The calculation of spin-orbit splitting and g tensors for small molecules and radicals

Abstract

The spin-orbit coupling terms in the molecular electronic Hamiltonian have important, spectroscopically observable, effects. In states possessing an orbital degeneracy (e.g. II states of diatomic molecules) they produce a first-order splitting of the various multiplet levels; and in states which are degenerate in spin only the y give second-order effects embodied in a n effective g tensor. Owing to the complexity of the spin-orbit operators, such effects are usually discussed using simple approximate form s and semi-empirical wave-functions. In this paper, the complete operators are employed inab initiocalculations of (i) the spin-orb it splitting of the2II ground states of NO and CH, and (ii) the g tensors of CN and NO2. The results are in good agreement with experiment. Detailed analysis of the calculations indicates a firm basis for semi-empirical procedures which could easily be applied to larger molecules. The evaluation of new integrals, involving the spin-orbit operators, is discussed in an appendix.