Basis sets¶

Modern quantum chemistry has converged on a small number of well-engineered basis-set families. This page is a practical guide to picking the right one for your system, with explicit notes on what vibe-qc ships today and what’s on the roadmap.

Theory¶

Contracted Gaussians. A basis function on centre $\mathbf A$ is a fixed contraction of $K$ primitive Gaussians sharing that centre and angular part,

\[ \chi_\mu(\mathbf r) = \sum_{p=1}^{K} d_{p\mu}\, N_p\, x_A^{\,i}\, y_A^{\,j}\, z_A^{\,k}\, e^{-\alpha_p r_A^2}, \qquad \mathbf r_A = \mathbf r - \mathbf A,\quad \ell = i + j + k , \]

with $\alpha_p$ and $d_{p\mu}$ fixed by the published set. Gaussians stand in for Slater functions because a product of Gaussians on two centres is a Gaussian on a third, which makes every integral analytic; STO-nG fits $n$ Gaussians to one Slater function (Hehre, W. J., Stewart, R. F., and Pople, J. A. (1969). *Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals.* Journal of Chemical Physics, **51**(6), 2657–2664. doi:[10.1063/1.1672392](https://doi.org/10.1063/1.1672392)). Chapters 6 and 8 of Helgaker, Trygve, Jørgensen, Poul, and Olsen, Jeppe (2000). *Molecular Electronic-Structure Theory.* Wiley. doi:[10.1002/9781119019572](https://doi.org/10.1002/9781119019572) treat this material in full.

Pure and Cartesian shells. A shell has $(\ell+1)(\ell+2)/2$ Cartesian or $2\ell+1$ pure (real solid harmonic) functions. The Cartesian $d$ shell contains the $s$-type combination $x^2+y^2+z^2$, so the two span different spaces and give different energies; the representation a set was optimised in is part of its definition (Schlegel, H. Bernhard and Frisch, Michael J. (1995). *Transformation between Cartesian and pure spherical harmonic Gaussians.* International Journal of Quantum Chemistry, **54**(2), 83-87. doi:[10.1002/qua.560540202](https://doi.org/10.1002/qua.560540202) gives the transformation).

Segmented and general contraction. In a segmented set (Pople, def2, pcseg) each primitive enters essentially one contracted function; in a general contraction (ANO, cc-pVnZ) every contracted function of a given $\ell$ combines the same primitives. Jensen’s P-orthogonalisation turns a general set into a cheaper segmented one of the same accuracy (Jensen, Frank (2014). *Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent Basis Sets.* Journal of Chemical Theory and Computation, **10**(3), 1074–1085. doi:[10.1021/ct401026a](https://doi.org/10.1021/ct401026a)).

The cc-pVnZ and def2 families. The cc-pVnZ sets (Dunning, Thom H. (1989). *Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen.* Journal of Chemical Physics, **90**(2), 1007–1023. doi:[10.1063/1.456153](https://doi.org/10.1063/1.456153)) add polarisation shells in groups that recover similar amounts of correlation energy, so correlated energies converge systematically with the cardinal number $X$ (2 for D, 3 for T, …), which supports the extrapolation $E^{\rm corr}_X = E^{\rm corr}_\infty + A X^{-3}$ (T. Helgaker, W. Klopper, H. Koch, J. Noga, J. Chem. Phys. 106, 9639 (1997), doi:10.1063/1.473863); aug- adds one diffuse function per angular momentum (Kendall, Rick A., Dunning, Thom H., and Harrison, Robert J. (1992). *Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions.* Journal of Chemical Physics, **96**(9), 6796–6806. doi:[10.1063/1.462569](https://doi.org/10.1063/1.462569)). The segmented def2 sets (Weigend, Florian and Ahlrichs, Reinhart (2005). *Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy.* Physical Chemistry Chemical Physics, **7**(18), 3297–3305. doi:[10.1039/B508541A](https://doi.org/10.1039/B508541A), built on Schäfer, Ansgar, Horn, Hans, and Ahlrichs, Reinhart (1992). *Fully optimized contracted Gaussian basis sets for atoms Li to Kr.* Journal of Chemical Physics, **97**(4), 2571–2577. doi:[10.1063/1.463096](https://doi.org/10.1063/1.463096)) target Hartree-Fock and DFT with balanced errors from H to Rn, with Stuttgart-Cologne core potentials beyond Kr.

Auxiliary sets. Density fitting (density fitting) expands orbital products in a second basis $\{P\}$ with Coulomb metric $J_{PQ} = (P|Q)$, $(\mu\nu|\lambda\sigma) \approx \sum_{PQ} (\mu\nu|P)\,[\mathbf J^{-1}]_{PQ}\,(Q|\lambda\sigma)$. Each fitting set matches an orbital family and a task: def2/J for Coulomb (Weigend, Florian (2006). *Accurate Coulomb-fitting basis sets for H to Rn.* Physical Chemistry Chemical Physics, **8**(9), 1057–1065. doi:[10.1039/B515623H](https://doi.org/10.1039/B515623H)), def2 JK sets for exchange (Weigend, Florian (2008). *Hartree-Fock exchange fitting basis sets for H to Rn.* Journal of Computational Chemistry, **29**(2), 167–175. doi:[10.1002/jcc.20702](https://doi.org/10.1002/jcc.20702)), cc-pVnZ-JKFIT (Weigend, Florian (2002). *A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency.* Physical Chemistry Chemical Physics, **4**(18), 4285–4291. doi:[10.1039/B204199P](https://doi.org/10.1039/B204199P)) and cc-pVnZ-RIFIT for RI-MP2 (Weigend, Florian, Köhn, Andreas, and Hättig, Christof (2002). *Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations.* Journal of Chemical Physics, **116**(8), 3175–3183. doi:[10.1063/1.1445115](https://doi.org/10.1063/1.1445115)).

BSSE and counterpoise. In a finite basis each fragment of a complex borrows its partner’s functions, so interaction energies come out too negative. The Boys-Bernardi counterpoise correction (Boys, S. F. and Bernardi, F. (1970). *The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors.* Molecular Physics, **19**(4), 553–566. doi:[10.1080/00268977000101561](https://doi.org/10.1080/00268977000101561)) evaluates every term in the full dimer basis (superscript) at the dimer geometry, $\Delta E^{\rm CP} = E_{AB}^{AB} - E_{A}^{AB} - E_{B}^{AB}$. The geometrical counterpoise gCP (Kruse, Holger and Grimme, Stefan (2012). *A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations.* Journal of Chemical Physics, **136**(15), 154101. doi:[10.1063/1.3700154](https://doi.org/10.1063/1.3700154)) replaces the ghost-atom calculations by an atom-pairwise function of the geometry, and the pob-rev2 sets for solids were reoptimised with a BSSE-correction scheme (Vilela Oliveira, Daniel, Laun, Joachim, et al. (2019). *BSSE-correction scheme for consistent Gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations.* Journal of Computational Chemistry, **40**(27), 2364–2376. doi:[10.1002/jcc.26013](https://doi.org/10.1002/jcc.26013)).

How the bundled library is stored¶

Every bundled basis set is one QVF-Basis record, python/vibeqc/basis_library/qvf/<name>.qvf.json: shells, effective core potentials, originating publications and provenance in one schema-validated JSON file. The .g94 and .ecp text files libint and libecpint read are renderings of the records, written at full precision by vibeqc.basis_toolkit.library and pinned byte for byte to the records by the test suite; nothing edits them by hand. A record’s provenance says what it is (kind: vendor, bse, hand-written or vibe-basis), where it came from (upstream, retrieval_date), its content identity (content_sha256 of the numbers alone) and which publication covers which elements (citations). vibe-qc-basis inspect python/vibeqc/basis_library/qvf/pob-tzvp-rev2.qvf.json prints all of it.

The runtime overlay under build/basis_library/ that scripts/setup_basis_library.sh writes is rendered from the same records and carries a content receipt; an overlay whose bytes disagree with the committed rendering refuses to load before any integral is computed.

