs/BasisEcpProjector, strict) is a sum of terms in the conventional semi-local form,

U(r) = Σ_i c_i · r^(n_i − 2) · exp(−α_i r²)        r in bohr, U in hartree

Field	Type	Required	Meaning	Unit
l	integer ≥ 0	yes	Angular momentum of a semi-local channel; for the local part, its conventional label L.	—
exponents	≥ 1 numbers, each > 0	yes	The α_i.	bohr⁻²
coefficients	≥ 1 numbers	yes	The c_i.	hartree · bohr^(2 − n_i)
powers	≥ 1 integers	yes	The radial powers n_i: n_i = 2 is a plain Gaussian, n_i = 0 carries r⁻².	—
local	boolean	no	true: this function is the local part. Absent means false.	—

The three arrays are parallel and MUST have the same length. The potential of the centre is

V(r) = U_L(r) + Σ_channels Σ_{m=−l..l} |l m⟩ U_l(r) ⟨l m|

where U_L is the radial function with local: true (zero when there is none), which acts on every angular momentum, and each semi-local channel multiplies the projector |l m⟩⟨l m| onto angular momentum l about the centre. A centre has at most one local part, and its l is the highest l of the centre: the local part of a potential with s, p and d channels is labelled l = 3. As in the tabulations of Gaussian, Molpro and NWChem, a semi-local channel of a centre with a local part holds the difference U_l(r) − U_L(r): QVF stores the function that multiplies the projector, so a producer copies such a table without converting it.

mo_metadata payload — schema’d as $defs/MoMetadataPayload (strict). spin selects one of two shapes. "unrestricted" carries its orbitals in an alpha and a beta object, matching mo_coefficients_alpha and mo_coefficients_beta, and no top-level n_mo, energies, occupations or symmetry_labels. Every other spin value carries one set of orbitals at the top level, matching mo_coefficients, and no alpha or beta. Per-MO arrays are in the row order of the coefficient member.

Field	Type	Required	Meaning	Unit
spin	"restricted", "unrestricted", "restricted_open" or "generalized"	yes	restricted: one set of spatial orbitals shared by both spins. unrestricted: separate α and β sets. restricted_open: one set of spatial orbitals, singly or doubly occupied. generalized: one set of two-component spin orbitals that mix α and β. See Spin and complex coefficients below.	—
orbital_kind	"canonical", "natural", "localized", "nto", "nbo", "iao", "ibo", "boys", "pipek_mezey" or "custom"	no	What the orbitals are: eigenfunctions of the converged Fock or Kohn–Sham operator (canonical, the meaning when absent), natural orbitals, localized orbitals of an unnamed method, natural transition orbitals, natural bond orbitals, intrinsic atomic or bond orbitals, Foster–Boys or Pipek–Mezey localized orbitals, or anything else (custom).	—
n_ao	integer ≥ 0	no	Number of AOs; equals the basis payload’s n_ao.	—
n_mo	integer ≥ 0	no; single set only	Number of MOs; equals the row count of mo_coefficients.	—
energies	array of numbers	yes, single set only	Orbital energy of each MO.	Hartree
occupations	array of numbers	yes, single set only	Occupation of each MO: electrons per orbital, or a transition weight (see occupation_semantics).	electrons
symmetry_labels	array of strings	no; single set only	Irreducible-representation label of each MO, one per entry of energies.	—
alpha, beta	spin channels (below)	yes, unrestricted only	The α and the β orbitals.	—
occupation_semantics	"electron_occupation" or "transition_weight"	no	Meaning of occupations: electrons per orbital (the meaning when absent) or the weights of natural transition orbitals.	—
k_point	3 numbers	no	Crystal momentum of the orbitals, in fractional coordinates of the reciprocal lattice; absent or [0, 0, 0] means Γ.	—
complex	boolean	no; yes for generalized, with the value true	true: every coefficient member is complex, float64 [n_mo, n_ao, 2] with the last axis (real, imaginary). Absent or false: real [n_mo, n_ao].	—
coefficient_encoding	"real" or "complex_split_last_axis"	no	Alternative spelling of complex (false and true); when both are present they MUST agree.	—
coefficient_components	["real", "imag"]	no	Order of the last axis of complex coefficients.	—
state_ref	string	no	Reference to the electronic state the orbitals describe, for state-specific orbitals. For natural transition orbitals it is the id of the excited_states section (§ 5.12) of the state.	—
state_index	integer ≥ 1	no	The index of the state the orbitals describe, in the excited_states section that state_ref names.	—
nto_role	"hole" or "particle"	no	Which half of a state’s natural transition orbitals the section holds (below).	—
localization_method	string	no	Name of the method that localized the orbitals.	—
localization_reference_basis	string, non-empty	no	Name of the minimal reference basis of free-atom AOs from which the producer constructed intrinsic atomic orbitals (IAOs), for IAO-based localization and IAO charges, e.g. "minao". See below.	—
atom_populations	[n_mo, n_atoms] numbers	no	Fraction of each localized orbital on each atom; each row sums to 1.	—
centroids_bohr	[n_mo, 3] numbers	no	Centroid of each localized orbital.	bohr
n_centres	array of integers ≥ 0	no	Number of atoms each localized orbital is centred on.	—

A spin channel ($defs/MoSpinChannel, strict) carries energies (Hartree) and occupations (electrons, 0 to 1), both required, and optionally n_mo (the row count of its coefficient member) and symmetry_labels (one per entry of its energies). What state_ref refers to for orbitals other than natural transition orbitals is not yet specified.

The IAO reference basis. Intrinsic atomic orbitals (IAOs) are built from the occupied orbitals of the calculation and a minimal basis of free-atom AOs, and intrinsic bond orbitals (IBOs) by localizing the occupied orbitals on them (G. Knizia, J. Chem. Theory Comput. 2013, 9, 4834–4843, doi:10.1021/ct400687b). The construction takes the minimal basis as an input: the IAOs, the IAO charges and the IBOs change slightly with it (that paper uses free-atom AOs from cc-pVTZ, MINAO, and compares them with Huzinaga’s MINI and with ANO-RCC functions). A producer that localizes on IAOs SHOULD therefore name that basis in localization_reference_basis, by the name its program uses ("minao", "mini", …), beside localization_method.

Deprecated fields. Three keys that producers wrote before the canonical carriers existed remain valid, so that archives which carry them keep validating. The schema annotates them "deprecated": true; producers SHOULD NOT write them, consumers SHOULD prefer the canonical carrier when both are present, and they may be removed in a future major version.

Field	Type	Meaning	Canonical carrier
iao_charges	array of numbers, one per atom	IAO partial charges, in e.	The iao_charge member of an atom_properties section (§ 5.7).
excitation_index	integer ≥ 0	The excited state natural transition orbitals describe, in the producer’s numbering.	state_index, the state’s index in the excited_states section that state_ref names (§ 5.12).
excitation_energy_ev	number	That state’s excitation energy, in eV.	The state’s excitation_energy in that excited_states section.

Natural transition orbitals. The natural transition orbitals (NTOs) of an excited state (§ 5.12) are written as two wavefunction.gto sections with the basis of the reference wavefunction: one holds the hole orbitals, which span the occupied space of the reference, and one the particle orbitals, which span its virtual space. Both mo_metadata payloads carry orbital_kind: "nto", occupation_semantics: "transition_weight", the same state_ref (the id of the excited_states section) and state_index (the index of the state there), and nto_role: "hole" in one section, "particle" in the other. Row k of the hole section and row k of the particle section are the k-th hole–particle pair, so the two sections have the same number of rows, in order of decreasing weight, and the same occupations: the weight λₖ of each pair. λₖ is the k-th eigenvalue of T Tᵀ for the transition density matrix T in the orbital basis, the square of its k-th singular value, and the weights of a normalized state sum to 1. energies, which the payload requires, has no meaning for NTOs: producers SHOULD write zeros, and consumers ignore it. The state’s nto_ref names the hole section; a consumer finds the particle section as the wavefunction.gto section whose mo_metadata has the same state_ref and state_index and nto_role: "particle".

For an unrestricted reference, there are still two sections per state, not four. Both payloads use spin: "unrestricted", with alpha and beta objects and mo_coefficients_alpha / mo_coefficients_beta members. Each spin channel has its own corresponding-orbital transformation and its own hole–particle pairs. Row k of the hole’s α channel pairs with row k of the particle’s α channel, and likewise for β. Hole and particle MUST have the same row count and the same occupations in each spin channel. The α and β row counts may differ, including an empty channel. Each channel’s occupations MUST be nonnegative, in non-increasing order, with one weight per coefficient row; its energies and optional n_mo have that same length/count. The weights are squared singular values λₖ = σₖ², not singular values. For a normalized state, both spins together sum to 1; neither spin is separately normalized. The hole and particle each carry the same weights, so this sum counts each pair once. nto_ref still names the hole section and the particle lookup above is unchanged and unique. The state identified by state_ref and state_index MUST exist.

For compatibility, deprecated NTO metadata without nto_role remains accepted as in toolkit v0.3.0 and is exempt from the new unrestricted channel/pair checks. Consumers MUST NOT infer a missing role from section order. New writers use the complete canonical fields described above.

The normalization statement is conditional: full TDDFT/RPA transition densities can have a non-unit weight sum because of de-excitation terms. QVF does not label a transition density as normalized, and validators do not impose a unit sum. See R. L. Martin, J. Chem. Phys. 118, 4775 (2003), doi:10.1063/1.1558471, equations 4–9 and the spin-unrestricted extension. This clarification does not specify NTOs of restricted-open references.

Spin and complex coefficients

• restricted and restricted_open use the single-set shape: one mo_coefficients member and top-level energies and occupations. Occupations run from 0 to 2 electrons per spatial orbital. A restricted_open wavefunction has singly occupied orbitals (fractional occupations are allowed, for natural or ensemble orbitals); by the usual high-spin convention a singly occupied orbital carries an α electron.

• unrestricted uses the two-set shape: mo_coefficients_alpha and mo_coefficients_beta, described by the alpha and beta spin channels, with occupations from 0 to 1.

• generalized is a two-component (spinor) wavefunction in the single-set shape. Each MO is a spin orbital ψ_i = Σ_μ (C[i, μ] χ_μ α + C[i, n_ao + μ] χ_μ β): the AO axis of mo_coefficients has 2 n_ao entries in the spinor layout [α AOs…, β AOs…], the α components on the n_ao AOs of basis in their Appendix A.2 order, then the β components on the same AOs in the same order. n_ao in basis and mo_metadata stays the number of spatial AOs. Occupations run from 0 to 1. A generalized wavefunction MUST carry complex: true; a real one is written with a zero imaginary part.

• complex: true means that every coefficient member has a trailing axis of length 2, [re, im]: [n_mo, n_ao, 2], or [n_mo, 2 n_ao, 2] for generalized. With complex absent or false every coefficient member is real and has no such axis. coefficient_encoding: "complex_split_last_axis" is the same statement as complex: true (and "real" as false) and is read the same way when complex is absent.

AO overlap and density matrices

The optional members overlap, density_matrix, density_matrix_alpha and density_matrix_beta are float64 [n_ao, n_ao] matrices whose rows and columns follow the AO order of basis (Appendix A.2), real in every case, including a complex or generalized wavefunction.

• overlap is the AO overlap matrix S[μ, ν] = ⟨χ_μ | χ_ν⟩ of the contracted AOs exactly as basis defines them: primitives normalized with the N_i of Appendix A.1 and contracted with the stored coefficients. Producers SHOULD write it. Its diagonal lets any consumer check that the stored coefficients and AO order mean what the producer’s own integral code meant (Appendix A.1, Verifying with overlap), and validators do: a diagonal that disagrees with the basis is the error E_NORMALIZATION.

• density_matrix is the spin-summed (total) one-particle density matrix P in the AO basis of a single-set wavefunction, so that the electron density is ρ(r) = Σ_μν P[μ, ν] χ_μ(r) χ_ν(r) and tr(P S) is the number of electrons it describes. For orbitals that define it, such as an SCF wavefunction, P[μ, ν] = Σ_i n_i C[i, μ] C[i, ν] with the occupations n_i; a correlated method may store its own density, which its orbitals do not reproduce. For complex coefficients P is the real part of the Hermitian density matrix, all that ρ needs because the AOs are real; for generalized it is the spin-summed spatial density, P[μ, ν] = Re Σ_i n_i (C̄[i, μ] C[i, ν] + C̄[i, n_ao + μ] C[i, n_ao + ν]).

• density_matrix_alpha and density_matrix_beta are the α and the β density matrices of an unrestricted wavefunction; the total density is their sum and the spin density their difference.

The density members follow the coefficient members: density_matrix appears only with mo_coefficients, and density_matrix_alpha and density_matrix_beta appear only together and only with mo_coefficients_alpha and mo_coefficients_beta.

Checks

Besides the payload definitions, validators check (§ 6): the rank of every coefficient member against complex; the length of every symmetry_labels against its energies; the [n_ao, n_ao] shape of overlap and of the density members, and their pairing with the coefficient members; n_electrons against the occupations (all E_MEMBER_MALFORMED) and against provenance.n_electrons (E_ROOT_INCONSISTENT); and the diagonal of overlap against Appendix A.1 (E_NORMALIZATION).

5.3.1 wavefunction.bloch — k-resolved Bloch orbitals, provisional

Provisional. This kind was promoted from the vendor section x_vibeqc.bloch_wavefunction by maintainer decision before a second independent producer shipped it (GOVERNANCE.md, “Vendor → canonical promotion”); its registry.json promotions entry carries "status": "provisional". It is canonical in every other respect: the schema and the validators check it, and the conformance corpus exercises it. It becomes final when a second producer ships it, and any revision needed before then is additive (§ 7.2).

Carries the k-resolved crystalline orbitals of a periodic system: complex MO coefficients at every k-point of a set, for one or two spin channels, over the atom-centred Gaussian basis of the cell, with their energies and occupations. A producer whose orbitals live at Γ alone may keep using wavefunction.gto (§ 5.3); a producer with orbitals at several k-points, or at one k-point other than Γ, writes this kind.

{
  "id": "wf_bloch",
  "kind": "wavefunction.bloch",
  "members": {
    "basis":       {"path": "wf_bloch/basis.json", "format": "json", "sha256": "…"},
    "kpoints":     {"path": "wf_bloch/kpoints.json", "format": "json", "sha256": "…"},
    "mo_metadata": {"path": "wf_bloch/mo_metadata.json", "format": "json", "sha256": "…"},
    "mo_coefficients": {"path": "wf_bloch/mo_coefficients.bin", "format": "binary",
                        "dtype": "float64", "shape": [2, 2, 2, 2, 2], "sha256": "…"},
    "energies":    {"path": "wf_bloch/energies.bin", "format": "binary",
                    "dtype": "float64", "shape": [2, 2, 2], "sha256": "…"},
    "occupations": {"path": "wf_bloch/occupations.bin", "format": "binary",
                    "dtype": "float64", "shape": [2, 2, 2], "sha256": "…"}
  }
}

Bloch sum. The basis payload is the one of § 5.3, with the AO order and the primitive normalization of Appendix A; its shell center indices refer to the atoms of one cell. For each AO χ_μ the Bloch function at crystal momentum k is

φ_μk(r) = N^(−1/2) · Σ_T e^{+i k·T} · χ_μ(r − T)

where T runs over the lattice translations T = n₁a₁ + n₂a₂ + n₃a₃ along the periodic axes (n_i = 0 for an axis whose pbc entry is false) and N is the number of cells in the Born–von Kármán supercell. k is given in fractional coordinates of the reciprocal lattice, k = k₁b₁ + k₂b₂ + k₃b₃ with a_i · b_j = 2π δ_ij, so k·T = 2π (k₁n₁ + k₂n₂ + k₃n₃). The phase is e^{+ik·T}, and the AO’s position inside the cell is not part of it. Orbital m of spin channel s at k-point k is

ψ_msk(r) = Σ_μ C_ksmμ · φ_μk(r),   C_ksmμ = c[k, s, m, μ, 0] + i · c[k, s, m, μ, 1]

with c the mo_coefficients array. In this convention the overlap of two Bloch functions is S_μν(k) = Σ_T e^{ik·T} ⟨χ_μ(r) | χ_ν(r − T)⟩, and the orbitals of a converged calculation are orthonormal in that metric, C†S(k)C = 1. The electron density of the cell is ρ(r) = Σ_k w_k Σ_s Σ_m n_ksm |ψ_msk(r)|², with the weights w of the kpoints payload and the occupations n. An orbital multiplied by a phase e^{iθ} is the same state; consumers MUST NOT assume a particular gauge.

Member	Format	Required	Shape and meaning	Unit
basis	JSON, $defs/BasisPayload (strict)	yes	The contracted shells of the cell, as for wavefunction.gto (§ 5.3). Its structure_ref names the structure unless the section carries its own.	—
kpoints	JSON, $defs/BlochKpointsPayload (strict)	yes	The k-points, in the order of axis 0 of the binary members; table below.	—
mo_metadata	JSON, $defs/BlochMoMetadataPayload (strict)	yes	The orbital set; table below.	—
mo_coefficients	float64	yes	[n_k, n_spin, n_mo, n_ao, 2]: the coefficient of Bloch function μ in orbital m of spin channel s at k-point k, with the last axis (real, imaginary), as for complex wavefunction.gto coefficients.	—
energies	float64	yes	[n_k, n_spin, n_mo] orbital energies.	hartree
occupations	float64	yes	[n_k, n_spin, n_mo] electrons in each orbital at each k-point, not weighted by the k-point weights: 0 to 2 when n_spin is 1, 0 to 1 when it is 2.	electrons

Spin channel 0 is α and 1 is β. Unlike the arrays of § 5.6, whose spin axis leads, the orbital members keep the k-point axis first, so that the orbitals of one k-point are contiguous.

