In this study the idea of the topological similarity index has been ge
neralized so that its applicability reaches beyond a simple HMO model
to semi-empirical or even ab initio methods. The greatest advantage of
this new index is its complete positional invariance, which makes it
possible to avoid time consuming optimization with respect to the mutu
al position of molecules. As a consequence of this invariance, the ind
ex can find a number of interesting applications, especially in the de
sign of compounds with desired biological properties. The applicabilit
y of the index has been numerically tested on a series of isosteric an
d isoelectronic molecules.