Where a basis name resolves¶

A basis name is looked up in five layers, in this order. The first layer that answers wins, and nothing below it is consulted.

A LIBINT_DATA_PATH you set yourself, when it holds a complete library (the def2-svp, 6-311+g3df2p and pob-tzvp-rev2 files are the canaries). vibe-qc never changes it, verifies nothing in it, and consults no other layer.
The bundled library: the verified build/basis_library/ overlay when scripts/setup_basis_library.sh made one, else the copy inside the package. Both are renderings of the bundled records.
Your store ($VIBEQC_BASIS_STORE, else $XDG_DATA_HOME/vibeqc/basis, else ~/.local/share/vibeqc/basis): records you imported with vibe-qc-basis import, hand-written or produced by vibe-basis. A store record never shadows a bundled name unless you imported it with --replace-bundled; that choice is recorded in the store index and makes your record win for that one name.
The fetch cache ($VIBEQC_BSE_CACHE, else $XDG_CACHE_HOME/vibeqc/basis, else ~/.cache/vibeqc/basis): records rendered from the Basis Set Exchange on an earlier run. Each is stored once under the SHA-256 of its numerical content; the name index points at it.
Fetching from the catalogue, only when you opt in with run_job(fetch_from_bse=True) or VIBEQC_FETCH_BSE=1. The result lands in layer 4.

Layers 3 to 5 reach libint through a directory of symlinks composed over the bundled library, so a composed root is always a superset of the bundle: a fetched orbital basis with a bundled auxiliary keeps working. Before a store or cache record is used, its file is re-hashed against its recorded identity and its rendering is compared byte for byte with what the record renders to; a mismatch stops the run, naming the file, and nothing is substituted silently.

Every run records which layer answered. The .system manifest names the root libint read (resolved_root), one [[basis_library.fetched]] row per set rendered from the catalogue, and one [[basis_library.records]] row (name, kind, layer, content hash) per store or cache record the resolution added. To pin a result to a particular record, keep the record file the row points at, or import it under a distinct name; basis="name" always means the record the layers currently hold under that name. vibe-qc-basis resolve <name> ... prints which layer answers a name.

Your own basis sets¶

A hand-written set and a vibe-basis product enter through the same door as a bundled one and resolve by name with no other change (#410). Put the shells in a Gaussian94 file (an .ecp of the same stem beside it carries the potentials), a BSE JSON file, a CRYSTAL per-element file or directory, or a QVF-Basis record, and import it:

vibe-qc-basis import my-basis.g94 --kind hand-written --cite some_database_key
vibe-qc-basis import run-42/mgo-opt.g94      # a vibe-basis export: the sidecar names kind and run
vibe-qc-basis list
vibe-qc-basis resolve my-basis

basis = vq.BasisSet(mol, "my-basis")               # resolves in every new process
result = vq.run_job(mol, basis="my-basis", method="rhf")

The import refuses a name a bundled set already uses unless you pass --replace-bundled, and a name already in your store unless you pass --replace. The record it writes carries provenance.kind (hand-written or vibe-basis), the upstream you name, the import date, the content hash and the citation keys you give with --cite; the .references output of a run cites those keys and says “user-supplied” where there is no publication. Nothing under python/vibeqc/basis_library/ is ever written by the import. vibe-qc-basis remove <name> takes a record out again.

vibe-basis writes its optimised basis with vibe_basis.io.export.write_basis_for_import, which produces the .g94 and a <name>.provenance.json sidecar naming the run; importing that file needs no flags.

Store records are activated when vibeqc is imported, so BasisSet finds them on both the molecular and the periodic route. Fetched records (layer 4) are consulted by run_job; a periodic job constructs its BasisSet before the runner sees the name, so make a fetched set visible first:

from vibeqc import basis_store
basis_store.resolve(["sadlej pvtz"], fetch=True)     # composes the root and points libint at it
basis = vq.BasisSet(cell.unit_cell_molecule(), "sadlej pvtz")

Filtered-basis cache and resolution¶

make_basis(..., exp_to_discard=...) preserves the active library before adding its derived basis. The cache store resolves through VIBEQC_FILTERED_BASIS_DIR, then $XDG_CACHE_HOME/vibeqc/basis_filter, then ~/.cache/vibeqc/basis_filter. Cache stores inside the installed package, repository or source library are refused, including symlinks resolving there. Caller-supplied store and source aliases resolve to their actual locations; links inside owned cache roots and their content are refused.

Each complete root contains byte copies of every active library file, including stock orbital bases, sidecars and earlier filtered bases, plus the new filtered file. Its identity includes every filename and content hash. Reusing a root checks its complete receipt and bytes; a changed, missing, extra or linked cache file is a hard error. Source file symlinks are read and copied, never written through. Case-fold name collisions and conflicting explicit filtered names are refused. A generated filtered name includes the emitted content hash.

Libint reads one root. The filter switches LIBINT_DATA_PATH only after the complete new root is published and validated. Unfiltered calls still find the same stock bytes, and named reloads find every earlier filtered basis. Normal filtering never deletes old roots. Internal filter writers are serialized; external changes to the process environment remain the caller’s responsibility. Changing LIBINT_DATA_PATH manually can hide previously selected names.

clear_filtered_basis_cache() is an explicit global purge, not an operation safe alongside live calculations. Stop all cache readers and writers, retire filtered BasisSets, and restore a stock LIBINT_DATA_PATH first. Cleanup refuses a selected root, unknown staging entries, invalid receipts or linked cache entries/content, and validates all owned roots before removing any. It cannot infer another process’s use of a root. Its return value counts removed _vibeqc_filtered_*.g94 files across those roots; custom-name files are retired with their roots but excluded from that prefix-based count.

Reaching a basis vibe-qc does not bundle¶

The bundled library carries 255 .g94 files. The Basis Set Exchange catalogues 776, so a set you want may simply not be here. vibeqc.basis_fetch renders one from BSE into a per-user cache, in the same .g94 (plus .ecp sidecar) layout libint and libecpint already read:

from vibeqc.basis_fetch import fetch_basis_from_bse

got = fetch_basis_from_bse("sadlej pvtz", elements=[1, 8])
print(got.g94_path, got.bse_version, got.elements)

It needs the optional extra, which is not installed by default:

pip install 'vibe-qc[bse]'

Three things worth knowing before you rely on it.

It does not touch the network. The basis-set-exchange distribution ships the whole catalogue as package data (~334 MB), so a lookup is a local read: it works on an air-gapped machine, and what you get is pinned by that package’s version, which is recorded in the provenance file written beside every rendered basis. That is also why it is an optional extra rather than a dependency.

A bundled basis that is merely short cannot be completed this way. Eight bundled sets carry fewer elements than the Basis Set Exchange publishes for the same name, mostly inherited from libint’s own distribution: 6-31g (stops at Zn; BSE has Ga-Kr), cc-pvqz (has Mg, not Ca), cc-pv6z (no Be), sto-3g (has I, not Xe), the two sap_*_large potentials (superheavy tails), and vibe-qc’s own pob-tzvp and pob-dzvp-rev2, which BSE carries in later or extended revisions. Asking for cc-pVQZ on calcium fails even with the [bse] extra installed, because the name already resolves and fetching only handles names that do not. Closing one of those gaps means bundling the blocks as a reviewed import, the way the def2 beyond-Kr merge did, not patching at run time. tests/test_basis_integrity.py pins the list so it cannot grow unnoticed.

It supplies whole sets, and refuses to patch one. Pass elements= and a record that does not cover all of them is refused, with nothing written to the cache. Filling a gap in a bundled basis by grafting BSE blocks for the missing elements would put two sources under one basis name with no reviewed provenance for the join, so it is not offered. If a bundled basis is missing an element you need, the coverage guard refuses the calculation, and that is the intended outcome.

Nothing resolves differently until you ask. run_job takes the flag, and only then:

vq.run_job(mol, basis="sadlej pvtz", method="rhf", fetch_from_bse=True)

VIBEQC_FETCH_BSE=1 does the same for a whole session. Without either, an unbundled name refuses exactly as it always has. A bundled name is a complete no-op even with the flag on: no lookup, no cache entry, and resolution untouched.

