Methods: theory and status¶
This page is the map of everything vibe-qc can compute. Each method family gets a short account of the physics it rests on, the working equations that the code solves, the keyword that selects it, and the status label the project gives it. The feature matrix has the exhaustive option tables; the tutorials derive each method at length and run it; the user guide documents options, defaults and limits. Use this page to decide which method, then follow the links to learn how.
How to read the status labels¶
vibe-qc labels every route with one of four words. The label is not a judgement of the underlying theory; it says how far this implementation has been validated and whether the release gate protects it.
Label |
What it means |
How you can tell at runtime |
|---|---|---|
production |
Validated within its documented scope against an external reference (PySCF, ORCA, CRYSTAL, CP2K or a published number), covered by the T1 release gate, and stable across patch releases. |
No warning. The |
preview |
Reachable and maintained, but with a narrower validation envelope than production: a route that ships for one reference type, one dimensionality or one regime, with the rest fail-closed. |
The |
experimental |
Research output. It runs and it is cited, but its numbers are not validated for publication, it is not release-gated, and it may change without a deprecation cycle. |
Emits |
gated |
Fails closed. The spelling is recognised, but the route refuses with a scientific message naming the missing term rather than returning a number it cannot stand behind. |
|
Experimental lines never pretend to be production
The ab initio cyclic cluster model (AICCM, both the Gamma-CCM and the chi-CCM constructions), the semiempirical cyclic cluster model (SECCM), GAPW augmentation, periodic RIJCOSX, GFN2-xTB, PM6, the OMx family, SKALA, COSMO-RS, Green’s-function surface embedding and the MPI grid overlay are experimental today. Every one of them warns at runtime. Treat their results as research output. The roadmap is the authoritative list; the sections below repeat the label beside each method.
Silencing a warning is deliberate and per class, for example
warnings.filterwarnings("ignore", category=vibeqc.AICCM2026DevAExperimentalWarning),
so an experimental route never runs silently by accident.
The problem every method solves¶
Under the Born-Oppenheimer approximation the nuclei are clamped and the electrons obey the electronic Schroedinger equation with the Hamiltonian
in atomic units. Every method below is a different way of approximating the lowest eigenvalue \(E_0\) of this operator, or an excited eigenvalue, or a derivative of one of them with respect to the nuclear positions or an external field. The tutorial introduction develops this starting point at greater length. vibe-qc expands the one-electron orbitals in Gaussian basis functions, so the first decision after the molecule is the basis set; the second is the level of theory, which is what this page organises.
Mean-field methods¶
Hartree-Fock: RHF, UHF, ROHF¶
Theory. The wavefunction is a single Slater determinant of orthonormal spin orbitals. Minimising the energy over the orbitals gives the Fock equations \(\hat f \phi_p = \varepsilon_p \phi_p\), where the Fock operator contains the kinetic and nuclear-attraction terms plus the Coulomb (\(\hat J\)) and exchange (\(\hat K\)) operators built from the occupied orbitals. In a Gaussian basis they become the Roothaan-Hall generalised eigenproblem
solved self-consistently because \(\mathbf F\) depends on the density \(\mathbf P\) it produces. Each electron feels the others only through their average field, so HF misses the correlation energy, typically about one percent of the total energy but most of a bond energy.
RHF doubly occupies spatial orbitals; closed shells only.
UHF gives alpha and beta electrons separate orbitals; it describes radicals and bond breaking but its determinant is not a spin eigenfunction (spin contamination, reported as \(\langle \hat S^2\rangle\) in the output).
ROHF keeps one spatial orbital set with integer 2/1/0 occupations and couples the shells through the Roothaan or Guest-Saunders coupling (Roothaan, Clemens C. J. (1960). *Self-Consistent Field Theory for Open Shells of Electronic Systems.* Reviews of Modern Physics, **32**(2), 179–185. doi:[10.1103/RevModPhys.32.179](https://doi.org/10.1103/RevModPhys.32.179), Guest, M. F. and Saunders, V. R. (1974). *On methods for converging open-shell Hartree-Fock wave-functions.* Molecular Physics, **28**(3), 819–828. doi:[10.1080/00268977400102171](https://doi.org/10.1080/00268977400102171)), so the state is spin-pure.
Select it. run_job(mol, basis="...", method="rhf" | "uhf" | "rohf"),
or the drivers run_rhf, run_uhf, run_rohf. Open-shell multiplicity comes
from Molecule(..., multiplicity=).
Status. Production. Energies agree with PySCF to machine precision;
analytic gradients on all three, analytic Hessians on RHF and UHF, and
finite-difference Hessians everywhere. Read the
molecular HF tutorial, the
open-shell tutorial, the
ROHF guide and
examples/molecular/input-h2o-rhf.py.
Kohn-Sham density-functional theory: RKS, UKS, ROKS¶
Theory. Hohenberg and Kohn showed that the ground-state energy is a functional of the electron density alone. Kohn and Sham made it practical by introducing a fictitious non-interacting system with the same density, whose orbitals satisfy
Everything unknown is in the exchange-correlation functional \(E_{xc}[\rho]\), whose functional derivative is \(v_{xc}\). The approximations form Jacob’s ladder: the LDA uses the uniform-electron-gas energy at the local density; GGAs add the density gradient (PBE, BLYP); meta-GGAs add the kinetic energy density \(\tau\) (TPSS, SCAN, r²SCAN, M06-L); hybrids mix in a fraction of exact HF exchange (B3LYP, PBE0, PW1PW); range-separated hybrids split the Coulomb operator with an error function and use exact exchange at long range (ωB97X, ωB97X-D) or short range (HSE06); VV10-paired functionals add a nonlocal correlation kernel for dispersion (ωB97X-V, ωB97M-V); and double hybrids add a scaled MP2-like correlation term on the KS orbitals (B2PLYP, DSD-PBEP86, revDSD-PBEP86-D4). The XC integrals are evaluated on an atom-centred Becke grid.
Select it. run_job(mol, basis, method="rks" | "uks" | "roks", functional="pbe0").
More than 500 libxc functionals resolve by name; custom weighted sums such as
"0.2*HF + 0.8*GGA_X_PW91, GGA_C_PW91" and runtime-defined functionals are
accepted. Note the B3LYP convention: bare b3lyp is the VWN5 flavour that
ORCA, TURBOMOLE and CRYSTAL mean; b3lyp/g is the Gaussian flavour.
Status. Production for LDA, GGA, meta-GGA and global hybrids,
including analytic gradients. Range-separated hybrids and VV10 have
production energies, but their analytic gradient omits the long-range
exchange and nonlocal-correlation terms, so geometry optimisations on them
fall back to full-energy finite differences and say so in the .out
(GitLab #571). ROKS is spin-pure and gradient-by-finite-differences. Read the
molecular DFT tutorial, the
functionals guide, the
functional comparison,
range-separated hybrids,
VV10 and modern functionals and
examples/molecular/input-h2o-rks-pbe-d3-opt.py.
SKALA-1.1 neural exchange-correlation functional¶
Theory. SKALA replaces the analytic \(E_{xc}\) form with a neural network trained on high-level reference energies. It consumes the same grid quantities as a meta-GGA plus nonlocal features of the whole density, and vibe-qc calls it through an external full-grid provider rather than libxc.
Select it. run_job(..., method="rks", functional="skala-1.1") with the
[skala] extra installed (PyTorch; the MIT-licensed checkpoint is fetched on
first use).
Status. Experimental. Energies only at a fixed geometry; forces, Hessians, TDDFT and response fail closed. See SKALA and the worked tutorial.
Dispersion corrections: D3(BJ), D4, gCP and the 3c composites¶
Theory. Semilocal functionals miss London dispersion because it arises from correlated fluctuations between non-overlapping densities. Grimme’s schemes add an atom-pairwise term
with Becke-Johnson damping in D3(BJ) (Grimme, Stefan, Ehrlich, Stephan, and Goerigk, Lars (2011). *Effect of the damping function in dispersion corrected density functional theory.* Journal of Computational Chemistry, **32**(7), 1456–1465. doi:[10.1002/jcc.21759](https://doi.org/10.1002/jcc.21759)) and charge-dependent, geometry-dependent \(C_6\) coefficients in D4 (Caldeweyher, Eike, Ehlert, Sebastian, et al. (2019). *A generally applicable atomic-charge dependent London dispersion correction.* Journal of Chemical Physics, **150**(15), 154122. doi:[10.1063/1.5090222](https://doi.org/10.1063/1.5090222)). The geometric counterpoise (gCP) correction removes basis-set superposition error in small bases, and the 3c composite methods (HF-3c, PBEh-3c, B97-3c, B3LYP-3c, r²SCAN-3c, ωB97X-3c, HSE-3c) bundle a tuned small basis with D3 or D4, gCP and a short-range basis correction behind one keyword.
Select it. run_job(..., dispersion="d3bj" | "d4"); composites through
method="hf-3c" | "pbeh-3c" | "b97-3c" | "b3lyp-3c" | "r2scan-3c" | "wb97x-3c" | "hse-3c";
compute_d3bj, compute_d4 and vibeqc.gcp directly.
Status. Production for D3(BJ) and for D4 through the dftd4 package.
The native D4 backend is parity-validated for H, He and B to Ne only and
refuses other elements. Periodic runs support D3(BJ) only. The composites are production for
molecules; their periodic flavours need recalibration before being trusted.
Read the dispersion tutorial and the
composites guide.
DFT+U¶
Theory. Semilocal functionals over-delocalise localised d and f electrons because of self-interaction error. DFT+U adds a Hubbard penalty on the occupation matrix \(n^{I\sigma}\) of a chosen atomic shell in the rotationally invariant form of Dudarev (Dudarev, S. L., Botton, G. A., et al. (1998). *Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study.* Physical Review B, **57**(3), 1505–1509. doi:[10.1103/PhysRevB.57.1505](https://doi.org/10.1103/PhysRevB.57.1505)),
which pushes occupations toward integers and opens gaps in Mott insulators.
