Electronic Structure, with Its Checks
Hartree-Fock energies, gradients, geometries, IR spectra, thermochemistry and orbitals from our own engine, agreeing with PySCF and Psi4.
Five Tools, One Planner
You do not pick a tool. The planner chooses it from your request and shows the plan before anything runs. Live
Energy
Single-point RHF, UHF, RKS or UKS energy in Eh, kJ/mol and kcal/mol, with orbital energies, dipole moment, Mulliken charges and the analytic gradient.
Optimise Geometry
Analytic gradient and a Cartesian BFGS optimiser with a trust radius.
Frequencies
Central differences of analytic gradients with a Richardson step, plus IR intensities.
Bond Scan
Energy along a chosen bond length, angle or dihedral, plotted in the study.
Orbitals
Orbital energies, occupations and Gaussian cube files you can view in 3D or export.
Results a Scientist Can Use
Reviewed by our own chemists on 2026-10-18 and rebuilt view by view. Live
Thermochemistry
Rigid-rotor harmonic-oscillator values at 298.15 K (McQuarrie, Statistical Mechanics): zero-point energy, internal energy, enthalpy and entropy. Hand-checked for water at HF/STO-3G: ZPE 15.30, U 17.08, H 17.67 kcal/mol, translational entropy 34.6 cal mol⁻¹ K⁻¹.
IR Spectrum
Stick and broadened spectra with a chosen line width and a Lorentzian or Gaussian shape, scaled-frequency columns, imaginary modes shown with "i", and a check that 3N-6 modes were found.
Downloads
XYZ, MOL, SDF and PDB structures, Molden orbital files, CSV tables and a methods paragraph with citations, so a result can be checked and reused.
Geometry and Dipole
A geometry table of bonds and angles, and dipole components as well as the total.
Bond Scans
Scans are normalised and never mistaken for the molecule's own energy or structure. Example: H2 minimum -1.11687 Eh at 1.3 bohr on the scan grid.
Model Systems
Grid quantum mechanics (boxes, oscillators, tunnelling, wavepackets) sits inside this domain as a sub-area. See Model Systems
DFT and Basis Sets, from the Papers
Engine 0.7.0 to 0.7.11, each parameter traced to its paper, table and page. Pure functionals are complete with analytic gradients; hybrids are next. Live
Functionals
LDA (SVWN5, SVWN-RPA, SPW92), BLYP and PBE in restricted and unrestricted Kohn-Sham form (RKS, UKS), plus HF-LYP. Analytic gradients (Johnson, Gill and Pople 1993) give DFT optimisation, frequencies and scans.
Basis Sets
STO-3G (hydrogen to argon, re-entered from Hehre 1969 and 1970), 6-31G and the def2 family (SV(P) to QZVPP) to krypton, with RI-J density fitting of the Coulomb term for energies, orbitals and scans.
Dispersion
DFT-D2 (Grimme 2006) for PBE and BLYP. Example: water dimer PBE/def2-SVP dispersion -0.00109 Eh.
Checked against the papers' own numbers, for example PBE H2 atomisation 104.6 kcal/mol against 105 printed, and test-only against PySCF energies.
Reference Values, Reproduced
Hartree-Fock with STO-3G, on the engine. Where a published value exists it is shown beside ours.
- Analytic gradients match finite differences to 1.3e-9 (RHF water) and 9.6e-10 (UHF water cation)
- Oxygen molecule matches PySCF to 4e-12 Eh; hydrogen fluoride within 6e-9 Eh
- Energies agree between Windows with MSVC and macOS with clang
| System | Ours | Reference |
|---|---|---|
| H2, Eh | -1.1167143251 | Reference code, 1e-15 |
| He, Eh | -2.8077839575 | -2.80778 published |
| H2O Optimised, Eh | -74.9659011923 | Reference code |
| CH4, Eh | -39.7268636795 | -39.72686 published |
| H2O r(OH), Å | 0.98941 | Optimised, 100.027° |
| H2O Frequencies, cm-1 | 2170.0, 4140.0, 4391.1 | 2170, 4140, 4391 published |
Speed Against a Reference Program
Engine 0.7.9, RHF energies on 8 CPU threads of a Mac mini, against an established open-source program used only as a test reference. Energies agree to 1e-7 Eh or better.
Basis sets with f functions remain our largest gap; a faster shell-quartet recurrence is the next step.
| Molecule, Basis | Ours | Reference |
|---|---|---|
| Benzene, 6-31G | 0.22 s | 0.35 s |
| Caffeine, STO-3G | 1.11 s | 1.41 s |
| Benzene, def2-SVP | 1.22 s | 1.01 s |
| Caffeine, def2-SVP | 38.6 s | 37.2 s |
| Glucose, def2-SVP | 26.3 s | 22.3 s |
| Benzene, def2-TZVP | 192.7 s | 19.5 s |
SCF Machinery That Protects the Answer
Convergence
DIIS, level shift and damping (Saunders and Hillier, 1973) with an automatic retry when a run stalls.
Stability Analysis
Internal, RHF to UHF and real to complex instabilities (Seeger and Pople, 1977), and since engine 0.7.12 the same for Kohn-Sham DFT (Bauernschmitt and Ahlrichs, 1996). A real instability is followed to the lower solution by default.
Point Group
The full molecular point group is detected (27 of 27 NIST CCCBDB reference molecules) and its largest Abelian subgroup reported; the geometry can be symmetrised. Symmetry is not yet used to block the SCF.
Integral Screening
Schwarz screening, an in-core integral store (1024 MB by default) and threads on CPU.
Reproducible Keys
Every result carries a SHA-256 cache key. An identical request offers the stored result instead of recomputing, and never across engine versions.
Physical Sanity Checks
Inputs with atoms closer than 0.1 Å, coordinates beyond 1000 Å or an impossible electron count are refused.
Honest Limits
- No hybrid functionals such as B3LYP or PBE0 yet, no MP2 or coupled cluster
- RI-J has no nuclear gradient yet, so optimisation and frequencies use exact Coulomb
- Basis sets to krypton; no effective core potentials for heavier elements
- Frequencies are harmonic and above experiment, as expected for this method
- Every basis set is taken from its original publication; STO-3G was re-entered from Hehre 1969 and 1970 and verified in engine 0.7.11
- Up to 400 atoms for frequencies
| Task | GPU Server (Windows) | Mac Mini (CPU) |
|---|---|---|
| Benzene Energy and Stability | 2.9 s | 1.3 s |
| Benzene Optimisation | 12.8 s | 6.1 s |
| Water Frequencies | 0.63 s | 0.18 s |
Quantum Chemistry Questions
Which quantum chemistry methods are available?
Which basis sets and elements are supported?
Why are Hartree-Fock frequencies higher than experiment?
Does it use the GPU?
How do I know a stored SCF solution is stable?
Run Your Next Molecule Through AiMolSim
See your own molecule optimised, its frequencies computed and the checks printed beside the result. A demo takes about 30 minutes.