Relativistic Effects on Atomic Shell Structure

Our concepts of molecules are based on our concepts of atoms. Molecular orbitals are conveniently viewed in terms of linear combinations of atomic orbitals. Thus, our 

The results obtained for the spinor eigenvalues (which relate to mean spinor radii through the virial theorem) are presented in table 22.1. For the s shell, the screening effects have little influence on the energy. The major influence is the change from nonrelativistic to relativistic dynamics. For the p shell, both the dynamics and the potential are important. The contributions are almost the same for the pi/2 subshell, but for the p3/2 subshell the effect of the dynamics is smaller by about a factor of three. For the d shell the dominant effect is the change in potential. 

The effect of the dynamics is termed the direct relativistic effect, and the effect of the potential—the screening—is termed the indirccf relativistic effect. The direct effects dominate for and pi/2 subshells, which both contract. Both have s-character, either in the large or the small component. One consequence of the contraction is that for the 6p elements, the 6 subshell stabilization contributes to the stability of the oxidation state n-2, where n is the valence occupation. This is often termed the inert pair effect. The pi/2 shells contract less, but in the superheavy Ip elements both the Is and the lpi/2 form inert filled shells for the later members. For the p3/2 subshell the dynamics and screening approximately cancel, and the behavior of the late p block elements shows little effect of relativity on many properties. For orbitals with 1, the screening effect dominates and the shells are destabilized. The 5d expands, for example, and contributes substantially to the bonding in third-row transition metals. Likewise, the 5/ of the actinide series participates in bonding past the middle of the series, whereas in the lanthanides, the 4/ forms a relatively inert shell inside the 5p shell early in the series. 

Dynamics Potential Dirac Rel Dirac Nonrel Schrodinger Rel Schrodinger Nonrel 

Data taken from table 2 of Rose S. J., Publishing Ltd). 

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