Limitations of roby'stheorem

Roby'stheorem establishes that, under certain conditions, electron interaction matrix elements over symmetrically orthogonalized (Löwdin) orbitals may be obtained from those over the ordinary nonorthogonal basis by simply discarding all integrals containing products of orbitals centered on different atoms (nddo approximation). We present evidence of the existence of many important cases where the error of this approximation, in practice, varies so rapidly with internuclear distance as to constitute a serious problem.