On several alternatives for Lِwdin orthogonalization

Several alternative procedures of orthogonalization involving the metric of the linear vector space formed by columns of the matrix of LCAO MO coefficients are briefly discussed and exemplified using electron population analyzes and orbital-atom assignment descriptors. The newly proposed procedures put emphasis on the resemblance constraints between the relevant non-orthogonal and pre-orthogonalized LCAO MO column matrices representing the subspace of occupied molecular orbitals in the final orthogonalization step. Since only the subspaces of occupied MOs completely determines the electronic structure of chemical species they give rise to definitely more adequate and chemically meaningful orthogonal atomic orbitals than the original Löwdin’s atomic orbitals.