Symmetrical orthogonalization within linear space of molecular orbitals

An alternative procedure of orthogonalization involving a metric matrix of the linear vector space formed by the columns of LCAO matrix is introduced. It is proved that this procedure is fully equivalent the original Löwdin’s scheme. Also, a few modifications involving a two-step orthogonalization scheme are outlined and briefly discussed. Numerical results of test calculations of atomic charges for several representative molecules seem to fully validate the newly proposed methodology.