Lecture: ab initio Methods Post Hartree-Fock Introduction

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, tex2html_wrap_inline671 over the atomic basis set tex2html_wrap_inline653, and produces the matrix elements tex2html_wrap_inline675 over the molecular orbital set tex2html_wrap_inline677,

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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.



Author: Ken Flurchick