Nonrelativistic effects, transition

The various transition energies of the gold atom and its ions are shown and compared with experiment [53] in table 2. The nonrelativistic results have errors of several eV. The RCC values, on the other hand, are highly accurate, with an average error of 0.06 eV. The inclusion of the Breit effect does not change the result by much, except for a some improvement of the fine-structure splittings. 

In this simple case there is no advantage to the pseudopotential calculation (the 3-21G( ) geometry is actually better ), but more challenging calculations on very-heavy-atom molecules, particularly transition metal molecules, rely heavily on ab initio or DFT (Chapter 7) calculations with pseudopotentials. Nevertheless, ordinary nonrelativistic all-electron basis sets sometimes give good results with quite heavy atoms [64]. A concise description of pseudopotential theory and specific relativistic effects on molecules, with several references, is given by Levine [65]. Reviews oriented toward transition metal molecules [66a,b,c] and the lanthanides [66d] have appeared, as well as detailed reviews of the more technical aspects of the theory [67]. See too Section 8.3. 

For the computational investigation of molecular systems containing heavy atoms, such as transition metals, lanthanides, and actinides, we could neglect neither relativity nor electron correlation. Relativistic effects, both spin-free and spin-orbit, increase with the nuclear charge of atoms. Therefore, instead of the nonrelativistic Schrodinger equation, we must start with the Dirac equation, which has four-component solutions. For many-electron systems, the four-component Hamiltonian is constructed from the one-electron Dirac operator with an approximated relativistic two-electron operator, such as the Coulomb, Breit, or Gaunt operator, within the nopair approximation. The four-component method is relativistically rigorous, which includes both spin-free and spin-orbit effects in a balanced way. However it requires much computational time since it contains more variational parameters than the approximated, one or two-component method. 

The transition metal atom has a possibility to possess a magnetic moment in metaUic material, then an investigation of the spin polarization of the cluster from a microscopic point of view is very important in understanding the magnetism of the metallic materials. We try to explain the spin polarization and the magnetic interactions of the cluster in terms of the molecular orbital. For the heavy element in the periodic table whose atomic number is beyond 50, it is mentioned that the relativistic effects become very important even in the valence electronic state. We perform the relativistic DV-Dirac-Slater calculation in addition to the nonrelativistic DV-Xa calculation for the small clusters of the 3d, 4d and 5d transition elements to clarify the importance of the relativistic effects on the valence state especially for the 5d elements. 

The chemistry of transition metals, lanthanides and actinides is significantly influenced by relativistic effects. Qualitatively, these effects become apparent in the comparison of certain structural properties or reactivity patterns for a group of metals, for example, trends in the chemistry of copper, silver and gold. Quantification of relativistic effects can, however, only be achieved by relating the experimental findings to the results of adequate ab initio studies. Reference to theory is required because nonrelativistic properties cannot be probed directly. Thus, elements behave relativis-tically in any kind of experiment, whether one deals with the spectrum of Hj or the properties of transuranium compounds. 

It was also proposed that the significant s and p orbital contraction at row four (Cu) is caused by the post-transition metal effect (d contraction), caused by an increase of the effective nuclear charge for the 4s electrons due to filling the first d shell (3d). A similar interpretation is possible for the row six (Au). This effect is commonly called lanthanoid contraction due to the effect of filling the 4f shell. The traditional explanation for the smaller size of gold (compared to Ag) is the lanthanoid contraction. However, this effect is only sufficient to cancel the shell-structure expansion, to make Au (nonrelativistic) similar to Ag (nonrelativistic). 

The most common feature in the electronic structure found for all compounds in both DFT [142-148] and RECP [126] calculations was an increase in covalency (a decrease in effective charges, Qm, and an increase in the overlap population, OP) in going down the transition element groups, as shown in Fig. 16. A comparison of relativistic with nonrelativistic calculations shows that this increase is a purely relativistic effect due to the increasing contribution of the relativistically stabilized and contracted 7s and 7pm AOs, as well as of expanded 6d AO in the bonding (Figs. 17 and 18) [148]. 

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