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arXiv · 2109.12693

Relativistic variational methods and the Virial Theorem

Charlotte Froese Fischer·Michel Godefroid
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Abstract

In the case of the one-electron Dirac equation with a point nucleus the Virial Theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly $-1$, a ratio that can be an independent test of the accuracy of a computed solution. This paper studies the virial theorem for subshells of equivalent electrons and their interactions in many-electron atoms. It shows that some Slater integrals impose conditions on a single subshell but others impose conditions between subshells. The latter slow the rate of convergence of the self-consistent field process in which radial functions are updated one at a time. Several cases are considered.

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Charlotte Froese Fischer, Michel Godefroid. 2021-09-26. Relativistic variational methods and the Virial Theorem. https://arxiv.org/abs/2109.12693

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