Select it. dft_plus_u=[vibeqc.HubbardSite(atom_index=0, l=2, U_ev=4.0)]
on run_periodic_job(..., jk_method="gpw") or the molecular drivers.
Status. Production on the GPW route for Gamma RHF/RKS/UHF/UKS and multi-k RKS. See DFT+U and its tutorial.
Density fitting: RI-J, RIJK and RIJCOSX¶
Theory. The four-index electron-repulsion integrals \((\mu\nu|\lambda\sigma)\) are the cost of every Fock build. The resolution of the identity expands each orbital product in an auxiliary basis \(\{P\}\), \((\mu\nu|\lambda\sigma) \approx \sum_{PQ}(\mu\nu|P)(P|Q)^{-1}(Q|\lambda\sigma)\), which turns the Coulomb build into three-index work (Eichkorn, Karin, Treutler, Oliver, et al. (1995). *Auxiliary basis sets to approximate Coulomb potentials.* Chemical Physics Letters, **240**(4), 283–290. doi:[10.1016/0009-2614(95)00621-A](https://doi.org/10.1016/0009-2614(95)00621-A)). RIJK fits exchange the same way; RIJCOSX keeps RI for Coulomb and evaluates exchange seminumerically on a grid with the chain-of-spheres algorithm (Neese, Frank, Wennmohs, Frank, et al. (2009). *Efficient, approximate and parallel Hartree-Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree-Fock exchange.* Chemical Physics, **356**(1–3), 98–109. doi:[10.1016/j.chemphys.2008.10.036](https://doi.org/10.1016/j.chemphys.2008.10.036)), which scales better for large molecules.
Select it. run_job(..., density_fit=True, aux_basis="def2-universal-jkfit"),
plus cosx=True for RIJCOSX. The JKBuilder abstraction dispatches to
FourIndexJKBuilder, DFJKBuilder or COSXJKBuilder.
Status. Production. RIJCOSX energies sit within 0.26 mHa of ORCA 6.1.1 on glycine/def2-TZVP; the RIJCOSX gradient matches finite differences of its own energy up to the neglected grid-motion band. Read density fitting and the RIJCOSX glycine tutorial.
A second integral engine. Independently of these routes, run_job and
run_periodic_job can select the experimental MANTA engine and choose the
Coulomb build (exact, RI, BUPO multipole far field, RI-BUPO) and the
exchange build (exact, RI) separately, with an explicit resource budget and
an executed-provider record in every artifact. Its exact build reproduces
libint to 1e-10 Ha on water; it is slower and refuses most workflows beyond
the SCF and its static properties. See
integral engines.
Effective core potentials¶
Theory. Core electrons of heavy atoms are chemically inert but expensive and, past the fourth row, relativistic. An ECP replaces them with a semilocal operator \(\hat U_\text{ECP} = U_L(r) + \sum_{l<L}\sum_m |lm\rangle [U_l(r)-U_L(r)]\langle lm|\) fitted to all-electron relativistic atomic calculations, so only valence electrons are treated explicitly and scalar relativistic effects enter implicitly. Integrals come from libecpint.
Select it. A bundled basis with an .ecp sidecar (def2, cc-pVnZ-PP,
LANL2DZ, pob-TZVP-rev2 for lanthanides) attaches its ECP automatically;
explicit ecp_centers and ecp_library="ecp28mdf" pick a Stuttgart-Koeln
potential.
Status. Production for SCF energies and ECP-aware analytic gradients on RHF, UHF, RKS and UKS. MP2, CC, DLPNO and the double hybrids consume an ECP reference and OVGF runs on one (without a dedicated validation); CASCI/CASSCF, NEVPT2 and CASPT2 still refuse one. Analytic ECP Hessians and CPCM-with-ECP forces fail closed. See ECPs and the Pt cluster tutorial.
Implicit solvation: CPCM, COSMO and COSMO-RS¶
Theory. A continuum of dielectric constant \(\varepsilon\) surrounds a molecular cavity built from atom-centred spheres. The conductor-like models solve for apparent surface charges \(q\) on the cavity such that the potential vanishes on a perfect conductor, then scale by \(f(\varepsilon) = (\varepsilon-1)/(\varepsilon+x)\) with \(x=0\) (CPCM) or \(x = 1/2\) (COSMO). The charges enter the Fock matrix as an extra one-electron potential and the SCF is macro-iterated to self-consistency between charges and density. COSMO-RS goes further and turns the surface charge density (“sigma profile”) into a statistical-thermodynamic model of the liquid, giving chemical potentials, activity coefficients and solvation free energies.
Select it. run_job(..., solvent="water") or a custom SolventModel;
vibeqc.solvation.cosmors on a ConductorSurface.
Status. CPCM/COSMO energies and analytic gradients are production for RHF, UHF, RKS and UKS; MSINDO has its own COSMO driver. COSMO-RS is experimental (the shipped cavity differs from the one the published constants were fitted on). Solvent with correlated, CAS, semiempirical (except MSINDO) or MLIP methods is gated. Read solvation and the water tutorial.
Getting the SCF to converge¶
Theory. The Roothaan-Hall fixed point is reached by iteration, and plain iteration oscillates or diverges whenever the HOMO-LUMO gap is small. DIIS (Pulay, Péter (1980). *Convergence acceleration of iterative sequences. The case of SCF iteration.* Chemical Physics Letters, **73**(2), 393–398. doi:[10.1016/0009-2614(80)80396-4](https://doi.org/10.1016/0009-2614(80)80396-4)) extrapolates the next Fock matrix from a history of previous ones by minimising the commutator error \(\mathbf e = \mathbf F\mathbf P\mathbf S - \mathbf S\mathbf P\mathbf F\); EDIIS and ADIIS (Kudin, Konstantin N., Scuseria, Gustavo E., and Cancès, Eric (2002). *A black-box self-consistent field convergence algorithm: One step closer.* Journal of Chemical Physics, **116**(19), 8255–8261. doi:[10.1063/1.1470195](https://doi.org/10.1063/1.1470195), Hu, Xiangqian and Yang, Weitao (2010). *Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function.* Journal of Chemical Physics, **132**(5), 054109. doi:[10.1063/1.3304922](https://doi.org/10.1063/1.3304922)) minimise an energy model instead and are robust far from convergence, so the default is an EDIIS-then-DIIS hybrid. Damping and level shifting (Saunders, V. R. and Hillier, I. H. (1973). *A “Level-Shifting” method for converging closed shell Hartree-Fock wave functions.* International Journal of Quantum Chemistry, **7**(4), 699–705. doi:[10.1002/qua.560070407](https://doi.org/10.1002/qua.560070407)) slow the density update or push virtual orbitals up; second-order methods (SOSCF, Newton, trust-region augmented Hessian, and the external OpenTrustRegion optimiser) use the orbital Hessian near convergence; stability analysis (Seeger, Rolf and Pople, John A. (1977). *Self-consistent molecular orbital methods. XVIII. Constraints and stability in Hartree-Fock theory.* Journal of Chemical Physics, **66**(7), 3045–3050. doi:[10.1063/1.434318](https://doi.org/10.1063/1.434318)) checks that the converged determinant is a minimum, not a saddle. The initial guess (SAD, PATOM, SAP, core Hamiltonian, or a READ restart) decides which stationary state the iteration lands on.
Select it. The *_options objects (RHFOptions, RKSOptions, …) carry
scf_accelerator, damping, level_shift, soscf_threshold, newton_threshold,
initial_guess and friends; the keyword index
lists defaults.
Status. Production for the whole DIIS family, damping, level shifts
and the second-order finalisers on molecules; periodic coverage is route by
route as SCF convergence documents.
run_job(solver=...) accepts dense, davidson and lobpcg; the
Jacobi-Davidson and GPLHR eigensolvers, reachable through
vibeqc.solvers.eigensolver.solve_eigenproblem(solver="jd" | "gplhr"), are
experimental.
Read the EDIIS/DIIS tutorial,
second-order SCF,
OpenTrustRegion and the
initial guess walkthrough.
Single-reference correlation¶
Everything in this section starts from a converged Hartree-Fock (or, for the double hybrids, Kohn-Sham) determinant and recovers the correlation energy \(E_\text{corr} = E_\text{exact} - E_\text{HF}\) that the mean field leaves out. The methods form a hierarchy of cost and accuracy; the correlated-energies learning path walks it in order.
Moller-Plesset perturbation theory: MP2, RI-MP2, SCS/SOS-MP2, UMP2¶
Theory. Treat the difference between the true electron repulsion and the HF mean field as a perturbation (Møller, Christian and Plesset, Milton S. (1934). *Note on an Approximation Treatment for Many-Electron Systems.* Physical Review, **46**(7), 618–622. doi:[10.1103/PhysRev.46.618](https://doi.org/10.1103/PhysRev.46.618)). First order returns the HF energy; second order gives
which scales as \(O(N^5)\) and captures most of the dispersion and pair correlation HF misses. RI-MP2 fits the \((ia|jb)\) integrals in an auxiliary basis (Feyereisen, Martin, Fitzgerald, George, and Komornicki, Andrew (1993). *Use of approximate integrals in ab initio theory. An application in MP2 energy calculations.* Chemical Physics Letters, **208**(5), 359–363. doi:[10.1016/0009-2614(93)87156-W](https://doi.org/10.1016/0009-2614(93)87156-W)) with negligible error; SCS- and SOS-MP2 rescale the same-spin and opposite-spin pair energies (Grimme, Stefan (2003). *Improved second-order Møller-Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies.* Journal of Chemical Physics, **118**(20), 9095–9102. doi:[10.1063/1.1569242](https://doi.org/10.1063/1.1569242), Jung, Yousung, Lochan, Rohini C., et al. (2004). *Scaled opposite-spin second order Møller-Plesset correlation energy: An economical electronic structure method.* Journal of Chemical Physics, **121**(20), 9793–9802. doi:[10.1063/1.1809602](https://doi.org/10.1063/1.1809602)); UMP2 and ROHF-MP2 extend the formula to open shells.
