Relativistic Effects in Model Potentials

Spin-free relativistic effects are readily incorporated into the ab initio model potential approximation by using a one-component spin-free relativistic method for the atom, such as the Cowan-Griffin method or the Douglas-Kroll-Hess method. 

In the case of the Cowan-Griffin method, the spin-free one-electron relativistic operators are incorporated into the spectral representation of the exchange potential  

M is the matrix of the combined core exchange and spin-free relativistic operator, given by 

The potential in this definition is the SCF potential, not merely the nuclear attraction potential. The model potential therefore includes both one- and two-electron relativistic corrections. The principal quantum number is that of the outermost valence orbital. Note that this makes the model potential dependent on the valence orbitals. For model 

In the case of the Douglas-Kroll-Hess method, no special treatment of relativistic effects is required apart from the use of the one-electron Douglas-Kroll-Hess operator for the valence electrons. The direct and exchange potentials for the core electrons are treated in exactly the same way as in the nonrelativistic case but using the atomic Douglas-Kroll-Hess orbitals. However, only the unmodified part of the nuclear attraction is partitioned into a core and a valence part the core part is included with the core direct potential just as in the nonrelativistic case. 

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Model potential methods and their utilization in atomic structure calculations are reviewed in [139], main attention being paid to analytic effective model potentials in the Coulomb and non-Coulomb approximations, to effective model potentials based on the Thomas-Fermi statistical model of the atom, as well as employing a self-consistent field core potential. Relativistic effects in model potential calculations are discussed there, too. Paper [140] has examples of numerous model potential calculations of various atomic spectroscopic properties. 

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