Payload kpoints ($defs/BlochKpointsPayload, strict; kpoints is required):

Field	Type	Meaning	Unit
kpoints	≥ 1 arrays of 3 numbers	Every k-point, in fractional reciprocal-lattice coordinates (see above). n_k is their number.	—
weights	array of numbers ≥ 0	Integration weight of each k-point, one per k-point, summing to 1 within 1e-6. Absent when the k-points are not an integration set, such as points along a path.	—
labels	array of strings	One label per k-point, such as a high-symmetry name; "" marks an unlabelled point.	—
mesh	3 integers ≥ 1	Dimensions of the uniform mesh the k-points were taken from, when they were: the k-points are its points, or the irreducible subset of them that the weights account for.	—
shift	3 numbers	Fractional reciprocal-lattice position of mesh point (0, 0, 0); absent means a Γ-centred mesh.	—
time_reversal	boolean	true when the set was reduced with time-reversal symmetry: the orbitals at −k are the complex conjugates of those at k, and the weight of k includes that of −k. Absent means false.	—
units	object	Optional declaration (§ 4.3, Declared units) restating that kpoints, weights and shift are dimensionless.	—

Payload mo_metadata ($defs/BlochMoMetadataPayload, strict). Per-orbital energies and occupations are the binary members above, not fields of this payload.

Field	Type	Required	Meaning
spin	"restricted" or "unrestricted"	yes	One set of spatial orbitals for both spins (n_spin 1), or separate α and β sets (n_spin 2).
n_spin	1 or 2	yes	Axis 1 of the binary members; 1 for restricted, 2 for unrestricted.
n_mo	integer ≥ 0	yes	Axis 2 of the binary members: the orbitals at each k-point and spin.
n_ao	integer ≥ 0	yes	Axis 3 of mo_coefficients; equals the basis payload’s n_ao.
complex	true	yes	The coefficients are complex; always true.
k_point_convention	"fractional"	yes	kpoints are fractional reciprocal-lattice coordinates; the only value in v1.
orbital_kind	as in § 5.3	no	What the orbitals are; absent means canonical.
n_mo_per_k	array of integers ≥ 0	no	The number of orbitals that are defined at each k-point, one entry per k-point, each at most n_mo, for a producer whose orbital count differs between k-points (canonical orthogonalisation removing a different number of near-linear-dependent combinations at each k). Orbitals n_mo_per_k[k] to n_mo − 1 at k-point k are padding with zero coefficients and zero occupations, and consumers ignore them. Absent means n_mo everywhere.
fermi_energy	{value, units}	no	Fermi level, on the absolute scale of energies.
units	object	no	Optional declaration restating that energies is hartree.

Structure. The section’s structure is the one its section-level structure_ref names, else the one basis.structure_ref names (§ 4.1). It MUST be a structure section with at least one periodic axis (§ 5.1).

Rules a validator checks (§ 6): mo_coefficients is [n_k, n_spin, n_mo, n_ao, 2] with n_spin 1 or 2; energies and occupations have its [n_k, n_spin, n_mo]; the kpoints payload lists n_k k-points and, when present, n_k labels and n_k weights that sum to 1 within 1e-6; mo_metadata states the n_spin that spin implies and the n_spin, n_mo and n_ao of the binary members, and n_mo_per_k has n_k entries of at most n_mo; basis.n_ao equals n_ao. A disagreement, or a structure with no periodic axis, is E_MEMBER_MALFORMED; a basis.structure_ref that does not name a structure section (when the section names none itself) is E_REF_UNRESOLVED.

With bands. When an archive carries both a wavefunction.bloch section and a bands section (§ 5.6) whose k-points include some of the Bloch section’s, the band energies at those k-points SHOULD agree with energies once converted from hartree to eV (mind the axis orders, [n_spin, n_k, n_bands] against [n_k, n_spin, n_mo]). Validators do not check this.

5.4 Spectra

Every spectra.* section carries exactly one JSON member, spectrum. The six one-dimensional kinds share one payload, $defs/SpectrumPayload; spectra.nmr and spectra.epr carry object-shaped parameter sets, $defs/NmrSpectrumPayload and $defs/EprSpectrumPayload.

Each payload definition in § 5 has one of three strictness levels:

• strict — no keys other than the listed ones, at the root and in every listed object, except extension keys whose names begin with x_;

• typed-open — the listed fields are typed; the root stays open for forward growth;

• permissive — the listed fields are typed and every object stays open; a later revision may tighten the definition once producer conventions settle.

A consumer ignores keys it does not know in an open object.

One-dimensional spectra

spectra.ir, spectra.raman, spectra.uvvis, spectra.ecd, spectra.vcd and spectra.generic. Payload: $defs/SpectrumPayload, typed-open.

Field	Type	Required	Meaning	Unit
frequencies	number[]	yes	The x value of every point or line.	the kind’s § 4.3 unit, or x_units
intensities	number[]	yes	The y value of each frequencies entry, in the same order.	the kind’s § 4.3 unit, or y_units
x	number[]	no	Alias of frequencies under a quantity-neutral name: the same values in the same order.	as frequencies
x_units	unit name (§ 4.3)	no	Unit of frequencies and x.	—
y_units	unit name (§ 4.3)	no	Unit of intensities.	—
peaks	object[]	no	Annotated peaks: x (number, required), y (number), width (number ≥ 0, full width at half maximum), label (string), assignment ({mode_index?, state_index?}, integers ≥ 0).	x, width as frequencies; y as intensities
broadening	object	no	The line shape the producer applied, or recommends: type (required: none, gaussian or lorentzian), fwhm (number > 0), units (unit name).	fwhm in units, else in the x unit
temperature_k	number > 0	no	Temperature the spectrum refers to.	K
raman	object	no	laser_nm (number > 0): excitation wavelength; depolarization_ratios (number[]): one per line, in frequencies order.	nm; dimensionless
uvvis	object	no	x_axis (energy_ev or wavelength_nm): the x quantity the producer recommends for display. It does not change the stored values.	—
states_ref	string	no	id of the excited_states section (§ 5.12) whose states the peaks’ assignment.state_index values name.	—

The x axis. frequencies carries the x axis in the unit § 4.3 gives the kind — cm⁻¹ for spectra.ir, eV for spectra.uvvis — unless x_units declares another unit. The name is historical and is kept for every kind, including those whose x values are energies (UV-Vis, ECD); x is an optional quantity-neutral alias, and a rename is left to a future major version. For a kind § 4.3 gives no unit (spectra.raman, spectra.ecd, spectra.vcd, spectra.generic) producers SHOULD declare x_units and y_units; consumers conventionally assume cm⁻¹ for Raman and VCD and eV for ECD. A declared unit is a declaration, not a conversion: the values are stored in it, and a consumer MUST NOT read them in the kind’s default unit. x_units, y_units and broadening.units are unit names of § 4.3 (Declared units).

One length. frequencies, intensities and, when present, x MUST have the same length. JSON Schema cannot express this rule, so a validator checks it separately (§ 6).

peaks[].assignment.mode_index is a 0-based index into the modes of the archive’s vibrations section (§ 5.5); state_index identifies the electronic state a transition reaches. When the payload carries states_ref, every state_index is the index of a state of the excited_states section that states_ref names (§ 5.12), and a validator checks both (§ 6); without states_ref, states are numbered as the producer numbers them. The raman and uvvis blocks are meaningful only in the kind they name.

spectra.nmr

Payload: $defs/NmrSpectrumPayload, permissive. Atom indices (atom_index, i, j) are 0-based indices into the atoms of the archive’s structure.

Field	Type	Required	Meaning	Unit
isotope	string	no	Observed nucleus, e.g. "1H", "13C".	—
reference	string	no	Shift reference, e.g. "TMS".	—
solvent	string	no	Solvent or solvation model, when one was used.	—
chemical_shifts	object[]	no	One entry per nucleus: atom_index (integer ≥ 0, required), symbol, isotropic_shift_ppm (required), anisotropy_ppm, asymmetry.	ppm; asymmetry dimensionless
shielding_tensors	object[]	no	One entry per nucleus: atom_index (integer ≥ 0), tensor (3 × 3), isotropic_ppm.	ppm
j_couplings	object[]	no	One entry per atom pair: i, j (integers ≥ 0, required), value_hz (required), isotope_i, isotope_j.	Hz

spectra.epr

Payload: $defs/EprSpectrumPayload, permissive. Units are fixed: g-values are dimensionless; hyperfine and zero-field-splitting parameters are in MHz.

Field	Type	Required	Meaning	Unit
g_tensor	object	no	matrix (3 × 3), isotropic (one third of the trace), principal (three principal values).	dimensionless
hyperfine	object[]	no	One entry per magnetic nucleus: atom_index (integer ≥ 0, required), symbol, isotope, a_iso_mhz, a_tensor_mhz (3 × 3), a_principal_mhz (three values).	MHz
zero_field_splitting	object	no	d_mhz (axial D), e_mhz (rhombic E), tensor_mhz (3 × 3).	MHz

A 3 × 3 tensor of either payload is written as three rows in the Cartesian frame of the structure.

5.5 Trajectories, reactions, vibrations

trajectory: JSON metadata (atom identities, per-frame metadata) + coords [n_frames, n_atoms, 3] in Å, plus optional per-frame members (the cell, velocities, gradients, times, energies, cell volumes, temperatures; below). reaction.path uses the same layout and adds waypoint records ({frame_index, label, kind, energy_eh?}, kind ∈ reactant/transition_state/intermediate/product/point). reaction.waypoints carries only annotations and references an existing trajectory section via the section-level trajectory_ref. vibrations: JSON metadata (frequencies in cm⁻¹) + displacements float64 [n_modes, n_atoms, 3]. scan.surface: JSON metadata + the 1-D coordinate values axis_a and axis_b + energies [nA, nB], with optional relaxed geometries.

trajectory members. Every binary member is little-endian and C-ordered (§ 4.2), in the frame order and atom order of coords. The per-frame members are optional and independent: an optimization may carry only energies, a molecular-dynamics run all of them.

Role	dtype	Shape	Required	Meaning	Unit
metadata	JSON	—	yes	Atom identities and per-frame metadata ($defs/TrajectoryMetadataPayload, below).	—
coords	float64, or float32	[n_frames, n_atoms, 3]	yes	Cartesian position of every atom in every frame. float32 only when metadata.precision is "float32".	Å
lattice	float64	[3, 3] or [n_frames, 3, 3]	no	The cell, in the structure convention: rows, row i the lattice vector of axis i, paired with metadata.pbc[i]. [3, 3] is one cell for every frame; [n_frames, 3, 3] one cell per frame (variable-cell, NPT).	Å
velocities	float64	[n_frames, n_atoms, 3]	no	Velocity of every atom in every frame.	Å / fs
gradient	float64	[n_frames, n_atoms, 3]	no	The energy gradient dE/dR of every atom in every frame, as the gradient of a forces section (§ 5.10): the forces are its negative. The role is named for what it stores, not forces, so that the sign cannot be misread.	hartree / bohr
times	float64	[n_frames]	no	Time of each frame.	fs
energies	float64	[n_frames]	no	Energy of each frame: the binary form of metadata.energies, preferred for long runs.	hartree
cell_volumes	float64	[n_frames]	no	Volume of the cell of each frame.	ų
temperatures	float64	[n_frames]	no	Instantaneous temperature of each frame.	kelvin

The schema types these members as $defs/TrajectoryCoords, $defs/TrajectoryLattice, $defs/TrajectoryFrameVectors (velocities, gradient) and $defs/TrajectoryFrameScalars (the [n_frames] members). The rules that relate the members to each other are semantic, and a validator checks them (§ 6):

• Extents. n_frames and n_atoms are the first two extents of coords. Every per-frame member has n_frames as its leading extent, and velocities and gradient have n_atoms as their second; a [n_frames, 3, 3] lattice has one cell per frame.

• Precision. coords MAY be float32 when metadata.precision is "float32", which halves the size of a long run; precision, when present, MUST name the dtype of coords, and float32 coords without it are an error. Every other member is float64.

• Periodicity. A trajectory that carries lattice MUST carry metadata.pbc, and a true entry of metadata.pbc MUST be accompanied by lattice, mirroring the structure contract of § 5.1: pbc is the normative carrier of periodicity, and a row of an aperiodic axis is bookkeeping, not a cell edge. A trajectory without lattice is molecular.

• Energies. When both the binary energies and metadata.energies are present they MUST agree within 1e-10 hartree, frame by frame. Producers SHOULD prefer the binary member for long runs and MAY then omit the JSON array.

• Times. When times is absent and metadata.timestep_fs is present, frame k (0-based) is at k × timestep_fs. When times is present it is the time of each frame, whatever timestep_fs says.

trajectory.lattice is not the convention of reaction.path.lattice (columns, bohr); Lattice conventions in § 4.3 states both. A validator reads each in its own convention and never mixes them.

reaction.path members. A reaction.path has the metadata and coords of a trajectory, with the same rules, and may carry the per-frame members velocities, gradient, times and energies of the table above, with the same shapes, units and rules. It carries neither cell_volumes nor temperatures, and its cell is its own lattice member, below. The frame_volumes and volume_grid members carry per-frame volumetric data ($defs/Volume4DBinary, $defs/VolumeGridPayload).

Periodic reaction paths. reaction.path may carry an optional lattice binary member: float64 with shape [3, 3] (fixed cell — the common case) or [n_frames, 3, 3] (variable cell), columns = a, b, c in bohr. Its presence is what marks the path periodic — a reaction.path without lattice is unambiguously molecular and renderers must draw no cell. This is capability detection by member presence, per § 7.1; it does not involve a qvf_version bump. This is not the layout or unit of structure.lattice_vectors or of trajectory.lattice (rows, Å); see Lattice conventions in § 4.3 for the side-by-side comparison and the conversion.

trajectory metadata payload — schema’d as $defs/TrajectoryMetadataPayload (typed-open), which extends $defs/TrajectoryMetadataCommon, the keys it shares with the reaction.path metadata. It names the atoms, in the atom order of coords, through at least one of symbols, atomic_numbers and atoms; when more than one is present they MUST describe the same atoms. Per-frame arrays are in frame order.

Field	Type	Required	Meaning	Unit
symbols	array of strings	one of three	Element symbol of each atom.	—
atomic_numbers	array of integers ≥ 0	one of three	Atomic number of each atom.	—
atoms	array of {symbol, atomic_number} ($defs/TrajectoryAtom)	one of three	Atom identities as objects.	—
energies	array of numbers	no	Energy of each frame; equal to the binary energies member within 1e-10 hartree when both are present.	Hartree
n_frames	integer ≥ 0	no	Number of frames; equals the leading dimension of coords.	—
kind	"optimization", "irc", "md", "neb", "scan" or "custom"	no	What produced the frames: md is molecular dynamics; scan covers relaxed and rigid coordinate scans.	—
pbc	3 booleans	for a trajectory with lattice	Per-axis periodicity of the frames, as in the structure payload (§ 5.1); absent means molecular. REQUIRED when the section carries lattice, and a true entry requires lattice.	—
ensemble	"nve", "nvt", "npt", "nph" or "custom"	no	Thermodynamic ensemble of a molecular-dynamics run.	—
timestep_fs	number > 0	no	Time between consecutive frames; frame k is at k × timestep_fs when the section has no times member.	fs
precision	"float64" or "float32"	no	Precision of coords; absent means float64. It MUST agree with the member’s dtype; float32 coords require "float32".	—
units	object	no	Declared units (§ 4.3, Declared units), keyed by a field of this payload or a member role of the section. The units of this section remain the contract, so a declaration restates them: energies hartree, coords angstrom, times and timestep_fs fs, and for a trajectory lattice angstrom, cell_volumes a3 and temperatures kelvin (for reaction.path, lattice bohr). velocities (Å/fs) and gradient (hartree/bohr) have no unit name in the vocabulary and are not declared.	—

reaction.path metadata payload — schema’d as $defs/ReactionPathMetadataPayload (typed-open), which also extends $defs/TrajectoryMetadataCommon: every field of the trajectory table above, with the same rules except the pbc requirement, which belongs to a trajectory’s lattice (a reaction path is periodic when it carries its own lattice member), plus:

Field	Type	Required	Meaning	Unit
waypoints	array of waypoint records (below)	no	Annotated frames of the path.	—
reaction_coordinate	array of numbers	no	Value of the reaction coordinate at each frame: the abscissa of an energy profile.	reaction_coordinate_unit
reaction_coordinate_label	string	no	Display label of the reaction coordinate.	—
reaction_coordinate_unit	string	no	Unit of reaction_coordinate, e.g. "bohr" or "rad".	—
dim	integer, 0–3	no	Number of periodic dimensions, shared by every frame of a periodic path.	—
dim_per_frame	array of integers, 0–3	no	Number of periodic dimensions of each frame, for a path whose frames differ; used instead of dim.	—
volume_frame_index	array of integers ≥ 0	no	For each slab of frame_volumes, in order, the 0-based path frame it belongs to, so that volumes can be emitted for a subset of the frames. One entry per slab.	—
volume_label	string	no	Display label of the per-frame volumes.	—
volume_isovalue	number	no	Suggested isovalue for the per-frame volumes.	that of the volume data

The volume_grid member that accompanies frame_volumes is a grid payload (§ 5.2, $defs/VolumeGridPayload).

Per-frame volumes and volume.series. The frame_volumes and volume_grid members of a reaction.path are the older form of a volume.series section (§ 5.2) whose axis has kind: "frame", values equal to the path’s volume_frame_index (or 0, 1, …, n − 1 when it is absent) and trajectory_ref naming the path; volume_label corresponds to the section label of the series, and volume_isovalue to the isovalue of a section hint (§ 3.4.1). The two forms carry the same data, [n, nx, ny, nz] slabs on one grid. Producers SHOULD write per-frame volumes as a volume.series section, which any trajectory or reaction path can name; both forms remain valid in v1 and neither is deprecated, so a consumer that reads per-frame volumes SHOULD read both.