Select it. run_job(..., method="mp2" | "scs-mp2" | "sos-mp2"); add
density_fit=True for RI-MP2. An open-shell molecule dispatches to UMP2 on
the UHF reference, and run_rohf_mp2 gives the semicanonical ROHF-MP2
energy. The drivers run_mp2 and run_ump2 take a converged SCF result. A
frozen core follows the ORCA convention by default.
Status. Production. Validated to 1e-9 Ha against PySCF. The dense
routes are accuracy references at small-molecule size rather than
production-size solvers; the memory envelope is documented in the
MP2 guide. Read the
RI-MP2 auxiliary-basis tutorial,
natural orbitals and
examples/molecular/input-h2o-scs-mp2.py.
Double-hybrid functionals: B2PLYP, DSD-PBEP86, revDSD-PBEP86-D4¶
Theory. A double hybrid (Grimme, Stefan (2006). *Semiempirical hybrid density functional with perturbative second-order correlation.* Journal of Chemical Physics, **124**(3), 034108. doi:[10.1063/1.2148954](https://doi.org/10.1063/1.2148954)) runs a hybrid Kohn-Sham SCF with a large exact-exchange fraction, then adds a scaled MP2 correlation term computed on the KS orbitals, \(E = E_\text{KS}^\text{hybrid} + c_2 E^{(2)}_\text{KS}\). The DSD variants scale same- and opposite-spin contributions separately and pair the result with D3 or D4 dispersion.
Select it. run_job(..., method="b2plyp" | "dsd-pbep86" | "revdsd-pbep86" | "pwpb95").
A double hybrid names a complete method, so it is a method=, not a
functional=; the spelling method="rks", functional="b2plyp" is refused
because it would run only the SCF half.
Status. Production, validated to 1e-7 Ha against PySCF. Read the B2PLYP tutorial.
Coupled cluster: CCSD, CCSD(T) and the open-shell variants¶
Theory. Coupled-cluster theory (Čížek, Jiří (1966). *On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods.* Journal of Chemical Physics, **45**(11), 4256–4266. doi:[10.1063/1.1727484](https://doi.org/10.1063/1.1727484)) writes the wavefunction as an exponential of excitation operators acting on the reference, \(|\Psi\rangle = e^{\hat T}|\Phi_0\rangle\) with \(\hat T = \hat T_1 + \hat T_2 + \dots\). Truncating at doubles gives CCSD (Purvis, George D. III and Bartlett, Rodney J. (1982). *A full coupled-cluster singles and doubles model: The inclusion of disconnected triples.* Journal of Chemical Physics, **76**(4), 1910–1918. doi:[10.1063/1.443164](https://doi.org/10.1063/1.443164)), whose amplitude equations are solved iteratively at \(O(N^6)\); the exponential form makes the energy size extensive, unlike truncated CI. CCSD(T) adds the connected triples by non-iterative perturbation theory (Raghavachari, Krishnan, Trucks, Gary W., et al. (1989). *A fifth-order perturbation comparison of electron correlation theories.* Chemical Physics Letters, **157**(6), 479–483. doi:[10.1016/S0009-2614(89)87395-6](https://doi.org/10.1016/S0009-2614(89)87395-6)) at \(O(N^7)\) and is the accepted “gold standard” for single-reference molecules. A-CCSD(T) uses the Lambda-based asymmetric triples correction, and frozen natural orbitals (FNO) truncate the virtual space with MP2 natural orbitals to make the triples cheaper. Open-shell references run through UCCSD(T) on UHF orbitals and a spin-orbital kernel on ROHF orbitals.
Select it. run_job(..., method="ccsd" | "ccsd(t)"), or run_ccsd with
CCSDOptions (density fitting on by default; density_fit=False for the
conventional cross-code route; triples="A-CCSD(T)"; FNO thresholds).
Status. Production as a dense small-molecule accuracy reference, validated to microhartree against PySCF and cross-checked against ORCA 6.1. The dense CC iteration and the FNO setup remain production-size memory gates. Read the CCSD(T) tutorial and the coupled-cluster guide.
The wider coupled-cluster and coupled-pair family: CC2, CC3, CCSDT, QCISD(T), CEPA(n)¶
Theory. CC2 (Christiansen, Ove, Koch, Henrik, and Jørgensen, Poul (1995). *The second-order approximate coupled cluster singles and doubles model CC2.* Chemical Physics Letters, **243**(5–6), 409–418. doi:[10.1016/0009-2614(95)00841-Q](https://doi.org/10.1016/0009-2614(95)00841-Q)) keeps the singles equations exact and approximates the doubles to first order, an \(O(N^5)\) model mainly used for excitation energies and as a step between MP2 and CCSD. CC3 (Koch, Henrik, Christiansen, Ove, et al. (1997). *The CC3 model: An iterative coupled cluster approach including connected triples.* Journal of Chemical Physics, **106**(5), 1808–1818. doi:[10.1063/1.473322](https://doi.org/10.1063/1.473322)) treats triples iteratively but approximately, and full CCSDT (Noga, Jozef and Bartlett, Rodney J. (1987). *The full CCSDT model for molecular electronic structure.* Journal of Chemical Physics, **86**(12), 7041–7050. doi:[10.1063/1.452353](https://doi.org/10.1063/1.452353)) solves the triples exactly at \(O(N^8)\). QCISD and QCISD(T) (Pople, John A., Head-Gordon, Martin, and Raghavachari, Krishnan (1987). *Quadratic configuration interaction. A general technique for determining electron correlation energies.* Journal of Chemical Physics, **87**(10), 5968–5975. doi:[10.1063/1.453520](https://doi.org/10.1063/1.453520)) are size-consistent quadratic CI approximations to CCSD; CCD, LCCD, LCCSD and the CEPA(n) family (Meyer, Wilfried (1973). *PNO-CI Studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application to the ground state and ionized states of methane.* Journal of Chemical Physics, **58**(3), 1017–1035. doi:[10.1063/1.1679283](https://doi.org/10.1063/1.1679283)) drop or linearise terms of the CCSD equations, with CEPA adding pair-specific shifts that approximate the exclusion-principle-violating corrections.
Select it. run_job(..., method="cc2" | "cc3" | "ccsdt" | "qcisd" | "qcisd(t)" | "ccd" | "lccd" | "lccsd" | "cepa(0)" ... "cepa(3)" | "bccd" | "bccd(t)");
the last two are Brueckner coupled cluster (Handy, Nicholas C., Pople, John A., et al. (1989). *Size-consistent Brueckner theory limited to double substitutions.* Chemical Physics Letters, **164**(2–3), 185–192. doi:[10.1016/0009-2614(89)85013-4](https://doi.org/10.1016/0009-2614(89)85013-4)),
which rotates the orbitals until the singles amplitudes vanish. The same
variants are reachable through method="ci", citype=....
Status. Production at benchmark scale, closed-shell energies only. CC2 and QCISD(T) are pinned against ORCA; CEPA(n) to sub-microhartree against ORCA RI-CEPA. CC3 and CCSDT use a dense determinant-space representation that grows combinatorially, so they are references for small molecules, not production solvers. All are documented in the coupled-cluster guide.
Local correlation: DLPNO-MP2, DLPNO-CCSD(T), DLPNO-(T1) and the open-shell solvers¶
Theory. Canonical correlation methods scale steeply because canonical orbitals are delocalised. The domain-based local pair natural orbital scheme (Riplinger, Christoph and Neese, Frank (2013). *An efficient and near linear scaling pair natural orbital based local coupled cluster method.* Journal of Chemical Physics, **138**(3), 034106. doi:[10.1063/1.4773581](https://doi.org/10.1063/1.4773581), Pinski, Peter, Riplinger, Christoph, et al. (2015). *Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.* Journal of Chemical Physics, **143**(3), 034108. doi:[10.1063/1.4926879](https://doi.org/10.1063/1.4926879)) localises the occupied orbitals (Foster-Boys), assigns each occupied pair a domain of projected atomic orbitals, and compresses each pair’s virtual space into pair natural orbitals, the eigenvectors of the pair’s approximate MP2 density that carry occupation above a threshold (\(T_\text{CutPNO}\)). Pairs whose estimated correlation energy falls below \(T_\text{CutPairs}\) are treated at a cheaper level. The result is near-linear scaling with a controllable truncation error; at zero thresholds the equations reduce exactly to the canonical ones, which is the test the implementation pins. The (T1) correction restores the off-diagonal Fock coupling in the triples (Guo, Yang, Riplinger, Christoph, et al. (2018). *Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)].* Journal of Chemical Physics, **148**(1), 011101. doi:[10.1063/1.5011798](https://doi.org/10.1063/1.5011798)), and the open-shell solvers keep independent alpha and beta PNO spaces (Saitow, Masaaki, Becker, Ute, et al. (2017). *A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory.* Journal of Chemical Physics, **146**(16), 164105. doi:[10.1063/1.4981521](https://doi.org/10.1063/1.4981521)).
Select it. run_job(..., method="dlpno-mp2" | "dlpno-ccsd" | "dlpno-ccsd(t)")
with dlpno_options=DLPNOMP2Options(...) (from vibeqc.dlpno), dlpno_ccsd_options= or
dlpno_thresholds= for thresholds; open-shell molecules
route to the spin-orbital DLPNO-UMP2 and DLPNO-UCCSD(T) solvers
automatically.
Status. Production for the molecular closed- and open-shell solvers. At the shipped defaults (chemical frozen core, NormalPNO, cc-pVDZ) on 17 closed-shell molecules from water to C₁₀H₂₂ the mean absolute error against canonical DF-CCSD(T) is 0.26 kcal/mol for CCSD and 0.38 for CCSD(T), and TightPNO brings it to 0.14 and 0.19; the per-molecule table is in the DLPNO guide. State the thresholds when you publish. The dense \(O(N^6)\) open-shell pilot is opt-in only.
