Chapter 18 - Evaluation of molecular integrals

Abstract

The molecular two-electron integrals may be classified into one-, two-, three-, and four-centre integrals, according to the number of nuclei to which atomic orbitals are referred, while one-electron integrals can imply three centres at most. The difficulty in their analytical evaluation greatly increases with the number of centres involved, three- and four-centre integrals being necessarily evaluated by numerical techniques. Particularly refined molecular energy calculations involving the interelectronic distance r12 directly into the wavefunction require still more difficult three- and four-electron many-centre integrals. After the explicit calculation of all two-centre molecular integrals over 1s Slater-type orbitals (STOs) occurring in the study of the H2 molecule, we illustrate two different strategies for the evaluation of two-centre integrals over general STOs in spheroidal or spherical coordinates, giving a short outline of a possible way of evaluating three- and four-centre integrals over 1s STOs. The last section gives an outlook of the calculation of molecular multicentre integrals over Gaussian-type orbitals.