am1-rs

A Rust-native implementation of the AM1 (Austin Model 1) semiempirical NDDO quantum-chemistry method. It provides AM1 heats of formation, Mulliken and AM1-BCC partial charges (for AMBER), nuclear gradients, and L-BFGS geometry optimization, with Rust, Python-native and ASE front ends.

AM1 is a genuine NDDO self-consistent-field method (Roothaan–Hall over a density matrix with the Dewar–Sabelli–Klopman semiempirical two-electron integrals).

Scope

Capability	Status
RHF/UHF NDDO SCF with SAD guess + A-DIIS→CDIIS convergence acceleration	✅ validated
AM1 Mulliken charges, dipole, HOMO/LUMO	✅
Nuclear gradient — fully closed-form (dual-number AD), RHF & UHF, all elements, no finite differences	✅ matches full-SCF FD to ~1e-7
L-BFGS geometry optimization (Rust)	✅
Analytic Hessian (CPHF/UCPHF orbital Hessian) + harmonic frequencies — RHF & UHF, all elements, no finite differences	✅ rayon-parallel, faer-diagonalized; matches FD Hessian to ~1e-5
Open-shell UHF (radicals, odd-electron ions, multiplicity > 1)	✅
AM1-BCC partial charges + mol2 export	✅ exact antechamber BCCPARM.DAT (405 params) + faithful typing
Rust API, Python-native API, ASE Calculator	✅
Elements	full published AM1 main-group set: H, C, N, O, F, Al, Si, P, S, Cl (n ≤ 3, exact analytic overlap) and Zn, Ge, As, Se, Br, Sb, Te, I, Hg (n ≥ 4, general numerical overlap)
Periodic boundary conditions (PBC)	⛔ roadmap (AM1 is molecular)

Validation. Optimized AM1 heat of formation of water is −59.24 kcal/mol and dipole 1.86 D, matching MOPAC AM1. See tests/.

Build

cargo build --release            # library + CLI (am1_rs_cli)
cargo test                       # unit + validation tests

Linear algebra uses faer (a pure-Rust symmetric eigensolver and LU — no LAPACK/BLAS) and hot loops are parallelized with rayon (gradient displacements, pair-integral construction, Hessian columns). pyo3 is pulled in only for the Python extension (--features python).

Units

The semiempirical block is computed in eV with distances in Bohr, using MOPAC7's model constants (ev = 27.21, a0 = 0.529167 Å) so published AM1 numbers reproduce. At the API boundary:

• Rust-native and Python-native APIs return atomic units (Hartree, Bohr).
• The ASE Calculator returns eV / Å (AM1 energies are natively eV).
• Heat of formation is additionally reported in kcal/mol.

Parameters

The standard published AM1 parameter set (U_ss … alpha plus the AM1 core-core Gaussian K/L/M triples) is embedded from src/data/am1_parameters.csv; isolated-atom energies and experimental atomic heats of formation reproduce MOPAC's calpar.f/block.f. No external parameter file is required.

Provenance / attribution. The AM1 parameter values are published scientific constants (Dewar et al. 1985 + the element-extension papers, consolidated in MOPAC). The specific machine-readable table, and the integral/overlap/Fock formulas that am1-rs was ported from, come from the PySEQM reference implementation (LANL, BSD-3-Clause). Every parameter's origin is documented in THIRD_PARTY_NOTICES.md, the retained license at third_party/pyseqm/LICENSE, the CSV header, and the module doc-comments that name the corresponding PySEQM source for each ported piece.

CLI

am1_rs_cli energy    examples/water.xyz            # ΔHf, charges, dipole, HOMO/LUMO
am1_rs_cli gradient  examples/methane.xyz          # energy + forces (eV/Å)
am1_rs_cli optimize  examples/water.xyz --opt-output opt.xyz
am1_rs_cli frequencies opt.xyz                             # harmonic frequencies (cm^-1)
am1_rs_cli charges   examples/ethanol.xyz --mol2-output ethanol.mol2   # AM1-BCC
am1_rs_cli charges   examples/ethanol.xyz --mulliken                   # raw AM1 charges

Options: --charge Q, --multiplicity M (M > 1 requires UHF), --reference auto|rhf|uhf (or the --rhf / --uhf shortcuts — --uhf runs a singlet unrestricted), --opt-output, --mol2-output.