On crystals. run_periodic_job(method="dlpno-ccsd(t)") correlates an
RHF or UHF reference on the GDF route at the Gamma point or on a
Gamma-centred mesh folded to the real BvK supercell, with the molecular
engine and the reference’s own retained fit as the correlation factors. At
full domains it reproduces PySCF KRCCSD(T) to the fit tolerance; its
accuracy at the shipped thresholds on real crystals is not measured yet, so
it is preview. See
local correlation on crystals
and the crystal tutorial.
Read the
DLPNO tutorial, the
DLPNO-MP2 guide and
examples/mlip/07_dlpno_ccsdt_on_mace_geometry.py.
Configuration interaction with singles and doubles: CISD¶
Theory. Diagonalise the Hamiltonian in the space of the reference plus all single and double excitations (Pople, J. A., Seeger, R., and Krishnan, R. (1977). *Variational configuration interaction methods and comparison with perturbation theory.* International Journal of Quantum Chemistry, **12**(S11), 149–163. doi:[10.1002/qua.560120820](https://doi.org/10.1002/qua.560120820)). CISD is variational but not size extensive: the missing quadruples make the recovered correlation energy per molecule shrink as the system grows, which is why the coupled-pair and coupled-cluster methods above are preferred for energies. It remains a clean benchmark and the natural entry point to multi-root excited states.
Select it. run_job(..., method="cisd") with CISDOptions for roots and
determinant-space guards.
Status. Production for small molecules; see the post-HF table in the feature matrix.
Multireference and exact methods¶
When one determinant is qualitatively wrong, at a stretched bond, a diradical, a transition-metal d shell or an avoided crossing, the methods above break down no matter how many excitations they include. The remedy is to treat a small set of strongly correlated orbitals exactly and correct the rest perturbatively. The CASSCF tutorial derives this section in detail.
CASCI and CASSCF¶
Theory. Choose an active space of \(n\) electrons in \(m\) orbitals, written CAS(\(n\),\(m\)). CASCI performs a full CI within that window on fixed (usually HF) orbitals; CASSCF additionally optimises the orbitals, so the inactive, active and virtual spaces rotate to minimise the CI energy (Roos, Björn O., Taylor, Peter R., and Siegbahn, Per E. M. (1980). *A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach.* Chemical Physics, **48**(2), 157–173. doi:[10.1016/0301-0104(80)80045-0](https://doi.org/10.1016/0301-0104(80)80045-0)). State averaging optimises one orbital set for several roots at once, which is what excited-state and conical-intersection work needs. The inactive core enters through the frozen-core dressing of the one-electron integrals, \(\tilde h_{pq} = h_{pq} + \sum_c [2(pq|cc) - (pc|cq)]\).
Select it. run_job(..., method="casci" | "casscf", active_space=(n_orbitals, n_electrons), casscf_options=CASSCFOptions(nroots=N)).
Status. Production. The state-specific closed-shell CASSCF analytic nuclear gradient is finite-difference tight to about 1e-7; state-averaged and open-shell CASSCF gradients fall back to finite differences. ECP references are refused.
CASPT2, NEVPT2 and MRCI¶
Theory. Dynamic correlation outside the active space is added on top of the CAS reference. CASPT2 (Andersson, Kerstin, Malmqvist, Per-Åke, et al. (1990). *Second-order perturbation theory with a CASSCF reference function.* Journal of Physical Chemistry, **94**(14), 5483–5488. doi:[10.1021/j100377a012](https://doi.org/10.1021/j100377a012), Andersson, Kerstin, Malmqvist, Per-Åke, and Roos, Björn O. (1992). *Second-order perturbation theory with a complete active space self-consistent field reference function.* Journal of Chemical Physics, **96**(2), 1218–1226. doi:[10.1063/1.462209](https://doi.org/10.1063/1.462209)) is second-order perturbation theory with a one-electron zeroth-order Hamiltonian, internally contracted here, with the optional IPEA shift; NEVPT2 (Angeli, Celestino, Cimiraglia, Renzo, et al. (2001). *Introduction of n-electron valence states for multireference perturbation theory.* Journal of Chemical Physics, **114**(23), 10252–10264. doi:[10.1063/1.1361246](https://doi.org/10.1063/1.1361246)) uses the Dyall Hamiltonian, which makes it intruder-free and size consistent without shifts. MRCI (Werner, Hans-Joachim and Knowles, Peter J. (1988). *An efficient internally contracted multiconfiguration-reference configuration interaction method.* Journal of Chemical Physics, **89**(9), 5803–5814. doi:[10.1063/1.455556](https://doi.org/10.1063/1.455556)) diagonalises singles and doubles out of every reference configuration and is the most accurate, and most expensive, of the three; the Davidson correction estimates the missing size-extensivity error.
Select it. run_job(..., method="caspt2" | "nevpt2" | "mrci", active_space=...),
optionally with casscf_options to use CASSCF rather than CASCI orbitals as
the reference.
Status. Production energies; CASPT2 was un-gated at v0.12.0 with a large-basis direct active-CI path. Analytic PT2 gradients exist only in a narrow envelope (state-specific, closed-shell, unshifted, explicit engine) and every other case uses full-energy finite differences, so treat multireference geometry optimisation as preview. Read the CASSCF tutorial and the non-HF solver guide.
Excited states and response properties¶
Linear-response TDDFT: Casida, Tamm-Dancoff, CIS¶
Theory. A weak oscillating field perturbs the ground-state density; the poles of the linear density response are the excitation energies. In the Casida formulation this becomes the non-Hermitian eigenproblem
where \(f_{xc}\) is the adiabatic exchange-correlation kernel and \(c_x\) the exact-exchange fraction. Setting \(\mathbf B = 0\) gives the Tamm-Dancoff approximation, which on a HF reference is CIS. Oscillator strengths follow from the transition dipoles, and natural transition orbitals (Martin, Richard L. (2003). *Natural transition orbitals.* Journal of Chemical Physics, **118**(11), 4775–4777. doi:[10.1063/1.1558471](https://doi.org/10.1063/1.1558471)) compress each excitation into a dominant hole-particle pair.
Select it. run_job(..., tddft=True, tddft_type="tda" | "casida", tddft_n_states=N, nto=True, tddft_spectrum=True),
or run_tddft_tda / run_tddft_casida; the vibeqc tddft CLI.
Status. Excitation energies are production for RHF, RKS, UHF and UKS with
LDA, GGA and global hybrid kernels (they match PySCF to 1e-4 eV); ROHF
supports TDA only; range-separated kernels are gated. Two known defects
matter: the oscillator strengths are currently too large (a factor of about 2
on closed-shell and 4 on unrestricted references, from the transition-dipole
normalisation), and run_job(tddft_gradient=True) differentiates a geometry
stretched by the bohr-to-angstrom factor. Excited-state gradients are finite
differences on the closed-shell RHF/CIS surface only (preview). Periodic
Gamma-point TDDFT is reachable through run_periodic_job(tddft=True); the
wrapper currently fails on GDF Gamma results until the leading k axis is
sliced off. See the TDDFT guide for the details. Read the
TDDFT tutorial.
Green’s-function ionisation energies: GF2 and OVGF¶
Theory. The one-particle Green’s function has poles at the exact
ionisation potentials and electron affinities. Solving the diagonal
quasiparticle equation \(\omega = \varepsilon_p + \Sigma_{pp}(\omega)\) with
the second-order self-energy gives the GF2 ionisation potentials, Koopmans
energies corrected for relaxation and correlation; the outer valence Green’s
function (Cederbaum, L. S. (1975). *One-body Green’s function for atoms and molecules: theory and application.* Journal of Physics B: Atomic and Molecular Physics, **8**(2), 290–303. doi:[10.1088/0022-3700/8/2/018](https://doi.org/10.1088/0022-3700/8/2/018), von Niessen, W., Schirmer, J., and Cederbaum, L. S. (1984). *Computational methods for the one-particle Green’s function.* Computer Physics Reports, **1**(2), 57–125. doi:[10.1016/0167-7977(84)90002-9](https://doi.org/10.1016/0167-7977(84)90002-9))
adds third-order terms with a renormalisation factor. In vibe-qc result.ovgf
holds the diagonal second-order solution and pole strength for each orbital;
the renormalised third-order value is printed for the HOMO when the system is
small enough (at most 60 spin orbitals), and the literal OVGF A/B/C variants
are not implemented.
Select it. run_job(..., method="ovgf") and read result.ovgf; MSINDO
has msindo_ovgf.
Status. Production for HF references including the open-shell propagator; renormalised GF2 prints automatically for small systems.
Static polarizability and analytic Hessians: coupled-perturbed SCF¶
Theory. Second derivatives of the energy need the first-order response of the orbitals. Differentiating the SCF conditions with respect to a perturbation gives the coupled-perturbed Hartree-Fock or Kohn-Sham equations (Pople, J. A., Krishnan, R., et al. (1979). *Derivative studies in Hartree-Fock and Møller-Plesset theories.* International Journal of Quantum Chemistry, **16**(S13), 225–241. doi:[10.1002/qua.560160825](https://doi.org/10.1002/qua.560160825)), a linear system in the occupied-virtual rotation parameters. With an electric-field perturbation the solution gives the static dipole polarizability \(\alpha_{ij} = -\partial^2 E/\partial F_i\partial F_j\); with nuclear displacements it gives the analytic Hessian, hence harmonic frequencies and IR intensities without finite differences.
