Electron properties, molecular systems Dirac theory

Heavy-element systems are involved in many important chemical and physical phenomena. However, they still present difficulties to theoretical study, especially in the case of solids containing atoms of heavy elements (with the nuclear charge Z > 50). In this short description of relativistic electronic-structure theory for molecular systems we follow [496] and add a more detailed explanation of the Dirac-Kohn-Sham (DKS) method. For a long time the relativistic effects underlying in heavy atoms had not been regarded as such an important effect for chemical properties because the relativistic effects appear primarily in the core atomic region. However, now the importance of the relativistic effects, which play essential and vital roles in the total natures of electronic structures for heavy-element molecular and periodic qrstems, is recognized [496]. 

The idea of calculating atomic and molecular properties from electron density appears to have arisen from calculations made independently by Enrico Fermi and P.A.M. Dirac in the 1920s on an ideal electron gas, work now well-known as the Fermi-Dirac statistics [19]. In independent work by Fermi [20] and Thomas [21], atoms were modelled as systems with a positive potential (the nucleus) located in a uniform (homogeneous) electron gas. This obviously unrealistic idealization, the Thomas-Fermi model [22], or with embellishments by Dirac the Thomas-Fermi-Dirac model [22], gave surprisingly good results for atoms, but failed completely for molecules it predicted all molecules to be unstable toward dissociation into their atoms (indeed, this is a theorem in Thomas-Fermi theory). 

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