Ab Initio Quantum Chemistry Methods

Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. Ab initio quantum chemistry methods attempt to solve the electronic Schrödinger equation given the positions of the nuclei and the number of electrons in order to yield useful information such as electron densities, energies and other properties of the system.  

Overall solutions

Methods Classifications
Hartree–Fock methods Hartree–Fock methods
Hartree–Fock (HF)
Restricted open-shell Hartree–Fock (ROHF)
Unrestricted Hartree–Fock (UHF) Post-Hartree–Fock methods
Moller–Plesset perturbation theory (MPn)
Configuration interaction (CI)
Post-Hartree–Fock methods
Coupled cluster (CC)
Quadratic configuration interaction (QCI)
Multi-reference methods Multi-configurational self-consistent field (MCSCF including CASSCF and RASSCF)
Multi-reference configuration interaction (MRCI)
n-electron valence state perturbation theory (NEVPT)
Complete active space perturbation theory (CASPTn)
State universal multi-reference coupled-cluster theory (SUMR-CC)

Method in details

Ab Initio Quantum Chemistry Methods

  • Hartree–Fock and post-Hartree–Fock methods

The simplest type of ab initio electronic structure calculation is the Hartree–Fock (HF) scheme, in which the instantaneous Coulombic electron-electron repulsion is not specifically taken into account. Only its average effect (mean field) is included in the calculation.

  • Valence bond methods

Valence bond (VB) methods are generally ab initio although some semi-empirical versions have been proposed. Current VB approaches are:
Generalized valence bond (GVB)
Modern valence bond theory (MVBT)

  • Quantum Monte Carlo methods

A method that avoids making the variational overestimation of HF in the first place is Quantum Monte Carlo (QMC), in its variational, diffusion, and Green's function forms.

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