Select it. dipole_polarizability_rhf and
vibeqc.cphf.dynamic_polarizability_rhf; the analytic Hessians are the
library functions
compute_hessian_{rhf,uhf,rks,uks}_analytic. Note that run_job(..., hessian=True)
uses compute_hessian_fd, finite differences of the analytic gradient, on
every route; run_periodic_job(hessian=True) computes the molecular
finite-difference Hessian of the isolated unit-cell molecule.
Status. Production for the RHF analytic Hessian, which matches PySCF
to 2.5e-9 Ha/bohr², and for the closed-shell polarizability. The UHF, RKS and
UKS analytic Hessians use the LDA kernel for the response, so GGA and hybrid
functionals differ from finite differences by up to about 12 cm⁻¹; treat them
as preview beyond LDA. run_job(hessian=True) ignores solvent= and
dispersion= without saying so. Read the vibrational frequencies tutorial
and the properties guide.
Semiempirical methods¶
Semiempirical Hamiltonians keep the self-consistent-field structure but replace most integrals with parametrised expressions fitted to experiment or to higher-level theory. They are one to three orders of magnitude faster than DFT and are meant for screening, preoptimisation, dynamics and very large systems. Their accuracy depends entirely on the parametrisation, which is why the status column below is more varied than anywhere else on this page. The semiempirical guide has the per-route status table that the tests pin.
MSINDO¶
Theory. MSINDO (Ahlswede, Bernd and Jug, Karl (1999). *Consistent modifications of SINDO1: I. Approximations and parameters.* Journal of Computational Chemistry, **20**(6), 563–571. doi:[10.1002/(SICI)1096-987X(19990430)20:6<563::AID-JCC1>3.0.CO;2-2](https://doi.org/10.1002/(SICI)1096-987X(19990430)20:6<563::AID-JCC1>3.0.CO;2-2)) is an INDO-type method with an orthogonalisation correction: overlap between atoms is kept in the one-electron terms, two-centre repulsion integrals are evaluated analytically over Slater orbitals, and pseudopotential-like terms model the core. It was built for solids as well as molecules, which is why the semiempirical cyclic cluster model was developed inside it. vibe-qc’s implementation is independent, covers H to Xe, and adds an NDDO mode for the main-group elements.
Select it. run_job(..., method="msindo"), with solvent= for its
own COSMO driver and the dynamics, metadynamics and MECI workflows below.
Status. Production within the documented scope: INDO energies for RHF and UHF, closed-shell analytic gradients, NDDO for H, Li to F and Na to Cl. Read the MSINDO guide and tutorial.
Density-functional tight binding: DFTB0 and SCC-DFTB¶
Theory. Expand the DFT energy around a reference density of superposed atoms (Porezag, D., Frauenheim, Th., et al. (1995). *Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon.* Physical Review B, **51**, 12947. doi:[10.1103/PhysRevB.51.12947](https://doi.org/10.1103/PhysRevB.51.12947)). The zeroth-order term gives a non-self-consistent tight-binding Hamiltonian with precomputed two-centre matrix elements plus a repulsive pair potential (DFTB0). The second-order term adds Mulliken-charge fluctuations interacting through a distance-dependent gamma function (SCC-DFTB, Elstner, M., Porezag, D., et al. (1998). *Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties.* Physical Review B, **58**, 7260. doi:[10.1103/PhysRevB.58.7260](https://doi.org/10.1103/PhysRevB.58.7260)), solved self-consistently and capturing charge transfer.
Select it. run_job(..., method="dftb0" | "scc_dftb"); periodic Gamma
and full-k routes through run_periodic_job.
Status. Preview, for screening and preoptimisation only. The parameters are in-house, there is no DFTB+ (mio-1-1) parity, and absolute energies are not claimable while the repulsive is a placeholder (issue #306); fixed-geometry differences remain valid. Read the DFTB tutorial.
GFN2-xTB¶
Theory. The extended tight-binding family (Bannwarth, Christoph, Ehlert, Sebastian, and Grimme, Stefan (2019). *GFN2-xTB—An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions.* Journal of Chemical Theory and Computation, **15**(3), 1652. doi:[10.1021/acs.jctc.8b01176](https://doi.org/10.1021/acs.jctc.8b01176)) adds to SCC-DFTB an anisotropic electrostatic term (atomic multipoles), shell-resolved charges, a third-order on-site term and a built-in D4 dispersion, parametrised across the periodic table for geometries, frequencies and non-covalent interactions.
Select it. run_job(..., method="gfn2_xtb"); parameters are fetched on
demand.
Status. Experimental. Molecular energies, analytic gradients and
the Gamma-periodic derivatives are implemented and finite-difference
validated, but external xtb parity and faithful periodic multipole
electrostatics remain production gates; the route is closed-shell only. Read
the GFN2-xTB workshop and
PM6 and GFN2.
NDDO methods: PM6, OM1, OM2, OM3 and the PM7 gate¶
Theory. Neglect of diatomic differential overlap keeps only one- and two-centre two-electron integrals, evaluated from multipole expansions with element-pair parameters. PM6 (Stewart, James J. P. (2007). *Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements.* Journal of Molecular Modeling, **13**, 1173–1213. doi:[10.1007/s00894-007-0233-4](https://doi.org/10.1007/s00894-007-0233-4)) is the widely used MOPAC parametrisation; the orthogonalisation-corrected OMx methods (Weber, Wolfgang and Thiel, Walter (2000). *Orthogonalization corrections for semiempirical methods.* Theoretical Chemistry Accounts, **103**, 495–506. doi:[10.1007/s002149900083](https://doi.org/10.1007/s002149900083), Scholten, Mirjam (2003). *Semiempirische Verfahren mit Orthogonalisierungskorrekturen: Die OM3 Methode.*) add explicit orthogonalisation and effective core potential terms that improve conformational energies and excited states.
Select it. run_job(..., method="pm6" | "om1" | "om2" | "om3"). PM7 is
recognised and refuses.
Status. PM6 is experimental (heat-of-formation parity with MOPAC is open; periodic PM6 is experimental). OM1, OM2 and OM3 are experimental and a retirement target: still executable as molecular prescreening, but scheduled to leave the public portfolio. PM7 is gated: it has never been executable in any release because the feathered electrostatics are not implemented.
SECCM: the semiempirical cyclic cluster model¶
Theory. Instead of Bloch functions and a k-mesh, the cyclic cluster model (Bredow, Thomas, Geudtner, Gerald, and Jug, Karl (2001). *Development of the cyclic cluster approach for ionic systems.* Journal of Computational Chemistry, **22**(1), 89–101. doi:[10.1002/1096-987X(20010115)22:1<89::AID-JCC9>3.0.CO;2-7](https://doi.org/10.1002/1096-987X(20010115)22:1<89::AID-JCC9>3.0.CO;2-7)) takes one supercell, imposes cyclic (Born-von Karman) boundary conditions on it directly in real space, and weights every interaction by whether it lies inside the Wigner-Seitz cell of the cluster. The result is a finite, molecule-like Hamiltonian that has the full translational symmetry of the crystal and no k-points at all, which makes defects, surfaces and localised states natural. The long-range Coulomb field is restored through an Ewald-summed Madelung embedding.
Select it. run_job(..., method="seccm") (normalised to "ccm") with
ccm_options carrying the supercell lattice vectors; the semiempirical
package also exposes per-family drivers such as
vibeqc.semiempirical.seccm.run_pm6_seccm for MSINDO, DFTB0, SCC-DFTB,
GFN2-xTB, PM6 and OMx.
Status. Experimental. The MSINDO route is the most mature (closed shell, 1-D to 3-D, native C++ for H to Kr); the DFTB, GFN2 and PM6 routes are gated experimental with energy-only or acknowledgement-gated envelopes. The Madelung embedding is opt-in and 1-D/2-D only. Read the cyclic cluster model guide and the CCM tutorial.
Machine-learned interatomic potentials¶
MACE¶
Theory. MACE (Batatia, Ilyes, Kovács, Dávid Péter, et al. (2022). *MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields.* Advances in Neural Information Processing Systems, **35**, 11423–11436. doi:[10.52202/068431-0830](https://doi.org/10.52202/068431-0830)) is an equivariant message-passing neural network that predicts energies and forces from atomic environments, trained on large DFT datasets (MACE-MP for materials, MACE-OFF for organic molecules). It is not an electronic-structure method: there are no orbitals, no density and no wavefunction, and its absolute energy scale is that of its training functional.
Select it. run_job(..., method="mace") for molecules; run_periodic_mace,
PeriodicMACEEvaluator, optimize_periodic_mace_positions and
optimize_periodic_mace_cell for periodic systems. Needs the [mace] extra
on Python 3.13 or earlier.
Status. The interface is production; the model is an external pre-trained potential, attributed as such in the citations, and its numbers are the model’s, not vibe-qc’s. Use it for geometries, screening and pre-relaxation, then hand the structure to an electronic-structure method. Read the MLIP guide, the MACE tutorial and from MACE geometry to electronic structure.
Periodic systems¶
Bloch’s theorem and k-point sampling¶
Theory. In a crystal the one-electron Hamiltonian commutes with lattice translations, so its eigenfunctions can be chosen as Bloch functions \(\psi_{n\mathbf k}(\mathbf r + \mathbf T) = e^{i\mathbf k\cdot\mathbf T} \psi_{n\mathbf k}(\mathbf r)\). Expanding them in Bloch sums of the Gaussian atomic orbitals, \(\phi_\mu^{\mathbf k} = \sum_{\mathbf T} e^{i\mathbf k\cdot\mathbf T}\chi_\mu(\mathbf r - \mathbf T)\), turns the crystal problem into an independent Roothaan-Hall problem at every crystal momentum \(\mathbf k\) in the first Brillouin zone,
coupled only through the density, which is a Brillouin-zone integral approximated by a Monkhorst-Pack mesh (Monkhorst, Hendrik J. and Pack, James D. (1976). *Special points for Brillouin-zone integrations.* Physical Review B, **13**(12), 5188–5192. doi:[10.1103/PhysRevB.13.5188](https://doi.org/10.1103/PhysRevB.13.5188)) reduced by symmetry to the irreducible wedge. Insulators converge quickly with \(\mathbf k\); metals need dense meshes plus a smearing of the occupation numbers (Fermi-Dirac, Methfessel-Paxton or Marzari-Vanderbilt) so that the Fermi surface is sampled smoothly, and a density mixer (Anderson, Broyden, Kerker) to damp charge sloshing.
