A generalization of the löwdin orthogonalization

The Löwdin orthonormalized set consists of those unique orthonormal functions which minimize the quantity Σi∫|gi — fi|2 dv, i.e., the sum of the squared distances in the Hilbert space between each initial function ff and a corresponding function gg of the orthonormal set. In this paper, the Löwdin orthogonalization is extended to a more general transformation. The new transformation also minimizes the sum Σi∫|gi — fi|2 dv dv, but the overlap matrix of the resultant functions gg is an arbitrary positive definite matrix in contrast to the unit matrix in the Löwdin orthogonalization. The new orbital set may be useful as a basis set for some many-electron problems in which the smallness of the sum Σi∫|gi — fi|2 dv and a particular form of the overlap matrix are requested at the same time.