Matrix representation of the relativistic kinetic energy operator: Two-component variational procedure for the treatment of many-electron atoms and molecules

Abstract

A matrix representation for the relativistic free-particle energy (p2c2 + m2c4)12 is proposed. Unlike the usual expansion term - p48m3c2, which is shown to lead to very compact states far below the ground state, this operator yields satisfactory charge distributions when included in the LCAO SCF and MRD CI procedure. Variational calculations employing the square-root matrix representation and a Coulomb potential (plus one-electron Darwin term) are carried out for a series of one-electron atoms (Z = 1, 5 and 8) and very good agreement is obtained with experiment for at least the 2s and 2p IPs; the corresponding 1s values are in somewhat worse agreement, however. When the same method is applied to the many-electron systems Br and I, results for the 2Pu valence-shell spin-orbit splittings are obtained in first-order perturbation theory which agree within 10% of their experimental values, indicating that such an ab initio variational treatment retains a high degree of reliability for the calculation of valence-shell properties even for relatively heavy elements.