Waypoint record — $defs/ReactionWaypoint (strict), used by reaction.path metadata and by reaction.waypoints:

Field	Type	Required	Meaning	Unit
frame_index	integer ≥ 0	yes	0-based index of the annotated frame: of the section’s own coords for reaction.path, of the coords of the trajectory named by trajectory_ref for reaction.waypoints.	—
label	string	yes	Display label, e.g. "TS1".	—
kind	"reactant", "transition_state", "intermediate", "product" or "point"	yes	Role of the frame on the path; point marks any other annotated frame.	—
energy_eh	number	no	Energy of the frame.	Hartree

reaction.waypoints waypoints payload — schema’d as $defs/ReactionWaypointsPayload (strict):

Field	Type	Required	Meaning	Unit
waypoints	array of waypoint records	yes	Annotated frames of the referenced trajectory.	—
reaction_coordinate	array of numbers	no	Value of the reaction coordinate at each frame of that trajectory, in frame order.	—

scan.surface metadata payload — schema’d as $defs/ScanSurfaceMetadataPayload (typed-open). The axis objects axis_a and axis_b are the preferred form. The flat label and unit keys are recognised alternatives that producers already write; when both forms are present, the objects take precedence.

Field	Type	Required	Meaning	Unit
axis_a, axis_b	axis objects (below)	no	The first driven coordinate (along the rows of energies) and the second (along its columns).	—
axis_a_label, axis_b_label	string	no	Flat alternatives to axis_a.label and axis_b.label.	—
coordinate_a_label, coordinate_b_label	string	no	Flat alternatives to axis_a.label and axis_b.label.	—
coordinate_a_unit, coordinate_b_unit	string	no	Flat alternatives to axis_a.unit and axis_b.unit.	—
atoms	array of {symbol, atomic_number}	no	Atom identities, in the atom order of geometries.	—
energy_unit	string	no	Unit of the energies member; absent means Hartree.	—
units	object	no	Declared units, as for trajectory; the usual keys are the member roles axis_a, axis_b, energies and geometries, none of which has a fixed unit.	—

An axis object ($defs/ScanSurfaceAxis, typed-open) carries label (string, required), unit (string: the unit of the values in the matching axis_a or axis_b binary member, e.g. "bohr" or "rad") and atoms (the 0-based indices of the atoms that define the coordinate: two for a distance, three for an angle, four for a dihedral).

vibrations metadata payload — schema’d as $defs/VibrationsMetadataPayload (typed-open). Per-mode arrays hold one entry per mode, in the mode order of displacements. An imaginary mode is written as a negative frequency whose magnitude is the imaginary wavenumber: a mode at 512i cm⁻¹ is written -512.0. imaginary, when present, MUST agree with the sign of frequencies.

Field	Type	Required	Meaning	Unit
frequencies	array of numbers	yes	Harmonic wavenumber of each mode; negative for an imaginary mode.	cm⁻¹
ir_intensities	array of numbers	no	IR intensity of each mode.	km·mol⁻¹
raman_activities	array of numbers	no	Raman scattering activity of each mode.	Å⁴·amu⁻¹
reduced_masses	array of numbers	no	Reduced mass of each mode.	amu
force_constants	array of numbers	no	Force constant of each mode.	mdyn·Å⁻¹
symmetry_labels	array of strings	no	Irreducible-representation label of each mode.	—
imaginary	array of booleans	no	true for an imaginary mode.	—
n_modes	integer ≥ 0	no	Number of modes; equals the leading dimension of displacements.	—
symbols	array of strings	no	Element symbol of each atom, in the atom order of displacements.	—
atoms	array of atoms as in the structure payload ($defs/StructureAtom)	no	Reference geometry: one atom per atom of displacements, in the same order, with Cartesian positions.	Å

vibrations hessian_ref. A vibrations section MAY carry the section field hessian_ref (a peer of members), the id of the hessian section (§ 5.11) its modes were derived from. A validator checks that it names a hessian section (§ 6).

5.6 Bands, DOS, and periodic kinds

Each kind below lists its members; each JSON member names the schema definition its payload conforms to ($defs/…), and a validator checks it against that definition. A payload is strict when it allows only the fields of its table plus vendor keys beginning x_, and typed-open when the fields of its table are typed and further keys are allowed. Units are those of § 4.3; the Unit columns restate them. All indices are 0-based.

Spin axis

An array that resolves spin carries it as its leading axis, of length n_spin (1 or 2; index 0 is α, 1 is β), as bands.eigenvalues [n_spin, n_k, n_bands] always has. Several members also have an older, lower-rank form without that axis:

Member	With the spin axis	Lower-rank form (means n_spin = 1)
bands.projections	[n_spin, n_k, n_bands, n_channels]	[n_k, n_bands, n_channels]
bands.occupations	[n_spin, n_k, n_bands]	—
dos.total.dos	[n_spin, n_points]	[n_points]
dos.projected.projections	[n_spin, n_channels, n_points]	[n_channels, n_points]
dos.coop / dos.cohp projections	[n_spin, n_pairs, n_points]	[n_pairs, n_points]
dos.coop / dos.cohp integrated	[n_spin, n_pairs]	[n_pairs]

Both forms are legal, and a consumer reads the lower-rank form as n_spin = 1. In a bands section a rank-4 projections and an occupations MUST have the [n_spin, n_k, n_bands] extents of eigenvalues, and a rank-3 projections its [n_k, n_bands]; a validator reports a disagreement as E_MEMBER_MALFORMED (§ 6). A producer whose eigenvalues have two spin channels SHOULD write projections with the spin axis; a rank-3 projections beside two spin channels carries one set of weights, which a consumer MAY apply to both. A DOS section with a spin axis also states n_spin (a section field of dos.total and dos.projected, a field of the meta payload of dos.coop and dos.cohp), and it MUST equal the length of that axis. For two-component (spinor) bands n_spin is 1.

bands

Member	Format	Required	Shape and meaning	Unit
kpath	JSON, $defs/KpathPayload (strict)	yes	The path, the Fermi level and the fat-band channels; table below.	—
eigenvalues	float64	yes	[n_spin, n_k, n_bands] band energies on the absolute scale (not shifted by the Fermi level).	eV
projections	float64, $defs/BandsProjections	no	Fat-band weights, [n_spin, n_k, n_bands, n_channels] or [n_k, n_bands, n_channels]; slice c of the last axis belongs to kpath.channels[c].	—
occupations	float64, $defs/BandsOccupations	no	[n_spin, n_k, n_bands]: electrons in each state, not weighted by k-point weights (0 to 2 when n_spin is 1 and the bands are not spinors, otherwise 0 to 1).	electrons

Payload kpath ($defs/KpathPayload, strict; no field is required):

Field	Type	Meaning	Unit
kpoints	array of [3] numbers	Every k-point of the path in the order of eigenvalues axis 1, in fractional reciprocal-lattice coordinates.	—
labels	array of strings	One label per k-point, parallel to kpoints; "" marks an unlabelled point.	—
segments	array of segment objects	The straight segments of the path, in path order; table below.	—
fermi	number	Fermi level, on the scale of eigenvalues.	eV
fermi_energy_ev	number	The same Fermi level under the name the DOS kinds use; equal to fermi when both are present.	eV
spinor	boolean	true for two-component (spin–orbit) bands, each band one spinor state. Default false.	—
n_spin	integer, 1 or 2	Equal to eigenvalues axis 0.	—
n_kpoints	integer ≥ 1	Equal to eigenvalues axis 1.	—
n_bands	integer ≥ 1	Equal to eigenvalues axis 2.	—
channels	array of channel objects or strings	One per last-axis slice of projections; table below. A string is shorthand for a channel object with only that label.	—
title	string	Display title.	—
units	object	Optional declaration, field name or member role → unit name, restating the units of this table (§ 4.3, Declared units): fermi, fermi_energy_ev and eigenvalues are ev.	—
kind, version, reciprocal_space	"bands", string, boolean	Informational keys that existing producers write; a consumer needs none of them.	—

Segment object ($defs/KpathSegment, strict; also used by qpath):

Field	Type	Meaning
start	integer ≥ 0	Index of the segment’s first point along the path axis. Absent: the previous segment’s end, or 0 for the first segment.
end	integer ≥ 0	Index of its last point, inclusive. Absent: start + n_points − 1.
n_points	integer ≥ 1	Number of points on the segment, both ends included.
label_start, label_end	string	High-symmetry labels of the two end points; may be empty.
k_start, k_end	[3] numbers	Fractional reciprocal-lattice coordinates of the two end points.

Consecutive segments therefore share their boundary point, unless the later one gives an explicit start; that is how a path with a jump (X|U) is written.

Channel object ($defs/DosChannel, typed-open; also used by the DOS and phonon payloads below):

Field	Type	Meaning
label	string, required	Display label, e.g. "Fe-3d".
atom	integer ≥ 0	Atom index into the structure section. Absent: summed over atoms.
l	integer ≥ 0	Shell angular momentum. Absent: summed over shells.
m	integer	Component of a spherical shell, −l to l, as in Appendix A.2. Absent: summed over the shell.
spin	0 or 1	For a channel that is itself spin-resolved, which arises only in a projection without a spin axis.

Further keys, such as an element symbol, are allowed.

dos.total and dos.projected

Member	Format	Required	Shape and meaning	Unit
energies	float64	yes	[n_points] energy grid, referenced to E_F at 0.	eV
dos (dos.total)	float64	yes	[n_points] or [n_spin, n_points].	states / eV
projections (dos.projected)	$defs/DOSProjectedProjections	yes	[n_spin, n_channels, n_points] or [n_channels, n_points]; row c belongs to entry c of the section’s channels list.	states / eV

dos.coop and dos.cohp

Crystal orbital overlap (COOP) and Hamilton (COHP) populations of atom pairs.

Member	Format	Required	Shape and meaning	Unit
energies	float64	yes	[n_points] energy grid, referenced to E_F at 0.	eV
projections	float64	yes	[n_pairs, n_points] or [n_spin, n_pairs, n_points]: the population curve of each pair.	—
integrated	float64	yes	[n_pairs] or [n_spin, n_pairs]: each curve integrated up to E_F.	—
meta	JSON, $defs/DosMetaPayload (typed-open)	yes	What the pair axis means; table below.	—

Payload meta ($defs/DosMetaPayload, typed-open):

Field	Type	Meaning	Unit
method	string	"coop" or "cohp", conventionally matching the kind.	—
n_spin	integer, 1 or 2	Number of spin channels: the length of the spin axis, or 1 without one.	—
fermi_energy_ev	number	Absolute Fermi level that energies are referenced to.	eV
smearing	number ≥ 0	Broadening width.	eV
smearing_type	string	Broadening function, e.g. "gaussian".	—
pairs	array	One entry per pair: [i, j], or an object {i, j, label?, symbol_i?, symbol_j?, distance_ang?}; i and j are atom indices.	Å (distance_ang)
pair_labels	array of strings	Display labels, one per pair.	—
channels	array of channel objects	One per pair, naming its two atoms as i and j.	—
units	object	Optional declaration, field name or member role → unit name (§ 4.3, Declared units): fermi_energy_ev and energies are ev.	—

fermi_surface

Member	Format	Required	Shape and meaning	Unit
mesh	JSON, $defs/FermiMeshPayload (strict)	yes	The k-point mesh and the cell; table below.	—
energies	float32 or float64	yes	[nk1, nk2, nk3, n_bands]: E(k) − E_F of each band at each grid point.	eV

Grid point (i1, i2, i3) of a uniform mesh lies at the fractional reciprocal-lattice coordinates (i1/nk1 + shift[0], i2/nk2 + shift[1], i3/nk3 + shift[2]), modulo the reciprocal lattice; without a shift, index 0 on every axis is Γ. A producer SHOULD write lattice_vectors or reciprocal_lattice: without either, a consumer can place the surface only in fractional coordinates. When both are present they MUST agree.

Payload mesh ($defs/FermiMeshPayload, strict; no field is required):

Field	Type	Meaning	Unit
shape	[3] integers ≥ 1	[nk1, nk2, nk3], the first three axes of energies.	—
nk1, nk2, nk3	integers ≥ 1	The same three numbers as separate keys, the form existing producers write; equal to shape when both are present.	—
shift	[3] numbers	Position of grid point (0, 0, 0), in fractional reciprocal-lattice coordinates. Default [0, 0, 0] (Γ-centred).	—
symmetry_expanded	boolean	true when the full mesh was filled by applying symmetry operations to an irreducible set of computed k-points.	—
kpoints	array of [3] numbers	For a mesh that is not uniform: the fractional coordinates of every grid point, entry (i1·nk2 + i2)·nk3 + i3 for point (i1, i2, i3). Replaces the uniform formula.	—
fermi_energy_ev	number	Absolute Fermi level that energies are referenced to.	eV
n_spin	integer, 1 or 2	Number of spin channels of the underlying calculation.	—
band_indices	array of integers ≥ 0	Index, in the producer’s full band list, of each band along the last axis of energies.	—
lattice_vectors	[3, 3] numbers	Real-space cell, rows, in the convention of structure.lattice_vectors (§ 4.3).	Å
reciprocal_lattice	[3, 3] numbers	b1, b2, b3 as rows, including the 2π factor: a_i · b_j = 2π δ_ij.	Å⁻¹
units	object	Optional declaration, field name or member role → unit name (§ 4.3, Declared units): fermi_energy_ev and energies are ev, lattice_vectors is angstrom.	—

phonon_bands

Member	Format	Required	Shape and meaning	Unit
qpath	JSON, $defs/QpathPayload (strict)	yes	The q-point path; table below.	—
frequencies	float64	yes	[n_q, n_modes] phonon frequencies along the path.	cm⁻¹

Payload qpath ($defs/QpathPayload, strict; no field is required) is laid out like kpath: kpoints, labels, segments (segment objects counting q-points along frequencies axis 0), channels (channel objects), title and units mean what they mean there, without the electronic fields fermi, fermi_energy_ev, spinor and n_spin; a declared units.frequencies is cm-1. It adds:

Field	Type	Meaning
n_kpoints	integer ≥ 1	Number of q-points along the path, equal to frequencies axis 0 (the name is shared with kpath).
n_atoms	integer ≥ 1	Number of atoms in the cell.
n_modes	integer ≥ 1	Number of phonon branches, 3 · n_atoms; equal to frequencies axis 1.
has_eigenvectors	boolean	Whether the section carries mode eigenvectors.

phonon_dos

Member	Format	Required	Shape and meaning	Unit
meta	JSON, $defs/PhononMetaPayload (typed-open)	yes	Counts, broadening and channels; table below. An empty object is valid.	—
frequencies	float64	yes	[n_points] frequency grid.	cm⁻¹
dos	float64	yes	[n_points] phonon density of states.	states / cm⁻¹

Payload meta ($defs/PhononMetaPayload, typed-open):

Field	Type	Meaning	Unit
n_atoms	integer ≥ 1	Number of atoms in the cell.	—
n_modes	integer ≥ 1	Number of phonon branches, 3 · n_atoms.	—
smearing	number ≥ 0	Broadening width.	cm⁻¹
smearing_type	string	Broadening function, e.g. "gaussian".	—
channels	array of channel objects	Channels of a projected phonon DOS, one per projection row.	—
units	object	Optional declaration, field name or member role → unit name (§ 4.3, Declared units): frequencies is cm-1.	—

equation_of_state

Member	Format	Required	Shape and meaning	Unit
volumes	float64	yes	[n_points] cell volumes.	ų
energies	float64	yes	[n_points] total energies, parallel to volumes.	eV
fit	JSON, $defs/EosFitPayload (strict)	yes	The fitted model; table below.	—

Payload fit ($defs/EosFitPayload, strict):

Field	Type	Meaning	Unit
model	string, required	birch_murnaghan (third-order Birch–Murnaghan), murnaghan, vinet, poirier_tarantola (third-order Poirier–Tarantola), or polynomial (a polynomial E(V), from which the parameters below are derived).	—
V0	number	Equilibrium volume.	ų
E0	number	Energy at V0.	eV
B0	number	Bulk modulus at V0.	GPa
B0_prime	number	Pressure derivative of the bulk modulus at V0.	dimensionless
residual_rms	number ≥ 0	Root-mean-square residual of the fit over the points.	eV
n_points	integer ≥ 0	Number of points the fit used.	—
pressures_gpa	array of numbers	Pressure of the fitted model at each volume, parallel to volumes.	GPa
energy_unit, volume_unit, pressure_unit	string	Informational restatements of eV, ų and GPa.	—

Model-specific values, such as polynomial coefficients, go under x_ keys.

DOS section fields. dos.total and dos.projected carry their metadata as optional fields on the section object (§ 4.1), not as members:

Field	Type	Meaning
n_spin	integer, 1 or 2	Number of spin channels: 1 spin-unpolarized, 2 spin-polarized.
smearing	number ≥ 0, eV	Width of the broadening applied to the DOS.
smearing_type	string	Name of the broadening function, e.g. "gaussian"; free text in v1.
fermi_energy_ev	number, eV	Fermi energy.
n_electrons	number ≥ 0	Number of electrons; may be fractional.
channels	array of objects (dos.projected only)	One label object per row of projections, in row order.

A channels item may carry atom (integer ≥ 0, the 0-based index of the projected atom in the structure section), l (integer ≥ 0), m (integer), spin (0 = α/up, 1 = β/down), and label (a display string such as "O-2p"). Every item field is optional. An item may carry further fields; a consumer ignores those it does not understand.

Phonon eigenvectors and projected phonon DOS. phonon_bands may carry an optional binary member eigenvectors, float64 with shape [n_q, n_modes, n_atoms, 3] when the eigenvectors are real or [n_q, n_modes, n_atoms, 3, 2] when they are complex. The last axis of the complex form holds [re, im], as for complex wavefunction.gto coefficients. The first two axes index the same q-points and modes as frequencies, and the axis of length 3 holds the Cartesian x, y, z components. The member stores the eigenvectors as the producer computed them; v1 does not fix their normalization or mass weighting.

phonon_dos may carry an optional binary member projected, float64 [n_channels, n_points]: row c is the phonon DOS projected on channel c, sampled on the n_points values of frequencies. The meta member then SHOULD carry a channels array with one object per row, in row order. An item has the shape of a dos.projected channel, typically {"atom": 0, "label": "Mg"}, with every field optional.

