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Two-Electron Terms and the Douglas-Kroll-Hess Approximation

Two-Electron Terms and the Douglas-Kroll-Hess Approximation [Pg.308]

So far we have made no reference to the two-electron terms of the Hamiltonian. Performing the free-particle Foldy-Wouthuysen transformation took the potential from an even operator to a combination of even and odd operators. The same will be true of the two-electron terms, except that a transformation must be performed on both electron coordinates. For the Coulomb interaction the resulting operator is [Pg.308]

To be entirely consistent with the one-particle terms, a second transformation should be applied to this operator. However, it has been found that this first transformation of the two-electron operators is about as important in scalar relativistic calculations as the transformations of the one-electron operators up to fifth order (Wolf et al. 2002). The second transformation of the two-electron operators is therefore unlikely to be of great significance. The reason is the strength of the nuclear potential, which is a factor of Z larger than the electron-electron interaction and is attractive rather than repulsive. [Pg.308]

The transformed two-electron operator bears a striking resemblance to the operator from the modified Dirac equation given in (15.43). We need only define [f = and t = [c /( p- -mc )],4 [f andtheidentityiscomplete. Theanalysisoftheterms of the modified Dirac equation into scalar and spin-orbit terms in section 15.4 can then be transferred directly to the above equation. The kinematic factors are reintroduced at the end to obtain the final expressions. [Pg.308]

Even though the number of transformed integrals is no larger than in a nonrelativistic calculation, the cost of the integral evaluation remains. What we would like is an approximation that is no more severe than the truncation of the transformed one-electron operator and that reduces the integral evaluation work. [Pg.309]




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