Dirac‐Fock self‐consistent field method for closed‐shell molecules with kinetic balance and finite nuclear size

Abstract

AbstractWe present a general method of implementing the kinetic balance condition within the Dirac‐Fock (DF) self‐consistent field (SCF) formalism for closed‐shell molecular structure. We review the steps leading to the derivation of DF SCF equations for closed‐shell molecules, particularly as formulated by Matsuoka et al. In the present approach, the large component of the molecular spinors are expanded in terms of atomic basis spinors of spherical‐type Gaussian functions, with the small component related to the large component by the kinetic balance condition. It is shown that imposing the kinetic balance condition on geometric Gaussian‐type basis functions allows us to obtain the Fock matrix elements, involving both the large and the small components, form the standard nonrelativistic Cartesian‐type matrix elements. By using properties of orthogonal polynomials, the solid spherical harmonics are expressed in Cartesian form, thus providing a general basis for transformation of one‐ and two‐electron‐matrix elements, obtained from a Cartesian Gaussian‐type basis, to a spherical Gaussian‐type basis. The advantages of using kinetically balanced geometric Gaussian‐type basis functions in molecular DF calculations including finite‐size nucleus effects are emphasized. For the sake of completeness, we have added in an appendix corrections to the nuclear attraction matrix elements for the finite‐size nucleus already derived by Matsuoka.