Post-Hartree-Fock Methods and Electron Correlation: A Very Brief Overview

‘This chapter sketches how the electron correlation is treated in post-Hartree-Fock (HF) wavefunction methods. The distinction between static and dynamic correlation is explained. A configuration interaction (CI) wavefunction is a linear combination of several or many Slater determinants (SDs). Following a HF calculation, different SDs can be constructed by replacing 1, 2, 3, … occupied orbitals in the HF wavefunction with 1, 2, 3,… unoccupied or virtual orbitals, leading to pseudo-excited electron configurations at the singles, doubles, triples, … (S, D, T, …) level. The virtual orbitals are usually available as a by-product of the HF calculation in a basis set. Full CI (FCI) considers all possible substitutions, up to N-fold for an N-electron system. FCI is impractical for all but the smallest molecules. CI truncated at a lower level, e.g. S and D, suffers from lack of size extensitivity. Truncated coupled-cluster (CC) is size extensive. Open-shell systems generally require a multi-reference treatment. The chapter concludes with a treatment of the static correlation in the bond breaking of H2.