Select it. PeriodicSystem(lattice, atoms, dim=1|2|3), KPoints.monkhorst_pack,
run_periodic_job(system, basis, method=..., kpoints=..., smearing_temperature=..., density_mixer=...).
Status. Production. Read k-points, the Brillouin zone and Bloch functions, the k-point guide, smearing and the metallic BZ integration guide.
The periodic Coulomb problem and Ewald summation¶
Theory. In an infinite lattice the bare Coulomb sums over nuclei, electrons and their cross terms are each conditionally convergent; only the total for a neutral cell is defined. Ewald’s method (Ewald, Paul Peter (1921). *Die Berechnung optischer und elektrostatischer Gitterpotentiale.* Annalen der Physik, **369**(3), 253-287. doi:[10.1002/andp.19213690304](https://doi.org/10.1002/andp.19213690304)) splits \(1/r\) into a short-range part summed in real space and a smooth long-range part summed in reciprocal space with a Gaussian screening parameter \(\alpha\) that cancels between the two. vibe-qc uses one shared \(\alpha\) gauge for the nuclear, one-electron and two-electron pieces, which is what makes the total energy independent of the gauge; the two-dimensional analogue (Parry, D. E. (1975). *The electrostatic potential in the surface region of an ionic crystal.* Surface Science, **49**, 433–440. doi:[10.1016/0039-6028(75)90362-3](https://doi.org/10.1016/0039-6028(75)90362-3)) treats slabs without a vacuum gap. The Madelung constants of NaCl, CsCl and ZnS are reproduced to 1e-8 as the regression check.
Select it. Automatic on every periodic route; ewald_point_charge_energy
exposes the classical sum.
Status. Production. Read the Ewald guide and the Madelung tutorial.
GDF: Gaussian density fitting, with RSGDF and MDF¶
Theory. The periodic four-index integrals are fitted in an auxiliary Gaussian basis exactly as in the molecular RI, but every fitting quantity is Bloch-summed and the \(G = 0\) divergence of the Coulomb kernel is handled separately (Sun, Qiming, Berkelbach, Timothy C., et al. (2017). *Gaussian and plane-wave mixed density fitting for periodic systems.* Journal of Chemical Physics, **147**(16), 164119. doi:[10.1063/1.4998644](https://doi.org/10.1063/1.4998644)). Range-separated GDF (Ye, Hong-Zhou and Berkelbach, Timothy C. (2021). *Fast periodic Gaussian density fitting by range separation.* Journal of Chemical Physics, **154**(13), 131104. doi:[10.1063/5.0046617](https://doi.org/10.1063/5.0046617)) evaluates the short-range part of the fit analytically and the long-range part on a plane-wave grid, which removes the lattice-sum truncation; mixed density fitting adds plane waves to the auxiliary set to close the all-electron accuracy floor in dense crystals. Exact exchange at \(\mathbf k\) meshes uses the Ewald probe-charge correction for the \(\mathbf q = 0\) singularity (Gygi, F. and Baldereschi, A. (1986). *Self-consistent Hartree-Fock and screened-exchange calculations in solids: Application to silicon.* Physical Review B, **34**, 4405–4408. doi:[10.1103/PhysRevB.34.4405](https://doi.org/10.1103/PhysRevB.34.4405)).
Select it. run_periodic_job(..., jk_method="gdf", gdf_method="rsgdf" | "compcell" | "mdf", kpoints=...);
drivers run_rhf_periodic_gamma_gdf, run_krhf_periodic_gdf, run_krks_periodic_gdf,
run_kuhf_periodic_gdf, run_kuks_periodic_gdf, run_krohf_periodic_gdf.
Status. Production for Gamma and multi-k RHF, RKS, UHF, UKS in 3-D and Gamma-only in 1-D (a 1-D cell with a k mesh currently fails closed for want of a consistent Coulomb gauge), with microhartree parity against PySCF on LiH and MgO, and for the bounded closed-shell 2-D slab route with analytic gradients. Periodic ROHF on GDF is preview (Gamma and full multi-k, no gradients or smearing). Read periodic methods, multi-k SCF, density fitting and the LiH multi-k tutorial.
GPW and GAPW: the plane-wave route¶
Theory. The Gaussian and plane-wave method (VandeVondele, Joost and Hutter, Jürg (2003). *An efficient orbital transformation method for electronic structure calculations.* Journal of Chemical Physics, **118**(10), 4365–4369. doi:[10.1063/1.1543154](https://doi.org/10.1063/1.1543154) lineage, as in CP2K) keeps Gaussian orbitals but represents the density on a regular grid, so the Hartree potential comes from one FFT-based Poisson solve and the XC potential from grid quadrature; only the smooth valence density fits on an affordable grid, which is why GPW pairs naturally with pseudopotentials. GAPW (Blöchl, P. E. (1994). *Projector augmented-wave method.* Physical Review B, **50**(24), 17953–17979. doi:[10.1103/PhysRevB.50.17953](https://doi.org/10.1103/PhysRevB.50.17953) lineage) restores all-electron accuracy by augmenting the grid density with one-centre atomic expansions near each nucleus, so the hard core density never touches the plane-wave grid.
Select it. run_periodic_job(..., jk_method="gpw" | "gapw"); GAPW needs
gapw_molecular_limit=True for RHF/UHF.
Status. GPW is the serial production plane-wave route within its
shipped envelope (Gamma RHF, UHF, RKS, UKS; multi-k pure-DFT RKS, ROKS, UKS;
Gamma analytic gradients; DFT+U; D3-BJ). The .out route description still
carries an experimental tag while the surrounding GPW/GAPW family is
completed, and the grid and J-builder infrastructure emit
GAPWExperimentalWarning once per build even through run_periodic_job
(the runner silences only the driver-level warning); read it as a scope
reminder. GAPW itself is experimental: not the automatic default, with molecular-limit
Gamma HF and block-construction DFT shipped and compact-crystal augmentation
validation pending. GPW ROHF/ROKS are a maintained preview. The MPI grid
overlay is experimental. Read GPW and GAPW, the
GPW tutorial and the GAPW tutorial.
BIPOLE: the exact Ewald J split¶
Theory. BIPOLE (Saunders, V. R., Freyria-Fava, C., et al. (1992). *On the electrostatic potential in crystalline systems where the charge density is expanded in Gaussian functions.* Molecular Physics, **77**, 629–665. doi:[10.1080/00268979200102671](https://doi.org/10.1080/00268979200102671)) is the CRYSTAL-style treatment of the periodic Coulomb term: the Hartree interaction of each atomic-orbital product with the infinite lattice is split into an exact near-field sum over overlapping distributions and a far field represented by multipoles and summed with Ewald’s method. vibe-qc’s implementation evaluates the far field exactly rather than through the multipole approximation, so the total is gauge-independent, and applies the same split to nuclei and electrons.
Select it. run_periodic_job(..., jk_method="bipole"); drivers
run_pbc_bipole_rhf, _uhf, _rks, _uks.
Status. Production energies for Gamma and multi-k RHF, UHF, RKS and
UKS in 3-D, with finite-difference forces and fixed-cell relaxation. The
analytic gradients are a preview, and the quartet multipole far-field
prototype is gated (every driver refuses use_multipole_far_field=True).
Read the BIPOLE guide and the
physical-domain tutorial.
Periodic RIJCOSX and the 2-D slab route¶
Theory. Periodic RIJCOSX takes the RI-J Coulomb from the GDF loop and builds exact exchange seminumerically on a periodic Becke grid, extending the molecular chain-of-spheres idea to Bloch orbitals. The 2-D slab route uses the rigorous vacuum-free two-dimensional Ewald sum (Parry, D. E. (1975). *The electrostatic potential in the surface region of an ionic crystal.* Surface Science, **49**, 433–440. doi:[10.1016/0039-6028(75)90362-3](https://doi.org/10.1016/0039-6028(75)90362-3), de Leeuw, S. W. and Perram, J. W. (1979). *Electrostatic lattice sums for semi-infinite lattices.* Molecular Physics, **37**(4), 1313–1322. doi:[10.1080/00268977900100951](https://doi.org/10.1080/00268977900100951)), so the third lattice vector is pure bookkeeping and the energy is independent of it.
Select it. run_periodic_job(..., jk_method="rijcosx"); slabs through
vibeqc.slab_2d(a1, a2, atoms) with jk_method="auto".
Status. Periodic RIJCOSX is experimental. The 2-D slab Ewald route is production for RHF, RKS and UKS (no smearing yet). Read slabs and adsorbates and the slab adsorbate tutorial.
Electronic structure of solids: bands, DOS, COOP/COHP, bond orders, QTAIM¶
Theory. Once the periodic SCF has converged, diagonalising \(\mathbf F(\mathbf k)\) along a path of high-symmetry \(\mathbf k\) gives the band structure; histogramming the eigenvalues over a dense mesh with Gaussian broadening gives the density of states, and weighting each state by its Mulliken population on an atom or orbital gives the projected DOS and fat bands. The crystal orbital overlap population (Hughbanks, Timothy and Hoffmann, Roald (1983). *Chains of trans-edge-sharing molybdenum octahedra: metal-metal bonding in extended systems.* Journal of the American Chemical Society, **105**(11), 3528–3537. doi:[10.1021/ja00349a027](https://doi.org/10.1021/ja00349a027)) and Hamilton population (Dronskowski, Richard and Blöchl, Peter E. (1993). *Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations.* Journal of Physical Chemistry, **97**(33), 8617–8624. doi:[10.1021/j100135a014](https://doi.org/10.1021/j100135a014)) resolve the DOS into bonding and antibonding contributions between atom pairs by weighting with \(S_{\mu\nu}\) or \(H_{\mu\nu}\) respectively. Periodic Mayer bond orders generalise the molecular index over the k mesh, and QTAIM (Bader, R. F. W. (1985). *Atoms in molecules.* Accounts of Chemical Research, **18**(1), 9–15. doi:[10.1021/ar00109a003](https://doi.org/10.1021/ar00109a003)) partitions space by the zero-flux surfaces of the density gradient, locating bond critical points and bond paths.
