Contraction, relativistic

M. Seth, M. Dolg, P. Fulde, P. Schwerdt-feger. Lanthanide and actinide contractions relativistic and shell structure effects. /. Am. Chem. Soc., 117 (1995) 6597-6598. 

All hydrogen-like atomic orbitals contract relativistically if we compare the orbital densities obtained by the Schrbdinger... 

SBKJC VDZ Available for Li(4.v4/>) through Hg(7.v7/ 5d), this is a relativistic basis set created by Stevens and coworkers to replace all but the outermost electrons. The double-zeta valence contraction is designed to have an accuracy comparable to that of the 3—21G all-electron basis set. Hay-Wadt MB Available for K(5.v5/>) through Au(5.v6/ 5r/), this basis set contains the valence region with the outermost electrons and the previous shell of electrons. Elements beyond Kr are relativistic core potentials. This basis set uses a minimal valence contraction scheme. These sets are also given names starting with LA for Los Alamos, where they were developed. 

Relativistic effects are cited for changes in energy levels, resulting in the yellow color of gold and the fact that mercury is a liquid. Relativistic effects are also cited as being responsible for about 10% of lanthanide contraction. Many more specific examples of relativistic effects are reviewed by Pyykko (1988). 

Figure 4.47 Relativistic contraction of the 6s shell in the elements Cs (Z = 55) to Fm (Z = 100) showing how relativistic effects on electrons become most pronounced at gold. (Reprinted with permission from Acc. Chem. Res., 1979,12, 226. Copyright (1979) American Chemical Society.)...

Figure 4.4 Valence relativistic s-shell contraction (/ )r/(/ )nr (4s for Cu, 5s forAg, SsforAu and 7s for Fr). Here the ns-shell remains singly occupied and the x-axis gives the total number of electrons N with additional electrons filled in successively from the inner shells. For example N = 3 for Au describes the occupation ls 6s and N — 11 the occupation ls 2s 2p 6s ...

Due to the relativistic 6s contraction in gold, the 6s shell becomes more compact (inert, hence the nobility of gold) and the (static dipole) polarizability an decreases substantially from 9.50 (NR) to 5.20 (R) [99], Table 4.3. The relativistic enhance-... 

AuH and Au2 serve as benchmark molecules to test the performance of various relativistic approximations. Figure 4.7 shows predictions for relativistic bond contractions of Au2 from various quantum chemical calculations over more than a decade. In the early years of relativistic quantum chemistry these predictions varied significantly (between 0.2 and 0.3 A), but as the methods and algorithms became more refined, and the computers more powerful, the relativistic bond contraction for Au2 converged and is now at 0.26 A. 

Figure4.7 Relativistic bond contractions A re for Au2 calculated in the years from 1989 to 2001 using different quantum chemical methods. Electron correlation effects Acte = te(corn) — /"e(HF) at the relativistic level are shown on the right hand side of each bar if available. From the left to the right in chronological order Hartree-Fock-Slater results from Ziegler et al. [147] AIMP coupled pair functional results from Stbmberg and Wahlgren [148] EC-ARPP results from Schwerdtfeger [5] EDA results from Haberlen and Rdsch [149] Dirac-Fock-Slater...

Figure 4.10 Calculated relativistic bond contractions ARte in A (circles and solid line, axis on the left-hand side) and relativistic change in the dissociation energy contractions (triangles and dashed line, axis on the right-hand side) for various diatomic compounds as a function ofthe electronegativity of the ligand.

Baerends, E.J., Schwarz, W.H.E., Schwerdtfeger, P. and Snijders, J.G. (1990) Relativistic atomic orbital contractions and expansions magnitudes and explanations. Journal of Physics B-Atomic Molecular and Optical Physics, 23, 3225-3240. 

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

The electron density i/ (0)p at the nucleus primarily originates from the ability of s-electrons to penetrate the nucleus. The core-shell Is and 2s electrons make by far the major contributions. Valence orbitals of p-, d-, or/-character, in contrast, have nodes at r = 0 and cannot contribute to iA(0)p except for minor relativistic contributions of p-electrons. Nevertheless, the isomer shift is found to depend on various chemical parameters, of which the oxidation state as given by the number of valence electrons in p-, or d-, or /-orbitals of the Mossbauer atom is most important. In general, the effect is explained by the contraction of inner 5-orbitals due to shielding of the nuclear potential by the electron charge in the valence shell. In addition to this indirect effect, a direct contribution to the isomer shift arises from valence 5-orbitals due to their participation in the formation of molecular orbitals (MOs). It will be shown in Chap. 5 that the latter issue plays a decisive role. In the following section, an overview of experimental observations will be presented. 

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