5.7 Analysis kinds

atom_properties: per-atom scalar and vector results, one binary member per role; the role list, units and conventions are in the atom_properties subsection below. bond_orders: JSON {method, pairs: [{i, j, order, distance_ang?, symbol_i?, symbol_j?}]}.

citations: one binary references member of UTF-8 BibTeX bytes. basis.ao: a per-AO grid + ao_metadata (quantum numbers + provenance) — see Appendix A.3 for how a spherical and a Cartesian component are each named.

The JSON payloads of bonds (§ 5.1), bond_orders, scf_history, topology.qtaim and structure.symmetry are specified by the $defs entries named below, at the strictness levels defined in § 5.4. Atom indices are 0-based indices into the atoms of the archive’s structure; those of bonds address the structure § 5.1 assigns (the structure that holds a bonds member, or the one a bonds section’s structure_ref names, else the first structure).

bonds

Payload of a bonds section’s bonds member and of a structure section’s optional bonds member: $defs/BondsPayload, strict.

Field	Type	Required	Meaning	Unit
pairs	object[]	yes	One entry per bond.	—
pairs[].i, pairs[].j	integer ≥ 0	yes	The two atoms.	—
pairs[].order	number ≥ 0	no	Bond order; absent means 1.	—

bond_orders

Payload of the bond_orders member: $defs/BondOrdersPayload, strict.

Field	Type	Required	Meaning	Unit
method	string	yes	Bond-order definition. Lowercase names are recommended: "mayer", "wiberg", "nbo", …	—
pairs	object[]	yes	One entry per atom pair.	—
pairs[].i, pairs[].j	integer ≥ 0	yes	The two atoms.	—
pairs[].order	number	yes	Bond order under method; some definitions yield small negative values.	—
pairs[].distance_ang	number ≥ 0	no	Interatomic distance.	Å
pairs[].symbol_i, pairs[].symbol_j	string	no	Element symbols of the two atoms.	—

scf_history

Payload of the iterations member: $defs/ScfHistoryPayload, strict.

Field	Type	Required	Meaning	Unit
iterations	object[]	yes	One record per SCF iteration, in order.	—
iterations[].iter	integer ≥ 0	yes	Iteration number, as the producer counts them.	—
iterations[].energy_eh	number	yes	Total energy after the iteration.	Hartree
iterations[].delta_e	number	no	Energy change from the previous iteration.	Hartree
iterations[].diis_error	number	no	DIIS error norm.	atomic units
iterations[].rms_density_change	number	no	Root-mean-square change of the density matrix from the previous iteration.	atomic units
converged	boolean	no	Whether the SCF met its convergence criteria; absent means not stated.	—

topology.qtaim

Payload of the critical_points member: $defs/QtaimPayload, permissive at the root, with typed points.

Field	Type	Required	Meaning	Unit
points	object[]	yes	Critical points of the electron density.	—
points[].type	string	yes	bcp (3,−1), rcp (3,+1), ccp (3,+3) or ncp (3,−3).	—
points[].position	3 numbers	yes	Cartesian position.	units.position, default Å
points[].rho	number	no	Electron density at the point.	not fixed
points[].laplacian	number	no	Laplacian of the electron density at the point.	not fixed
points[].ellipticity	number	no	Ellipticity; meaningful for a bcp.	dimensionless
points[].atom_pair	2 integers ≥ 0	no	For a bcp: the two atoms it connects.	—
points[].atoms	integer[] ≥ 0	no	Atoms the point belongs to, e.g. the nucleus of an ncp or the ring atoms of an rcp.	—
bond_paths	object[]	no	Gradient paths joining two nuclei through a bcp.	—
bond_paths[].atoms	2 integers ≥ 0	no	The two atoms the path joins.	—
bond_paths[].path	array of 3-vectors	no	Vertices of the path as a polyline.	units.position, default Å
units	object	no	position (unit name of a length): unit of every position. Any other key names the unit of the point field of the same name. Values are unit names (§ 4.3).	—

Position unit. Every position — a point’s position and every vertex of a bond_paths[].path — is Cartesian, in the unit units.position declares. When units or units.position is absent, the unit is ångström ("angstrom"). This default was chosen to match the structure section (§ 5.1, Å) whose atoms the points overlay. It is provisional: it is subject to maintainer decision 2 (“QTAIM position unit”) in docs/format_review.md, and a later revision of this section will record that decision. Producers SHOULD therefore declare units.position explicitly, and a consumer MUST read positions in a declared unit. rho and laplacian have no fixed unit in v1, and the unit names of § 4.3 do not yet include a unit of electron density or of its Laplacian, so a producer cannot declare them; a consumer that does not know the producer’s convention presents them as written.

structure.symmetry

Payload of the data member: $defs/SymmetryPayload, permissive.

Field	Type	Required	Meaning	Unit
spacegroup_number	integer 1–230	no	Space-group number of the International Tables for Crystallography.	—
international	string	no	Short international (Hermann–Mauguin) space-group symbol, e.g. "Fm-3m".	—
hall	string	no	Hall symbol of the space group.	—
point_group	string	no	Point-group symbol; Schoenflies notation recommended, e.g. "C2v".	—
hermann_mauguin	string	no	The point group in Hermann–Mauguin notation, e.g. "mm2".	—
operations	object[]	no	Symmetry operations x′ = R x + t: rotation (3 × 3, required), translation (three values).	fractional coordinates of the structure’s lattice when periodic; Cartesian for a molecule, t zero or absent
wyckoffs	string[]	no	Wyckoff letter of each atom, in the order of the structure’s atoms.	—
equivalent_atoms	integer[] ≥ 0	no	For each atom, the index of the representative atom of its symmetry-equivalence class.	—
symprec	number > 0	no	Distance tolerance of the symmetry search.	Å
space_group_number, space_group_symbol	integer 1–230, string	no	The same quantities as spacegroup_number and international, under the names some producers write. When both spellings are present they MUST agree.	—

atom_properties

An atom_properties section holds per-atom results as binary members, one per role. Row i of every member belongs to atom i of the structure the section describes, and all roles of one section have the same n_atoms. A section carries one or more roles. A scalar role is float64 [n_atoms] ($defs/AtomChargeBinary); a vector role is float64 [n_atoms, 3] ($defs/AtomVectorBinary), whose last axis holds the Cartesian components x, y, z in the frame of the structure. The table is the one role list: the schema, the § 5 table, this table and both reference writers carry the same names in the same order.

Role	Shape	Quantity	Unit	Convention
mulliken_charge	[n_atoms]	Mulliken net atomic charge	e	Net charge (see below).
loewdin_charge	[n_atoms]	Löwdin net atomic charge	e	Net charge.
hirshfeld_charge	[n_atoms]	Hirshfeld (stockholder) net atomic charge	e	Net charge.
iao_charge	[n_atoms]	Net atomic charge from the intrinsic atomic orbital (IAO) partition	e	Net charge.
spin_population	[n_atoms]	Spin population, α minus β electrons on the atom	electrons	Positive for an excess of α electrons.
cm5_charge	[n_atoms]	Charge Model 5 (CM5) net atomic charge	e	Net charge.
chelpg_charge	[n_atoms]	Net atomic charge fitted to the molecular electrostatic potential on the CHELPG grid	e	Net charge.
resp_charge	[n_atoms]	Net atomic charge from the restrained electrostatic potential (RESP) fit	e	Net charge.
esp_charge	[n_atoms]	Net atomic charge from an unrestrained fit to the electrostatic potential	e	Net charge.
nbo_charge	[n_atoms]	Natural population analysis (NPA) net atomic charge of the NBO analysis	e	Net charge.
mbis_charge	[n_atoms]	Minimal basis iterative stockholder (MBIS) net atomic charge	e	Net charge.
bader_charge	[n_atoms]	Net atomic charge from integrating the electron density over the QTAIM (Bader) basin	e	Net charge.
ddec_charge	[n_atoms]	Density-derived electrostatic and chemical (DDEC) net atomic charge	e	Net charge.
valence	[n_atoms]	Total valence of the atom	dimensionless	Under the producer’s bond-order scheme; valence − bonded_valence is the free valence.
bonded_valence	[n_atoms]	Bonded valence: the sum of the bond orders between the atom and every other atom	dimensionless	Under the producer’s bond-order scheme.
fukui_plus	[n_atoms]	Condensed Fukui function f⁺ (nucleophilic attack)	dimensionless	f⁺ = p(N+1) − p(N) (see below).
fukui_minus	[n_atoms]	Condensed Fukui function f⁻ (electrophilic attack)	dimensionless	f⁻ = p(N) − p(N−1).
fukui_zero	[n_atoms]	Condensed Fukui function f⁰ (radical attack)	dimensionless	f⁰ = (f⁺ + f⁻) / 2.
dual_descriptor	[n_atoms]	Condensed dual descriptor Δf	dimensionless	Δf = fukui_plus − fukui_minus.
atomic_energy_eh	[n_atoms]	Energy assigned to the atom by the producer’s energy partition	hartree	The partition scheme is the producer’s.
atomic_volume_bohr3	[n_atoms]	Volume assigned to the atom by the producer’s partition	bohr3	The partition scheme is the producer’s.
nmr_shielding_iso_ppm	[n_atoms]	Isotropic NMR shielding σ of the atom’s nucleus	ppm	A shielding, not a chemical shift: no reference compound is subtracted.
magnetic_moment	[n_atoms, 3]	Atomic magnetic moment, Cartesian components	μB (Bohr magneton)	A collinear producer puts the moment on the quantisation axis (see below).
force_eh_bohr	[n_atoms, 3]	Energy gradient on the atom, ∂E/∂R, Cartesian components	hartree / bohr	A gradient, not a force: force = −gradient (see below).

Charges. Every *_charge role is a net atomic charge in units of the elementary charge e: the atom’s nuclear charge (its effective core charge where an effective core potential replaces core electrons) minus its electron population, so a positive value means electron loss. The role name is the partition scheme. The schemes give different numbers for the same density, and a consumer MUST NOT treat two charge roles as interchangeable. spin_population counts electrons, α minus β, and is positive for an excess of α electrons.

Fukui functions. The condensed Fukui functions are differences of atomic electron populations. With p_A(M) the electron population of atom A in the system of M electrons and N the electron count of the system, f⁺_A = p_A(N+1) − p_A(N), f⁻_A = p_A(N) − p_A(N−1), f⁰_A = (f⁺_A + f⁻_A) / 2, and the dual descriptor Δf_A = f⁺_A − f⁻_A. All are dimensionless. A producer that writes dual_descriptor together with fukui_plus and fukui_minus SHOULD write values that satisfy the identity to numerical precision. The population scheme behind the populations is the producer’s and is not named by the role.

magnetic_moment. The three components are the Cartesian components of the atomic moment in μB, in the frame of the structure. A collinear calculation has no spatial spin direction: its producer puts the signed moment on the quantisation axis, [0, 0, m] for the usual z axis, with the sign convention of spin_population (positive for an excess of α electrons). A non-collinear producer writes the full vector.

force_eh_bohr. The row of atom i is the gradient ∂E/∂R_i of the energy with respect to the position of atom i, in hartree/bohr, the sign convention of the gradient member of the forces kind (force = −gradient), despite the role’s name. The role lets a section show per-atom gradients next to charges; it is a display alias. When a forces section for the same structure is present and its gradient differs from this role, the forces section is authoritative.

Custom roles. A producer may add a quantity the list does not provide as a role named custom.<name>, where <name> is one or more characters of A–Z, a–z, 0–9 and _. A custom role is a scalar (float64 [n_atoms]) or a vector (float64 [n_atoms, 3]) member, like the listed roles. A section that has a custom.* member MUST also have a JSON member meta ($defs/AtomPropertiesMetaPayload, strict) with one entry per custom role, keyed by the role name. A validator reports E_MEMBER_MALFORMED for a custom.* member that meta does not describe, including when the section has no meta member (§ 6). Entries for roles the section does not carry are ignored. A consumer that does not know a custom role presents its description and units, or ignores it. Use a listed role when one fits, and a vendor kind (§ 7.3) for data that is not per-atom.

Field	Type	Required	Meaning	Unit
custom.<name>	object	yes, one per custom role	Description of the role of that name.	—
custom.<name>.units	string	yes	Unit of the values, spelled as in § 4.3 where it gives a spelling (for example e, bohr3, hartree, ppm); dimensionless for a pure number.	—
custom.<name>.description	string	yes	What the quantity is, with any sign convention.	—
custom.<name>.kind	scalar or vector	yes	scalar for a float64 [n_atoms] member, vector for a float64 [n_atoms, 3] member. It MUST agree with the member’s shape.	—

{
  "custom.born_charge_mean": {
    "units": "e",
    "description": "Trace of the Born effective-charge tensor divided by three.",
    "kind": "scalar"
  }
}

5.8 run.record — self-contained run records

A run.record section carries the verbatim artefacts of one program invocation: the input handed to a quantum-chemistry code, the full log/output it produced, and any auxiliary files. With it, a QVF archive is a self-contained record of a calculation — input, results, and log travel in one file.

Section fields (peers of members, like volume.difference’s operands):

Field	Required	Meaning
program	yes	The code the input/log belong to ("vibe-qc", "orca", …). Lowercase identifiers recommended.
program_version	no	Version string of that code.
command	no	Launch command line, as one string.
exit_status	no	Integer process exit status.
started_utc / finished_utc	no	ISO 8601 UTC timestamps.
sequence	no	Ordering index (≥ 0) when an archive carries multiple run records (multi-step workflows: opt → freq → …).
job_ref	no	Id of the job.spec section (§ 5.9) this run executed. A validator checks that it names a job.spec section (§ 6).
run_status	no	Outcome of this run: "running", "converged" or "failed", with the meanings of the root provenance.run_status (§ 3.2).

job_ref and run_status make the runs of a job set (§ 5.9) unambiguous: a job is pending until a run.record names it, and that run’s run_status is the job’s. In an archive with one job.spec, a run record without job_ref executed that job, as before.

program is deliberately distinct from the root source.program (§ 3.1): the root identifies the QVF producer, which may be a converter or packing tool; run.record.program identifies the code that actually ran. For a code writing its own archives the two coincide.

Members — at least one of input / log is REQUIRED:

• input — the verbatim main input, opaque binary bytes that MUST decode as UTF-8 text. Producers converting from another encoding transcode at write time.

• log — the full log/output of the program, opaque UTF-8 binary bytes. A producer that finalizes the archive before its own process ends SHOULD embed the log as complete as it can be at write time and note any truncation in the files index ("truncated": true on the log entry); a packing tool working from finished files embeds them whole.

• files — optional JSON index describing the stored members, schema’d as $defs/RunRecordFilesPayload: a map from member role to an entry that records the member’s original file. Every key MUST name a member that exists in the section (input, log, or an attachment.<suffix>), so the index has no vendor keys of its own. An entry is strict: only the fields below and vendor keys beginning x_.

  Field	Type	Meaning
  filename	string	Original file name, without directories.
  description	string	What the file is, for display.
  media_type	string	IANA media type of the bytes, e.g. text/plain or chemical/x-xyz.
  truncated	boolean	true when the stored bytes are not the complete file, e.g. a log embedded before the run ended.

  No field of an entry is required; producers SHOULD give filename whenever the member was read from a file.

• attachment.<suffix> — optional auxiliary files (structure includes, restart data, …), opaque binary bytes with no encoding requirement. <suffix> matches [A-Za-z0-9_.-]+. Describe each in the files index.

Producers SHOULD NOT duplicate large binary result files (wavefunctions, volumetric grids) as attachments when a canonical section kind exists for the data — attachments are for run artefacts, not a bypass of § 5.

A consumer renders input and log as plain text. Logs can reach tens of MB; consumers SHOULD size-gate rendering (the uncompressed size is available from the ZIP central directory without reading the member, and from the member’s size, § 4.2) and offer the full text on demand.

Sharing and sanitisation

A run.record embeds its artefacts verbatim, and archives are meant to be shared. Inputs and logs commonly contain absolute paths, user names, host names, and scratch-directory locations; attachment.* members may contain the same (in any encoding), and so may the command field and the original filenames recorded in the files index. The format does not redact anything: sanitising such content before an archive is shared is the responsibility of the producer or of the user. Producers SHOULD offer a way to suppress or redact it — for example, an option to omit the run record or individual members, or to rewrite paths at write time. The intended mechanism in the reference toolkit is a scrub operation that rewrites such content in an existing archive and reports each change for review (informative: the operation is not yet part of the toolkit, and it changes nothing in the format). Root provenance.hostname is deprecated for the same reason (§ 3.2).

5.9 job.spec — declarative job specification

A job.spec section describes the calculation an archive requests — before, and independent of, any results it carries. Together with a structure section (§ 5.1) it makes a QVF archive an executable input: a runner opens the container, reconstructs the job from the declarative payload, executes it, and writes the results — and a run.record (§ 5.8) — back into the same container. An archive whose provenance.run_status (§ 3.2) is "pending" carries at least one job.spec section and the structure sections they run on.

Members:

• spec — REQUIRED JSON member, schema’d as $defs/JobSpecPayload.

