OpenQuantum
OpenQuantum is an ab initio molecular orbital (MO) calculation program written in Rust. It performs Hartree–Fock, Kohn–Sham DFT, and post–Hartree–Fock calculations within the Linear Combination of Atomic Orbitals (LCAO) framework. Supports RHF, UHF, ROHF, and RKS/UKS for closed- and open-shell molecules; MP2 and CCSD(T) correlation energies; density functional theory with GGA, meta-GGA, hybrid, and range-separated hybrid functionals; implicit solvation (PCM-family, ddCOSMO/ddPCM, SMD) with analytical gradients and Hessians; geometry optimization (BFGS, Berny RFO, primitive/DLC/TRIC internal coordinates) with analytic gradients; IRC and NEB pathways; harmonic frequency analysis with analytical Hessians and thermochemistry; and effective core potentials (ECPs).
Note: The project is under active development and not yet ready for production use.
Feature Highlights
| Category | Features |
|---|---|
| Molecular Input | XYZ Cartesian geometry in Angstrom or Bohr units |
| Basis Sets | STO-3G, 3-21G, 6-31G, 6-31G*, 6-31G**, 6-31+G*, 6-311G, cc-pVDZ, cc-pVTZ, cc-pVQZ, def2-SVP, def2-TZVP, def2-TZVPP, def2-QZVP, LANL2DZ, and 520+ more built directly into the binary — spanning Pople, Dunning cc-pVXZ, Karlsruhe def2, ANO, Jensen PCseg, relativistic (DKH/ZORA/x2c), universal (UGBS/HGBS), SARC, Sapporo, ECP libraries, and specialized sets — with support for external JSON, GBS, and Orca BAS formats |
| One-Electron Integrals | Overlap (S), kinetic energy (T), and nuclear attraction (V) via Obara–Saika recurrences |
| Two-Electron Integrals | McMurchie–Davidson algorithm with 8-fold permutational symmetry; SP analytical fast paths for S/P shells (up to 10× speedup); Rys quadrature for D/F+ shells; direct SCF mode for large systems with symmetry-accelerated cache lookup; engine selection via the INT section (Eri auto/md/sp/rys) — applies uniformly to in-core ERI build, direct SCF, analytical gradients/Hessians, and semi-analytical (FD) Hessians |
| SCF Methods | RHF, UHF, and ROHF with DIIS, level shifting, damping, Fermi broadening, multiple initial guesses (core Hamiltonian, Hückel, SAD), and Quadratic Convergence SCF (QC-SCF) with Newton–Raphson orbital optimization |
| Post-HF | MP2 and CCSD(T) correlation energies |
| Analytical Gradients | RHF and UHF analytic nuclear gradients with symmetry-accelerated ERI derivatives (skips symmetry-equivalent shell quartets); used by BFGS optimizer |
| Analytical Hessians | Fully analytical RHF and UHF Hessians including CPHF response, occupied-occupied reorthonormalization, and analytic d²ERI integrals with symmetry acceleration (skips symmetry-equivalent quartets); semi-analytical (FD) path also propagates the selected ERI engine to all displaced SCF evaluations |
| Geometry Optimization | BFGS optimizer with analytic nuclear gradients; Berny RFO algorithm with trust-radius step control via the OPT section (Algorithm berny); backend-specific controls (dihedral, superweakdih, energynoise) can be invoked by setting Algorithm rberny (or RBerny in the task: line); Primitive, DLC, and TRIC internal-coordinate back-ends with topology-inferred primitive sets (bonds, angles, dihedrals, out-of-plane, linear-angle supplementary) and IC back-transform; IRC path; NEB pathway optimization with Henkelman energy-weighted tangent and climbing-image CI-NEB; Transition-state search with P-RFO step, Bofill Hessian update, initial TS Hessian initialization, periodic eigenvalue correction, and TS-specific trust radius (0.01 Å); saddle-point-aware IC optimizer with TS-BFGS Hessian update, P-RFO or Minimum Mode Following (MMF) step, sigma-based trust-radius schedule, and Davidson partial eigensolver (Algorithm sella or the Sella task token); GDIIS/GEDIIS geometry-space DIIS extrapolation in IC optimizers (Diis true); Bofill Hessian update for transition-state optimization (Update bofill) |
