The calculation thus far has given us an uncorrelated wave
function. That is, the dynamical correlations between the electrons has
been neglected. To proceed beyond the uncorrelated Hartree-Fock wave
function, i.e. to obtain correlation energies we must directly calculate
the molecular orbitals. This transformation takes the electron repulsion
matrix elements,
over the atomic basis set
,
and produces the matrix elements
over the molecular orbital set
,
Some of the typical post Hartree-Fock schemes:
Although this step appears simple it is a bottleneck to most ab initio calculations because of the memory requirements. This step scales as N5 to convert from the atomic orbital (AO) description to the molecular orbital (MO) description. Referred to as the 4-index transformation. Following the AO-MO transformation, the post Hartree-Fock schemes scale as N6 in computational complexity and N3 in storage requirements.