Relativistic contraction of orbitals

Minimizing the relativistie energy equation (3.65) leads to an equation for optimum  

The result differs remarkably from the non-relativistic value = Z, but ap-proaehes the non-relativistie value when c - oo. Note than the dilference between the two values increases with atomic number Z, and that the relativistic exponent is always larger that its non-relativistic counter-part. This means that the relativistic orbital decays faster with the electron-nucleus distance and therefore 

Let us see how it is for the hydrogen atom. In that case = 1.0000266 as compared to = Zh — 1- And what about l5 orbital of gold For gold 

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

It is not possible to use normal AO basis sets in relativistic calculations The relativistic contraction of the inner shells makes it necessary to design new basis sets to account for this effect. Specially designed basis sets have therefore been constructed using the DKH Flamiltonian. These basis sets are of the atomic natural orbital (ANO) type and are constructed such that semi-core electrons can also be correlated. They have been given the name ANO-RCC (relativistic with core correlation) and cover all atoms of the Periodic Table.36-38 They have been used in most applications presented in this review. ANO-RCC are all-electron basis sets. Deep core orbitals are described by a minimal basis set and are kept frozen in the wave function calculations. The extra cost compared with using effective core potentials (ECPs) is therefore limited. ECPs, however, have been used in some studies, and more details will be given in connection with the specific application. The ANO-RCC basis sets can be downloaded from the home page of the MOLCAS quantum chemistry software (http //www.teokem.lu.se/molcas). 

FIGURE 1. Relativistic contraction of 6s orbitals for heavy elements (atomic number from Z = 70 to 90). 

In compounds containing heavy main group elements, electron correlation depends on the particular spin-orbit component. The jj coupled 6p j2 and 6/73/2 orbitals of thallium, for example, exhibit very different radial amplitudes (Figure 13). As a consequence, electron correlation in the p shell, which has been computed at the spin-free level, is not transferable to the spin-orbit coupled case. This feature is named spin-polarization. It is best recovered in spin-orbit Cl procedures where electron correlation and spin-orbit interaction can be treated on the same footing—in principle at least. As illustrated below, complications arise when configuration selection is necessary to reduce the size of the Cl space. The relativistic contraction of the thallium 6s orbital, on the other hand, is mainly covered by scalar relativistic effects. 

The ionization energies of the relativistic Pb 6s electrons were found to be much higher than those calculated using nonrelativistic pseudopotentials, e.g. the ionization energy increases by 4.7 eV (Pb3+) and 3.7 eV (Pb2+), due to relativity107. This results from the relativistic contraction of the 6s orbital which is about 12% for the neutral Pb atom107. 

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],... 

The relativistic contraction of the 7s orbitals ( Group 11 maximum ) results in the atomic size of element 111 being similar to that of gold and smaller than that of silver. For compounds, where the 7s orbitals contribute predominantly to bonding, the smallest size of the element 111 species in the group is expected. 

The so-called inert-pair effect for Tl, Pb, and Bi as well as the low cohesive energy of elemental mercury arise from relativistic contraction of the 6s orbitals. 

It can be seen that the contributions of valence orbitals to the total second momentum (r2) are essential the inner shells contribute insignificantly. For example, within the series of Cu, Ag and Au atoms the contributions of valence nsi/2 orbitals are 40, 44 and 18% and those of (n — l)dy2 plus (n — l)d5/2 are 43, 37 and 50% of the total, respectively. The reduced contribution of the 6sl/2 orbital for the Au atom has roots in the relativistic contraction of this orbital, as is seen from the comparison with the non-relativistic limit. 

In basic research, the chemistry of gold and organogold compounds merits special interest because of the unique position of gold in the periodic table, which is characterized by the highest electron affinity, electronegativity, and redox potential of all metals. These properties have their origin in a pronounced maximum in the relativistic contraction of the valence electron orbitals and associated effects. Several reviews on organogold chemistry have been published. ... 

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