Rust API

All Rust entry points are in atomic units (Hartree, Bohr) except the AM1 block's native eV (the *_ev fields) and ΔHf in kcal/mol. Am1Options carries charge, multiplicity (2S+1), reference (Auto/Restricted/Unrestricted — restricted vs unrestricted, independent of the multiplicity), SCF tolerances, and the accelerator choice.

use am1_rs::{
    Molecule, Am1Parameters, Am1Calculator, Am1Options,
    closed_form_gradient, optimize, vibrational_analysis, am1_bcc_charges,
    OptOptions,
};

let params = Am1Parameters::standard()?;          // embedded AM1 parameter set
let mol = Molecule::from_xyz_file("examples/water.xyz", 0.0)?;   // charge = 0.0
let opts = Am1Options::default();                 // RHF, A-DIIS→CDIIS, SAD guess

// Single point: energy, Mulliken charges, dipole, HOMO/LUMO, ΔHf.
let r = Am1Calculator::with_options(params.clone(), opts.clone()).calculate(&mol)?;
println!("ΔHf = {:.3} kcal/mol   dipole = {:.3} D", r.heat_of_formation_kcal, r.dipole_magnitude);

// Analytic nuclear gradient (eV/Bohr in `.gradient`, forces = −gradient).
let g = closed_form_gradient(&mol, &params, &opts)?;
println!("|grad|max = {:.3e} eV/Bohr", g.max_gradient);

// L-BFGS geometry optimization.
let optd = optimize(&mol, &params, &opts, &OptOptions::default())?;
println!("relaxed ΔHf = {:.3} kcal/mol", optd.scf.heat_of_formation_kcal);

// Analytic Hessian → harmonic frequencies (evaluate at a minimum).
let vib = vibrational_analysis(&optd.molecule, &params, &opts, 1.0e-3)?;
println!("highest mode = {:.1} cm^-1", vib.frequencies_cm.last().copied().unwrap_or(0.0));

// AM1-BCC partial charges for AMBER.
let bcc = am1_bcc_charges(&mol, &params, &opts)?;
println!("BCC charges = {:?}", bcc.charges);

Python / ASE

Built with maturin (maturin develop --features python). The distribution is am1-rs-python (import module am1_rs):

ASE calculator (eV / Å convention; multiplicity > 1 selects UHF):

from am1_rs.ase import AM1
from ase.build import molecule

atoms = molecule("H2O")
atoms.calc = AM1(charge=0.0, multiplicity=1)   # ASE convention: eV, Å
print(atoms.get_potential_energy())            # eV
print(atoms.get_forces())                      # eV/Å
print(atoms.get_charges())                     # Mulliken, e
print(atoms.calc.get_hessian(atoms))           # analytic Hessian, eV/Ų

Charge, multiplicity and reference may be given at construction (e.g. AM1(reference="uhf")) or per structure at calculation time via atoms.info["charge"] / atoms.info["multiplicity"] / atoms.info["reference"] ("auto"/"rhf"/"uhf").

Native API — atomic units (Hartree, Bohr); input coordinates in Å. Each call takes (numbers, positions, charge=0.0, multiplicity=1, reference="auto") (reference = "auto" / "rhf" / "uhf") and returns a dict (keys documented in each function's docstring):

import am1_rs

Z = [8, 1, 1]
xyz = [[0.0, 0.0, 0.0], [0.9584, 0.0, 0.0], [-0.24, 0.9278, 0.0]]

sp   = am1_rs.single_point(Z, xyz)          # energy_hartree, heat_of_formation_kcal, charges, dipole_debye, homo/lumo_ev…
grad = am1_rs.gradient(Z, xyz)              # gradient_hartree_per_bohr, gradient_ev_per_angstrom
opt  = am1_rs.optimize(Z, xyz)              # positions_angstrom, energy_hartree, converged, iterations
freq = am1_rs.frequencies(Z, opt["positions_angstrom"])   # frequencies_cm (evaluate at a minimum)
hess = am1_rs.hessian(Z, xyz)               # hessian_hartree_per_bohr2, hessian_ev_per_angstrom2, ndof
bcc  = am1_rs.am1_bcc(Z, xyz)               # charges (AM1-BCC), mulliken, atom_types
print(sp["heat_of_formation_kcal"], bcc["charges"])

