Canonical orthonormalization and neglect of differential overlap

Löwdin's canonical orthonormalization procedure is non-unique if the overlap matrix has degenerate eigenvalues. A recent attempt by Roby to justify neglect of differential overlap is re-examined taking proper account of this lack of uniqueness. We conclude that his central result, eq. (6) in our paper, is formally correct in the limit of complete basis sets, but Roby's presentation lends a misleading interpretation to this equation. Consequently, some conclusions which are claimed to follow are, in fact, not valid. We briefly investigate the Roby approximation for finite basis sets and indicate the strengths and weaknesses when used for practical computations.