Spin‐orbit (core) and core potential integrals

Abstract

Molecular integral formulas and corresponding computational algorithms are developed for the relativistic spin-orbit and core potential operators that are obtained from atomic relativistic calculations by means of the effective core potential procedure. Much use is made of earlier work on core potential integrals by McMurchie and Davidson. The resulting computer code has been made part of the ARGOS (Argonne, Ohio State) program from the COLUMBUS suite of programs, which computes the needed integrals over symmetry-adapted combinations of generally contacted Gaussian atomic orbitals.

Configuration interaction calculation of electronicgtensors in transition metal complexes*

“…The matrix elements of the angular momentum and spin-orbit coupling operators can be readily calculated analytically with Gaussian-type orbitals (GTO) basis functions [49,50]. However, in the semiempirical treatment pursued here the (purely imaginary) reduced SOC matrix elements are calculated in a one-center approximation:…”

Analytical evaluation of pseudopotential matrix elements with Gaussian-type solid harmonics of arbitrary angular momentum

“…It is based on a technique originally introduced by Löwdin [19]. Many improvements have been suggested in the meantime, e.g., new recursion relations and alternative approaches to fundamental integrals [20] or techniques based on numerical quadrature [21]. However, the number of floating-point operations required in all these algorithms is still rather high, especially when basis functions of higher angular momentum are considered.…”

Spin–orbit interaction with nonlinear wave functions

“…However, the new nonlinear expansion formulation is not specific to the RECP method. The RECP valence spin-orbit operators are the basic technology already employed in many traditional spin-orbit CI schemes [24][25][26][27]. RECP methods can employ both one-electron and two-electron spin-orbit operators.…”