Semiempirical and MACE method comparison¶

Status date: 2026-06-04. This note compares the fast-method surface in vibe-qc for development and production planning: DFTB0/SCC-DFTB, GFN2-xTB, PM6/OM1/OM2/OM3, MSINDO, and MACE. It is intentionally conservative: a method can be executable and still not be production-validated.

Abstract¶

vibe-qc now contains two different kinds of fast energy engines. The semiempirical engines are electronic-structure methods implemented inside vibe-qc. They build Hamiltonians, solve SCF-like equations when required, and can expose electronic quantities such as densities or charges. MACE is different: it is an external pre-trained machine-learning interatomic potential (MLIP). It predicts a DFT-fitted potential-energy surface from a neural network and provides no wavefunction, orbitals, density, or charge model.

The production conclusion is therefore not “which method is best” but “which method is valid for this question.” Use MACE for fast structures, forces, stress, molecular dynamics, and relaxations inside a trained domain. Use MSINDO when the system lies inside its validated molecular scope and a semiempirical electronic model is needed. Use OM2/OM3 (and PM6, within its documented integral-model residuals) for molecular NDDO work. Use DFTB as a screening and preoptimization tool. Treat GFN2-xTB and OM1 as experimental until their gates lift.

Feature matrix¶

Engine	Model type	Energy scale	Electronic outputs	Gradients / stress	Periodic support	Open shell	Current scope	Production recommendation
DFTB0 / UDFTB0	non-self-consistent tight binding	vibe-qc in-house semiempirical total	density-like TB quantities, limited charges	analytic DFTB0 gradients; stress paths available	Gamma + k-point paths	yes	91 in-house estimated elements	Screening and preoptimization only; parameters are not DFTB+ parity parameters
SCC-DFTB / USCC	self-consistent-charge tight binding	vibe-qc in-house semiempirical total	charges, densities, SCC trace	fixed-charge approximate gradients; stress paths available	Gamma + k-point paths	yes	91 in-house estimated elements	Screening/preoptimization; do not publish quantitative energies without external validation
GFN2-xTB	self-consistent tight binding with multipole electrostatics	GFN2-style semiempirical total	charges and SCC state	approximate / FD-dependent paths; periodic stress still experimental	Gamma + k-point paths, experimental	yes	86 fetched GFN2 parameters	Keep experimental gate; remaining gates are self-consistent D4, periodic AES images, mixer tuning, and xTB parity
PM6 / UPM6	NDDO SCF	PM6-like total, not MOPAC heat of formation	density, SCF convergence, spin counts for UPM6	finite difference	Gamma periodic path, experimental	molecular yes	82 bundled MOPAC-derived parameters	Production (molecular); PES pinned by regression; spherical-integral fallback documented
OM2 / OM3	orthogonalization-corrected NDDO SCF (Dral 2016 eqs 6-20)	OMx total; published-benchmark relative energetics (H3- 0.1 kcal/mol, ethane barrier ±0.6); minima ~0.1-0.2 A long	density, SCF convergence, PES wells, published matrix elements + barriers	finite difference	Gamma periodic path, legacy-model parity only	yes (UHF)	H, C, N, O, F	Production (molecular)
OM1	orthogonalization-corrected NDDO SCF	OMx total; X-H bonds ~0.3 A short, close contacts can collapse (analytic ECP missing)	density, SCF convergence, documented-limitation pins	finite difference	Gamma periodic path, legacy-model parity only	yes (UHF)	H, C, N, O, F	Experimental (warns); unblocks when Kolb-Thiel 1993 ECP lands
MSINDO	INDO SCF over Slater orbitals	reference-MSINDO total	charges, density, binding energy, spin UHF state	no analytic gradients yet	none yet	UHF for s/p scope	H, He, C, N, O, F; Al, Si, P, S, Cl RHF via Python	Production within documented molecular scope; parity to reference MSINDO is closed
MACE-MPA / MACE-OFF	external pre-trained MLIP	model-specific reference-shifted DFT surface, not an electronic total	none	analytic forces; periodic stress and variable-cell relaxation	periodic direct drivers for materials models	spin not modeled as electronic state	model-dependent trained domain	Production for structures/forces inside domain; never compare absolute energies to SCF/semiempirical totals

Method-by-method comparison¶

DFTB0 and SCC-DFTB¶

DFTB is the fastest native electronic route in vibe-qc. DFTB0 has no charge self-consistency loop, so it is especially useful for cheap geometry preconditioning. SCC-DFTB adds charge response and is often more chemically reasonable for polar systems. The limitation is parameter provenance: the current tables are in-house estimates, not a published DFTB parameter set with fitted repulsive potentials. That makes these methods useful for workflow acceleration, not for quantitative publication claims.

Production guidance: keep using DFTB for preoptimization and regression coverage of fast periodic infrastructure. Do not promote the present parameter set to quantitative DFTB until fitted repulsives and external DFTB+ parity tests exist.

GFN2-xTB¶

GFN2-xTB is the most ambitious native fast method in the stack. The deep H0/overlap bug was fixed on 2026-06-01. Molecular AES dipole/quadrupole terms, the GAM3 third-order term, and post-SCF native D4-style dispersion have landed. The method remains gated because the defining GFN2 production surface still requires self-consistent D4, periodic AES image-cell multipole Ewald terms, robust non-simple SCC mixer tuning, and a closed parity matrix against external xtb over molecules, ions, radicals, and periodic test cells.