AM1-BCC charges for AMBER

am1_rs_cli charges runs the AM1 SCF for Mulliken charges, perceives the molecular graph, assigns antechamber BCC atom types (the numeric 11–91 scheme of ATOMTYPE_BCC.DEF), and applies the additive bond charge corrections from the exact antechamber BCCPARM.DAT (405 parameters, embedded from AmberTools, GPL-3). Ethanol charges match antechamber closely (O −0.60, hydroxyl-H +0.40, …). The atom/bond typing is faithful for common organic molecules but not guaranteed byte-identical to antechamber's full typing engine for every edge case — see THIRD_PARTY_NOTICES.md. Net charge is preserved.

Documentation

• docs/rust-api.md — complete Rust API (every public type and function, with examples).
• docs/python-api.md — complete Python API (native functions + ASE calculator).
• docs/scope.md — feature matrix and units contract.
• docs/theory.md — AM1 equations and references.

Limitations

• Open-shell systems use spin-unrestricted UHF (--multiplicity M, M > 1); no spin-contamination annihilation or ROHF yet.
• Gradients use the exact NDDO Hellmann–Feynman formula (no Pulay term — the AO basis is orthonormal) and are fully closed-form for every case — RHF and UHF, all elements. Each term (two-electron, core-attraction, overlap radial and angular, core-core) is forward-mode dual-number AD with no finite differences; for heavy elements (n ≥ 4) the derivative is AD through the numerical Slater-overlap quadrature. Open-shell (UHF) uses the spin-resolved fixed-density gradient. All match a full-SCF finite difference to ~1e-7.
• The Hessian is fully analytic for every case — closed-shell RHF and open-shell UHF, all elements — with no finite differences. The skeleton (fixed-density) second derivative is closed-form second-order forward-AD (Dual2) of the integral kernels (through the quadrature for n ≥ 4); the orbital-relaxation term solves the CPHF equations against the orbital Hessian (RHF), or the coupled α/β UCPHF equations (UHF), in the compact MO occupied–virtual subspace. It agrees with an independent finite-difference Hessian to within that reference's own truncation error (~1e-5). Harmonic frequencies come from its mass-weighted diagonalization. (A finite-difference gradient/Hessian is retained only as a validation gate.)
• Overlaps for valence shells n ≤ 3 use the exact analytic Slater kernel; n ≥ 4 (heavy AM1 elements) use a general numerical Slater overlap (Gauss–Legendre quadrature) whose value and derivatives are both consistent (the derivatives are taken analytically through the quadrature), validated to reproduce the analytic kernel to ~1e-8.
• AM1-BCC uses the exact antechamber BCCPARM.DAT parameters; the atom/bond typing is faithful for common organic molecules but not byte-identical to antechamber's full engine for every edge case (see THIRD_PARTY_NOTICES.md).

References

• AM1 — M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, J. J. P. Stewart, J. Am. Chem. Soc. 107, 3902 (1985).
• MNDO integrals / core-core — M. J. S. Dewar, W. Thiel, J. Am. Chem. Soc. 99, 4899 (1977).
• AM1-BCC — A. Jakalian, B. L. Bush, D. B. Jack, C. I. Bayly, J. Comput. Chem. 21, 132 (2000); A. Jakalian, D. B. Jack, C. I. Bayly, J. Comput. Chem. 23, 1623 (2002).
• ASE — A. Hjorth Larsen et al., "The Atomic Simulation Environment — a Python library for working with atoms," J. Phys.: Condens. Matter 29, 273002 (2017).
• Reference integral/rotation formulas cross-checked against the PySEQM implementation (Zhou, Nebgen et al.), which reproduces MOPAC.

License

GPL-3.0-or-later.