Electric field gradient expressions for transition metal elements

1 Electric Field Gradient Expressions for Transition Metal Elements 

For transition metal atoms, the dominant contribution to the electric field gradient at a nucleus originates in the valence shell centered on that nucleus. The expressions for this central contribution are given in Eq. (8.43) for Slater-type, exponential, density functions, defined as in Eq. (3.34)  

Expressions (8.43) for the elements of the traceless quadrupole tensor can be written in a slightly different form as 

Substitution of Eq. (10.18) in Eq. (10.20), with the value of n(2) in Eq. (10.18) equal to 4 for 3d valence-shell density functions of first-row transition metal atoms (chapter 3), gives1 

The value of Qr is sensitive to the nature of the radial function. The Qr for the radial dependence of the Hartree-Fock isolated atom function can be evaluated analytically using the Clementi-Roetti Slater-type expansions, defined by expression (8.38) (dementi and Roetti 1974). The result is a weighted sum over terms of the type (k()3/[h,(H + l)(n, + 2)], each with the appropriate expansion coefficient. For the isolated Fe atom, one obtains 

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