“Ab initio” quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term “ab initio” indicates that the calculation is from the first principles and that no empirical data are used.
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 into the calculation. This is a variational procedure. Therefore, the obtained approximate energies, expressed in terms of the system wave function are always equal to or greater than the exact energy and tend to a limiting value called the Hartree-Fock limit as the size of the basis is increased.
Many types of calculations begin with a Hartree-Fock calculation and subsequently correct for electron-electron repulsion, referred to also as electronic correlation. Moller-Plesset perturbation theory (MPn) and coupled cluster theory (CC) are examples of these post-Hartree-Fock methods. In some cases, particularly for bond breaking processes, the Hartree-Fock method is inadequate and this single-determinant reference function is not a good basis for post-Hartree-Fock methods. It is then necessary to start with a wave function that includes more than one determinant such as multi-configurational self- consistent field (MCSCF) and the methods have been developed which use these multi-determinant references for some improvements.
Almost always the basis set which is usually built for LCAO used to solve the Schrodinger equation is not complete, and does not span the Hilbert space associated with ionization and scattering processes (see continuous spectrum for more details). In Hartree-Fock method and Configuration interaction method, this approximation allows one to treat the Schrodinger equation as a "simple" eigenvalue equation of the electronic molecular Hamiltonian, with a discrete set of solutions.