| Frequency Analysis | Harmonic vibrational frequencies via semi-analytical (finite-difference of gradients) or fully analytical Hessian; IR intensities, thermochemistry |
| Thermochemistry | Zero-point energy, thermal corrections (U, H, G), entropy (translational + rotational + vibrational) via RRHO model with symmetry number |
| ECP Support | Effective core potentials (LANL2DZ, Stuttgart, etc.) |
| DFT Methods | Restricted (RKS) and unrestricted (UKS) Kohn–Sham DFT across four rungs of Jacob's ladder — GGA (BP86, PBE), meta-GGA (TPSS, M06-L), hybrid GGA (B3LYP, PBE0), hybrid meta-GGA (M06-2X), and range-separated hybrid (ωB97X-D); Becke-style atom-centered quadrature with Mura–Knowles radial and Lebedev–Laikov angular grids (six built-in preset levels: Coarse through SuperFine); empirical dispersion corrections (D2, D3 zero-damping, D4 charge-scaled) |
| XC Integration | Shell-pair screening (product bound < 10⁻¹⁶ threshold); forward-mode autodiff functional derivatives (7-variable dual numbers) for exact analytic vρ, vσ, vτ; kinetic-energy density support for meta-GGAs; Stratmann–Scuseria compact cell function (f(μ), 3003/2048 normalization, |
| DFT SCF Coupling | Range-separated hybrids with short/long-range exchange splitting via error function; solvent-coupled SCF (RKS/UKS with reaction field); full re-use of SCF infrastructure (DIIS, damping, level shifting, checkpointing) |
| Implicit Solvation | Seven electrostatic models across three engine families — PCM-family (C-PCM, COSMO, IEF-PCM, SS(V)PE) with SWIG/ISWIG cavity discretization; domain-decomposition (ddCOSMO, ddPCM) with spherical-harmonic expansion; SMD with IEF-PCM electrostatics and CDS non-electrostatic term; 179-solvent SMD parameter database |
| Solvent Analytical Gradients | Full analytic PCM gradient (three contributions: grad_nuc, grad_solver, grad_qv) via adjoint-Lagrangian formulation for C-PCM/COSMO/IEF-PCM/SS(V)PE; ddCOSMO/ddPCM analytic gradient with regularized l=0 block |
| Solvent Analytical Hessians | Full analytic PCM Hessian (hess_nuc + hess_solver + hess_qv) including CPHF solvent response (AXPCM kernel) for C-PCM/COSMO/IEF-PCM/SS(V)PE; finite-difference fallback for ddCOSMO/ddPCM |
| Symmetry | Point group detection, character tables, irrep assignment; symmetry acceleration for all ERI-heavy computations — energy (in-core + direct SCF), analytical gradient, and analytical Hessian (matching GRAD2E SymShl — skips symmetry-equivalent shell quartets before expensive integral evaluation) |
| CPHF Solver | Coupled-perturbed Hartree–Fock equations for response properties; RHF and coupled 2×2 UHF spins |
| Analysis | Mulliken population analysis, orbital energies, spin contamination ⟨S²⟩, dipole moments, EFG |
| Checkpointing | Save and restart SCF from binary checkpoint files; checkpoint and other temporary files are written to a configurable scratch directory (see Environment Variables) |
Quick Navigation
- New to OpenQuantum? Start with Installation then Quick Start.
- Ready to run? See the Input File Format and Keyword Reference.
- Want to understand the algorithms? See Theoretical Background and Density Functional Theory.
- Running with solvent? See Implicit Solvent Models.
- Looking for the full API? See Developer Documentation.
Citation
If you use OpenQuantum in your research, please cite this preprint:
Pham, Le Nhan. OpenQuantum: A High-Performance Rust Implementation for Ab Initio Molecular Orbital Calculations. 2026.