When a render does happen, the record is stored in the fetch cache under its content hash (layer 4 above), its .g94 and .ecp are rendered beside it, and vibe-qc composes a library root that carries the bundled one plus the rendering, then points libint at that (see “Where a basis name resolves”). Each render prints a warning naming the basis, the catalogue version and the file, because a non-bundled basis is something a reader of your results needs to know about.

Every rendered file carries a header saying it is not a bundled vibe-qc basis, the catalogue version it came from, and BSE’s own originating publications. Cite them as you would for a bundled set; see license § 3a for the terms, which are the same.

Every run records where its basis data came from. The .system manifest gains a [basis_library] section naming the library root libint actually read, plus one [[basis_library.fetched]] row per rendered set:

[basis_library]
resolved_root  = "/.../build/basis_library"
fetched_count  = 1

[[basis_library.fetched]]
name            = "sadlej pvtz"
bse_version     = "0.12"
element_count   = 25
provenance_path = "/.../cache/basis/sadlej pvtz.provenance.json"

resolved_root is written on every run, fetching or not. vibe-qc prefers a build overlay over the committed library, so a result produced against a stale overlay is otherwise indistinguishable from one produced against current data; now the manifest says which answered. A [[basis_library.records]] row names every store or cache record the resolution added (records_count counts them). Branch on fetched_count and records_count, not on the arrays: an empty array of tables is dropped from the file, so on an ordinary run the keys are absent rather than empty.

What vibe-qc ships today¶

Available now

90 standard molecular bases bundled with libint (Pople, Dunning, def2, Sapporo, ANO, core-valence). Use the standard names ("sto-3g", "6-31g*", "cc-pvdz", "def2-tzvp", …).
pob-TZVP, pob-TZVP-rev2, pob-DZVP-rev2 — the Peintinger-Vilela-Oliveira-Bredow family for periodic calculations on solids (project author’s design papers).
vq.make_basis(mol, name, exp_to_discard=...) — primitive filter that drops diffuse Gaussians below an exponent threshold. PySCF-style; useful for using molecular bases in tight ionic crystals. See user guide § linear dependence.

Basis-set library coverage today

Most of the families discussed below resolve to a real load on a clean install. The bundled python/vibeqc/basis_library/ ships 255 Gaussian .g94 basis files: 90 libint-inherited standard files plus 165 custom / BSE-derived overlay files, with matching QVF-Basis sidecars for every set. (A further 11 custom files carry the same names as libint’s own def2 records and replace them, which is how the def2 family reaches past Kr.) That includes pob-TZVP, pob-DZVP-rev2, pob-TZVP-rev2, the def2 series, the cc-pVxZ family and the Pople sets. Forty-four of them are valence-only somewhere and ship their ECP as a .ecp sidecar that the molecular SCF wrappers attach automatically, per element: the def2 family from Rb to Rn (the libint H-Kr files extended with the Basis Set Exchange blocks and the def2-ECP; plain, unpolarized def2-SV is the exception, see below), the LANL and dhf families, vDZP, the 3c bases def2-mSVP / def2-mTZVP / def2-mTZVPP, pob-TZVP-rev2, and the 16 Peterson/Figgen {,aug-}cc-p{V,wCV}{D,T,Q,5}Z-PP sets (Cu-Kr, Y-Xe, Hf-Rn). x2c-TZVPall is all-electron (it needs no ECP, and none is attached). See user guide § ECPs.

def2-SV stops at Ar. The unpolarized def2-sv covers H-Ar only (18 elements) and is all-electron over that range. This is a deliberate boundary, not a gap in the fetch: the Basis Set Exchange has no def2-SV record past argon, and its “Ahlrichs VDZ” (the 1992 SV) is a different set. A K-Rn atom in def2-sv is refused with an error that names the element (has no functions for Z=19). For those elements use def2-sv(p) or def2-svp, which reach Rn with the def2-ECP.

Using a basis set¶

from vibeqc import BasisSet
basis = BasisSet(mol, "pob-tzvp")
print(basis.nbasis)      # number of basis functions

Names are matched on their letters, digits and + only, ignoring case, spaces and other punctuation. 6-31G(d,p), 6-31G(d, p) and 631gdp all load 6-31g**; sto3g, STO_3G and Sto 3G all load sto-3g. The basis registry (vibeqc.basis_registry.lookup, which supplies the default auxiliary sets and the ECP rules) resolves a name with the same function, so every spelling gets the same metadata as the file it loads. An aug-cc-pV* name loads its own bundled file when one ships (the cc-pVnZ-PP, -RIFIT and (n+d) families). Otherwise it loads the parent set plus its augmentation- file.

For periodic systems with diffuse molecular bases, optionally filter the most-diffuse primitives:

import vibeqc as vq
basis = vq.make_basis(mol, "def2-tzvp", exp_to_discard=0.1)
# — drops every primitive with α < 0.1 and prints the drop log

Discarding primitives reduces, but does not remove, the lattice-sum requirement

A diffuse AO tail forces the real-space lattice sums (overlap, kinetic, nuclear attraction) to reach further before they converge. exp_to_discard shortens that tail, at the cost of changing the basis and therefore the answer, but it does not make the requirement go away. Measure it, don’t guess:

from vibeqc.lattice_screening import bloch_overlap_cutoff_bohr
print(bloch_overlap_cutoff_bohr(basis, system))   # bohr

On a rocksalt LiF primitive cell (a = 4.03 Å), measured:

basis	full	with `exp_to_discard=0.1`
STO-3G	37.1 bohr	25.7 bohr
def2-SVP	51.5 bohr	25.0 bohr (23 → 18 functions)
def2-TZVP	45.3 bohr	25.0 bohr (45 → 40 functions)

vibeqc.lattice_screening.bloch_overlap_cutoff_bohr() carries a 25 bohr floor, so no amount of primitive-discarding brings the requirement below that. Compact ionic cells, and cells containing light loosely bound atoms (Li especially), are the demanding cases; a cell like MgO/STO-3G is far less so.

Where the cutoff is settable, set it: run_periodic_job(..., bipole_cutoff_bohr=...) on the BIPOLE route. To check how truncated a given choice actually is, vibeqc.pbc_bipole_common.s_fold_truncation_drift compares the folded overlap against the same sum at 1.5× the cutoff, using one-electron integrals only. A drift below 1e-4 is converged; above 1e-2 the BIPOLE drivers refuse to start. Measured on LiF/STO-3G/Γ, the drift predicts the total-energy error to within about a factor of three across four decades, so a drift of 1e-3 implies roughly 3 mHa.

Background and terminology¶

A basis set is the finite set of analytic functions used to expand the molecular orbitals. Modern molecular codes use contracted Gaussian-type orbitals (cGTOs), with the primitive radial part $G_\alpha(r) = N e^{-\alpha r^2}$. Solids more often use plane waves $e^{i\mathbf{k}\cdot \mathbf{r}}$, numerical atom-centred orbitals, or augmented plane waves.

