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

Abstract

The theory of special relativity is a topic not addressed in theoretical chemistry courses. Einstein's theory of relativity is mainly applied to high‐energy phenomena governed by physical laws not used to describe the chemical bond. Nevertheless, the electrons of heavy elements orbit around the nucleus with relativistic velocities. Here it is, then, the laws that appeared so unusual for chemistry became fundamental tools for investigating the properties of these atoms. Studying the electronic structure of heavy elements is the best place for chemists to learn to tame the pitfalls of a little‐known subject, such as Einstein's theory, and become familiar with its elegant formalism. In this paper, the main relativistic approaches to quantum chemistry are revisited. The problem of the finite nuclear size, the approximation methods used to solve the relativistic equations for k‐shell electrons, and the problem of the negative energy continuum are investigated. Some ansatzes to solve divergence's problem of relativistic corrections near the nucleus are proposed. Finally, a possible connection between the self‐consistent field method and bondonic chemistry is also investigated.

Relativistic Effects in Ligand Field Theory (I): Optical Properties of d1 Atoms in Oh′ Symmetry

“…However, we believe that our framework is founded on a stronger theoretical background, since relativistic effects are considered from the beginning through the Dirac equation. We note that the developed theory, when combined with relativistic calculations, is suited for studying relativistic effects , in ligand field states at any order. That is, it opens up the opportunity to study the relevance of spin–spin and spin-other-orbit interactions, the nuclear charge distribution function, , or even the forthcoming quantum electrodynamics corrections to atomic and molecular states. − All of these can be explored through the p / q ratio as described in eqs and .…”

“…15 For comprehensive discussions of relativistic effects in chemistry the reader is directed to Pyykkö1 6 and to Nanni. 17 Despite the huge success of the LFT, from the theoretical point of view, it is desired to count with a theory free of empirical parameters. Thus, a recently and continuously developing Ab Initio Ligand Field Theory (AILFT) has emerged.…”

“…A friendly introduction to the Dirac equation and its consequences in chemistry can be found in Kaltsoyannis’s review . For comprehensive discussions of relativistic effects in chemistry the reader is directed to Pyykkö and to Nanni . Despite the huge success of the LFT, from the theoretical point of view, it is desired to count with a theory free of empirical parameters.…”

“…In this article, the LFT is rederived using the wave functions obtained from the Dirac equation instead of using the wave functions obtained from the Schrödinger equation. In this sense, the spin–orbit interaction and others relativistic effects , are incorporated in theory from the beginning, without the need of having many terms in the Hamiltonian apart from the ligand field potential as a perturbation. This allows us not only to obtain algebraic expressions for the ligand field relativistic energy levels of d 1 octahedral complexes, but also to provide a bridge between the LFT and ab initio relavitistic calculations.…”