The payload:

Field	Required	Meaning
job_type	yes	"molecular" or "periodic" — which class of engine runs the job. A periodic job’s geometry carries pbc/lattice_vectors in the structure section; job_type selects the runner, it does not restate periodicity.
method	no	Method identifier (e.g. "rhf", "rks", "ccsd(t)", "gfn2"). Producer-neutral lowercase string recommended. Absent means the engine’s default.
basis	no	Basis-set name (e.g. "def2-svp"), or null: the method takes no basis set (a semiempirical or tight-binding method such as GFN2-xTB). Absent means the engine’s default.
functional	no	Exchange-correlation functional name, for DFT methods, or null: the method takes no functional (Hartree–Fock, a correlated wavefunction method, a semiempirical method). Absent means the engine’s default.
charge	no	Net charge, integer. Absent means 0. Authoritative for the job — a consumer never infers charge from the structure.
multiplicity	no	Spin multiplicity 2S+1, integer ≥ 1. Absent means 1.
kpoints	no	[n1, n2, n3] Monkhorst–Pack mesh (integers ≥ 1). Periodic jobs only.
tasks	no	Ordered list of task identifiers, e.g. ["single_point"], ["optimize", "hessian"]. Absent means a single point.
structure_ref	no	String: id of the structure section (§ 5.1) the job runs on. A validator resolves it to a section of kind structure (§ 6). Absent means the archive’s only structure section; with several structure sections and no structure_ref the job is ambiguous, and a runner MUST refuse it rather than guess. A structure_ref on the job.spec section object takes precedence over this one (§ 4.1); keep the two equal.
solvation	no	Object: implicit solvation, below. Absent means none.
dispersion	no	String: the dispersion correction by its conventional lowercase name, e.g. "d3bj", "d4". Absent means none beyond what the method implies.
relativistic	no	String: the scalar-relativistic treatment by its conventional lowercase name, e.g. "zora", "x2c", "dkh2". Absent means none.
scf	no	Object: SCF settings, below. Absent means the engine’s defaults.
geometry	no	Object: geometry-optimisation settings, below. Absent means the engine’s defaults.
resources	no	Object: the resources the job would like, below. Hints, not requirements.
options	no	Object of additional engine-specific keywords (JSON-safe values). A runner that does not recognize an option MUST refuse the job rather than silently drop the option.

null and absent differ. null states that the method takes no such input, and a runner MUST NOT supply one; an absent key leaves the choice to the engine, as for method. The empty string "" is a deprecated spelling of null, which earlier producers wrote for a semiempirical job’s basis: it remains valid, a consumer reads it as null, and producers SHOULD NOT write it.

The payload root is open (additionalProperties: true) for forward growth, but producers SHOULD put engine-specific keywords under options, keeping the typed top level portable across codes. The four objects below are strict, each a $defs entry of the schema: they carry only the fields listed and vendor keys beginning x_, so an engine keyword has no place in them and goes under options. Every field of them is optional, and an absent field means the engine’s default.

solvation ($defs/JobSpecSolvation):

Field	Type	Required	Meaning
model	string, non-empty	yes	The solvation model by its conventional lowercase name, e.g. "pcm", "cpcm", "smd", "cosmo".
solvent	string, non-empty	no	The solvent by name, e.g. "water".
epsilon	number > 0	no	Static dielectric constant, dimensionless. When given it is the constant the model uses, and solvent then only labels it.

scf ($defs/JobSpecScf):

Field	Type	Meaning	Unit
convergence	number > 0	Convergence threshold of the SCF energy change. An engine that converges on another measure maps it to its nearest criterion.	hartree
max_iterations	integer ≥ 1	Maximum number of SCF iterations.	—
guess	string, non-empty	The initial guess by its conventional lowercase name, e.g. "core", "sad", "huckel".	—
damping	number	Damping factor of the density or Fock update.	—

geometry ($defs/JobSpecGeometry):

Field	Type	Meaning	Unit
convergence	number > 0	Convergence threshold of the optimisation: the largest Cartesian gradient component. An engine with several criteria applies it to its gradient criterion and keeps its defaults for the others.	hartree/bohr
max_steps	integer ≥ 1	Maximum number of optimisation steps.	—
coordinates	"cartesian", "internal" or "redundant"	The coordinate system the optimiser steps in.	—

resources ($defs/JobSpecResources) are hints, not requirements: a runner uses what it has and may use less, and a run that used other resources has not failed to honour the spec. What a run actually used is recorded in provenance (n_threads, n_mpi_ranks, n_gpus, wall_seconds; § 3.2).

Field	Type	Meaning	Unit
n_cores	integer ≥ 1	Number of CPU cores to use.	—
memory_mb	integer ≥ 1	Memory to use.	megabytes
walltime_s	number > 0	Wall-clock time to allow.	s

A periodic job on a given structure:

{
  "job_type": "periodic",
  "method": "rks", "functional": "pbe", "basis": "pob-tzvp-rev2",
  "structure_ref": "structure",
  "kpoints": [4, 4, 1],
  "tasks": ["optimize"],
  "dispersion": "d3bj",
  "scf": {"convergence": 1e-8, "max_iterations": 100, "guess": "sad"},
  "geometry": {"convergence": 4.5e-4, "max_steps": 50, "coordinates": "redundant"},
  "resources": {"n_cores": 16, "memory_mb": 32000, "walltime_s": 86400}
}

A job.spec is declarative data, never code. Executing it involves no evaluation of an embedded program — deliberately distinct from run.record.input, which may be an arbitrary script and is a record of what ran, not a request. A runner MUST NOT execute run.record.input as a side effect of opening or running an archive.

Lifecycle: a runner that executes a pending archive updates the same container (§ 2.3) — result sections are added, a run.record is embedded, and provenance.run_status moves to "converged" or "failed". The runner also records what ran, with which resources and when, in provenance (software, git_commit, n_threads, n_mpi_ranks, n_gpus, started_utc, finished_utc; § 3.2). The job.spec section is preserved verbatim through this update, so a settled archive still records what was asked. Multi-step workflows append further run.record sections ordered by their sequence field.

Job sets

An archive MAY carry several job.spec sections, a job set: for example one calculation for each species of a reaction scheme (§ 5.14), or the same species at several levels of theory. Each job.spec section is one job, independent of the others.

• Each job names its structure. In an archive with more than one structure section, a job without a structure_ref is ambiguous, and a runner MUST refuse it, as above. The section-level structure_ref (§ 4.1) is the preferred carrier, because a consumer reads it from the manifest without opening the payload; a structure_ref inside the spec payload remains valid, the section’s takes precedence, and producers SHOULD keep the two equal.

• Runs name their job. A runner executes any subset of the jobs, in any order or in parallel. For each job it runs it adds a run.record whose job_ref names the job’s section and whose run_status gives the job’s outcome (§ 5.8), and the result sections of that run SHOULD carry run_ref naming the run record and structure_ref naming the structure (§ 4.1), so that a reader attributes every result to its job. A job that no run.record names has not run.

• The set has one status. provenance.run_status summarises the set: pending, running, then converged or failed (§ 3.2).

• One refusal does not stop the set. A runner that refuses or fails one job still runs the others it was asked to run, and records the failed one with run_status: "failed".

Jobs of a set do not depend on each other. A sequence within one job, such as an optimisation followed by a frequency calculation on the optimised geometry, is that job’s tasks list.

A pending job set with two species, each job naming its structure on the section object:

"provenance": {"run_status": "pending"},
"sections": [
  {"id": "structure_s1", "kind": "structure", "label": "1", "charge": 0,
   "multiplicity": 1, "members": {"structure": {"path": "…", "format": "json", "sha256": "…"}}},
  {"id": "structure_s2", "kind": "structure", "label": "2", "charge": 0,
   "multiplicity": 2, "members": {"structure": {"path": "…", "format": "json", "sha256": "…"}}},
  {"id": "job_s1_opt", "kind": "job.spec", "structure_ref": "structure_s1",
   "members": {"spec": {"path": "…", "format": "json", "sha256": "…"}}},
  {"id": "job_s2_opt", "kind": "job.spec", "structure_ref": "structure_s2",
   "members": {"spec": {"path": "…", "format": "json", "sha256": "…"}}}
]

5.10 forces — nuclear gradient and stress

A forces section carries the first derivatives of the energy at one geometry: the derivatives with respect to the nuclear positions and, for a periodic system, the stress. The stored quantity is the energy gradient, not the force: gradient[a][c] is ∂E/∂R, the derivative of the energy with respect to Cartesian coordinate c (0 = x, 1 = y, 2 = z) of atom a. The force on atom a is the negative of row a, F = −∇E. A consumer that draws forces MUST negate the stored values.

The rows follow the atoms of one structure section (§ 5.1), in the order of its atoms, and the Cartesian axes are that structure’s. The structure is the one the section-level structure_ref names when the section carries one (§ 4.1), else the one meta.structure_ref names; when neither is given, it is the archive’s structure section if the archive has exactly one. Producers SHOULD name the structure whenever the archive has more than one.

Member	Format	Required	Shape and meaning	Unit
gradient	float64	yes	[n_atoms, 3] energy gradient ∂E/∂R; row a belongs to atom a of the structure.	hartree / bohr
stress	float64	no	[3, 3] stress tensor of a periodic system, σ_ij = (1/V) ∂E/∂ε_ij for the strain ε and the cell volume V, in the Cartesian axes of the structure. It is symmetric, and the pressure is p = −(σ_xx + σ_yy + σ_zz)/3, so a compressed cell has a negative trace.	hartree / bohr³
meta	JSON, $defs/ForcesMetaPayload (strict)	no	Table below.	—

Payload meta ($defs/ForcesMetaPayload, strict; no field is required):

Field	Type	Meaning
structure_ref	string	id of the structure section the rows belong to. The section-level structure_ref takes precedence when both are present.
method	string	Method of the energy that was differentiated, e.g. "rks".
convention	"gradient"	What gradient holds. "gradient", the energy gradient, is the only value in v1; absent means "gradient".
units	object ($defs/DerivativeUnits)	Declared units: energy ("hartree") and length ("bohr"). v1 fixes both, so a declaration restates them and cannot name another unit.

A validator checks that gradient is [n_atoms, 3] and stress [3, 3]; when it can resolve the structure, it checks that n_atoms is that structure’s atom count, and a meta.structure_ref that names no structure section is an unresolved reference (§ 6).

5.11 hessian — Cartesian second derivatives

A hessian section carries the matrix of second derivatives of the energy with respect to the nuclear Cartesian coordinates at one geometry, from which harmonic frequencies and normal modes follow; a vibrations section names the Hessian its modes come from through hessian_ref (§ 5.5).

matrix[i][j] is ∂²E/∂x_i∂x_j, where index i = 3a + c belongs to Cartesian coordinate c (0 = x, 1 = y, 2 = z) of atom a: the order is x₀, y₀, z₀, x₁, y₁, z₁, … for N atoms. The atoms and axes are those of the section’s structure, resolved as for forces (§ 5.10). The matrix is symmetric; a producer whose Hessian is not exactly symmetric, as a finite-difference one is, SHOULD write (H + Hᵀ)/2.

Member	Format	Required	Shape and meaning	Unit
matrix	float64	yes	[3N, 3N], as above.	hartree / bohr²; hartree / (bohr² · amu) when meta.mass_weighted is true
meta	JSON, $defs/HessianMetaPayload (strict)	no	Table below.	—

Payload meta ($defs/HessianMetaPayload, strict; no field is required, but a mass-weighted matrix requires atom_masses_amu):

Field	Type	Meaning	Unit
structure_ref	string	id of the structure section whose atoms index the matrix, as for forces.	—
mass_weighted	boolean	true: the matrix is mass-weighted, element (i, j) divided by √(m_a m_b) for the atoms a and b of i and j, with the masses of atom_masses_amu, which is then required. Absent means false.	—
projected	boolean	true: the rigid-body motions have been projected out of the matrix (translations and, for a non-periodic system, rotations), so their eigenvalues are zero. Absent means false: the plain second derivatives.	—
atom_masses_amu	array of numbers > 0	Mass of each atom in atom order, N entries: the masses of the mass weighting, or the masses frequencies derived from the matrix are to use.	amu (unified atomic mass unit)
units	object ($defs/DerivativeUnits)	Declared units, as for forces: energy ("hartree") and length ("bohr").	—

A validator checks that matrix is square with an extent divisible by 3, that atom_masses_amu has N entries, and, when it can resolve the structure, that N is that structure’s atom count (§ 6).

5.12 excited_states — excited states and transition properties

An excited_states section carries the electronically excited states of one calculation, from TD-DFT, CIS, ADC, EOM-CC or any other method that yields a table of states: their energies, transition properties and dominant orbital excitations. Every state is a vertical excitation from one reference state, usually the ground state that the archive’s wavefunction.gto and provenance describe. The section has one member:

Member	Format	Required	Meaning
states	JSON, $defs/ExcitedStatesPayload (strict)	yes	The states and a description of the calculation (tables below).

Besides the generic fields of § 4.1 (its structure_ref names the structure whose axes the transition dipoles use), the section may carry one field of its own, a peer of members:

Section field	Type	Meaning
wavefunction_ref	string	id of the wavefunction.gto section of the reference state. The from_mo and to_mo of every contribution are rows of its coefficient member.

Payload states ($defs/ExcitedStatesPayload, strict):

Field	Type	Required	Meaning
states	array of states (below)	yes	The states, in ascending order of index.
meta	object (below)	no	The calculation the states come from.

Each state ($defs/ExcitedState, strict):

Field	Type	Required	Meaning	Unit
index	integer ≥ 1	yes	Number of the state, unique within the payload, counted from 1 in the producer’s order (normally by increasing energy); the reference state has no entry. Spectrum peaks (§ 5.4), natural transition orbitals (§ 5.3) and transition densities (§ 5.2) name a state by this number.	—
excitation_energy	{value, units}	yes	Vertical excitation energy: the energy of the state minus that of the reference state.	producers SHOULD write ev
total_energy	{value, units}	no	Total energy of the state.	producers SHOULD write hartree
multiplicity	integer ≥ 1	no	Spin multiplicity 2S + 1.	—
symmetry	string	no	Irreducible representation of the state, e.g. "B1".	—
oscillator_strength	number ≥ 0	no	Oscillator strength f of the transition from the reference state.	dimensionless
rotatory_strength_cgs	number	no	Rotatory strength R of the transition, signed.	10⁻⁴⁰ esu²·cm²
transition_dipole	3 numbers	no	Electric transition dipole moment ⟨0|μ̂|n⟩.	e·bohr (atomic units)
transition_magnetic_dipole	3 numbers	no	Magnetic transition dipole moment ⟨0|m̂|n⟩.	e·ħ/mₑ (atomic units, = 2 μ_B)
contributions	array (below)	no	The dominant orbital excitations of the state.	—
nto_ref	string	no	id of the wavefunction.gto section of the state’s hole natural transition orbitals (§ 5.3, Natural transition orbitals).	—
density_ref	string	no	id of a volume.transition_density section holding the transition density of the state (§ 5.2), or of a volume.difference section holding its difference density, the density of the state minus that of the reference state.	—

The two dipoles are Cartesian vectors in the axes of the section’s structure. The sign of a transition dipole is arbitrary, as is the phase of the state; f and R are not. In the length gauge f = (2/3) ΔE |μ|², with the excitation energy ΔE in hartree and the transition dipole μ in atomic units. The rotatory strength unit is the one quantum-chemistry programs print as “10⁻⁴⁰ cgs”; the vocabulary of § 4.3 has no name for it, nor for the atomic units of the dipoles, so this table fixes the units of these three fields and meta.units does not declare them.

Each contribution ($defs/ExcitedStateContribution, strict):

Field	Type	Required	Meaning
from_mo	integer ≥ 0	yes	The orbital the electron leaves: a 0-based row of the coefficient member of the reference wavefunction.
to_mo	integer ≥ 0	yes	The orbital the electron enters, indexed the same way.
spin	"alpha" or "beta"	no	For an unrestricted reference, the spin channel: alpha rows index mo_coefficients_alpha, beta rows mo_coefficients_beta. Absent for a reference with one set of orbitals.
weight	number	yes	Weight of the excitation in the state: the squared amplitude X² (CIS, TDA) or X² − Y² (full TD-DFT, RPA), normalized so that the weights of all excitations of the state sum to 1. A list of the dominant ones sums to a little less.

Without wavefunction_ref the orbital rows refer to the reference calculation as the producer numbers its orbitals, which a consumer cannot check; producers SHOULD set wavefunction_ref whenever they write contributions, and give spin for every contribution of an unrestricted reference. A contribution without spin in an unrestricted reference indexes a row that both coefficient members have.

Payload meta ($defs/ExcitedStatesMeta, strict; no field is required):

Field	Type	Meaning
method	string	The excited-state method, e.g. "tddft", "cis", "adc2", "eom-ccsd".
reference_state	string	Label of the reference state, e.g. "S0".
n_states	integer ≥ 0	Number of states; when present it MUST equal the length of states.
tda	boolean	true: the Tamm–Dancoff approximation was used.
spin_flip	boolean	true: the states come from a spin-flip calculation.
units	object	Declared units (§ 4.3), keyed by a field of the states, each value a unit name: excitation_energy and total_energy restate the units of those objects of every state, and oscillator_strength is "dimensionless". The dipoles and rotatory_strength_cgs are not declared (above).

Linked sections. The table of states is the hub of an excited-state calculation:

• wavefunction_ref names the reference wavefunction.gto (§ 5.3).

• A state’s nto_ref names the wavefunction.gto section of its hole NTOs; that section and its particle partner carry this section’s id as state_ref and the state’s index as state_index (§ 5.3).

• A state’s density_ref names its volume.transition_density, which carries this section’s id as excited_states_ref and the state’s index as state_index (§ 5.2), or a volume.difference.

• A one-dimensional spectrum names this section with states_ref, and its peaks name states by assignment.state_index (§ 5.4). A stick UV-Vis spectrum derived from the table has one line per state at its excitation energy, with the oscillator strength as intensity (y_units "dimensionless"); an ECD stick spectrum uses the rotatory strengths.

A validator checks that the index values are unique and ascending, that meta.n_states, when present, equals the number of states, that wavefunction_ref and every nto_ref name wavefunction.gto sections and every density_ref a volume.transition_density or volume.difference section, and, when wavefunction_ref names a wavefunction.gto section, that every from_mo and to_mo is a row of its coefficient member (§ 6).

5.13 Property kinds

Three kinds carry properties of the system as a single JSON payload each: properties.electric (electric multipole moments and polarizabilities), properties.elastic (the elastic constants of a periodic system) and properties.dielectric (the dielectric tensors, Born charges and piezoelectric tensor of a periodic system). A section of one of these kinds has exactly one member, properties, a JSON member whose payload is strict (§ 5): the keys of its table, and keys that begin with x_, are allowed, and the same holds for every object inside it. No field is required unless its table says so; a field that is absent was not computed.

Conventions common to the three kinds:

• Axes. Cartesian components x, y, z are those of the structure the section describes: the one the section-level structure_ref names when the section carries one (§ 4.1), else the archive’s structure section if it has exactly one. Producers SHOULD name the structure whenever the archive has more than one.

