Capabilities in full

Every method and basis set, in one reference.

The complete, honestly-labelled list of what Hilbeon can compute — from a minimal STO-3G single point to DLPNO-CCSD(T) on a drug-sized molecule, excited states with analytic gradients, and real-space bonding analysis. Every method below runs on our own validated integral engine.

analytic gradient — opt · freq · spectra energy — single-point only recommended / gold standard local correlation relativistic frontier / specialist

SCF reference wavefunctions

The mean-field starting point for every method on this page.

Self-consistent field with DIIS / EDIIS acceleration, level shifting and a choice of SAP, SAD or GWH initial guess. Odd-electron systems are promoted to an unrestricted reference automatically.

Reference	Shell	Capability	Use it for
RHF	Closed-shell restricted	gradient	Default reference for even-electron molecules.
UHF	Open-shell unrestricted	gradient	Radicals and odd-electron systems; auto-selected when the electron count is odd.
ROHF	Restricted open-shell	energy	Spin-contamination-free open-shell reference for high-spin states.

Density-functional theory 11 functionals

LDA through hybrid meta-GGA, plus dispersion and composite corrections.

Three functionals carry a full analytic nuclear gradient — they drive geometry optimization, frequencies and simulated spectra. The remaining functionals (via libxc) give accurate single-point energies for benchmarking and method comparison.

Analytic gradient — opt · freq · spectra

Functional	Rung	Capability	Notes
LDA SVWN	LDA	gradient	Local density approximation; fast and robust.
PBE	GGA	gradient	Non-empirical GGA; solid all-rounder.
B3LYP VWN5	Global hybrid	gradientgold for organics	The reference B3LYP in Hilbeon (VWN5 correlation). An alternative VWN3/RPA-convention variant is listed below for cross-code number matching.

Single-point energy — via libxc

Functional	Rung	Exact exchange	Notes
B3LYP VWN3/RPA	Global hybrid	20%	The alternative VWN3/RPA convention used by several other codes, for cross-code number matching.
PBE0	Global hybrid	25%	Parameter-free hybrid; excellent general accuracy.
BLYP	GGA	0%	Classic pure GGA.
r2SCAN	meta-GGA	0%	Modern non-empirical meta-GGA.
M06	meta-GGA hybrid	27%	Minnesota functional tuned for main-group and transition-metal chemistry.
M06-2X	meta-GGA hybrid	54%	Main-group thermochemistry, kinetics and non-covalent interactions.
TPSSh	meta-GGA hybrid	10%	Popular for transition-metal complexes.
B97-D	GGA	0%	Designed to be paired with a D3 dispersion correction.

Dispersion corrections

Correction	Model	Notes
D4	Charge-dependent (EEQ)	Latest-generation Grimme dispersion.
D3(BJ)	Becke–Johnson damping	Native implementation — analytic energy and gradient.
D2	Pairwise C6	Legacy fallback.

Composite / low-cost methods

Method	Recipe	Notes
HF-3c	HF/MINIX + corrections	Fast geometries and interaction energies.
HF/6-31G*	Small-basis HF	Quick structures.
B3LYP/6-31G*	Small-basis hybrid	Screening-quality energetics.

Correlation & post-Hartree-Fock

Møller-Plesset through coupled cluster — canonical and local correlation.

From perturbation theory to the CCSD(T) "gold standard". For medium-to-large molecules the DLPNO local-correlation path recovers the same accuracy at a fraction of the cost, and is validated against the canonical result on every release.

Method	Family	Scaling	Notes
MP2	2nd-order perturbation	O(N⁵)	Matches an established reference code on internal tests; analytic AO path.
SCS-MP2	Spin-component-scaled	O(N⁵)	1.2·OS + 0.333·SS — improved thermochemistry.
SOS-MP2	Scaled opposite-spin	O(N⁴)*	1.3·OS; opposite-spin only.
MP3	3rd-order perturbation	O(N⁶)	RHF reference + AO integrals; small molecules.
RI-MP2	Density-fitted MP2	O(N⁵)	Resolution-of-identity acceleration for larger systems.
DLPNO-MP2	Local MP2	reduced	Pair natural orbitals; drug-sized molecules.
CCSD(T) canonical	Coupled cluster	O(N⁷)	exact reference Dumped-integral path, practical to ~20–30 atoms.
DLPNO-CCSD(T0)	Local coupled cluster	reduced	gold standardlocal ≥ 99.9% of the correlation energy at the Normal setting; frozen core by default. Auto-switches to a memory-compact mode on large molecules (a badge signals it during the run).

* Opposite-spin-only scaling; the MP2/MP3 AO paths target small molecules. DLPNO kernels are generated by the internal tensor compiler and validated against an established reference code to tight tolerances (CCSD 2e-9, (T) 2e-10).

