The expressions for the 2nd-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities

摘要

In a recent publication it has been shown how to generate derivatives withrespect to atom coordinates of Slater-Koster matrix elements for the tightbinding (TB) modelling of a system. For the special case of a mixed secondpartial derivative at coordinate singularities only the results were stated inthat publication. In this work, the derivation of these results is given indetail. Though it may seem rather `technical' and only applicable to a veryspecial case, atomic configurations where the connecting vector between the twoatoms involved in a two-centre matrix element is aligned along the z-axis (inthe usual approach) require results for precisely this case. The expressionsderived in this work have been implemented in the DINAMO code.