• Matrices are nested arrays of rows: entry [i][j] is row i, column j, with the Cartesian order x, y, z for a 3 × 3 matrix. In Voigt notation the six indices are, in this order, xx, yy, zz, yz, xz, xy.

• Units are fixed; the tables give them (§ 4.3). The optional units object of each payload maps a field name to a unit name and may only restate the unit that is fixed, as for the other payloads (§ 4.3, Declared units). It can name only the fields whose unit is in the vocabulary: a compound unit such as debye · Å or GPa⁻¹ has no name there (§ 9), so those fields are fixed by their table alone.

• One section, one state. A section holds the properties of one geometry and, for an electric field response, one frequency. A producer with several (a static and a dynamic polarizability, say) writes several sections with distinct ids and MAY tie them together with group (§ 4.1).

properties.electric

Payload properties ($defs/ElectricPropertiesPayload, strict; at least one of dipole, quadrupole, octupole, polarizability and hyperpolarizability is required):

Field	Type	Meaning	Unit
origin	string or [3] numbers	Reference point of the multipole moments, with the meaning of dipole_moment.origin (§ 3.3): a conventional name ("center_of_mass", "center_of_nuclear_charge", "origin") or an explicit 3-vector.	bohr, for a vector
dipole	object	vector ([3] numbers, required): the dipole components; total (number ≥ 0): its magnitude; units: "debye".	debye
quadrupole	object	matrix (3 × 3, symmetric), traceless (boolean) and convention ("buckingham" or "cartesian"), all required; defined below.	debye · Å
octupole	object	tensor (27 numbers, row-major [3, 3, 3], required): element (a, b, c) is at index 9a + 3b + c; convention ("buckingham" or "cartesian"; absent means "cartesian").	debye · Ų
polarizability	object	matrix (3 × 3, required): α_ab; frequency_ev (number ≥ 0; 0, the default, is the static polarizability); isotropic (number): ⅓ tr α.	atomic units, e² a₀² / E_h; frequency_ev in eV
hyperpolarizability	object	tensor (27 numbers, row-major [3, 3, 3], required): β_abc; frequencies_ev ([2] numbers, default [0, 0]): the photon energies ω₁, ω₂ of β(−(ω₁ + ω₂); ω₁, ω₂).	atomic units, e³ a₀³ / E_h²; frequencies_ev in eV
units	object	Declared units: dipole is debye, origin is bohr.	—

With the charges q_i of the nuclei and of the electrons (the electron’s is −e) at the positions r_i, taken relative to origin, the multipole moments are:

• the dipole μ_a = Σ q_i r_a;

• the Buckingham quadrupole Θ_ab = ½ Σ q_i (3 r_a r_b − r² δ_ab), which is traceless, and the Cartesian quadrupole Q_ab = Σ q_i r_a r_b, whose trace is Σ q_i r². traceless says whether the stored matrix has zero trace: it is always true for "buckingham", and for "cartesian" it says that the trace has been removed, Q_ab − ⅓ δ_ab Σ_c Q_cc;

• the Buckingham octupole Ω_abc = ½ Σ q_i (5 r_a r_b r_c − r² (r_a δ_bc + r_b δ_ac + r_c δ_ab)) and the Cartesian octupole Σ q_i r_a r_b r_c.

For a charged system the moments depend on origin; for a neutral one the dipole does not, but the quadrupole does as long as the dipole is non-zero. The polarizability and hyperpolarizability are the responses of the dipole to a uniform electric field F: μ_a(F) = μ_a + α_ab F_b + ½ β_abc F_b F_c + …, with the dynamic versions at the stated frequencies; α is symmetric for a static field.

Consistency with the root dipole. The root block dipole_moment (§ 3.3) stays the canonical place for a bare dipole. When both it and a properties.electric dipole are present, the two state one dipole: vector MUST equal vector_debye, and total MUST equal total_debye, each within 1e-6 debye, for every field both state. A producer that restates the dipole SHOULD also give the same origin; the check compares the dipole values only. A validator reports a disagreement as E_ROOT_INCONSISTENT (§ 6), located at the section’s properties member.

properties.elastic

Payload properties ($defs/ElasticPropertiesPayload, strict; stiffness is required):

Field	Type	Meaning	Unit
stiffness	6 × 6 numbers, required	The stiffness matrix C_IJ = ∂σ_I/∂ε_J in Voigt notation, with the engineering shear strains 2ε_yz, 2ε_xz, 2ε_xy. Symmetric.	GPa
compliance	6 × 6 numbers	The compliance matrix S, the inverse of stiffness, in the same notation. Symmetric.	GPa⁻¹
bulk_modulus_gpa	number	Bulk modulus K.	GPa
shear_modulus_gpa	number	Shear modulus G.	GPa
youngs_modulus_gpa	number	Young’s modulus E.	GPa
poisson_ratio	number	Poisson’s ratio ν.	—
average	"voigt", "reuss" or "hill"	The averaging scheme the four isotropic numbers come from: Voigt (uniform strain, from the stiffness), Reuss (uniform stress, from the compliance) or Hill (the arithmetic mean of the two). Absent means that the scheme is not stated; a producer SHOULD state it whenever it writes a modulus, because the schemes differ for an anisotropic crystal.	—
units	object	Declared units: stiffness and the three moduli are gpa, poisson_ratio is dimensionless.	—

A validator checks that stiffness and, when present, compliance are symmetric: entries [I][J] and [J][I] differ by at most 1e-6 times the largest absolute entry of the matrix. A violation is E_MEMBER_MALFORMED (§ 6). The payload carries no positive-definiteness rule: the stiffness of a mechanically unstable structure is legitimate data.

properties.dielectric

Payload properties ($defs/DielectricPropertiesPayload, strict; electronic is required):

Field	Type	Meaning	Unit
electronic	3 × 3 numbers, required	The electronic dielectric tensor ε∞, the high-frequency response with the ions held fixed.	— (relative permittivity)
ionic	3 × 3 numbers	The ionic (lattice) contribution to the static dielectric tensor.	—
static	3 × 3 numbers	The static dielectric tensor ε₀.	—
born_charges	array of 3 × 3 numbers	The Born effective charge tensor Z* of each atom, one per atom in the atom order of the structure: Z*[i][j] is the polarization along i per unit displacement of the atom along j (equivalently the force on the atom along j per unit field along i), in units of the elementary charge.	e
piezoelectric	3 × 6 numbers	The piezoelectric stress tensor e_iα = ∂P_i/∂ε_α, row i the polarization component and column α the Voigt strain index, at zero field with the ions relaxed.	C / m²
units	object	Declared units: electronic, ionic and static are dimensionless, born_charges is e.	—

Two rules need the payload as a whole, so a validator checks them (§ 6):

• when electronic, ionic and static are all present, static MUST equal electronic + ionic, entry by entry, within 1e-6;

• when the section’s structure resolves (the section-level structure_ref, else the archive’s only structure), born_charges MUST have exactly one tensor per atom of it.

A violation of either is E_MEMBER_MALFORMED.

5.14 reaction.scheme — reaction schemes

A reaction.scheme section relates structure sections (§ 5.1) as the reactants, reagents and products of one or more reaction steps, the way a scheme in a paper does: which species react, what is drawn at the arrow, the kind of arrow, the conditions written beside it and the yield. It carries the chemistry of a drawn scheme, not its drawing; the species are the archive’s structure sections, with their chemical identity (§ 5.1, Chemical identity), so every reader knows the molecules and their roles without the program that drew them.

Members:

• scheme — REQUIRED JSON member, schema’d as $defs/ReactionSchemePayload (strict).

The section has no kind-specific fields; its generic label (§ 4.1) titles the scheme. An archive MAY carry several schemes.

Payload scheme ($defs/ReactionSchemePayload, strict):

Field	Type	Required	Meaning
steps	array of step objects, at least one	yes	The steps of the scheme, in reading order. Steps that share a species form a sequence: the product of one step is a reactant of the next.

A step ($defs/ReactionStep, strict):

Field	Type	Required	Meaning
id	string, ^[A-Za-z0-9_.-]+$	yes	Identifier of the step, unique within the payload.
label	string	no	Display label of the step, e.g. "a" or "step 2".
reactants	array of participants, at least one	yes	The species the step consumes.
products	array of participants, at least one	yes	The species the step forms.
reagents	array of participants	no	Species drawn at the arrow rather than on either side: reagents, catalysts, solvents drawn as structures.
arrow	"forward", "equilibrium", "retrosynthetic" or "resonance"	no	The kind of arrow; absent means "forward".
conditions	array of strings	no	The text written at the arrow, one entry per line, in reading order, e.g. ["THF, −78 °C", "2 h"].
yield_percent	number, 0 to 100	no	Yield of the step’s products, in percent.
yield_text	string	no	The yield as printed, e.g. "87%", ">95%" or "quant."; with yield_percent it is the display form of that number.

A participant ($defs/ReactionParticipant, strict):

Field	Type	Required	Meaning
structure_ref	string	yes	Id of the structure section of the species.
coefficient	number > 0	no	Stoichiometric coefficient of the species in the step; absent means 1.

Every object of the payload may carry vendor keys beginning x_.

Roles are chemical, the arrow is how the step is drawn. reactants are consumed and products formed in the step’s forward direction whatever the arrow, so a quantity of the step such as a reaction energy is always products minus reactants:

• forward — reactants → products.

• equilibrium — reactants ⇌ products; the forward direction is the one written.

• retrosynthetic — products ⇒ reactants: the target, the step’s products, sits at the tail of the arrow and the precursors, its reactants, at the head. A producer whose drawing records the species by their place at the arrow swaps them when it writes a retrosynthetic step.

• resonance — reactants ↔ products: two resonance structures of one species, at the tail and the head. No reaction takes place; producers SHOULD NOT write reagents, conditions or a yield for it.

A species that appears in several steps is one structure section named by each of them. A species without a three-dimensional structure cannot be a participant, because every participant names a structure section; a producer writes such a reagent into conditions instead.

A validator checks (§ 6), reporting E_REF_UNRESOLVED for the first rule and E_MEMBER_MALFORMED for the others:

• every structure_ref names a structure section;

• the step id values are unique within the payload;

• within one role of one step, no structure_ref occurs twice (a coefficient says how many).

Reaction energies (reserved). A later revision will add the energies of each step, computed from energies of its participants and their coefficients; the key energies of a step is reserved for it, and the strict payload rejects it until then. A producer that has such numbers now writes them under an x_ key.

A two-step synthesis, the second step an equilibrium with a reagent drawn at the arrow (the structures are sections of the same archive):

{
  "steps": [
    {"id": "r1", "label": "a",
     "reactants": [{"structure_ref": "structure_s1"},
                   {"structure_ref": "structure_s2", "coefficient": 2}],
     "products": [{"structure_ref": "structure_s3"}],
     "conditions": ["THF, −78 °C", "2 h"],
     "yield_percent": 87, "yield_text": "87%"},
    {"id": "r2", "label": "b", "arrow": "equilibrium",
     "reactants": [{"structure_ref": "structure_s3"}],
     "reagents": [{"structure_ref": "structure_s4"}],
     "products": [{"structure_ref": "structure_s5"}]}
  ]
}

5.15 preview — a picture of the archive

A preview section carries a picture of the archive’s contents, so that a file manager, a quick-look panel or a catalogue can show the archive without understanding any other section.

Role	Format	Required	Meaning
thumbnail	opaque binary with media_type image/png or image/jpeg	yes	A raster image, the picture a file manager shows.
image	opaque binary with media_type image/svg+xml, image/png or image/jpeg	no	A larger or vector rendering of the same picture, for a preview pane.

Both members are opaque binary members (§ 4.2) and MUST carry their media_type ($defs/PreviewThumbnail, $defs/PreviewImage): a reader learns the image type from the manifest and does not sniff the bytes.

• Which picture. The picture of the archive is the thumbnail of the first preview section in sections order. Further preview sections MAY show parts of the archive and say which with structure_ref or group (§ 4.1).

• Size. The longest side of a thumbnail SHOULD be between 256 and 1024 pixels, and the member SHOULD be at most 1 MiB, so that a file manager reads it cheaply. An already compressed image gains nothing from DEFLATE, so a producer MAY store both members uncompressed.

• The bytes are what the type says. A PNG member begins with the PNG signature (bytes 89 50 4E 47 0D 0A 1A 0A), a JPEG member with FF D8 FF, and an SVG member is a UTF-8 SVG document.

• SVG is inert. An SVG member MUST be self-contained: it references no external resource (no remote href, image, font or style sheet) and contains no script or event-handler attribute. A consumer that renders it MUST NOT run scripts or fetch external resources, whatever the document contains.

The picture describes the archive and is not data: a consumer MUST NOT read chemistry from it, and a producer that updates an archive (§ 2.3) so that the picture no longer matches SHOULD replace or remove the preview section.

A validator checks that each member’s bytes begin with the signature of its raster media_type, and that an image/svg+xml member decodes as UTF-8 and contains an <svg element (§ 6). The media_type values themselves are checked by the JSON Schema.

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6. Validation semantics

A validator treats every archive as untrusted input. A conforming validator performs the checks below and reports each problem as a finding with a severity: an error makes the archive invalid; a warning does not. Every check is an error except the orphan rule, the unit-name rule and the withdrawn version 2, which are warnings. The JSON Schema check is structural; the other checks are semantic rules that a validator performs whether or not it can run a JSON Schema engine.

Container — checked from the ZIP central directory before any member is decompressed:

• The archive is a readable ZIP, and every entry the validator reads decompresses to exactly the uncompressed size recorded for it and matches its ZIP CRC-32.

• ZIP entry names are unique (§ 2.1), except manifest.json: any other duplicated name is an error. Of several manifest.json entries the one whose central-directory record comes last is the manifest, and each earlier copy is superseded and reported as the warning W_ORPHAN_MEMBER (§ 2.3).

• Every ZIP entry name follows the path rules of § 2.1.

• No entry exceeds the per-member uncompressed-size cap; the uncompressed sizes of all entries together do not exceed the total cap (§ 6.1). A validator MUST NOT decompress an entry that exceeds a cap, nor any member payload once the total cap is exceeded.

• Warning: every entry other than the current manifest.json and directory entries is referenced by a member path (orphans, § 2.1, § 2.3).

Manifest:

• manifest.json exists (the last entry of that name, § 2.3), is within the JSON size and depth caps, and parses as UTF-8 JSON to an object; it conforms to the JSON Schema. Among other things the schema check rejects a root byte_order other than "little" (§ 2.2).

• qvf_version is 1, or the withdrawn 2, which a validator reads as 1 for every check, the JSON Schema check included, and reports as the warning W_VERSION_WITHDRAWN (§ 3.1); source carries program, version, and calculation, with program and version non-empty.

• sections is an array of objects, each with a string id, a string kind, and a members object.

• Section id values are unique, and none is auto_open, bookmarks, camera or crossfade (reserved viewer_defaults keys, § 3.1, § 3.4).

• Every kind is canonical (§ 5) or a vendor kind x_<vendor>.* (§ 7.3).

• Extension governance (§ 7): a critical: true section whose kind is neither canonical nor a declared vendor namespace is an error.

• Root blocks agree (§ 3.6): every energy of energies stated for the method that provenance.method names agrees with provenance.scf_energy, and energies.components.zpve with thermochemistry.zpve_eh, within 1e-8 hartree. In an archive with exactly one structure section, its charge and multiplicity equal provenance.charge and provenance.multiplicity where both are present (§ 5.1).

Members and kind-specific rules:

• Every member spec is an object with a string path that follows § 2.1.

• Every declared member path exists in the archive.

• Every member size, when present, is a non-negative integer equal to the uncompressed size the ZIP central directory records for the member’s entry (§ 4.2). The check needs no decompression and is made before the member is read.

• Every declared member sha256 matches the stored bytes.

• Every JSON member is within the JSON size and depth caps and parses as UTF-8 JSON.

• Every binary member that declares a dtype uses a § 4.2 dtype name, and its byte length equals itemsize × ∏(shape).

• Every JSON member whose section kind and role have a payload definition (§ 5) conforms to that $defs entry of the JSON Schema. This is part of the JSON Schema check.

• A structure payload’s periodicity contract (§ 5.1) holds: pbc is present whenever lattice_vectors is non-null; lattice_vectors is non-null whenever any pbc[i] is true; and dimensionality, when present, equals the number of true entries in pbc.

• A structure section’s charge and multiplicity are possible for the atoms of its payload (§ 5.1, Chemical identity): with charge, the electron count N = Σ atomic_number − charge is not negative, and with multiplicity too, multiplicity − 1 is at most N and has the parity of N.

• volume.difference.operand_a/operand_b resolve when present.

• reaction.waypoints.trajectory_ref resolves to a trajectory section.

• A section’s structure_ref, when present, resolves to a structure section, and its run_ref to a run.record section (§ 4.1).

• A standalone bonds section whose structure_ref names a structure section: every pair’s i and j is an atom of that structure, from 0 to its atom count − 1 (§ 5.1). A bonds section without structure_ref, and the bonds member of a structure section, are not checked against an atom count.

• bands: a rank-4 projections and an occupations have the [n_spin, n_k, n_bands] extents of eigenvalues, and a rank-3 projections has its [n_k, n_bands] (§ 5.6).

• trajectory and reaction.path (§ 5.5): coords are float32 only when metadata.precision is "float32", and precision, when present, names the dtype of coords. Against a coords of shape [n_frames, n_atoms, 3], velocities and gradient are [n_frames, n_atoms, 3], times, energies and, for a trajectory, cell_volumes and temperatures are [n_frames], and lattice is [3, 3] or [n_frames, 3, 3]. The binary energies agree with metadata.energies within 1e-10 hartree. A trajectory that carries lattice has metadata.pbc, and one whose metadata.pbc has a true entry carries lattice. Each lattice is read in its own convention (§ 4.3); a validator never compares or converts one carrier against another.