Frontier & multireference

Static correlation, quasiparticles and open-shell coupled cluster.

A specialist suite for problems the single-reference methods above cannot describe — bond breaking, strong correlation, charged/neutral excitations. Run and interpreted by a domain expert; ask us if your case needs one of these.

Method	Describes	Notes
CASSCF	Static correlation	specialist Complete active space; bond dissociation, diradicals, near-degeneracies.
NEVPT2	Dynamic on top of CAS	specialist Second-order perturbation on a CASSCF reference.
GW-BSE	Quasiparticle + optical	specialist Many-body ionization energies and neutral excitations.
UCCSD(T)	Open-shell coupled cluster	specialist Gold standard for radicals.
SOC-CIS	Spin-orbit coupling	specialist Intersystem crossing and phosphorescence rates.

Excited states & spectroscopy

Linear-response excited states with analytic gradients, plus simulated spectra.

CIS, TDA and full TD-DFT (Casida) all carry analytic excited-state gradients — you can optimize and vibrate an excited state, not just read off vertical energies. Validated against a reference implementation to ~1e-8.

Excited-state methods

Method	Theory	Capability	Notes
CIS	Configuration interaction singles (HF)	gradient	Excited-state geometry and frequencies.
TDA-DFT	Tamm–Dancoff approximation	gradient	Robust, well-behaved excitation energies.
TD-DFT	Full Casida linear response	gradient	Standard for UV-Vis; B3LYP / PBE / LDA / TDHF.

Analysis & simulated spectra

Output	Notes
UV-Vis spectrum	Broadened absorption curve (selectable line shape) with peak assignment.
NTO analysis	Natural transition orbitals — a compact hole/particle picture of each state.
Singlet–triplet SOC	Spin-orbit couplings for phosphorescence and intersystem crossing.
Solvated excited states	C-PCM implicit solvent applied to the excited-state calculation.
IR / Raman	Vibrational spectra from harmonic frequencies with intensities.
GIAO NMR	Gauge-including atomic-orbital shieldings and simulated 1D spectra.
Photoelectron (PES)	Simulated He I / He II photoelectron spectrum from orbital energies.

Basis sets 30+ sets

Minimal to quadruple-zeta, diffuse-augmented, and relativistic all-electron.

Grouped by family. "Diffuse" functions matter for anions, pKa and electron affinities; f/g polarization matters for correlated methods and complete-basis-set extrapolation. Element ranges are the validated support ranges.

Minimal

Basis	Character	Elements	Notes
STO-2G	Minimal	H–Ar	Smallest; qualitative only.
STO-3G	Minimal	H–Ar	The classic minimal basis (default).
STO-6G	Minimal	H–Ar	Six-primitive contraction.

Pople — split & triple valence

Basis	Character	Diffuse	Elements
3-21G	Split valence	—	H–Ar
4-31G	Split valence	—	H–Ar
6-31G	Split valence	—	H–Ar
6-31G(d)	+ d polarization	—	H–Ar
6-31G(d,p)	+ d,p polarization	—	H–Ar
6-31+G	Split valence	heavy atoms	H–Ar
6-31++G	Split valence	all atoms	H–Ar
6-31+G(d)	+ d polarization	heavy atoms	H–Ar
6-31+G(d,p)	+ d,p polarization	heavy atoms	H–Ar
6-31++G(d,p)	+ d,p polarization	all atoms	H–Ar
6-311G	Triple valence	—	H–Ar
6-311G(d,p)	+ d,p polarization	—	H–Ar
6-311+G(d,p)	+ d,p polarization	heavy atoms	H–Ar
6-311+G(2d,p)	+ 2d,p polarization	heavy atoms	H–Ar
6-311++G(d,p)	+ d,p polarization	all atoms	H, Li–Ar
6-311++G(2d,2p)	+ 2d,2p polarization	all atoms	H, Li–Ar
6-311G(2df,2pd)	+ f functions	—	H–Ne, K, Ca
6-311++G(3df,3pd)	+ 3df,3pd (max Pople)	all atoms	H, Li–Ar

Dunning — correlation-consistent

Basis	Character	Diffuse	Elements
cc-pVDZ	Double-zeta	—	H–Ar
cc-pVTZ	Triple-zeta	—	H–Ar
cc-pVQZ	Quadruple-zeta (with g)	—	H–Ar
aug-cc-pVDZ	Double-zeta	full augmentation	H–Ar
aug-cc-pVTZ	Triple-zeta	full augmentation	H–Ar

Karlsruhe — def2

Basis	Character	Diffuse	Elements
def2-SVP	Split valence + polarization	—	H–Rn*
def2-SVPD	SVP + diffuse	yes	H–Ar
ma-def2-SVP	SVP minimally augmented	light	H–Ar
def2-TZVP	Triple-zeta + polarization	—	H–Rn*
def2-TZVPD	TZVP + diffuse	yes	H–Ar
ma-def2-TZVP	TZVP minimally augmented	light	H–Ar
def2-TZVPP	Triple-zeta + double polarization	—	H–Kr
def2-QZVP	Quadruple-zeta + polarization (with g)	—	H–Kr