Key descriptors:

Zeta level (n-zeta), number of basis functions used to describe each valence orbital. STO-3G is single-zeta. 6-31G, def2-SVP, cc-pVDZ are double-zeta. def2-TZVP, cc-pVTZ, pcseg-2 are triple-zeta. cc-pVQZ, def2-QZVP are quadruple-zeta.
Polarisation functions, higher-angular-momentum functions (d on C, p on H, f on transition metals, etc.) that allow the electron density to deform on bond formation. Modern usage demands them: unpolarised basis sets like 6-31G or cc-pVDZ-without-d should never be used for production.
Diffuse functions, low-exponent functions needed for anions, weakly bound species, Rydberg states, and many response properties (polarisabilities, NMR shielding, TDDFT excitations). Indicated by +, ++, aug-, or ma- prefixes.
Contraction, segmented vs. general. Segmented (Pople, def2, pcseg) is faster in most integral codes. Generally contracted (cc, ANO) is more compact and accurate per primitive but needs a code that exploits it (Jensen, Frank (2014). *Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent Basis Sets.* Journal of Chemical Theory and Computation, **10**(3), 1074–1085. doi:[10.1021/ct401026a](https://doi.org/10.1021/ct401026a) converts one form into the other).
Effective core potential (ECP), replaces inner-shell electrons with a parameterised potential. Reduces cost, builds in scalar relativistic effects. The Stuttgart/Cologne ECPs (Andrae, D., Häußermann, U., et al. (1990). *Energy-adjusted ab initio pseudopotentials for the second and third row transition elements.* Theoretica Chimica Acta, **77**(2), 123–141. doi:[10.1007/BF01114537](https://doi.org/10.1007/BF01114537) for the 4d and 5d transition metals) paired with def2 valence sets are the de facto standard above Kr.
Polarisation-consistent vs. correlation-consistent, cc-pVnZ was optimised to recover correlation energy in CCSD/CCSD(T) (Dunning, Thom H. (1989). *Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen.* Journal of Chemical Physics, **90**(2), 1007–1023. doi:[10.1063/1.456153](https://doi.org/10.1063/1.456153)). pc-n / pcseg-n was optimised to converge HF and DFT energies (Jensen, Frank (2001). *Polarization consistent basis sets: Principles.* Journal of Chemical Physics, **115**(20), 9113–9125. doi:[10.1063/1.1413524](https://doi.org/10.1063/1.1413524), Jensen, Frank (2014). *Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent Basis Sets.* Journal of Chemical Theory and Computation, **10**(3), 1074–1085. doi:[10.1021/ct401026a](https://doi.org/10.1021/ct401026a)). For DFT, pcseg-n is technically the better-targeted choice, but def2-TZVP achieves nearly the same accuracy at lower cost in practice.

A note on basis set superposition error (BSSE) and basis set incompleteness error (BSIE): these are large at the double-zeta level (several kcal/mol on noncovalent interactions) and are the reason a triple-zeta basis is now the recommended floor for any quantitative molecular work. The Boys-Bernardi counterpoise correction (Boys, S. F. and Bernardi, F. (1970). *The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors.* Molecular Physics, **19**(4), 553–566. doi:[10.1080/00268977000101561](https://doi.org/10.1080/00268977000101561)) corrects for BSSE with ghost-basis calculations. The geometrical counterpoise correction (gCP) of Kruse and Grimme (Kruse, Holger and Grimme, Stefan (2012). *A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations.* Journal of Chemical Physics, **136**(15), 154101. doi:[10.1063/1.3700154](https://doi.org/10.1063/1.3700154)) is the cheapest practical fix and is built into the 3c composite methods below.

Choosing a molecular basis set¶

Small, fast-screening / pedagogical tier¶

Basis	Zeta	Notes
STO-3G	SZ	Single-zeta minimal, no polarisation. Useful only for initial guesses, very large systems where qualitative geometries suffice, or pedagogy.
MINI / MINIs (Huzinaga)	SZ	Slightly better than STO-3G atomic energies. Niche use.
3-21G	DZ (unpol)	Old Pople split-valence. Faster than 6-31G but unpolarised. Avoid for production.
pcseg-0 / pc-0	DZ (unpol)	Jensen DZ without polarisation. Better-balanced than 3-21G.
6-31G	DZ (unpol)	Historical workhorse without polarisation. Pitman et al. (2023) showed unpolarised DZ basis sets perform poorly and should not be used.

Bottom line. Support STO-3G (legacy + pedagogical) and 3-21G (rare speed-dominated contexts). All other small basis sets should carry a “not for production” warning.

Medium, polarised double-zeta, the everyday tier¶

Basis	Notes
def2-SVP	Karlsruhe segmented DZ with polarisation on heavy atoms. The most widely used DZ basis in modern DFT codes. Best speed/accuracy balance for routine geometry optimisation.
vDZP (Grimme 2023)	Custom polarised DZ used inside ωB97X-3c. Large-core ECPs and deep contraction. On TorsionNet206 drug-like benchmark, vDZP-based methods give MAEs of 0.4-0.5 kcal/mol, comparable to triple-zeta hybrid methods.
6-31++G(d,p)	Pitman et al. (2023) found this the best-performing DZ basis on diet-GMTKN55. Diffuse functions matter.
6-31G(d,p) / 6-31G**	Classic Pople workhorse. Acceptable for organic structures, inferior to def2-SVP at similar cost.
pcseg-1	Jensen segmented DZ-polarised. Slightly better than def2-SVP for HF/DFT energies, less widely supported.
cc-pVDZ	Dunning DZ. Designed for correlation; for pure DFT less efficient than pcseg-1 or def2-SVP. Useful as a stepping stone in cc-pVnZ extrapolations.
def2-mSVP	Modified def2-SVP used inside PBEh-3c and B3LYP-3c. Not for standalone use.
LANL2DZ	Hay-Wadt ECP plus DZ valence. Historically common for transition metals but inferior to def2-SVP/TZVP plus def2-ECP. Should be deprecated.

Bottom line. def2-SVP is the default. vDZP is a strong contender for any system with heavy atoms.

Large, triple-zeta and above, production accuracy¶

Basis	Notes
def2-TZVP	The de facto reference for hybrid-DFT calculations on molecules of any size where it is affordable. Within 0.5 kcal/mol of def2-QZVPD for main-group thermochemistry.
def2-TZVPP	Extra polarisation on hydrogen. Recommended for transition metals, weak interactions, properties beyond geometries.
pcseg-2	Best-performing TZ basis for DFT thermochemistry on diet-GMTKN55. Slightly better than def2-TZVP, less widely available.
cc-pVTZ / aug-cc-pVTZ	Dunning TZ, the reference for post-HF (MP2, CCSD(T)). Use aug- variant for anions, noncovalent, response.
def2-QZVP / def2-QZVPP	Quadruple-zeta. For benchmarking small molecules, basis-set-limit reference, double-hybrid functionals.
cc-pVQZ / aug-cc-pVQZ	Quadruple-zeta correlation-consistent. Standard for CCSD(T)/CBS extrapolation in `(T,Q)` or `(Q,5)` schemes.
pcseg-3 / pcseg-4	Larger pc-n family members. Excellent DFT convergence but rarely needed in practice.
def2-TZVPD / ma-def2-TZVP	TZ with diffuse functions. Use for anions, TDDFT, polarisabilities. The “ma-” (minimally augmented) Truhlar-Zheng variants are a cheaper alternative to full aug-.
cc-pV5Z, cc-pV6Z, aug-cc-pV5Z	For very small systems and CBS extrapolation only.
ANO-RCC-VTZP, ANO-RCC-VQZP	Generally contracted relativistic ANOs. Standard for CASPT2/NEVPT2/MS-CASPT2. Compact per primitive, ideal for multireference.

Bottom line. def2-TZVP is the production-quality default. cc-pVTZ family is the reference for post-HF. ANO-RCC is mandatory for multireference.

By chemical category¶

Organic molecules (C, H, N, O, S, halogens, P)¶

Tier	Recommendation
Small (geometry, screening)	def2-SVP or B97-3c (def2-mTZVP + D3 + gCP)
Medium (production)	def2-TZVP with a hybrid functional (ωB97X-D, ωB97M-V, M06-2X, B3LYP-D3)
Large (benchmark)	aug-cc-pVTZ → aug-cc-pVQZ extrapolation, or ωB97M-V/def2-QZVPP
Anions, Rydberg, response	aug- variants required (aug-cc-pVTZ, ma-def2-TZVP, aug-pcseg-2)

Pople basis sets (6-31G(d), 6-311G(2df,p)) remain in widespread use due to inertia. The polarised 6-311G family is poorly parameterised (Pitman et al. 2023 explicitly recommends avoiding it). For new work, support 6-31G(d) and 6-31++G(d,p) for compatibility but encourage def2.