• forces and hessian (§ 5.10, § 5.11): gradient is [n_atoms, 3], stress is [3, 3], matrix is square with an extent 3N divisible by 3, and hessian meta.atom_masses_amu, when present, has N entries. When the section’s structure resolves (the section-level structure_ref, else meta.structure_ref, else the archive’s only structure section), n_atoms and N equal its number of atoms. A meta.structure_ref names a structure section.

• vibrations.hessian_ref, when present, names a hessian section (§ 5.5).

• excited_states (§ 5.12): the index values of states are unique and ascending, and meta.n_states, when present, equals the number of states. The section’s wavefunction_ref and every state’s nto_ref name wavefunction.gto sections, and every density_ref a volume.transition_density or volume.difference section. When wavefunction_ref names a wavefunction.gto section, every contribution’s from_mo and to_mo is a row of its coefficient member: of mo_coefficients, else of mo_coefficients_alpha or mo_coefficients_beta as spin selects, and of both when spin is absent. The rows are read from the manifest shape of the member.

• Unrestricted NTOs (wavefunction.gto, § 5.3): each alpha/beta metadata channel has one nonnegative, non-increasing weight and one energy per coefficient row; optional n_mo agrees. The state reference resolves, and exactly one opposite-role section exists for the same state, with the same spin layout and equal row counts and weights per spin. Findings use E_MEMBER_MALFORMED for channel/pair inconsistencies and E_REF_UNRESOLVED for missing/ambiguous partners or state references, located at the affected section’s members/mo_metadata. A unit weight sum is not imposed because normalization is conditional.

• A one-dimensional spectrum’s states_ref, when present, names an excited_states section, and every peaks[].assignment.state_index is the index of one of its states (§ 5.4).

• A volume.transition_density section’s excited_states_ref, when present, names an excited_states section, and its state_index is the index of one of its states (§ 5.2).

• job.spec: the structure_ref of the spec payload, when present, names a structure section (§ 5.9). The payload’s solvation, scf, geometry and resources objects are checked by the JSON Schema check like the rest of the payload. A run.record job_ref, when present, names a job.spec section (§ 5.8).

• reaction.scheme (§ 5.14): every participant’s structure_ref names a structure section; the step id values are unique within the payload; and no structure_ref occurs twice within one role of one step.

• preview (§ 5.15): a member whose media_type is image/png begins with the PNG signature and one whose media_type is image/jpeg with FF D8 FF; an image/svg+xml member decodes as UTF-8 and contains <svg.

• wavefunction.gto (§ 5.3): every coefficient member has rank 3 with a last extent of 2 when mo_metadata says complex: true (or coefficient_encoding: "complex_split_last_axis"), and rank 2 otherwise; every symmetry_labels array, at the top level or in a spin channel, has one entry per entry of its energies; overlap and the density members are [n_ao, n_ao], with n_ao counted from the basis shells (its n_ao when the shells cannot be read); density_matrix appears only with mo_coefficients, and density_matrix_alpha and density_matrix_beta only together and only with the α and β coefficients; and basis.n_electrons, when present, equals the sum of the occupations over both spin channels within 1e-6, unless occupation_semantics is transition_weight.

• A basis.n_electrons and a root provenance.n_electrons that are both present are equal (§ 3.2, § 5.3).

• When a wavefunction.gto section carries overlap, its diagonal agrees with the self-overlaps that Appendix A.1 gives for the basis payload, to a relative tolerance of 1e-6 (Appendix A.1, Verifying with overlap).

• Volumes (§ 5.2): the data of volume.laplacian is [nx, ny, nz], of volume.vector [nx, ny, nz, 3], of volume.complex [nx, ny, nz, 2] and of volume.series [n, nx, ny, nz]; a volume.series axis has one values entry, and one labels entry when it has labels, per slab, and its trajectory_ref, when present, names a trajectory or reaction.path section.

• Grids (§ 5.2): a grid payload’s structure_ref, when present, names a structure section. When periodic[a] is true and the grid’s structure resolves (the section-level structure_ref, else the grid’s structure_ref, else the archive’s only structure section), that structure’s pbc[a] is true, and voxel_vectors[a] × (shape[a] − 1) when includes_endpoint is true or absent, or voxel_vectors[a] × shape[a] when it is false, equals lattice row a of the structure converted to bohr within 10⁻⁶ relative.

• The property kinds (§ 5.13): a properties.elastic stiffness and compliance are symmetric to within 1e-6 of their largest entry; in a properties.dielectric payload, static equals electronic + ionic within 1e-6 when all three are present, and born_charges has one tensor per atom of the section’s structure when that resolves (the section-level structure_ref, else the archive’s only structure section); each violation is E_MEMBER_MALFORMED. A properties.electric dipole agrees with the root dipole_moment within 1e-6 debye (vector against vector_debye, total against total_debye), or the finding is E_ROOT_INCONSISTENT. The payloads properties.electric, properties.elastic and properties.dielectric conform to the $defs definitions of § 5.13.

• wavefunction.bloch (§ 5.3.1): mo_coefficients is [n_k, n_spin, n_mo, n_ao, 2] with n_spin 1 or 2, and energies and occupations have its [n_k, n_spin, n_mo]; the kpoints payload lists n_k k-points and, when present, n_k labels and n_k weights that sum to 1 within 1e-6; mo_metadata n_spin (1 for restricted, 2 for unrestricted), n_mo and n_ao, and basis.n_ao, agree with those axes, and mo_metadata.n_mo_per_k has n_k entries of at most n_mo. The section’s structure (the section-level structure_ref, else basis.structure_ref) is a structure section with at least one periodic axis.

• The JSON members bands.kpath, dos.coop.meta, dos.cohp.meta, fermi_surface.mesh, phonon_bands.qpath, phonon_dos.meta, equation_of_state.fit and run.record.files conform to the $defs payload definitions their tables name (§ 5.6, § 5.8).

• run.record: input and log members decode as UTF-8; every key of the files index names a member that exists in the section.

• atom_properties: every custom.<name> member has an entry named custom.<name>, a JSON object, in the section’s meta member (§ 5.7); a missing meta member, or one without that entry, is an error for that member. The meta payload itself is checked against $defs/AtomPropertiesMetaPayload like any payload definition.

• A one-dimensional spectrum’s frequencies, intensities and, when present, x have the same length — a part of SpectrumPayload that JSON Schema cannot express (§ 5.4).

• Warning: every declared unit is a unit name of § 4.3 (Declared units): each value of the units object of a JSON member of a canonical kind, and of the meta.units object of an excited_states payload; a one-dimensional spectrum’s x_units, y_units and broadening.units; the units of a volume.series axis; and the units of every {value, units} object directly under provenance, which may also be a legacy spelling. This rule needs no JSON Schema engine. The schema types the same strings, so a validator that runs it also reports the schema finding.

6.1 Resource limits

A validator reports an error when an archive exceeds one of the caps below. Validators SHOULD use the reference values, which are the defaults of the reference validators; producers SHOULD stay within them so that their archives validate everywhere.

Quantity	Reference value
Uncompressed size of one ZIP entry	8 GiB
Total uncompressed size of all ZIP entries	64 GiB
Size of manifest.json or of one JSON member	256 MiB
Nesting depth of JSON arrays and objects	64 — a top-level [] or {} has depth 1, a scalar depth 0

Compression ratio is not a format validity limit: valid constant arrays can compress by more than 1000:1. The size caps above and the requirement never to inflate past the declared uncompressed size bound decompression independently of compression ratio. Readers MUST reject a mismatch between actual and declared size or a CRC-32 mismatch as E_ZIP_UNREADABLE.

The reference APIs retain max_ratio as an optional, stricter application policy for compatibility, with 0 disabling it by default. A positive value applies to compressed entries of at least ratio_exempt_bytes (default 1 MiB); STORE entries remain exempt. E_COMPRESSION_RATIO identifies rejection by this explicit policy, not a malformed QVF archive.

6.2 Finding codes

Conforming validators SHOULD report each finding with the stable code listed in Appendix B (“Validation finding codes”), so that tools, bindings, and test suites match findings by code rather than by message text. A finding carries exactly one code: E_… codes are errors, W_… codes are warnings. The conformance suite’s negative corpus (conformance/negative/) holds a must-fail archive for each rule, naming the code it must produce.

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7. Extension and versioning model

7.1 qvf_version

Integer. v1 = 1. A value > 1 signals breaking changes; a v1-only consumer MUST refuse such files, except the withdrawn 2, which it SHOULD read as 1 (§ 3.1). Minor, backward-compatible growth (new optional kinds, new optional members) does not bump the integer — capability is detected via supported-kind checking and the extensions block.

7.2 Canonical kinds

Canonical kinds appear in the schema and § 5. They may grow in minor revisions; no canonical kind may be removed or have its required members changed without a major version bump.

7.3 Vendor namespace x_<vendor>.*

Any kind matching x_<vendor>.<specific> is a vendor extension. <vendor> SHOULD be a DNS-like identifier (x_orca, x_pyscf, x_vasp). Vendor members must be valid JSON, binary or opaque binary member specs (§ 4.2); an opaque member, such as an image, SHOULD carry its media_type. Registering the namespace in registry.json (vendor_namespaces) records who uses it and is advisory (GOVERNANCE.md). A consumer MUST list vendor sections as present-but-unsupported unless the extension is critical: true. Unknown non-vendor kinds are not valid QVF.

7.4 Root extensions block and per-section critical

The manifest root may declare vendor extensions:

{ "extensions": { "x_orca": { "version": "1.0", "schema_uri": "…", "critical": false } } }

Each section may carry critical (default false). If critical: true and the consumer does not support the kind, the consumer MUST refuse to open the file rather than silently drop the section. Use critical: true only when the section changes correct interpretation of the rest of the file (e.g. an ECP that alters the effective electron count).

7.5 Promoting a vendor kind to canonical

1. The kind is used in production by ≥ 2 independent producers for ≥ 1 minor cycle.

2. A spec PR adds it to § 5, the schema oneOf branches, and the validator.

3. Its member contract is stable across the two producers.

4. At least one reference consumer renders it.

The maintainer may promote a kind before the first criterion is met, as a maintainer decision recorded in GOVERNANCE.md and registry.json; spectra.epr and wavefunction.bloch (§ 5.3.1) were promoted that way. A kind promoted before a second independent producer ships it carries "status": "provisional" in its registry.json promotions entry. A provisional kind is canonical in every respect (§ 7.2): producers may emit it, consumers may rely on it, and any revision it needs is additive. It becomes final, and loses the status, when a second producer ships it.

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8. Conformance

8.1 Producer conformance

A conforming producer MUST:

• write a valid ZIP with manifest.json at the root;

• set qvf_version to 1;

• include source.program, source.version, source.calculation;

• use unique section ids matching ^[A-Za-z0-9_.-]+$, other than the reserved auto_open, bookmarks, camera and crossfade (§ 3.4);

• use canonical kinds or x_<vendor>.*;

• include only member paths that exist in the ZIP and follow § 2.1 (relative, /-separated, no .. segments), and write each ZIP entry name once — except manifest.json when updating an archive in place, whose new manifest is the last entry (§ 2.3);

• compute sha256 over the exact stored bytes of each member, and write a member’s size, when it writes one, as the uncompressed byte count of the member’s entry (§ 4.2);

• write byte_order, when it writes it, as "little" (§ 2.2);

• write numeric fields in the units of § 4.3, and name every declared unit with a unit name of § 4.3;

• write binary payloads matching the declared dtype and shape, little-endian;

• ensure JSON members parse as UTF-8 JSON, and that every JSON member with a payload definition (§ 5) conforms to it;

• write pbc in every structure payload that carries lattice_vectors, and keep dimensionality — if emitted at all — equal to sum(pbc) (§ 5.1);

• point every structure_ref, run_ref and trajectory_ref on a section at a section of the kind it names (§ 4.1, § 5.5), and likewise every reference of an excited-state calculation: wavefunction_ref, nto_ref, density_ref, states_ref and excited_states_ref (§ 5.12), every participant of a reaction.scheme (§ 5.14) and every run.record job_ref (§ 5.8);

• write a structure’s charge and multiplicity only as values possible for its atoms, and equal to those of provenance in an archive with one structure section (§ 5.1);

• write the atom indices of a standalone bonds section that carries a structure_ref as atoms of the structure it names (§ 5.1);

• give every preview member its media_type, and write an SVG image that references no external resource and contains no script (§ 5.15);

• declare each x_<vendor> namespace in root extensions when any section in that namespace is critical: true;

• set critical: true only when consumer support is truly required.

A conforming producer SHOULD include provenance when known; include citations when results depend on citable methods/bases/functionals; prefer a specific volume.* kind over volume.generic; use a vendor namespace for experimental payloads; set structure_ref on every standalone bonds section of an archive with several structures (§ 5.1); stay within the reference resource limits of § 6.1; and run a validator on its own output in tests.

8.2 Consumer conformance

A conforming consumer MUST:

• read manifest.json by name, not by ZIP entry order, and use the entry whose central-directory record comes last when there are several (§ 2.3);

• ignore every ZIP entry the manifest does not reference: orphans and superseded manifests (§ 2.1, § 2.3);

• sanity-check qvf_version, source, and sections;

• verify sha256 before using a member’s bytes;

• interpret only kinds it supports;

• report unsupported vendor sections without corrupting or misinterpreting them;

• respect declared dtype, shape, and units, reading a legacy unit spelling as the unit name it stands for (§ 4.3);

• take per-axis periodicity from pbc, and never draw, replicate along, or measure an extent from a lattice row whose axis is non-periodic (§ 5.1);

• read a payload’s atom indices against the structure named by the section’s structure_ref when the section has one, in preference to a structure_ref inside the payload (§ 4.1), and the bonds of a standalone bonds section without one against the first structure (§ 5.1);

• find sections by kind and reference, never by a conventional id such as structure, and open an archive with several structures, none of them named structure, showing its first structure (§ 4.1);

• open a file whose viewer_defaults carries a malformed or unknown hint, ignoring that hint (§ 3.4);

• render an SVG preview member, if at all, without running scripts or fetching external resources (§ 5.15);

• honor the per-section critical flag and the root extensions critical flags, refusing to open when an unsupported extension is critical.

A conforming consumer SHOULD read an archive stamped qvf_version: 2 as 1 (§ 3.1), refuse an archive with duplicate ZIP entry names other than manifest.json, refuse an archive whose byte_order is not "little" (§ 2.2), and apply the § 6.1 resource limits before decompressing or parsing a member (§ 2.1).

A consumer MAY require specific kinds for a given operation (a band plotter may refuse a file without bands; a structure viewer may open it and ignore all scalar fields).

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9. Known open items (informative)

These are acknowledged limitations of v1, not defects:

1. Endianness tag. dtype names do not carry byte order. v1 archives are little-endian and may say so once, with the root byte_order (§ 2.2); a per-dtype prefix such as <f8 changes the dtype vocabulary and is a candidate for the next major version.

2. k-resolved Bloch wavefunctions. wavefunction.gto covers molecular systems and the Γ-point; k-resolved orbitals over an atom-centred Gaussian basis are carried by wavefunction.bloch (§ 5.3.1), which is provisional until a second producer ships it. Not yet covered: k-resolved density matrices (the spin-density restart payload of x_vibeqc.bloch_wavefunction stays in that vendor section), two-component (spinor) Bloch orbitals, and Bloch orbitals over other bases such as plane waves or numeric atomic orbitals; producers may use x_<vendor>.* for those meanwhile.

3. NMR and EPR schema tightening. The spectra.nmr and spectra.epr payloads are typed but permissive in v1 (§ 5.4): their known fields are checked and every object stays open until producer conventions settle.

4. Fermi-surface meshes. v1 assumes a Γ-centered uniform Monkhorst-Pack grid.

5. Cartesian wavefunction.gto shells have little mileage. The convention is fully specified (Appendix A.1: one N_i per shell, from the total l), but pure: false has far less cross-consumer mileage than pure: true, and the per-component normalization trap described there has already been hit in practice — by the reference producer’s own two readers, which is how it was found. A producer can now make its archives checkable: with the overlap member (§ 5.3) every reference validator compares the stored diagonal with Appendix A.1 and reports a d_xy self-overlap of 1 rather than 1/3 as E_NORMALIZATION. The check covers producers only; a consumer that evaluates AOs still has to test its own evaluator on a Cartesian d shell (the corpus archives wavefunction_cartesian.qvf and wavefunction_overlap.qvf carry the numbers), because a spherical-only test will not catch the trap.

6. QTAIM position unit. The ångström default for topology.qtaim positions (§ 5.7) is provisional pending a maintainer decision; producers should declare units.position.

7. Unit names of compound quantities. The unit vocabulary of § 4.3 names the units that QVF payloads declare today. It has no name yet for compound units such as an electron density (e·bohr⁻³), its Laplacian (e·bohr⁻⁵, volume.laplacian), a reciprocal length (Å⁻¹) or a density of states (states·eV⁻¹), so such fields cannot be declared; their units are those of § 4.3 and the payload tables. A later revision may add names, which is an additive change.

8. Two-dimensional drawings. v1 has no canonical kind for an editable drawing of molecules or of a scheme: the drawing formats in use (Ketcher’s KET, ChemDraw’s CDXML, the 2-D coordinates of an MDL molfile) are program-specific, and one producer writes drawings into QVF today. Such a drawing travels in its producer’s vendor section, as vibe-sketch’s x_vibesketch.document does. What a drawing means has canonical carriers: the identity of each species on its structure section (§ 5.1), the scheme as reaction.scheme (§ 5.14) and the picture as preview (§ 5.15).

9. Reaction energies. reaction.scheme (§ 5.14) reserves the step key energies for the energies of a step, to be specified when a producer computes them from the energies of the participants.

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10. Governance and stewardship

QVF is an open standard. It was created by and is stewarded by the vibe-qc project — that origin is explicit — but the format is producer-neutral by design (§ 1) and its specification and reference implementations are Apache-2.0, so any code may implement a conforming producer or consumer, including a proprietary one, with no obligation back to vibe-qc. vibe-qc’s own non-standard data lives under the x_vibeqc.* vendor namespace, exactly like any other adopter’s.

