Relativistic effects Relaxation

Finally, a comment regarding relativistic effects and the calculation of one-electron energies and monopole relaxation shifts. The most convenient way to obtain relativistic zlSCF one-electron energies is to use the Dirac-Fock-Slater (DFS) zlSCF values tabulated by Huang et al.82). These are very close (a few tenths of an eV) to DF JSCF, and the relativistic monopole relaxation shift is the given by... 

Equation (45) is to be preferred to the non-relativistic Eq. (36 b) in the case of heavy atoms with large spin-orbit slittings. zlf° now measures monopole relaxation and screening including relativistic effects and is extremely useful for the calculation of approximate binding energies of double and multiple vacancy levels (Eq. (38)-(40)) for which zlSCF results are very scarce. 

DV-Xa molecular orbital calculation is demonstrated to be very efficient for theoretical analysis of the photoelectron and x-ray spectroscopies. For photoelectron spectroscopy, Slater s transition state calculation is very effective to give an accurate peak energy, taking account of the orbital relaxation effect. The more careful analysis including the spin-polarized and the relativistic effects substantially improves the theoretical results for the core level spectrum. By consideration of the photoionization cross section, better theoretical spectrum can be obtained for the valence band structure than the ordinary DOS spectrum. The realistic model cluster reproduce very well the valence state spectrum in details. 

This theorem is recognized as an approximation as, apart from the inaccuracies inherent in the S.C.F. method (such as neglect of electron correlation and relativistic effects), it assumes that the molecular orbitals are the same for the molecule and the molecular ion. Many ASCF calculations have shown (see for example 14 16)) that if an electron is removed from a metal localized orbital, considerable charge migration towards the metal occurs this is termed relaxation. These relaxation effects give ionization energies smaller values than those expected on the basis of Koopmans theorem. For ionization from ligand based orbitals, relaxation effects are smaller and more constant. 

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