Orbital contraction, relativistic effect

The DF and HF calculations [139] for the 5d and 6d elements widi and without the 4f and 5f shells, respectively, have shown that the shell-structure contraction is, indeed, enhanced by relativistic effects and that the orbital and relativistic effects are not additive. 

Snijders, J.G. and Pyykko, P. (1980) Is the relativistic contraction of bond lengths an orbital contraction effect Chemical Physics Letters, 75, 5-8. 

An important advantage of ECP basis sets is their ability to incorporate approximately the physical effects of relativistic core contraction and associated changes in screening on valence orbitals, by suitable adjustments of the radius of the effective core potential. Thus, the ECP valence atomic orbitals can approximately mimic those of a fully relativistic (spinor) atomic calculation, rather than the non-relativistic all-electron orbitals they are nominally serving to replace. The partial inclusion of relativistic effects is an important physical correction for heavier atoms, particularly of the second transition series and beyond. Thus, an ECP-like treatment of heavy atoms is necessary in the non-relativistic framework of standard electronic-structure packages, even if the reduction in number of... 

One-center expansion was first applied to whole molecules by Desclaux Pyykko in relativistic and nonrelativistic Hartree-Fock calculations for the series CH4 to PbH4 [81] and then in the Dirac-Fock calculations of CuH, AgH and AuH [82] and other molecules [83]. A large bond length contraction due to the relativistic effects was estimated. However, the accuracy of such calculations is limited in practice because the orbitals of the hydrogen atom are reexpanded on a heavy nucleus in the entire coordinate space. It is notable that the RFCP and one-center expansion approaches were considered earlier as alternatives to each other [84, 85]. 

Further aspects governing computational effort and accuracy are related to the explicit treatment of relativistic effects, which are pronounced for atoms with high atomic numbers, as their core electrons reach velocities that make the influence of special relativity significant. Contraction of bond lengths and a shifting of orbital energies are observed compared to the non-relativistic treatment. An efficient way to include a major fraction of these... 

While the contraction resulting from the poor shielding of 4/ electrons ceases at hafnium, the relativistic effect continues across the sixth row of the periodic table. It is largely responsible for the stabilization of the 6. orbital and the inert s pair effect shown by the elements Hg-Bi. It also stabilizes one40 of the 6p orbitals of bismuth allowing the unusual i-l oxidation state in addition to +3 and + 5.4 ... 

That is, relativistic effects have effectively contracted the Is orbital by 19%. 

In contrast, the valence d and f orbitals in heavy atoms are expanded and destabilized by the relativistic effects. This is because the contraction of the s orbitals increases the shielding effect, which gives rise to a smaller effective nuclear charge for the d and f electrons. This is known as the indirect relativistic orbital expansion and destabilization. In addition, if a filled d or f subshell lies just inside a valence orbital, that orbital will experience a larger effective nuclear charge which will lead to orbital contraction and stabilization. This is because the d and f orbitals have been expanded and their shielding effect accordingly lowered. 

For heavy atoms with different Z values and various numbers of d and f electrons, the two aforementioned relativistic effects will lead to different degrees of 6s orbital contraction. Figure 2.4.5 shows the ratio R / NR as a function of Z. 

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