The governance model, versioning policy, change process, and the vendor→canonical promotion process are described in GOVERNANCE.md; the machine-readable list of canonical kinds and registered vendor namespaces is in registry.json (kept in lock-step with the schema). Stewardship is intended to broaden as independent producers adopt the format.

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Appendix A. AO ordering, primitive normalization, and component naming

A wavefunction.gto or wavefunction.bloch section is only correct if the MO coefficients, the AO ordering, and the primitive normalization all agree with A.1–A.2 of this appendix. This is the part most producers get subtly wrong. A.3 applies to basis.ao, which names a single AO rather than ordering a whole matrix, and depends on the same in-shell ordering.

A.1 Contraction and the normalization convention

Each contracted basis function is reconstructed as

χ(r) = Σ_i c_i · φ_i(r)

where each primitive φ_i is normalized as:

φ_i(r) = N_i · (x−A_x)^{l_x} (y−A_y)^{l_y} (z−A_z)^{l_z} · exp(−α_i r²)

N_i = (2 α_i / π)^{3/4} · (4 α_i)^{l/2} / √((2l − 1)!!),   l = l_x + l_y + l_z

The coefficients c_i written into basis.json MUST apply to primitives normalized exactly this way.

N_i depends only on l, not on (l_x, l_y, l_z). This matters for Cartesian shells, and it is deliberate: N_i is the normalization of the axial component (l, 0, 0) and is applied uniformly to the whole shell. It is what libint and libcint store, so a producer divides by one factor per primitive and is done.

The consequence is that for pure: false shells the primitives are not individually unit-normalized. Only the axial components (x^l, y^l, z^l) have unit norm; a mixed component such as d_xy does not. Concretely, for a single Cartesian d shell the overlap diagonal in this convention is ⟨xx|xx⟩ = 1 but ⟨xy|xy⟩ = 1/3. A genuinely unit-normalized Cartesian Gaussian would divide by √((2l_x−1)!!(2l_y−1)!!(2l_z−1)!!) instead of √((2l−1)!!), which for d_xy differs by a factor of √3.

Consumers MUST NOT apply a per-component correction on top of N_i. Doing so scales every mixed Cartesian AO by that factor and the resulting density is wrong by its square — a factor of 3 for d_xy. This is a real, observed failure mode, not a hypothetical one. For pure: true shells the question does not arise: the solid-harmonic transform absorbs it and the two conventions coincide, which is why the discrepancy can sit unnoticed in a spherical-only pipeline.

This is not a hypothetical warning. Both of vibe-qc’s AO evaluators shipped that per-component correction — its own evaluate_ao and the vibe-view reader — while its writer divided by N_i exactly as specified. Writer and readers therefore disagreed by that factor on pure: false shells, and nothing failed loudly, because spherical shells (everything a named basis produces) are unaffected. Both readers were corrected on 2026-08-05. If you are implementing a consumer, this is the single easiest thing here to get wrong, and a spherical-only test will not catch it.

The trap. Integral libraries such as libint and libcint (used by PySCF, and by many other codes including patterns ORCA developers will recognize from GBW-style storage) store contraction coefficients already pre-multiplied by N_i — i.e. the stored coefficient is c_i · N_i, so it multiplies an un-normalized primitive. If your engine stores coefficients that way, you MUST divide each stored coefficient by N_i before writing it into basis.json. Writing the engine-native (pre-scaled) coefficients produces orbitals that look plausible but are quantitatively wrong, especially for high-l and tightly contracted shells.

Reference implementation of N_i (Python; the C++ toolkit has the identical routine as qvf::primitive_norm):

import math
def primitive_norm(alpha: float, l: int) -> float:
    radial  = (2.0 * alpha / math.pi) ** 0.75
    angular = (4.0 * alpha) ** (l / 2.0)
    df = 1.0
    for k in range(1, 2 * l, 2):   # (2l-1)!!
        df *= k
    return radial * angular / math.sqrt(df)

Both reference writers expose a flag: pass your coefficients as-is if they are already on N_i-normalized primitives, or ask the writer to divide by N_i if they are libint/libcint-style. When in doubt, verify against a known orbital: the HOMO of H₂O/STO-3G evaluated on a grid should integrate to ~1 electron per spin. Better still, write the overlap member and let a validator check it, as described next.

Verifying with overlap

The self-overlap of every AO follows from basis.json alone. For a shell of angular momentum l with exponents α_i and coefficients c_i, the self-overlap of its axial component (l, 0, 0) is

S_axial = Σ_i Σ_j c_i c_j · ( 2 √(α_i α_j) / (α_i + α_j) )^(l + 3/2)

which is Σ_ij c_i c_j N_i N_j ⟨x^l e^(−α_i r²) | x^l e^(−α_j r²)⟩ with the N_i above folded in. The diagonal of the AO overlap matrix, at the AO index of each component of the shell (A.2), is then:

• spherical shell: S_axial for every m, because a real solid harmonic built on N_i-normalized primitives is normalized like the axial component;

• Cartesian shell: S_axial · (2l_x−1)!! (2l_y−1)!! (2l_z−1)!! / (2l−1)!! for the component (l_x, l_y, l_z): S_axial for an axial component, S_axial / 3 for d_xy, S_axial / 5 for f_xxy, S_axial / 15 for f_xyz.

A contraction normalized in the usual way has S_axial = 1, so the diagonal is 1 for every spherical AO and every axial Cartesian AO, and 1/3 for d_xy.

A wavefunction.gto section may carry the overlap matrix its producer computed with its own integral code (the overlap member, § 5.3), and producers SHOULD write it. A validator then computes the values above from basis.json and compares each with the stored diagonal at that AO’s index, to a relative tolerance of 1e-6. A disagreement is the error E_NORMALIZATION (Appendix B): the coefficients in basis.json are not on N_i-normalized primitives (the libint/libcint trap above), a per-component correction has been applied to a Cartesian shell (a d_xy diagonal of 1 rather than 1/3), or the AO order disagrees with A.2. The check sees the diagonal only, so it cannot tell apart the components of a spherical shell, whose diagonal entries are all equal: a permutation of m within a spherical shell passes it.

This is the most valuable interoperability check the format has. The normalization trap produces orbitals that look plausible and are wrong; with overlap in the archive it fails validation at write time instead.

A.2 AO ordering within a shell

AO order is part of the contract and MUST match the pure flag:

• Spherical (pure: true): functions are ordered m = −l, −l+1, …, +l.

• Cartesian (pure: false): libint lexicographic ordering of (l_x, l_y, l_z) with l_x + l_y + l_z = l, decreasing l_x first, then l_y.

The row/column index of an AO in mo_coefficients is its position in the concatenation of all shells (shell order = shells array order), each shell contributing 2l+1 (spherical) or (l+1)(l+2)/2 (Cartesian) functions.

If your engine uses a different in-shell order (common differences: p as x,y,z vs m = −1,0,+1; d as xx,yy,zz,xy,xz,yz vs m = −2…+2), you MUST permute the coefficient rows into QVF order before writing.

A.3 Naming a single component (basis.ao)

A basis.ao section carries one component of one shell, so its ao_metadata has to name which — and the two shell kinds above are named differently:

• Spherical (pure: true): angular_momentum is [l, m] with m ∈ [−l, +l], the harmonic’s own index under the A.2 ordering.

• Cartesian (pure: false): there is no magnetic quantum number. The component is named by cartesian_powers, the [l_x, l_y, l_z] of the monomial, so a d shell’s six components are [2,0,0] … [0,0,2] in the A.2 order. angular_momentum[1] is then 0 by convention and carries no meaning.

cartesian_powers is present if and only if the component is Cartesian, and l_x + l_y + l_z MUST equal angular_momentum[0]. A consumer therefore reads l from angular_momentum[0] for either kind, but MUST NOT read angular_momentum[1] as an m when cartesian_powers is present — [2, 0] on a Cartesian d component does not mean d_z².

The trap. Deriving m as component index − l is correct for a spherical shell and wrong for a Cartesian one, where it runs past +l: a Cartesian d shell comes out as m = −2 … +3 over its six components. A producer that emits basis.ao for Cartesian shells MUST branch on the shell’s pure flag.

cartesian_powers is an optional member added under v1 — the additive case per GOVERNANCE.md, so there is no qvf_version bump, and a spherical-only producer is unaffected.

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Appendix B. Validation finding codes (informative)

Stable identifiers for the findings of § 6. A code is never renamed or reused; a new check gets a new code. Messages are free text for people; tools match on the code. The Python reference validator (python/qvf_reader.py), the C++ reference validator (qvf::QvfReader::validate_findings) and the JavaScript validator (@qvf/core) emit these codes. All three run the JSON Schema check: Python through jsonschema, C++ and JavaScript through the checker generated from the schema (scripts/gen_kinds.py). A validator that runs without the check (jsonschema missing, or the check disabled) reports W_SCHEMA_SKIPPED instead of E_SCHEMA / E_PAYLOAD_SCHEMA.

A finding is {severity, code, where, message}. where locates it: archive (the ZIP as a whole), entry:<name> (one ZIP entry), manifest.json (the manifest document as a whole), or a JSON Pointer (RFC 6901) into manifest.json, such as /sections/2/members/data. A finding about a member’s payload points at the member spec that declares it.

Code	Severity	Rule	Meaning
E_ZIP_UNREADABLE	error	§ 2.1	The archive is not a readable ZIP, or an entry cannot be decompressed (corrupt data, CRC mismatch, unsupported method, data that does not inflate to its recorded size).
E_ZIP_DUPLICATE_ENTRY	error	§ 2.1, § 2.3	Two or more ZIP entries share a name other than manifest.json. (Several manifest.json entries are an archive updated in place: the last is the manifest and each earlier one is a W_ORPHAN_MEMBER.)
E_MEMBER_PATH	error	§ 2.1	A ZIP entry name or a member path contains a backslash or a NUL, begins with / or a drive letter, or has a .. segment.
E_MEMBER_TOO_LARGE	error	§ 6.1	An entry’s uncompressed size exceeds the per-member cap; it is not decompressed.
E_TOTAL_TOO_LARGE	error	§ 6.1	The entries’ total uncompressed size exceeds the total cap; no member payload is decompressed.
E_COMPRESSION_RATIO	error	§ 6.1	An explicitly enabled application ratio policy rejects a compressed entry; it is not decompressed. Disabled by default; not a format validity rule.
W_ORPHAN_MEMBER	warning	§ 2.1, § 2.3	A ZIP entry, other than the current manifest.json or a directory entry, that no member path references, or a superseded manifest.json: an earlier entry of that name in an archive updated in place (where is entry:manifest.json).
E_MANIFEST_MISSING	error	§ 2.1	There is no manifest.json at the archive root.
E_MANIFEST_JSON	error	§ 3	manifest.json is not UTF-8 JSON, or not a JSON object.
E_JSON_TOO_LARGE	error	§ 6.1	manifest.json or a JSON member exceeds the JSON size cap.
E_JSON_TOO_DEEP	error	§ 6.1	manifest.json or a JSON member nests arrays and objects deeper than the depth cap.
E_SCHEMA	error	§ 6	manifest.json violates the JSON Schema (one finding per schema error), for example with a root byte_order other than "little" (§ 2.2).
W_SCHEMA_SKIPPED	warning	§ 6	The validator could not run the JSON Schema check; the semantic checks still ran.
E_VERSION	error	§ 3.1	qvf_version is neither 1 nor the withdrawn 2.
W_VERSION_WITHDRAWN	warning	§ 3.1	qvf_version is the withdrawn 2. The validator checks the archive as version 1; producers MUST NOT write 2, and consumers SHOULD read it as 1.
E_SOURCE	error	§ 3.1	source is not an object, lacks program, version, or calculation, or has an empty program or version.
E_SECTION_MALFORMED	error	§ 4.1	sections is not an array, or a section is not an object, has no string id or kind, or has no members object.
E_SECTION_ID_DUPLICATE	error	§ 4.1	Two sections share an id.
E_RESERVED_ID	error	§ 3.1, § 3.4	A section id is auto_open, bookmarks, camera or crossfade.
E_KIND_UNKNOWN	error	§ 7.3	A kind is neither canonical nor x_<vendor>.*.
E_CRITICAL_UNDECLARED	error	§ 7.4	A critical: true vendor section’s namespace is not declared in root extensions.
E_MEMBER_MALFORMED	error	§ 4.2, § 5.1, § 5.2, § 5.3, § 5.3.1, § 5.5, § 5.6, § 5.7, § 5.10, § 5.11, § 5.12, § 5.13, § 5.14, § 5.15	A member spec is not an object or has no string path; a binary member’s shape is not a list of non-negative integers; a pair of a standalone bonds section names an atom index i or j that is not an atom of the structure its structure_ref names; a wavefunction.gto coefficient member’s rank disagrees with complex, a symmetry_labels array differs in length from its energies, an overlap or density member is not [n_ao, n_ao] or does not pair with the coefficient members, or basis.n_electrons differs from the sum of the occupations; a per-frame member of a trajectory or reaction.path disagrees in shape with its coords, its coords are float32 without metadata.precision "float32" (or precision names the other dtype), its binary energies disagree with metadata.energies, or a trajectory carries lattice without metadata.pbc or a true pbc entry without lattice; the projections or occupations of a bands section disagree in shape with its eigenvalues; a custom.<name> member of an atom_properties section has no entry in the section’s meta member; a forces gradient or stress, a hessian matrix or its meta.atom_masses_amu has the wrong shape or disagrees with the atom count of the section’s structure; the states of an excited_states section repeat an index or list it out of order, disagree in number with meta.n_states, or have a contribution whose from_mo or to_mo is not a row of the reference wavefunction; the data of a volume.laplacian, volume.vector, volume.complex or volume.series section has the wrong rank or trailing axis, or a volume.series axis has not one values (or labels) entry per slab; a periodic grid axis is aperiodic in the grid’s structure or does not span its lattice vector; a properties.elastic stiffness or compliance is not symmetric; a properties.dielectric static is not electronic + ionic, or its born_charges do not number the atoms of the section’s structure; the members of a wavefunction.bloch section disagree in shape, its k-point weights do not sum to 1, or its structure has no periodic axis; two steps of a reaction.scheme share an id, or a structure_ref occurs twice within one role of a step; a preview member does not begin with the signature of its raster media_type, or an image/svg+xml member has no <svg element; or a member’s size is not a non-negative integer.
E_MEMBER_MISSING	error	§ 4.2	A declared member path is not in the archive.
E_SHA256_MISMATCH	error	§ 4.2	A member’s bytes do not match its sha256.
E_JSON_INVALID	error	§ 4.2	A JSON member is not UTF-8 JSON.
E_DTYPE	error	§ 4.2	A binary member’s dtype is not a § 4.2 dtype name.
E_BINARY_SIZE	error	§ 4.2	A binary member’s byte length differs from itemsize × ∏(shape), or a member’s declared size (JSON, binary or opaque) differs from the uncompressed size the ZIP central directory records for its entry.
E_UTF8	error	§ 5.8, § 5.15	A run.record input or log member, or a preview member of media_type image/svg+xml, does not decode as UTF-8.
E_PAYLOAD_SCHEMA	error	§ 6	A JSON member violates the payload definition (§ 5) of its section kind and role (one finding per schema error), or a one-dimensional spectrum’s arrays differ in length (§ 5.4).
E_STRUCTURE_PERIODICITY	error	§ 5.1	A structure payload breaks the periodicity contract, or is not a JSON object.
E_CHARGE_MULTIPLICITY	error	§ 5.1	A structure section’s charge and multiplicity are impossible for the atoms of its payload: the electron count Σ atomic_number − charge is negative, or multiplicity − 1 exceeds it or differs from it in parity.
E_REF_UNRESOLVED	error	§ 4.1, § 5.2, § 5.3.1, § 5.4, § 5.5, § 5.8, § 5.9, § 5.10, § 5.11, § 5.12, § 5.14	A volume.difference operand does not name a section in the archive; a reaction.waypoints trajectory_ref does not name a trajectory section; a section’s structure_ref or run_ref does not name a section of kind structure or run.record respectively; a job.spec payload’s structure_ref or a forces or hessian meta.structure_ref does not name a structure section; a wavefunction.bloch basis.structure_ref, in a section without a section-level structure_ref, does not name a structure section; a vibrations hessian_ref does not name a hessian section; an excited_states wavefunction_ref or nto_ref does not name a wavefunction.gto section, or a density_ref a volume.transition_density or volume.difference section; a grid structure_ref does not name a structure section; a volume.series axis trajectory_ref does not name a trajectory or reaction.path section; or a spectrum’s states_ref or a volume.transition_density excited_states_ref does not name an excited_states section, or a state_index it qualifies names no state of that section; a reaction.scheme participant’s structure_ref does not name a structure section; or a run.record job_ref does not name a job.spec section.
E_FILES_INDEX	error	§ 5.8	A run.record files index names a role with no member in the section.
W_UNIT_UNKNOWN	warning	§ 4.3	A declared unit is not a unit name: a value of a payload’s units object (of an excited_states payload’s meta.units), a one-dimensional spectrum’s x_units, y_units or broadening.units, the units of a volume.series axis, or the units of a {value, units} object in provenance that is not a legacy spelling either. A validator with a JSON Schema engine also reports E_SCHEMA or E_PAYLOAD_SCHEMA for it.
E_ROOT_INCONSISTENT	error	§ 3.6, § 5.1, § 5.3, § 5.13	Two statements of the same quantity differ: an energy of energies stated for the method provenance.method names differs from provenance.scf_energy, or energies.components.zpve from thermochemistry.zpve_eh, by more than 1e-8 hartree; a wavefunction.gto basis.n_electrons differs from provenance.n_electrons; the dipole of a properties.electric section differs from the root dipole_moment by more than 1e-6 debye; or, in an archive with one structure section, its charge or multiplicity differs from provenance.charge or provenance.multiplicity.
E_NORMALIZATION	error	§ 5.3, Appendix A.1	The diagonal of a wavefunction.gto overlap member disagrees with the self-overlaps Appendix A.1 gives for its basis payload: basis.json coefficients are not on N_i-normalized primitives, or the AO order disagrees with Appendix A.2.