Relativistic effects spin-orbit splitting

Kotzian et al. (1991) and Kotzian and Rosch (1992) applied their INDO/1 and INDO/S-CI methods to hydrated cerium(III), i.e. model complexes [Ce(H20) ] (n=8,9), in order to rationalize the electronic structure and the electronic spectrum of these species. Besides the scalar relativistic effects spin-orbit coupling was also included in the INDO/S-CI studies. The spin-orbit splitting of the 4f F and 5d states of the free Ce " ion was calculated as 2175cm" and 2320cm in excellent agreement with the experimental values of 2253 cm and 2489 cm" , respectively. The calculated energy separation between the F and states of approximately 44000cm" (estimated fi-om fig. 5 in Kotzian and Rosch 1992) is somewhat lower than the experimental value of 49943 cm" (Martin et al. 1978). 

Thus, the main relativistic effects are (1) the radical contraction and energetic stabilization of the s and p orbitals which in turn induce the radial expansion and energetic destabilization of the outer d and f orbitals, and (2) the well-known spin-orbit splitting. These effects will be pronounced upon going from As to Sb to Bi. Associated with effect (1), it is interesting to note that the Bi atom has a tendency to form compounds in which Bi is trivalent with the 6s 6p valence configuration. For this tendency of the 6s electron pair to remain formally unoxidized in bismuth compounds (i.e. core-like nature of the 6s electrons), the term inert pair effect or nonhybridization effect has been often used for a reasonable explanation. In this context, the relatively inert 4s pair of the As atom (compared with the 5s pair of Sb) may be ascribed to the stabilization due to the d-block contraction , rather than effect (1) . On the other hand, effect (2) plays an important role in the electronic and spectroscopic properties of atoms and molecules especially in the open-shell states. It not only splits the electronic states but also mixes the states which would not mix in the absence of spin-orbit interaction. As an example, it was calculated that even the ground state ( 2 " ) of Bij is 25% contaminated by Hg. In the Pauli Hamiltonian approximation there is one more relativistic effect called the Dawin term. This will tend to counteract partially the mass-velocity effect. 

As discussed in section 2.8, relativistic effects on the valence electronic structure of atoms are dominated by spin-orbit splitting of (nl) states into (nlj) subshells, and stabilization of s- and p-states relative to d- and f-states. Here we examine consequences of relativistic interactions for cubo-octahedral metal-cluster complexes of the type [M6X8Xfi] where M=Mo, Nb, W and X=halogen, which have a well defined solution chemistry, and are building blocks for many interesting crystal structures. 

It was not until the 1970s that the full relevance of relativistic effects in heavy-element chemistry was discovered. However, for the sixth row (W---Bi), relativistic effects are comparable to usual shell-structure effects and therefore provide an explanation for many unusual properties of gold chemistry155-159. The main effects on atomic orbitals are (i) the relativistic radial contraction and energetic stabilization of the s and p shells, (ii) the spin-orbit splitting and (iii) the relativistic radial expansion and energetic destabilization of the outer d and f shells. 

If spin-orbit effects are considered in ECP calculations, additional complications for the choice of the valence basis sets arise, especially when the radial shape of the / -f-1/2- and / — 1/2-spinors differs significantly. A noticeable influence of spin-orbit interaction on the radial shape may even be present in medium-heavy elements as 53I, as it is seen from Fig. 21. In many computational schemes the orbitals used in correlated calculations are generated in scalar-relativistic calculations, spin-orbit terms being included at the Cl step [244] or even after the Cl step [245,246]. It therefore appears reasonable to determine also the basis set contraction coefficients in scalar-relativistic calculations. Table 9 probes the performance of such basis sets for the fine structure splitting of the 531 P ground state in Kramers-restricted Hartree-Fock [247] and subsequent MRCI calculations [248-250], which allow the largest flexibility of... 

The information obtainable from photoelectron polarization measurements is reviewed, for both atoms and molecules, by Heinzmann and Cherepkov (1996). Even at non-relativistic excitation energy, photoelectrons can be spin-polarized (Fano, 1969). For l / 0 atoms, due to the spin-orbit splitting of the initial atomic and/or the final ionic state, photoelectrons are in most cases highly spin-polarized (up to 100%) when photoexcited with circularly polarized light. Analogous effects occur in molecular photoionization, but systematic studies have only been made for hydrogen halide molecules, HX. The electronic ground state of HX+ is X2n. 

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