pm6-rs-python 0.1.2

PM6 semiempirical method (pm6-rs) with a Python-native API and an ASE calculator, including PM6-D3/D3H4/D3H4X corrections

pm6-rs

Rust-native implementation of the PM6 semiempirical NDDO method (J. J. P. Stewart, J. Mol. Model. 13, 1173 (2007)). Non-periodic heats of formation, fully analytic nuclear gradients and Hessians, L-BFGS geometry optimization, P-RFO transition-state search, and the PM6-D3 / PM6-D3H4 / PM6-D3H4X post-SCF corrections, with Rust, Python-native and ASE APIs.

• Author: ss0832
• License: GPL-3.0-or-later
• Pure Rust linear algebra (faer + rayon); no LAPACK/BLAS.

Scope and validation status

Validated against the MOPAC v23.2.5 oracle (openmopac/mopac, Apache-2.0); parameters are extracted from the same release.

Capability	Status
SCF energy (RHF + UHF), heats of formation	✅ frozen molecular set; s/p ≤1e-6, hypervalent/TM ≤1e-4 kcal/mol vs MOPAC; see limitations below
d-orbital two-center integrals (S, P, Cl, transition metals, …)	✅ e.g. TiCl₄ ≤2e-5, HCl ≤1e-8 kcal/mol
Analytic gradient (dual-number, Hellmann–Feynman)	✅ s/p and d, matches MOPAC & FD
Analytic Hessian + frequencies	✅ closed-shell s/p/d CPHF; open-shell d uses FD-of-analytic-gradient
L-BFGS geometry optimization	✅ all elements, matches MOPAC minima
Mulliken charges, dipole	✅ (≤1e-5 e / ≤1e-4 D)
Lanthanide sparkles (Ce…Yb)	⚠️ functional (0-orbital cores, oracle-derived ΔH_f); energy ~10 kcal/mol from MOPAC
D3 dispersion (PM6-D3)	⚠️ implemented, ~0.25 kcal/mol vs MOPAC
H4 / X corrections (PM6-D3H4 / -D3H4X)	⚠️ implemented per source; full PM6-D3H4 parity pending
Python native + ASE APIs (energy/grad/forces/Hessian/opt/freq)	✅
PBC	⛔ out of scope (PM6 is molecular)

✅ = validated to the stated tolerance; ⚠️ = implemented and functional, not yet bit-exact. See docs/scope.md and THIRD_PARTY_NOTICES.md.

Units

Internal computation uses eV and Bohr with MOPAC's 2018-CODATA model constants (src/constants.rs). At the boundaries:

• Rust and Python-native APIs return atomic units (Hartree, Bohr), plus convenience eV fields and ΔH_f in kcal/mol.
• The ASE calculator uses eV / Å (PM6 is natively eV, so no round-trip).

Build

cargo build --release        # library + pm6_rs_cli
cargo test                   # unit + MOPAC-oracle regression tests

CLI

pm6_rs_cli energy      water.xyz
pm6_rs_cli gradient    water.xyz
pm6_rs_cli optimize    water.xyz            # writes water.pm6opt.xyz
pm6_rs_cli frequencies water.pm6opt.xyz
pm6_rs_cli charges     water.xyz --charge 0 --multiplicity 1
pm6_rs_cli energy      dimer.xyz --method PM6-D3H4X   # PM6 | PM6-D3 | PM6-D3H4 | PM6-D3H4X

Rust API

use pm6_rs::{Molecule, Pm6Parameters, Pm6Options, run_pm6};

let mol = Molecule::from_xyz_file("water.xyz", 0.0)?;
let params = Pm6Parameters::standard()?;
let r = run_pm6(&mol, &params, &Pm6Options::default())?;
println!("ΔHf = {} kcal/mol", r.heat_of_formation_kcal);

Python

pip install maturin
maturin develop --release --features python   # or: pip install pm6-rs-python

import pm6_rs
import numpy as np

numbers = [8, 1, 1]
positions = np.array([[0.0, 0.0, 0.0], [0.9584, 0.0, 0.0], [-0.24, 0.9278, 0.0]])

# charge, multiplicity and reference ("auto"/"rhf"/"uhf") are per-call arguments.
out = pm6_rs.single_point(numbers, positions, charge=0.0, multiplicity=1, reference="auto")
print(out["heat_of_formation_kcal"], out["charges"])

g = pm6_rs.gradient(numbers, positions)          # dE/dR (Hartree/Bohr and eV/Å)
f = pm6_rs.forces(numbers, positions)            # −dE/dR
h = pm6_rs.hessian(numbers, positions)           # Hartree/Bohr², 3N×3N
w = pm6_rs.frequencies(numbers, positions)       # cm⁻¹ (evaluate at a minimum)

ASE

from ase.build import molecule
from pm6_rs.ase import PM6

atoms = molecule("H2O")
atoms.calc = PM6(charge=0, multiplicity=1, reference="auto")
print(atoms.get_potential_energy())   # eV
print(atoms.get_forces())             # eV/Å
print(atoms.calc.get_gradient())      # eV/Å  (= −forces)
print(atoms.calc.get_hessian())       # eV/Ų, 3N×3N

References

• J. J. P. Stewart, J. Mol. Model. 13, 1173 (2007) — PM6.
• W. Thiel, A. A. Voityuk, J. Phys. Chem. 100, 616 (1996) — MNDO-d.
• S. Grimme et al., J. Chem. Phys. 132, 154104 (2010) — D3.
• J. Řezáč, P. Hobza, J. Chem. Theory Comput. 8, 141 (2012) — H4.
• J. J. P. Moussa, J. J. P. Stewart, J. Open Source Softw. 11(119), 8025 (2026) — MOPAC.