Relativistic quantum chemistry involving heavy atoms

Quantum chemistry is nowadays a term referring to a wide set of theoretical frameworks and models mainly relying on non-relativistic quantum mechanics. While, in most cases, the picture of the molecular structure and of the chemical reality provided by non-relativistic quantum chemistry is appropriate, we live in a universe with a finite speed of light. While neglecting variation of mass and velocity in the interaction of electrons and atomic nuclei is often safe, this is no more the case when heavy atoms are involved. In the present paper, we will briefly review the most rigorous way to include relativity in the modeling of molecular systems, that is to use the full 4-component (4c) formalism derived from the Dirac equation. Specifically, we will review the implementation that has been carried out in an effective 4c code called BERTHA. A recently developed method to gain deep insights into chemical bond is also presented and discussed in the 4c Dirac–Kohn–Sham context, the so-called natural orbitals for chemical valence/charge-displacement analysis.