Multipole sum rules

Abstract

Many molecular properties are related to the (2 l -pole)-(2 l′ -pole) spectral moments Sl,l′ (k) for the molecule. Sum rule expressions are derived for the S l,l′ (k) for k=2, 1, 0, -1 and arbitrary (l, l′) some of the difficulties associated with using MO-LCAO-SCF wavefunctions, in place of exact wavefunctions, to evaluate the multipole properties are discussed. SCF results have been obtained for H2, BH3, CH4, NH3, H2O, HF, N2, CO, CO2, and N2O for (l, l′)=(1, 1), (1, 2), (1, 3) and (2, 2) with k = 1, 0, -1 and for (l, l′ = (1, 1) with k = 2 and are used to discuss certain calculational and physical features of the S l,l′ (k): basis set incompleteness problems, the importance of two-electron contributions, additivity (core versus valence MO contributions), their anisotropy, and the importance of the nuclear framework of the molecule. The use of the sum rules greatly simplifies the evaluation of the S l ,l′(k) for k=2, 1, 0, -1 and apparently a double-zeta basis set is adequate for the determination of SC...