Metal-organic / organometallics (TM complexes, MOFs)¶

Tier	Recommendation
Small (screening)	def2-SVP (with def2-ECP for 4d/5d) plus dispersion correction
Medium (production)	def2-TZVP / def2-TZVPP on the metal, def2-TZVP on ligands. Use a TM-tested functional: TPSSh, B3LYP*-D3(BJ), or PWPB95-D3(BJ) for benchmarking.
Large (benchmark)	def2-QZVPP, x2c-TZVPPall for explicit relativity
Multireference	ANO-RCC-VTZP / VQZP with CASPT2, NEVPT2, or DMRG-CASPT2
Spin states	Truhlar’s group recommends def2-TZVP for spin-splitting energies; extra polarisation does not help

Avoid LANL2DZ for new work, Stuttgart/Cologne ECPs (built into def2) are more accurate.

For 4d / 5d transition metals, scalar relativistic effects matter. Either use def2-ECP, or for explicit treatment use dhf-TZVP / x2c-TZVPall (Pollak-Weigend 2017, Pollak, Patrik and Weigend, Florian (2017). *Segmented Contracted Error-Consistent Basis Sets of Double- and Triple-ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations.* Journal of Chemical Theory and Computation, **13**(8), 3696–3705. doi:[10.1021/acs.jctc.7b00593](https://doi.org/10.1021/acs.jctc.7b00593)) or DKH-recontracted def2 (def2-TZVP-DKH).

Inorganic main-group (clusters, oxides, halides, hypervalent)¶

Tier	Recommendation
Small	def2-SVP (with care for hypervalent S, P needing extra d)
Medium	def2-TZVPPD (the extra d and diffuse matter) or aug-cc-pV(T+d)Z for second-row hypervalent
Large	def2-QZVP, aug-cc-pwCVTZ-DK for explicit core-valence
Anions, halide complexes	aug- variants required
Heavy main group (Sn, Pb, Bi)	def2-TZVP plus ECP, or all-electron x2c-TZVPall

For second-row hypervalent (SO₃²⁻, SF₆, PF₅, ClO₄⁻), the “tight d” variants (e.g. aug-cc-pV(T+d)Z, Dunning et al. 2001, Dunning, Thom H., Peterson, Kirk A., and Wilson, Angela K. (2001). *Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited.* Journal of Chemical Physics, **114**(21), 9244–9253. doi:[10.1063/1.1367373](https://doi.org/10.1063/1.1367373)) are essential. The def2 family already includes appropriate d-functions for these atoms.

Biomolecules (peptides, nucleic acids, lipids, sugars)¶

Tier	Recommendation
Screening (large fragments)	r2SCAN-3c (def2-mTZVPP + D4 + gCP) or B97-3c
Production (single-point on optimised fragments)	def2-TZVP with ωB97X-D or B3LYP-D3(BJ)
Noncovalent / hydrogen bonding	def2-TZVPPD or ma-def2-TZVP, with explicit dispersion (D4 preferred)
Vibrational, NMR	property-specific basis sets (pcS-n for shielding, pcJ-n for J couplings)

The 3c composite methods are particularly well-suited here because gCP corrects for the BSSE that dominates large-biomolecule binding-energy errors. Recent benchmarks (Behara et al. 2024, TorsionNet206) showed B3LYP-D3BJ/6-31G(d) is now clearly inferior to vDZP-based or 3c methods at comparable cost.

Pharma / drug-like molecules¶

Tier	Recommendation
High-throughput conformer / torsion scans	ωB97X-3c (vDZP) or r2SCAN-3c
Reference single-points for force-field parametrisation	ωB97M-V/def2-TZVPPD or DLPNO-CCSD(T)/def2-TZVPP
QM/MM cores	def2-SVP (QM region), with def2-TZVP single-point refinement

vDZP deserves particular attention here. The Rowan/Wagen TorsionNet206 study showed vDZP-based methods give 0.4-0.5 kcal/mol MAE on torsion energies (versus CCSD(T)/def2-TZVP), comparable to standard hybrid functionals with triple-zeta basis sets. The use of ECPs makes it especially efficient for halogenated and metal-containing drug candidates.

Choosing a basis set for solids¶

Periodic codes split into three philosophical camps:

Plane waves + pseudopotentials. VASP, Quantum ESPRESSO, ABINIT, CASTEP, GPAW. A single cutoff energy parameter controls the basis. No BSSE. Smooth convergence. Heavy reliance on the quality of the pseudopotential or PAW dataset.
Gaussian basis sets. CRYSTAL, CP2K (mixed Gaussian-plane wave), Turbomole-Riper, FHI-aims (in some modes). Inherits molecular-style basis sets, but they need re-optimisation for solids, diffuse functions in molecular bases lead to linear dependencies in periodic systems.
Numerical atomic orbitals or augmented plane waves. FHI-aims, SIESTA, OpenMX (NAO); WIEN2k, exciting, ELK (LAPW+lo). Highly accurate, smaller basis sizes but slower per evaluation.

vibe-qc is family 2 (Gaussian basis, with periodic-image folding for solid-state). For users moving back and forth between codes, the surveys below cover all three.

Plane-wave pseudopotential libraries¶

The pseudopotential is the basis-set-equivalent choice for plane-wave codes. The cutoff is the convergence parameter.

Library	Code	Type	Characteristics
VASP PAW (PBE / PBE.54 / PBE.64)	VASP	PAW	The de facto industry standard for materials science. `_GW`, `_sv` / `_pv` variants for semicore. Closed source. Cutoffs 250-600 eV by element.
SSSP precision (1.3.0)	Quantum ESPRESSO	mixed PAW + USPP + ONCV	EPFL/Marzari curated. Most accurate open-source PSP library: avg Δ-factor below 0.4 meV/atom against all-electron references (Prandini et al. 2018).
SSSP efficiency (1.3.0)	QE	mixed	Same protocol with lower cutoffs, faster, slightly less accurate. Standard for high-throughput.
PseudoDojo (ONCV, NC SR/FR)	abinit, QE, others	norm-conserving (ONCV)	Hamann-Schlüter-Chiang; scalar and fully-relativistic versions. State of the art for systematic, hybrid-functional, and GW calculations.
SG15	many	ONCV	Schlipf-Gygi 2015. Solid alternative to PseudoDojo, well-tested.
GBRV	QE, ABINIT	USPP, PAW	Garrity-Bennett-Rabe-Vanderbilt high-throughput library.
JTH PAW	ABINIT	PAW	Jollet-Torrent-Holzwarth. ABINIT-native PAW.

The 2016 multi-code Δ-factor study (Lejaeghere et al., Science) showed that all of these libraries now agree with all-electron LAPW codes (WIEN2k, exciting) to within roughly 1 meV/atom on equation-of-state data, the practical floor for DFT precision.

Gaussian basis sets for periodic systems¶

Basis	Code	Notes
pob-TZVP	CRYSTAL, vibe-qc	Peintinger-Vilela Oliveira-Bredow 2013 (project author). TZ polarised for solids, derived from def2-TZVP by re-optimisation to remove diffuse linear dependencies. CRYSTAL community standard.
pob-TZVP-rev2	CRYSTAL, vibe-qc	Vilela Oliveira et al. 2019. Improved performance for transition metals. Use this over the original pob-TZVP for any new work.
pob-DZVP-rev2	CRYSTAL, vibe-qc	DZ companion to pob-TZVP-rev2.
MOLOPT (SZV/DZVP/TZVP/TZV2P)	CP2K	Optimised by VandeVondele-Hutter for numerical stability in periodic systems with the GPW approach. CP2K standard.
dcm-TZVP	CRYSTAL	Daga-Civalleri-Maschio 2020. System-specific re-optimisations for diamond, graphene, carbyne. Illustrative of all-purpose-library limits.
MOLOPT-aug (aug-MOLOPT-ae)	CP2K	Augmented MOLOPT for excited states (TDDFT, BSE-GW). Recent.

vibe-qc users default to pob-TZVP-rev2 (Vilela Oliveira, Daniel, Laun, Joachim, et al. (2019). *BSSE-correction scheme for consistent Gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations.* Journal of Computational Chemistry, **40**(27), 2364–2376. doi:[10.1002/jcc.26013](https://doi.org/10.1002/jcc.26013)) for ionic crystals; see the pob basis sets in detail section further down this page and user guide § linear dependence for the design philosophy.