Relativistic — all-electron (X2C)

Basis	Character	Capability	Elements
x2c-SVPall	Split valence, all-electron	X2C	H–Rn
x2c-TZVPall	Triple-zeta, all-electron	X2C	H–Rn

* def2 sets pair automatically with the def2 effective core potential (def2-ECP) for heavy elements — see the relativistic section below. The x2c-*all sets describe heavy cores explicitly and switch on scalar X2C automatically; don't combine them with an ECP.

Relativistic treatment

Two independent routes for heavy elements.

Approach	Kind	Notes
sf-X2C-1e	All-electron scalar relativistic	X2C Exact-two-component, one-electron. Activated automatically by the x2c-*all basis sets. Cross-checked against a reference implementation to ~1e-9 (Au⁺).
def2-ECP	Effective core potential	Scalar-relativistic pseudopotential for heavy elements, paired with def2 valence bases. Basis-aware selection.

Implicit solvation

C-PCM continuum solvent for ground and excited states.

The conductor-like polarizable continuum model (C-PCM) is available for SCF, DFT and excited-state calculations. Preset solvents below, or supply a custom dielectric constant ε.

Solvent	ε	Solvent	ε
Water	78.39	DMSO	46.83
Methanol	32.61	Acetone	20.49
Ethanol	24.85	Chloroform	4.71
Toluene	2.37	Benzene	2.27
Custom ε	any	—	—

Geometry, thermochemistry & properties

What you do with a gradient: optimize, vibrate, and derive.

Task	Notes
Geometry optimization	Analytic gradients; Cartesian or redundant internal coordinates; linear or geodesic interpolation.
Transition-state search	Saddle-point optimization for reaction barriers.
IRC	Intrinsic reaction coordinate to connect a TS to its minima.
Harmonic frequencies	Analytic or numerical Hessian; IR intensities; imaginary-mode checks.
RRHO thermochemistry	ZPE, enthalpy, entropy and Gibbs free energy (ΔG, ΔH, ΔS).
Reaction thermochemistry	ΔG / ΔH / ΔS, equilibrium constant K, Eyring rate from a barrier.
Conformer ensembles	Generation plus Boltzmann-weighted properties.
Coordinate scans	Relaxed or rigid scans along a bond, angle or dihedral.
Polarizability	Static dipole polarizability via CPHF.
Absolute pKa	Thermodynamic-cycle estimate (anchored to a reference acid — reported as a trend/ranking).

Real-space & population analysis

Turn the wavefunction into bonding insight and figures.

Analysis	Notes
QTAIM topology	Bond, ring and cage critical points; the atoms-in-molecules picture of bonding.
NCI / IGM	Non-covalent interaction and independent-gradient-model surfaces you can show.
Atomic charges	Mulliken, Löwdin, NPA, MBIS, DMA and ESP-fitted charges.
Fukui functions	Electrophilic / nucleophilic / radical reactive-site maps.
ESP surfaces	Electrostatic potential mapped onto the molecular surface.
Frontier orbitals	HOMO / LUMO energies and the electrophilicity index ω.
Cube export	Electron density ρ, molecular orbitals and ESP on a grid for external viewers.

Workflows & automation

From a SMILES string to a full portrait — by command, GUI, API or sentence.

Capability	Notes
Build from SMILES	Sensible 3D structure generation (RDKit) — or load your own geometry.
Batch screening campaigns	Run a property across a series of molecules in one job.
Natural-language assistant	Drive calculations conversationally from a built-in chatbot.
MCP / HTTP API	Wire Hilbeon into your own agents, notebooks and scripts.
Interactive 3D GUI	Rotate molecules, paint orbitals and densities, explore results in a viewer.
Reproducibility	A fully owned two-electron integral engine — bit-identical across machines, validated to ~1e-10 Hartree against reference codes.

Honesty first. Every method above is shipped and runs on our own engine, but they don't all carry the same weight. Methods tagged analytic gradient drive optimization, frequencies and spectra; energy-only functionals are single points for benchmarking. Canonical CCSD(T) uses a dumped-integral path practical for small molecules — for larger systems the DLPNO local-correlation path takes over, verified against the canonical result on every release. Absolute pKa carries a known offset anchored to a reference acid, and the frontier / specialist suite is best run with expert guidance. When in doubt, ask us which method fits your question.

Not sure which method fits your molecule?

Tell us the question. A PhD computational chemist will pick the method and basis, run it on our engine, and hand you a clear answer — or set you up to run it yourself.

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