L-S term energy equations for complex electronic configurations

Abstract

A computer program has been written to calculate L-S term energy expressions for all configurations of s, p, d, f, g, and h electrons, subject to the usual restriction to no more than one open shell of each symmetry species. The coefficients of Slater integrals occurring in these expressions are also converted to vector-coupling coefficients useful in self-consistent- field calculations of atomic wave functions. This program is fully automatic and requires no data except for the occupation numbers of the six symmetry species. A listing of the program is presented, along with tables of Slater-integral coefficients and vector- coupling coefficients for several representative configurations. Such coefficients have appeared previously for only four configurations of the types pmfq and dnfq; none have appeared for any configurations that include open shells of g or h electrons. The immediate use of the results now made available is anticipated to be in the calculation of atomic wave functions for states arising from excited configurations of lanthanide ions. In fact, there is one ion, Gd2+, for which the normal configuration--4f75d--is one of those treated here for the first time. These atomic wave functions are useful in the determination of numerous atomic properties and may also be used as the starting point for configuration interaction studies. Slater's treatment of complex atomic systems provides the method used in the computer program, and an exposition of this method is included. The application to the configuration p2d is provided as a detailed illustration of the method.