Numerical atomic orbitals + (L)APW+lo¶

Basis / tier	Code	Notes
FHI-aims tier 1	FHI-aims	“Light” species defaults. Polarised DZ-equivalent. Sub-meV precision for many energy differences.
FHI-aims tier 2	FHI-aims	“Tight” species defaults. Roughly QZVP-quality but smaller. FHI-aims production standard.
FHI-aims tier 3 / 4	FHI-aims	Reference quality. For benchmarking only.
tier2_aug2	FHI-aims	tier 2 plus two lowest-l aug-cc functions. Required for excited-state and weakly-bound-anion calculations.
SIESTA SZ / DZ / DZP / TZP	SIESTA	Numerical pseudo-atomic orbitals with confinement. DZP is the standard SIESTA production basis.
(L)APW+lo	WIEN2k, exciting	Augmented plane waves. The all-electron gold standard for periodic DFT. Slower than PAW but no pseudopotential approximation.

By solid type¶

Metals (elemental, alloys, intermetallics)¶

Tier	Recommendation
Small (screening)	PAW with default cutoff (e.g. VASP `ENCUT` from POTCAR), dense k-mesh (Methfessel-Paxton smearing)
Medium (production)	PseudoDojo standard ONCV or VASP PAW with semicore states (`_sv`, `_pv`) for early TMs, cutoff 400-500 eV
Large (benchmark)	LAPW+lo (WIEN2k, exciting) with all-electron references
Magnetic systems	Always include semicore states. For 3d magnetism use `_pv` or `_sv` variants. For spin-orbit use fully-relativistic ONCV.

Common pitfalls: forgetting semicore p-states in early transition metals (Sc-Cr), too-low cutoff for d-block elements, underconverged k-meshes. Choudhary-Tavazza 2019 NIST study on 30,000+ materials provides good convergence heuristics by element.

Oxides (binary oxides, perovskites, TM oxides)¶

Tier	Recommendation
Small	PAW with O standard, screening-functional (PBEsol or SCAN)
Medium	VASP PAW with O_h or O_s + high cutoff (520 eV minimum, often 600-700 eV). Materials Project standard is 520 eV with O standard. SSSP precision in QE.
Large	PAW + DFT+U (Dudarev) or hybrid (HSE06) for correlated TM oxides. For benchmarking, all-electron LAPW.
Strongly correlated	DFT+U with carefully chosen U (e.g. Materials Project tabulated values), or hybrid (HSE06, PBE0).
Defects, polarons	Hybrid (HSE06) and large supercell.

Oxygen p-states are deep and the O 2s semicore needs a cutoff substantially above what alkali-halide systems require. The 520 eV Materials Project default is widely accepted.

Semiconductors (Si, Ge, III-V, II-VI, halide perovskites)¶

Tier	Recommendation
Small	PAW with PBE, modest cutoff (300-400 eV)
Medium	PAW or ONCV (PseudoDojo) with PBE for structure, hybrid (HSE06) or G₀W₀ for band gaps. Include spin-orbit for heavy elements (GaAs, halide perovskites).
Large (band-gap accuracy)	G₀W₀ on top of HSE06 or PBE, with NAO tier 2 + aug2 (FHI-aims) or LAPW + high-energy local orbitals (HLO).
Excitonic absorption	BSE-GW with appropriate basis (aug-MOLOPT-ae in CP2K, tier2+aug2 in FHI-aims, LAPW+HLO+lo in exciting).

For halide perovskites and other heavy-element semiconductors, scalar + spin-orbit relativity is essential. Use fully-relativistic PseudoDojo or VASP PAW with LSORBIT = .TRUE..

Composite “3c” methods¶

These bundle a tailored basis with corrections (geometric counterpoise gCP, Kruse, Holger and Grimme, Stefan (2012). *A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations.* Journal of Chemical Physics, **136**(15), 154101. doi:[10.1063/1.3700154](https://doi.org/10.1063/1.3700154); dispersion D3/D4, Grimme, Stefan, Antony, Jens, et al. (2010). *A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.* Journal of Chemical Physics, **132**(15), 154104. doi:[10.1063/1.3382344](https://doi.org/10.1063/1.3382344) and Caldeweyher, Eike, Ehlert, Sebastian, et al. (2019). *A generally applicable atomic-charge dependent London dispersion correction.* Journal of Chemical Physics, **150**(15), 154122. doi:[10.1063/1.5090222](https://doi.org/10.1063/1.5090222); sometimes a modified short-range correction).

Method	Functional	Basis	Year	Notes
HF-3c	Hartree-Fock	MINIX	2013	Cheapest. Useful for very large systems where mean-field qualitative behaviour suffices.
PBEh-3c	PBE0 (42% HF)	def2-mSVP	2015	Hybrid. Strong for noncovalent geometries.
HSE-3c	HSE	def2-mSVP	2016	Screened-exchange variant of PBEh-3c. Same basis and short-range potential, but its own D3(BJ) damping.
B97-3c	B97 GGA	def2-mTZVP	2018	Workhorse GGA. Especially recommended for transition-metal systems.
r2SCAN-3c	r²SCAN meta-GGA	def2-mTZVPP	2021	Current “Swiss army knife” recommendation. Excellent default for routine work, geometries, thermochemistry, noncovalent.
B3LYP-3c	B3LYP	def2-mSVP	2022	Tailored for IR spectra (B3LYP frequencies are particularly accurate).
ωB97X-3c	ωB97X-V	vDZP	2023	Range-separated hybrid plus vDZP. Often the best 3c for thermochemistry and barrier heights.

The published 3c benchmark MAEs on GMTKN55 are competitive with much more expensive calculations. First-class support for the modified bases (def2-mSVP, def2-mTZVP, def2-mTZVPP, vDZP) plus gCP and D4 corrections is the path to making these turnkey, roadmap item.

Property-specific basis sets¶

Critical to know about, but not “general-purpose” so they don’t appear in the main rankings:

Property	Basis family	Reference
NMR shielding	pcS-n (Jensen)	Jensen 2008, J. Chem. Theory Comput. 4, 719
NMR J-coupling	pcJ-n (Jensen)	Jensen 2006, J. Chem. Theory Comput. 2, 1360
NMR (relativistic)	x2c-TZVPall-s (Franzke-Weigend)	Franzke et al. 2019, Phys. Chem. Chem. Phys. 21, 16658
EPR (g-tensor, hyperfine)	EPR-II, EPR-III, x2c-TZVPall-s	Barone 1996; Franzke et al.
Core-level X-ray (XPS, NEXAFS)	cc-pCVnZ, aug-cc-pCVnZ, ccX-DK	Peterson et al.; Hanson-Heine et al.
Polarisability, hyperpolarisability	Sadlej, aug-cc-pVnZ, LPolX	Sadlej 1988; Bauernschmitt-Ahlrichs 1996
Excited states (TDDFT)	aug-cc-pVTZ, ma-def2-TZVPP, aug-pcseg-2	Many

Master recommendation table¶

Compact view of the recommended sets at each tier and category. Everything listed is freely available from the Basis Set Exchange or built into common open-source codes.

