Relativistic stabilization

Figure 4.2 The relativistic stabilization of the ns shell for the elements Kto Kr (n = 4), RbtoXe (n = 5), Csto Rn (n = 6), and Fr to element 118 (n = 7). Redrawn from the data of Desclaux [32] and Schwerdtfeger and Seth [33]. Pd is ground state d °s° and is therefore missing in this graph.

Comparisons of gold and silver further illustrate the point. The Au—H bond is much stronger than the Ag—H bond and Aul, is much more stable than Agl ". The relatively high effective nuclear charge leads to relativistic stabilization (contraction) of 6s orbitals and destabilization (expansion) of 5d orbitals. The net result is greater participation in M—L bonding by the 5d orbitals and thus stronger bonds.4... 

The second (indirect) relativistic effect is the expansion of outer d and f orbitals The relativistic contraction of the s and pi/2 shells results in a more efficient screening of the nuclear charge, so that the outer orbitals which never come to the core become more expanded and energetically destabilized. While the direct relativistic effect originates in the immediate vicinity of the nucleus, the indirect relativistic effect is influenced by the outer core orbitals. It should be realized that though contracted s and pi/2 core (innermore) orbitals cause indirect destabilization of the outer orbitals, relativistically expanded d and f orbitals cause the indirect stabilization of the valence s and p-orbitals. That partially explains the very large relativistic stabilization of the 6s and 7s orbitals in Au and element 112, respectively Since d shells (it is also valid for the f shells) become fully populated at the end of the nd series, there will occur a maximum of the indirect stabilization of the valence s and p orbitals [34],... 

Fig. 4. The relativistic stabilization of the 6s and 7s orbitals in the 6th and 7lh row of the Periodic Table. Re-drawn from the data of [17]. The relativistic DF data are from [23].

Figure 5 demonstrates the relativistic stabilization of the ns orbitals, as well as the destabilization of the (n-l)d orbitals for group-8 elements, as an example. One can see that trends in the relativistic and non-relativistic energies of the valence electrons are opposite from the 5d to the 6d elements. Thus, the non-relativistic description of the wave function would still give the right trend in properties from the 4d to the 5d elements, while it would result in the opposite and consequently wrong trend from the 5d to the 6d elements. 

Fig. 6. Relativistic stabilization of the ns and npi/2 orbitals and the spin-orbit splitting of the np orbitals for the noble gases Xe, Rn and element 118. The DF atomic energies are from [23] and the HF values are from [17].

The relativistic stabilization of the 7p electrons manifests itself in some excited states different than those of the lighter homologues, e.g., 6d7s27p(3D2) of Rf lying 0.3 eV higher in energy in contrast to the 6d27s2(3F3) state of Hf. 

For some time, the relativistic stabilization of the 7s2 and 7pi/2 electrons was a reason to suggest an enhanced stability of lower oxidation states like Lr+, Db3+ or Sg4+, and to design gas-phase experiments to detect a p-character of Lr and Rf taking into account different volatilities of d- and p-element compounds. The MCDF calculations of multiple IPs for elements 104 through 108 [26-29] and estimates of redox potentials (see Section 7.1) did not confirm the stability of lower oxidation states. Neither was the character of Rf confirmed by molecular calculations, see [15,16]. 

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