Effective nonrelativistic

Further, the emphasis of our review is on calculations that include both relativistic and electron correlation effects. Nonrelativistic calculations are usually only mentioned when a corresponding relativistic calculation is available and allows us to determine relativistic effects. Uncorrelated calculations will not be discussed whenever corresponding results including correlation effects are available. There exists far more experimental than theoretical information on lanthanide systems, and only a few of the important experimental papers can be cited in this article. We refer to the theoretical papers reviewed here for a more complete list of citations. 

Section VI shows the power of the modulus-phase formalism and is included in this chapter partly for methodological purposes. In this formalism, the equations of continuity and the Hamilton-Jacobi equations can be naturally derived in both the nonrelativistic and the relativistic (Dirac) theories of the electron. It is shown that in the four-component (spinor) theory of electrons, the two exha components in the spinor wave function will have only a minor effect on the topological phase, provided certain conditions are met (nearly nonrelativistic velocities and external fields that are not excessively large). 

Table 4.2 Nonrelativistic (NR) and relativistic (R) ionization potentials A p and electron affinities AEp (positive values and in eV), relativistic effects Ap and relativistic enhancement factors y for the Group 11 elements of the periodic table.

Table 4.3 Nonrelativistic (NR) and relativistic (R) static dipole polarizabilities tto (in A ), relativistic effects Af.aD, and relativistic enhancementfactors Yaforthe Croup 11 elements ofthe periodic table.

Relativistic quantum mechanics yields the same type of expressions for the isomer shift as the classical approach described earlier. Relativistic effects have to be considered for the calculation of the electron density. The corresponding contributions to i/ (0)p may amount to about 30% for iron, but much more for heavier atoms. In Appendix D, a few examples of correction factors for nonrelativistically calculated charge densities are collected. Even the nonrelativistically calculated p(0) values accurately follow the chemical variations and provide a reliable tool for the prediction of Mossbauer properties [16]. 

The twin facts that heavy-atom compounds like BaF, T1F, and YbF contain many electrons and that the behavior of these electrons must be treated relati-vistically introduce severe impediments to theoretical treatments, that is, to the inclusion of sufficient electron correlation in this kind of molecule. Due to this computational complexity, calculations of P,T-odd interaction constants have been carried out with relativistic matching of nonrelativistic wavefunctions (approximate relativistic spinors) [42], relativistic effective core potentials (RECP) [43, 34], or at the all-electron Dirac-Fock (DF) level [35, 44]. For example, the first calculation of P,T-odd interactions in T1F was carried out in 1980 by Hinds and Sandars [42] using approximate relativistic wavefunctions generated from nonrelativistic single particle orbitals. 

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