Expressions for the second-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities
Matthias Meister · Physical Review B · 2005
In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding modeling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather technical and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-center matrix element is aligned along the $z$ axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.