Production guidance: keep GFN2ExperimentalWarning. Use it for development and targeted comparisons, not production numbers. The next production milestone should be parity-first, not threshold tuning.

PM6 and OMx¶

PM6 and OMx share the NDDO family shape: minimal valence basis, parameterized one- and two-electron approximations, and SCF over a small Hamiltonian. PM6 has wider element reach through the bundled MOPAC-derived parameter cache. OM1/OM2/OM3 have a narrower H/C/N/O/F surface but include the orthogonalization corrections that distinguish the OMx family.

As of 2026-06 the molecular PM6/OM2/OM3 paths are production: the PES shape is pinned by tests/test_semiempirical_pes.py (proper wells for H2O/N2/CO/CH4, geometry-opt smoke), open-shell SCF converges (UPM6 + UOMx), and the OMx relative energetics reproduce the published benchmarks — Weber & Thiel 2000 H3- bending curve to 0.1 kcal/mol, matrix elements to <0.01 eV, and the ethane rotation barrier (the signature ORT observable: OM2 3.1 vs published 2.8, OM3 3.0 vs 2.4 kcal/mol) — see TestOMxV2AgainstWeber2000. Two documented accuracy residuals remain: PM6 falls back to a spherical Klopman–Ohno integral model where MOPAC diatomic multipole data is absent, and the OMx two-centre integrals use Klopman-scaled STO monopole densities in place of the published scaled-Gaussian multipole integrals (omx_fock.cpp documents every approximation inline). Both bias bond minima systematically ~0.1–0.2 Å long while leaving the PES shape and relative energetics intact. OM1 is the one experimental member: its analytically-evaluated core-valence ECP (Kolb & Thiel 1993) is not implemented yet — X–H bonds come out ~0.3 Å short, close non-bonded contacts can variationally collapse (the uncapped F2 term), and run_job(method="om1") warns accordingly.

Production guidance: prefer OM2/OM3 for H/C/N/O/F molecular energetics and geometries within the documented residuals; quote PM6 results as PM6-like totals, not MOPAC heats of formation, until out-of-process MOPAC parity is demonstrated. Method-paper citations are emitted on every run.

MSINDO¶

MSINDO is the strongest production semiempirical path today within its documented scope. The implementation is independent, validated out-of-process against a reference MSINDO build, and reproduces total energies to microhartree scale for the supported closed-shell and UHF test sets. The tradeoff is scope: there are no analytic gradients, no periodic Cyclic Cluster Model yet, no ROHF, no open-shell d-block path, and no transition-metal table.

Production guidance: MSINDO can be used for molecular energies and charges inside the validated element/spin scope. The next production implementation steps are analytic or stable finite-difference gradients, the remaining parameter table, open-shell d-block support, and then the CCM periodic port.

MACE¶

MACE is the fastest route to high-quality structures and forces when the system is inside a trained domain. It is not an electronic-structure method: there is no SCF, no basis, no density, no orbitals, no charges, and no band structure. Its energy is a model-specific, reference-shifted DFT-surface quantity. For water, the default MACE-MPA-0 and MACE-OFF23 models sit on very different absolute energy scales, so absolute energies across MACE models or between MACE and SCF/semiempirical methods are not meaningful.

Production guidance: use MACE for optimization, molecular dynamics, stress, cell relaxation, and relative energies at fixed composition and fixed model. Keep the ASL gate strict for academic-only weights. For commercial or mixed licensing contexts, default to MIT MACE-MPA-0 or another explicitly verified MIT model.

Production implementation guidance¶

Keep method families separate in the user interface. Semiempirical methods are native electronic-structure engines; MACE is an external MLIP. The shared energy() / gradient() duck type is useful, but the provenance and energy interpretation are different.
Do not compare absolute energies across families. DFTB, GFN2, PM6, OMx, MSINDO, ab initio SCF, and MACE all use different references and fitted targets. Compare geometries, force directions, relative energies within one method/model, or externally validated observables.
Keep every user-facing method in the citation database. The 2026-06-04 audit found and fixed missing PM6 and OMx routes. Future method additions should update python/vibeqc/output/citations/database.toml and tests/test_citations.py in the same merge.
Preserve the no-runtime-wrapper rule for QC programs. xTB, MOPAC, DFTB+, and reference MSINDO belong in examples/regression/... subprocess runners, never imported into python/vibeqc/ or the C++ core.
Gate production claims on parity, not convergence. For semiempirical methods, a converged SCF is necessary but not sufficient. The acceptance bar should include external energies, gradients or finite-difference checks, rotation/translation invariance, size consistency, charge signs, open-shell cases, and periodic molecular-limit tests where relevant.
Prefer small shippable milestones. Each milestone should leave main taggable: method available only inside its honest scope, docs and changelog aligned, citations emitted, tests green, and experimental paths visibly gated.

Suggested next implementation sequence¶

GFN2-xTB: finish self-consistent D4, periodic AES image-cell multipole Ewald, and mixer tuning; then close the xTB parity matrix before removing the experimental warning.
PM6: close the MOPAC parity gap on a small molecule set, documenting energy convention differences explicitly. Only then expand claims around the 82-element cache.
OMx: add external reference fixtures for OM1/OM2/OM3 and decide whether run_omx_v2 should become the only public molecular path once parity is established.
MSINDO: add gradients and continue the staged port toward open-shell d-blocks, transition metals, and the CCM periodic implementation.
MACE: add a Python <=3.13 CI lane for the real MACE e2e tests and keep the model registry current as upstream weights and licenses evolve.