Domain	Small (fast)	Medium (production)	Large (benchmark)
Organic molecules	def2-SVP, B97-3c	def2-TZVP	def2-QZVPP, aug-cc-pVQZ
Metal-organic	def2-SVP + def2-ECP	def2-TZVPP + def2-ECP	def2-QZVPP, ANO-RCC-VTZP (multiref)
Inorganic main-group	def2-SVP	def2-TZVPPD	aug-cc-pV(Q+d)Z, def2-QZVPPD
Biomolecules	r2SCAN-3c, B97-3c	def2-TZVP + D4	DLPNO-CCSD(T)/def2-TZVPP
Pharma / drug-like	ωB97X-3c (vDZP)	def2-TZVPPD	ωB97M-V/def2-QZVPP
Excited states	def2-SVPD	ma-def2-TZVPP, aug-pcseg-2	aug-cc-pVQZ, tier2+aug2
Multireference	ANO-RCC-VDZP	ANO-RCC-VTZP	ANO-RCC-VQZP
Heavy elements (relativistic)	x2c-SVPall, dhf-SVP	x2c-TZVPall, dhf-TZVPP	x2c-QZVPPall
Solids: metals (PW)	PseudoDojo standard	PseudoDojo stringent / SSSP precision	LAPW+lo (WIEN2k)
Solids: oxides (PW)	VASP PAW (520 eV)	VASP PAW + HSE06, SSSP precision	LAPW+lo, all-electron
Solids: semiconductors (PW)	PAW + PBE	PAW + G₀W₀ on HSE06	LAPW+HLO, BSE-GW
Solids: Gaussian periodic	pob-DZVP	pob-TZVP-rev2, MOLOPT TZVP	dcm-TZVP (system-specific)
Solids: NAO all-electron	FHI-aims tier 1 (light)	FHI-aims tier 2 (tight)	FHI-aims tier 3, LAPW+lo

Bold entries are the “if you support exactly one thing in this category, support this” recommendations.

pob-* basis sets in detail¶

The pob-* sets were designed by the project author and collaborators around the CRYSTAL code’s requirements for solid-state calculations. Standard molecular TZVP bases contain very diffuse functions that, when periodic images overlap across unit cells, produce near-linear-dependent basis sets, SCF convergence suffers or fails outright. The pob family tightens those functions to make them usable in solids (Peintinger, Michael F., Vilela Oliveira, Daniel, and Bredow, Thomas (2013). *Consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations.* Journal of Computational Chemistry, **34**(6), 451–459. doi:[10.1002/jcc.23153](https://doi.org/10.1002/jcc.23153)).

Coverage¶

Name	Elements	Reference
pob-TZVP	H-Br, Rb-I (48)	Peintinger, Vilela Oliveira, Bredow, J. Comput. Chem. 34, 451 (2013); Rb-I: Laun, Vilela Oliveira, Bredow, J. Comput. Chem. 39, 1285 (2018)
pob-TZVP-rev2	H-Br, Rb-Po, La-Lu (78)	H-Br: Vilela Oliveira, Laun, Peintinger, Bredow, J. Comput. Chem. 40, 2364 (2019); Rb-Po and La-Lu: the three later papers named below the table
pob-DZVP-rev2	H-Br, Rb-I (48)	(same as above); Rb-I: Laun, Vilela Oliveira, Bredow, J. Comput. Chem. 39, 1285 (2018)

The pob-TZVP-rev2 records beyond Br come from three later papers: Rb-I (Laun, Joachim and Bredow, Thomas (2022). *BSSE-corrected consistent Gaussian basis sets of triple-zeta valence with polarization quality of the fifth period for solid-state calculations.* Journal of Computational Chemistry, **43**(12), 839–846. doi:[10.1002/jcc.26839](https://doi.org/10.1002/jcc.26839)), Cs-Ba and Hf-Po (Laun, Joachim and Bredow, Thomas (2021). *BSSE-corrected consistent Gaussian basis sets of triple-zeta valence with polarization quality of the sixth period for solid-state calculations.* Journal of Computational Chemistry, **42**(15), 1064–1072. doi:[10.1002/jcc.26521](https://doi.org/10.1002/jcc.26521)), and La-Lu (Seidler, Leopold Maximilian, Laun, Joachim, and Bredow, Thomas (2023). *BSSE-corrected consistent Gaussian basis sets of triple-zeta valence quality of the lanthanides La-Lu for solid-state calculations.* Journal of Computational Chemistry, **44**(15), 1418–1425. doi:[10.1002/jcc.27097](https://doi.org/10.1002/jcc.27097)).

Heavy elements¶

The pob-TZVP and pob-DZVP-rev2 records for Rb-I and the pob-TZVP-rev2 records for Rb-Po and La-Lu are valence-only: each carries a Stuttgart-Cologne effective core potential in CRYSTAL’s Z+200 format (the same potentials block for block across the three sets). vibe-qc bundles those records and ships the potentials as pob-tzvp.ecp, pob-dzvp-rev2.ecp and pob-tzvp-rev2.ecp sidecars, which are applied automatically on the molecular route and on the periodic k-point GDF route. No network access is needed.

Method scope¶

The pob-* basis sets are optimised for DFT and hybrid-DFT work on solids, that’s the regime the parameter re-optimisations in Peintinger 2013 / Vilela Oliveira 2019 (Peintinger, Michael F., Vilela Oliveira, Daniel, and Bredow, Thomas (2013). *Consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations.* Journal of Computational Chemistry, **34**(6), 451–459. doi:[10.1002/jcc.23153](https://doi.org/10.1002/jcc.23153), Vilela Oliveira, Daniel, Laun, Joachim, et al. (2019). *BSSE-correction scheme for consistent Gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations.* Journal of Computational Chemistry, **40**(27), 2364–2376. doi:[10.1002/jcc.26013](https://doi.org/10.1002/jcc.26013)) targeted, and the regime where the bundled .g94 files have been validated. For pure Hartree-Fock or correlated methods (MP2, CCSD, …) on periodic systems, pob-* is not the right basis choice: SCF convergence under defaults is unreliable (e.g. MgO RHF/pob-TZVP requires aggressive LEVSHIFT and 200+ cycles even in CRYSTAL14 itself), and the basis was never recommended for correlated treatment.

For periodic RHF / RKS-without-hybrid-mixing parity work, prefer either STO-3G (for cheap, robust baselines) or a hardened def2-family basis with diffuse primitives discarded (exp_to_discard=0.1). The bundled baseline_sto3g/ reference inputs follow this principle.

Re-fetching the pob-* library¶

The pob records ship in the repository (basis_library/qvf/pob-*.qvf.json, derived from the per-element CRYSTAL sources under basis_library/sources/), so a fresh clone has them. To re-fetch from the Bredow group server (for a future revision), write the archive’s .g94 conversion somewhere outside the package and turn it into a record:

python -m vibeqc.basis_crystal fetch --dest /tmp/pob-refetch
vibe-qc-basis convert /tmp/pob-refetch/pob-tzvp-rev2.g94 --ecp /tmp/pob-refetch/pob-tzvp-rev2.ecp \
    -o python/vibeqc/basis_library/qvf/pob-tzvp-rev2.qvf.json --kind vendor \
    --upstream "Bredow group basis-set archive" --retrieval-date 2026-10-11
./scripts/setup_basis_library.sh --target-dir python/vibeqc/basis_library

The fetcher writes only where --dest (or dest_dir= in Python) says; it has no default output directory, so a call that only needs the parsed records (return_atoms=True) never writes into an installed tree. scripts/basisset_dev/pob_basis_verify.py compares the sources with the records and renderings, and can regenerate the records from the sources.

Parsing a CRYSTAL-format basis directly¶

from vibeqc.basis_crystal import parse_crystal_atom_basis_file, emit_g94

atom = parse_crystal_atom_basis_file("path/to/06_C")
print(atom.element_symbol, len(atom.shells))
with open("my-basis.g94", "w") as f:
    f.write(emit_g94([atom]))

To use the result by name, turn it into a record with vibe-qc-basis convert my-basis.g94 -o my-basis.qvf.json --kind hand-written and point LIBINT_DATA_PATH at a directory holding its rendering, or, for a bundled set, save the record under basis_library/qvf/ and re-render (see the library README).

CRYSTAL format in one page¶

The per-element files that Bredow, CRYSTAL’s library, and most other solid-state QC projects distribute use CRYSTAL’s native input format:

Z  NSHELL                           ← header: atomic number, shell count
ITYPE  LAT  NG  CHE  SCAL           ← shell 1 header
  exp₁  coef₁                       ← NG primitive lines
  exp₂  coef₂
  ...
ITYPE  LAT  NG  CHE  SCAL           ← shell 2 header
  ...

