The external heavy atom effect: Theory of spin–orbit coupling of alkali and noble metals in rare gas matrices

Recent data from magnetic circular dichroism (MCD) and optical absorption studies of alkali and noble metal atoms in rare gas matrices have shown an interesting and significant influence of the rare gas on the spin–orbit (SO) splitting of the metal excited 2P state. The excited state SO coupling constants extracted from these data can be classified into three major categories: (I) positive and greater than gas phase values, (II) positive and less than gas phase values, and (III) negative and less than gas phase values. A theory for the spin–orbit coupling of a noble or alkali metal in a rare gas matrix is presented. A supermolecule model in which the metal is surrounded by 12 tetradecahedrally situated rare gas atoms is used to calculate the SO splitting. The splitting is found to depend on three quantities: the metal–rare gas σ- and π-type overlap integrals, the ratio of rare gas-to-metal SO coupling constants, and the metal–rare gas molecular orbital mixing coefficients. Using computed overlap integrals and empirical SO coupling constants it is shown that the model is capable of predicting qualitatively the three major categories of metal–rare gas spin–orbit constants. Finally, a semiempirical approach is utilized to estimate the mixing coefficients and quantitative SO ‘‘reduction’’ factors are determined. This parameterless theory is shown to predict all the important trends well.