Select it. band_structure, density_of_states, band_structure_projected,
compute_coop_cohp, periodic_mayer_bond_orders, vibeqc.qtaim.qtaim_analysis;
the vibeqc coop CLI; all written to QVF for vibe-view.
Status. Bands, DOS, PDOS, fat bands, periodic Mayer bond orders, QTAIM and COOP/COHP are production on the GDF routes. COHP is computed with the same spin Hamiltonian that produced the analysed eigenpairs, and the kernel refuses any other operator rather than labelling it COHP; on BIPOLE, AICCM and external-XC routes the DOS and COOP/COHP sections are skipped with a stated reason. Read the band structure tutorial, PDOS, COOP/COHP and QTAIM.
Phonons, stress and variable cells¶
Theory. Displacing each atom by a small step and differencing the analytic forces gives the force-constant matrix; mass-weighting and diagonalising it at \(\mathbf q = 0\) gives the Gamma-point phonons. The stress tensor is the strain derivative of the energy per volume; vibe-qc obtains it by central differences of the energy over strain with the basis rebuilt on each strained cell, so Hellmann-Feynman and Pulay terms arrive together. An equation-of-state fit (third-order Birch-Murnaghan) turns an energy-volume scan into the equilibrium volume and bulk modulus.
Select it. vibeqc.PhononCalculator, compute_stress_gpw, compute_stress_gapw,
vibeqc.eos.fit_birch_murnaghan.
Status. Phonons are a preview (Gamma only, GAPW forces). Stress is
finite-difference only and optimize_cell=True fails closed on every ab
initio route (gated); variable-cell relaxation is reachable on the full-k
semiempirical routes. The EOS fit is production. See the
periodic geometry optimisation tutorial.
Surface embedding¶
Theory. A semi-infinite surface is partitioned into a surface region treated explicitly and a bulk region whose influence enters through an energy-dependent self-energy built from the bulk Green’s function (Inglesfield, J. E. (1981). *A method of embedding.* Journal of Physics C: Solid State Physics, **14**(26), 3795-3806. doi:[10.1088/0022-3719/14/26/015](https://doi.org/10.1088/0022-3719/14/26/015)), so the surface sees the true bulk continuum instead of a truncated slab.
Select it. The embedded-surface calculator described in surface embedding.
Status. Experimental. The 3-D Gaussian foundation is validated; thick-slab GDF parity is pending, so absolute energies and densities are qualitative. Read the surface embedding tutorial.
AICCM: the ab initio cyclic cluster model¶
Theory. AICCM carries the cyclic cluster idea of SECCM to first principles (Peintinger, Michael F. and Bredow, Thomas (2014). *The cyclic cluster model at Hartree-Fock level.* Journal of Computational Chemistry, **35**(11), 839–846. doi:[10.1002/jcc.23550](https://doi.org/10.1002/jcc.23550)). A finite Born-von Karman torus of \(N_1\times N_2\times N_3\) unit cells replaces the k-mesh: the electronic structure of the crystal is represented by one real-space supercell with cyclic boundary conditions, and every two-electron integral is weighted by where the interacting charge distributions fall relative to the Wigner-Seitz cell of the torus. Because the Hamiltonian is a finite, molecule-like object, the whole molecular correlation hierarchy (MP2, CCSD, DLPNO) can be applied to it directly, which is the motivation for the approach. vibe-qc maintains two independent constructions on purpose:
Gamma-CCM is the neutral finite-torus construction with two admissible producers,
variant="real-gamma"(the real-Gamma supercell representation, which carries the exchange \(\mathbf q = 0\) seam explicitly) andvariant="neutral-bloch"(the same Hamiltonian in its Bloch representation). The same development line also keepsvariant="four-center", the 2014 union-and-weight / Wigner-Seitz lineage, which is a different construction rather than a third producer.chi-CCM (
variant="chi") builds the Hamiltonian from the characters of the finite translation group on a Gamma-centred character mesh, with four-centre, RI and RIJCOSX backends.
Agreement between the two under a matched Coulomb gauge is the evidence for a common limit; divergence decides which construction is admissible. No cross-approach delta is reportable yet.
Select it. run_periodic_job(system, basis, method="aiccm", variant=..., aiccm_lattice_extension=(N1, N2, N3), correlation="mp2" | "ccsd" | "dlpno-mp2" | "dlpno-ccsd").
variant is mandatory.
Status. Experimental, every variant, every driver. All are 3-D only; the 1-D and 2-D absolute-energy backends fail closed; results are research output and not part of any release gate. Read the AICCM guide, the quickstart, the Gamma-CCM and chi-CCM tutorials, and the chi-CCM reference.
Workflows on the energy surface¶
Geometry optimisation, relaxed scans and intrinsic reaction coordinates¶
Theory. A stationary point satisfies \(\partial E/\partial\mathbf R = 0\). Quasi-Newton optimisers (BFGS and its line-search variant through ASE, or the native optimiser) update an approximate Hessian from successive gradients and converge in tens of steps for molecules; forces come from the Hellmann-Feynman term plus the Pulay correction for the basis functions that move with the nuclei (Pulay, P. (1969). *Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. I. Theory.* Molecular Physics, **17**(2), 197–204. doi:[10.1080/00268976900100941](https://doi.org/10.1080/00268976900100941)). A relaxed scan freezes one internal coordinate at a series of values and relaxes the rest. The intrinsic reaction coordinate follows the mass-weighted steepest descent path from a transition state down to both minima (Ishida-Morokuma-Komornicki damped integrator).
Select it. run_job(..., optimize=True), optimize_molecule, the
VibeQC ASE calculator; vibeqc.relaxed_scan(...) for scans; run_irc;
periodic fixed-cell relaxation through run_periodic_job(..., optimize=True).
Status. Production for molecules on every method with a gradient
(analytic where it exists, finite differences otherwise, always stated in
the .out). Two caveats matter: optimize=True with a post-SCF method
(MP2, CC, DLPNO, OVGF) relaxes the mean-field reference surface and tags the
output with that energy_method, and the correlated methods without a fast
gradient (FCI, NEVPT2, CASPT2, MRCI) require optimizer_backend="native" or
"brent" for a finite-difference optimisation on their own surface (#357).
Periodic relaxation is production on BIPOLE (finite-difference forces) and the
analytic-gradient GDF routes; periodic IRC fails closed. Read
geometry optimisation,
relaxed PES scans and
periodic geometry optimisation.
Transition states: nudged elastic band, dimer and eigenvector following¶
Theory. A chain of images between reactant and product is relaxed under the true force perpendicular to the path plus a spring force along it; the climbing image is pushed uphill along the tangent until it sits on the saddle point, and the barrier is the energy of that image. The dimer method needs no second image: two close replicas are rotated to find the lowest curvature mode and translated uphill along it and downhill in every other direction. Eigenvector following (EF, P-RFO) does the same with an approximate Hessian and Bofill updates.
Select it. run_neb (HF, DFT, ROHF/ROKS, MACE, semiempirical and SECCM
surfaces) or the ASE NEB on VibeQC calculators; run_dimer;
run_job(..., geom_target="transition_state", geom_opt="dimer" | "ef" | "prfo").
Status. NEB, the dimer method and the IRC are production for molecules
(the dimer needs a sensible initial_direction); eigenvector following and
P-RFO through run_job are a preview, because they did not converge from
an approximate start on HCN/HNC and NH3 in testing and the .out does not
say when max iterations was reached. Periodic ROHF/ROKS, ECP and DFT+U
combinations are gated route by route. Read the
NEB tutorial, the NEB guide
and IRC and dimer.
Vibrational frequencies and thermochemistry¶
Theory. Diagonalising the mass-weighted Hessian after projecting out translations and rotations gives the harmonic normal modes and frequencies; the dipole derivative along each mode gives its IR intensity. The rigid-rotor harmonic-oscillator partition functions turn frequencies, moments of inertia and mass into zero-point energy, enthalpy, entropy, heat capacity and Gibbs free energy at a given temperature and pressure.
Select it. run_job(..., hessian=True) computes the Hessian, the
frequencies, the IR intensities and the RRHO thermochemistry in one pass;
thermo_options sets temperature and pressure. The pieces are also
callable on their own: compute_hessian_fd, compute_hessian_rhf_analytic,
ir_intensities, compute_thermochemistry.
Status. Production, validated against PySCF to 1e-7 Ha in the thermochemistry and below 0.01 cm⁻¹ in analytic frequencies. Read the frequencies tutorial and thermodynamics.
Molecular dynamics, metadynamics and conical intersections¶
Theory. Born-Oppenheimer molecular dynamics integrates Newton’s equations on the electronic energy surface with the velocity-Verlet scheme; energy conservation in the NVE ensemble is the consistency test between forces and energy. Well-tempered metadynamics adds a history-dependent bias of Gaussian hills along chosen collective variables so the trajectory escapes minima and the accumulated bias reconstructs the free-energy surface. A minimum-energy conical intersection is located by minimising the average of two state energies under a penalty on their gap.
