Vertical trends in transition-metal bonding

A convenient measure of the importance of relativistic corrections is given by the ratio Aei of Z to the fine-structure constant (e2/(hc) — 137, a dimensionless ratio of fundamental physical constants) 

For the lighter elements rei is much less than unity (e.g., rei = 0.15 for Sc) and the relativistic corrections are small. However, these corrections become much larger for heavier elements (e.g., ,ei = 0.58 for Hg, about four times larger than for Sc) and the perturbative correction procedure breaks down completely as rei approaches unity. Thus, while relativistic corrections are largely ignorable for the first transition series, these corrections become of dominant chemical importance in later series, particularly after filling of the lanthanide f shell. 

Two of the leading relativistic effects can be summarized in physical terms as follows. 

group 6 (Cr, Mo, W), and group 10 (Ni, Pd, Pt). (Note that CrH6 was optimized with MoH -like angular geometry to prevent formation of the Cr(H2)3 dihydrogen complex.) 

The computational bond-length variations in Table 4.53 exhibit the expected periodic trends. Most noticeably, third- and second-series elements for groups 4, 6, and 10 exhibit similar bond lengths, i.e., the post-lanthanide contraction with respect to the ordinary increase of atomic size with increasing Z. 

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