Each shell header has:

Token	Meaning
`ITYPE`	Format code; `0` = user-defined contracted Gaussians (what the Bredow files use).
`LAT`	Shell angular-momentum code: `0=S`, `1=SP`, `2=P`, `3=D`, `4=F`, `5=G`.
`NG`	Number of primitive Gaussians in the contraction.
`CHE`	Formal occupancy of the shell (electrons).
`SCAL`	Scale factor; primitive exponents are multiplied by $\text{SCAL}^2$.

For ECP-bearing atoms (heavy elements, Rb-I and beyond in the pob family), the first line uses 200+Z and an INPUT block follows the header describing the ECP.

vibeqc.basis_crystal.parse_crystal_atom_basis_file(path) returns a dataclass that mirrors this structure:

>>> atom = parse_crystal_atom_basis_file("pob-TZVP/06_C")
>>> atom.Z, atom.element_symbol
(6, 'C')
>>> atom.shells[0].shell_type, atom.shells[0].n_primitives
('S', 6)
>>> atom.shells[0].exponents[:2]
[13575.349682, 2035.2333680]

emit_g94(list_of_atom_basis) renders them to libint’s .g94 (NWChem-format) text.

Key references¶

Reviews and best-practice guides¶

Bursch, M., Mewes, J.-M., Hansen, A., Grimme, S. Best-Practice DFT Protocols for Basic Molecular Computational Chemistry. Angew. Chem. Int. Ed. 2022, 61, e202205735. doi:10.1002/anie.202205735
Karton, A. Good Practices in Database Generation for Benchmarking Density Functional Theory. WIREs Comput. Mol. Sci. 2025, 15, e1737. doi:10.1002/wcms.1737
Goerigk, L., Hansen, A., Bauer, C., Ehrlich, S., Najibi, A., Grimme, S. A look at the density functional theory zoo with the advanced GMTKN55 database. Phys. Chem. Chem. Phys. 2017, 19, 32184. doi:10.1039/C7CP04913G
Pitman, S. J., Evans, A. K., Ireland, R. T., Lempriere, F., McKemmish, L. K. Benchmarking Basis Sets for DFT Thermochemistry: Why Unpolarized Basis Sets and the Polarized 6-311G Family Should Be Avoided. J. Phys. Chem. A 2023, 127, 10295. doi:10.1021/acs.jpca.3c05573

Pople family¶

Hehre, W. J., Stewart, R. F., Pople, J. A. J. Chem. Phys. 1969, 51, 2657 (STO-nG).
Binkley, J. S., Pople, J. A., Hehre, W. J. J. Am. Chem. Soc. 1980, 102, 939 (3-21G).
Hariharan, P. C., Pople, J. A. Theor. Chim. Acta 1973, 28, 213 (6-31G(d,p)).
Krishnan, R., Binkley, J. S., Seeger, R., Pople, J. A. J. Chem. Phys. 1980, 72, 650 (6-311G).

Dunning correlation-consistent¶

Dunning, T. H. Jr. J. Chem. Phys. 1989, 90, 1007 (cc-pVnZ).
Kendall, R. A., Dunning, T. H. Jr., Harrison, R. J. J. Chem. Phys. 1992, 96, 6796 (aug-cc-pVnZ).
Dunning, T. H. Jr., Peterson, K. A., Wilson, A. K. J. Chem. Phys. 2001, 114, 9244 (cc-pV(n+d)Z).

Karlsruhe def2 family¶

Weigend, F., Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297 (def2 series).
Weigend, F. Phys. Chem. Chem. Phys. 2006, 8, 1057 (def2/J auxiliary).
Rappoport, D., Furche, F. J. Chem. Phys. 2010, 133, 134105 (def2-XVPD diffuse-augmented).

Jensen polarisation-consistent¶

Jensen, F. J. Chem. Phys. 2001, 115, 9113 (pc-n).
Jensen, F. J. Chem. Phys. 2002, 117, 9234 (aug-pc-n).
Jensen, F. J. Chem. Theory Comput. 2014, 10, 1074 (pcseg-n).

Relativistic and ANO¶

Pollak, P., Weigend, F. J. Chem. Theory Comput. 2017, 13, 3696 (x2c-XVPall).
Franzke, Y. J., Spiske, L., Pollak, P., Weigend, F. J. Chem. Theory Comput. 2020, 16, 5658 (x2c-QZVPPall).
Roos, B. O., Lindh, R., Malmqvist, P.-Å., Veryazov, V., Widmark, P.-O. J. Phys. Chem. A 2005, 109, 6575 (ANO-RCC TM).
Zobel, J. P., Widmark, P.-O., Veryazov, V. J. Chem. Theory Comput. 2020, 16, 278 (ANO-R).

Composite 3c methods¶

Sure, R., Grimme, S. J. Comput. Chem. 2013, 34, 1672 (HF-3c).
Grimme, S., Brandenburg, J. G., Bannwarth, C., Hansen, A. J. Chem. Phys. 2015, 143, 054107 (PBEh-3c).
Brandenburg, J. G., Bannwarth, C., Hansen, A., Grimme, S. J. Chem. Phys. 2018, 148, 064104 (B97-3c).
Grimme, S., Hansen, A., Ehlert, S., Mewes, J.-M. J. Chem. Phys. 2021, 154, 064103 (r2SCAN-3c).
Müller, M., Hansen, A., Grimme, S. J. Chem. Phys. 2023, 158, 014103 (ωB97X-3c, vDZP).
Wagen, C. C. The vDZP Basis Set Is Effective for Many Density Functionals. Rowan publication, 2024 (TorsionNet206 benchmarks).

Periodic Gaussian basis sets¶

Peintinger, M. F., Vilela Oliveira, D., Bredow, T. J. Comput. Chem. 2013, 34, 451 (pob-TZVP). doi:10.1002/jcc.23153
Vilela Oliveira, D., Laun, J., Peintinger, M. F., Bredow, T. J. Comput. Chem. 2019, 40, 2364 (pob-TZVP-rev2). doi:10.1002/jcc.26013
Laun, J., Vilela Oliveira, D., Bredow, T. J. Comput. Chem. 2018, 39, 1285.
VandeVondele, J., Hutter, J. J. Chem. Phys. 2007, 127, 114105 (MOLOPT).
Daga, L. E., Civalleri, B., Maschio, L. J. Chem. Theory Comput. 2020, 16, 2192 (dcm-TZVP).

Plane wave and PAW pseudopotentials¶

Blöchl, P. E. Phys. Rev. B 1994, 50, 17953.
Kresse, G., Joubert, D. Phys. Rev. B 1999, 59, 1758 (VASP PAW).
Hamann, D. R. Phys. Rev. B 2013, 88, 085117 (ONCV).
van Setten, M. J. et al. Comput. Phys. Commun. 2018, 226, 39 (PseudoDojo).
Schlipf, M., Gygi, F. Comput. Phys. Commun. 2015, 196, 36 (SG15).
Prandini, G., Marrazzo, A., Castelli, I. E., Mounet, N., Marzari, N. npj Comput. Mater. 2018, 4, 72 (SSSP).
Lejaeghere, K. et al. Science 2016, 351, aad3000 (Δ-factor benchmark across codes).
Garrity, K. F., Bennett, J. W., Rabe, K. M., Vanderbilt, D. Comput. Mater. Sci. 2014, 81, 446 (GBRV).

Numerical atomic orbitals¶

Blum, V. et al. Comput. Phys. Commun. 2009, 180, 2175 (FHI-aims).
Soler, J. M. et al. J. Phys.: Condens. Matter 2002, 14, 2745 (SIESTA).

Database¶

Pritchard, B. P., Altarawy, D., Didier, B., Gibson, T. D., Windus, T. L. J. Chem. Inf. Model. 2019, 59, 4814. Basis Set Exchange