Select it. from vibeqc.md import run_md, run_nvt for any method with
forces, or ASE VelocityVerlet on a VibeQC calculator;
vibeqc.metadynamics.run_metadynamics layers the well-tempered bias on the
same driver with distance and angle collective variables;
vibeqc.conical.optimize_conical_intersection implements the
Levine-Coe-Martinez penalty and takes any two tracked states with energies
and gradients, in practice the HF-CIS finite-difference surface or MSINDO
CIS. The top-level vibeqc.run_md / run_nve / run_nvt / run_npt names
are the GAPW periodic helpers and inherit that route’s label.
Status. Production for molecular dynamics, metadynamics and the MECI optimiser on any surface with forces; the GAPW periodic dynamics helpers follow GAPW. Read the MD tutorial and the MD guide.
Basis-set optimisation¶
Theory. The exponents and contraction coefficients of a Gaussian basis are variational parameters. vibe-basis minimises a molecular or cohesive energy objective over them with analytic energy gradients and a BDIIS update, which is how the pob family of solid-state bases was constructed.
Select it. optimize_molecular_basis, the vb command-line tool.
Status. Production; see basis optimisation and the basis convergence tutorial.
Analysis of the wavefunction¶
Charges, bond orders and localised orbitals¶
Theory. Mulliken populations split each overlap population equally between the two centres; Loewdin populations use the symmetrically orthogonalised basis and are less basis-set sensitive; Hirshfeld charges partition the real-space density in proportion to superposed free-atom densities (Hirshfeld, F. L. (1977). *Bonded-atom fragments for describing molecular charge densities.* Theoretica Chimica Acta, **44**(2), 129–138. doi:[10.1007/BF00549096](https://doi.org/10.1007/BF00549096)) and are the most stable of the three. Intrinsic atomic orbitals (Knizia, Gerald (2013). *Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts.* Journal of Chemical Theory and Computation, **9**(11), 4834–4843. doi:[10.1021/ct400687b](https://doi.org/10.1021/ct400687b)) build a minimal, polarised atomic basis that exactly spans the occupied space, giving basis-set-independent charges and, after localisation, intrinsic bond orbitals. Mayer (Mayer, I. (1983). *Charge, bond order and valence in the ab initio SCF theory.* Chemical Physics Letters, **97**(3), 270–274. doi:[10.1016/0009-2614(83)80005-0](https://doi.org/10.1016/0009-2614(83)80005-0)) and Wiberg (Wiberg, Kenneth B. (1968). *Application of the Pople-Santry-Segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane.* Tetrahedron, **24**(3), 1083–1096. doi:[10.1016/0040-4020(68)88057-3](https://doi.org/10.1016/0040-4020(68)88057-3)) bond orders and the delocalisation index measure electron sharing between atom pairs from the density matrix.
Select it. mulliken_charges, loewdin_charges, hirshfeld_charges,
vibeqc.bond_analysis, mayer_bond_orders; all emitted into the
.population.txt and .population.json sidecars by run_job.
Status. Production. NPA charges are gated (raise
NotImplementedError until natural atomic orbitals land) and the NBO search
is a provisional exploratory helper. Read properties,
bond analysis, IAO populations
and the post-SCF properties tutorial.
Energy decomposition and orbital entanglement¶
Theory. Energy decomposition analysis splits an interaction energy between two fragments into electrostatic, exchange, repulsion, polarisation and dispersion terms, in the LMO-EDA (Su, Peifeng and Li, Hui (2009). *Energy decomposition analysis of covalent bonds and intermolecular interactions.* Journal of Chemical Physics, **131**(1), 014102. doi:[10.1063/1.3159673](https://doi.org/10.1063/1.3159673)) and Morokuma (Morokuma, Keiji (1971). *Molecular orbital studies of hydrogen bonds. III. C=O…H-O hydrogen bond in H2CO…H2O and H2CO…2H2O.* Journal of Chemical Physics, **55**(3), 1236–1244. doi:[10.1063/1.1676210](https://doi.org/10.1063/1.1676210)) schemes. Orbital entanglement measures (Legeza, Ors and Solyom, Jeno (2003). *Optimizing the density-matrix renormalization group method using quantum information entropy.* Physical Review B, **68**(19), 195116. doi:[10.1103/PhysRevB.68.195116](https://doi.org/10.1103/PhysRevB.68.195116)) use the one- and two-orbital reduced density matrices to compute single-orbital entropies and mutual information, which reveal static correlation and guide active-space selection.
Select it. vibeqc.eda.eda_lmo, vibeqc.eda.eda_morokuma,
vibeqc.entanglement.single_orbital_entropy, mutual_information,
entanglement_bond_order.
Status. The entanglement measures on a correlated reduced density
matrix are production; the convenience wrapper
entanglement_from_density is an occupation-based approximation (its
overlap transform was corrected on main, #418). The EDA functions are
preview: they return the real LMO-EDA and Kitaura-Morokuma terms for two
closed-shell Hartree-Fock fragments computed in the dimer basis, and the terms
sum to the interaction energy. Kohn-Sham, ECP, open-shell and
other-basis inputs are refused with a ValueError; the Kohn-Sham form, open-shell
fragments, the Kitaura-Morokuma split of polarisation, charge transfer and
coupling, and a run_job keyword are not implemented. You assemble the three
SCF runs yourself, as the
EDA and entanglement tutorial shows.
Natural orbitals, natural transition orbitals and volumetric data¶
Theory. Diagonalising a correlated one-particle density matrix gives natural orbitals whose occupation numbers measure correlation; the same operation on a transition density gives natural transition orbitals. Any orbital or density can be sampled on a grid and written as a Gaussian cube, an XSF volume, or, for Fermi surfaces, a BXSF file.
Select it. natural_orbitals, run_job(..., nto=True),
write_cube_density, write_cube_mo, write_cube_mos and their periodic
siblings, write_bxsf; every run writes a Molden file and a QVF archive.
Status. Production. Read volumetric data, orbital visualisation and XSF and BXSF.
Input, output and interchange¶
Every user-facing file goes through vibeqc.output: the human-readable
.out, the .system manifest with provenance and method status, the .bibtex
and .references citation files for exactly the methods you used, the
population sidecars, Molden orbitals, ASE trajectories and the QVF
archive that carries the whole calculation for vibe-view.
Wavefunctions can also leave as TREXIO files for other correlated codes
and as QCSchema JSON for workflow engines, and structures come in from
XYZ, extended XYZ, POSCAR and CIF, or from public databases through
vqfetch (OPTIMADE, Materials Project, COD, NIST). All of these are
production; see output files,
TREXIO, QCSchema,
external structures and the
ASE integration guide.
Not in vibe-qc today¶
So that “every method” is a checkable claim, these standard capabilities are absent rather than experimental: equation-of-motion and STEOM coupled cluster for excited states, ADC, GW and Bethe-Salpeter, MP3 and higher MP orders, explicitly correlated F12 methods, symmetry-adapted perturbation theory, NMR shieldings and spin-spin couplings, EPR parameters, analytic Hessians beyond the four mean-field references, periodic D4, periodic IRC and variable-cell relaxation on the ab initio routes. The citation database carries route keys for several of them because the output layer is prepared for them, not because they run. The roadmap says which are planned.
Status at a glance¶
Family |
Production |
Preview |
Experimental |
Gated |
|---|---|---|---|---|
Mean field |
RHF, UHF, ROHF, RKS, UKS, ROKS; LDA to global hybrids with gradients; D3(BJ), D4; RIJK, RIJCOSX; ECPs; CPCM/COSMO; composites (molecular) |
Range-separated and VV10 gradients (finite differences); ROKS gradients |
SKALA; native D4 backend; COSMO-RS; Jacobi-Davidson and harmonic-Davidson (GPLHR) solvers; MANTA integral engine with its RI, BUPO and RI-BUPO J/K selectors |
Solvent with correlated, CAS, semiempirical (except MSINDO) or MLIP methods |
Single-reference correlation |
MP2 family, double hybrids, CCSD, CCSD(T), open-shell CC, CC2, CC3, CCSDT, QCISD(T), CEPA(n), CISD, DLPNO-MP2, DLPNO-CCSD(T), open-shell DLPNO |
Dense production-size memory envelopes; DLPNO-CCSD(T) on 3-D crystals (RHF or UHF GDF reference, Gamma or BvK-folded mesh) |
||
Multireference and exact |
CASCI, CASSCF (state-specific gradient), IC-CASPT2, NEVPT2, MRCI, FCI, selected CI, v2RDM |
PT2 and state-averaged gradients (finite differences); transcorrelated CI |
DMRG (toy, 6 spatial orbitals); SC-CASPT2 behind |
ECP references in CAS methods |
Excited states and response |
TDDFT Casida and TDA, NTOs, spectra; OVGF; CPHF polarizability; analytic Hessians |
Excited-state gradients (RHF/CIS, finite differences) |
Range-separated TDDFT kernels |
|
Semiempirical and MLIP |
MSINDO within scope; MACE interface |
DFTB0, SCC-DFTB |
GFN2-xTB, PM6, OM1/OM2/OM3, SECCM |
PM7 |
Periodic |
GDF, GPW, BIPOLE energies; 2-D slab Ewald; smearing, mixers; DFT+U; bands, DOS, PDOS, fat bands; COOP/COHP; periodic Mayer; QTAIM; EOS fits |
Periodic ROHF/ROKS; BIPOLE analytic gradients; Gamma phonons; finite-difference stress; symmetry-reduced exact exchange ( |
GAPW; periodic RIJCOSX; surface embedding; AICCM (all variants); MPI overlay; MANTA finite-domain periodic HF and KS |
Variable-cell relaxation on ab initio routes; BIPOLE quartet multipole |
Workflows and analysis |
Optimisation, scans, IRC, NEB, dimer, MD, metadynamics, MECI, frequencies, thermochemistry, basis optimisation; charges, bond orders, IAO, EDA, entanglement; all I/O routes |
Post-SCF |
NPA; periodic IRC; variable-cell relaxation on ab initio routes |
When this table and a method’s own page disagree, the method page wins and this table has a bug: please report it.