The relativistic crystal field

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Abstract
It is shown that approximate relativistic radial wavefunctions can be constructed from nonrelativistic wavefunctions by allowing for nl to n'l configuration interaction due to the spin-orbit coupling. This construction is used to demonstrate that the dominant contribution to the relativistic crystal field is not due to the mechanism which has frequently been proposed (i.e. the anisotropy of the electrostatic potential). A new model is employed to estimate the contribution of overlap and covalency effects to the relativistic crystal field, and the role of this field in splitting the ground state of Gd3+ is discussed. The method used by the author could be employed to calculate relativistic effects in the many cases where solutions of the relativistic Hartree-Fock equations are not readily available.

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