When solving equations of the form:
$$F(C)C = SC\epsilon$$
(e.g. Hartree-Fock-Roothan or Kohn-Sham-Roothan) where $F$ is the fock matrix, $C$ is the coefficient matrix and $S$ the overlap matrix, the usual way to proceed is to first perform a change of basis and orthonormalize the AOs (atomic orbitals) by performing a Lowdin (Symmetric) orthogonalization. I know at least one case (The Psi4 program) where a different orthogonalization scheme is used (Canonical) but I haven't been able to find any information of other alternative orthogonalization schemes implemented in any programs. Are any other schemes used? If so, where and why?