  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 (TB) modelling 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-centre 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.
