A new relativistic Hartree–Fock calculation scheme and its application to the evaluation of fine-structure intervals fornd (n= 3–40) series of sodium

Abstract

We present a new second-order representation of the relativistic Hartree-Fock equation, which can be solved by the standard Hartree-Fock technique. An alternative reduction for the magnetic part of the Breit interaction is presented in an explicit expression. A corresponding program has been developed, which improves significantly the scaled linear mesh introduced by Herman and Skillman. The structures for a number of atoms and ions are calculated and the agreement of our results with those published is excellent. We evaluate the fine-structure intervals of nd(n = 3-40) Rydberg series for sodium. The inverted fine-structure splitting values are obtained directly as the differences of eigenvalues obtained from a self-consistent field procedure. Taking into account the Gaunt effect enables the accuracy of the calculation to be substantially improved. The complete treatments reproduce very well the inverted fine structures along the Rydberg series and the relative difference between the present results and the experiments does not exceed 4.4%.

A discussion on the relativistic corrections of the electronic structures of multi‐electron atoms

“…To formulate the relativistic HF-SCF method, we make the opposite choice, namely not eliminating the small component. This approach, unconventional compared to those reported in the literature [43][44][45], leads to unexpected results that we will discuss shortly. Let us write the Fock operator for the ith electron as:…”

“…In Equation (45), the first term is the relativistic kinetic energy, the second term is the potential energy, and the third term is the contribution of the repulsive potential energy and the attractive exchange energy. Once again, it must be emphasized that, for inner electrons of heavy atoms, the potential U NÀe to be used is that which provides for the finiteness of the nuclear volume.…”