Relativistic integrals over Breit–Pauli operators using general Cartesian Gaussian functions. I. One-electron interactions

Abstract

Cartesian Gaussian functions are employed to derive general expressions for integrals over all one-electron operators of the Breit–Pauli Hamiltonian. It is shown that in atoms of higher atomic number p6, p8, ⋅⋅⋅ operators can be important in determining relativistic corrections to the kinetic energy. All other operators of this Hamiltonian can be expressed as some derivative of 1/r. Thus, a general expression is derived for the integral over the operator (∂1/∂x1) (∂m/∂ym) (∂n/∂zn) (1/r) by employing its Fourier transform. The operator and charge-distribution-dependent parts can be separately identified in the resulting expression and hence for a given charge distribution, integrals over any number of operators that can be expressed in the above form can be obtained simultaneously. In addition to nuclear attraction, these operators include the spin-orbit and Darwin terms of the Breit-Pauli Hamiltonian, as well as the electric field components and their derivatives, and other interactions over operators required in the study of magnetic shieldings. Furthermore, these expressions serve as a prototype for more difficult and numerous two-electron integrals, as discussed in the second paper in this series.