Weighted orthogonalization of atomic orbitals: A stable alternative to the Carlson–Keller method

In quantum chemistry, molecular orbitals are frequently orthogonalized. Often, some orbitals should change less than other orbitals during the orthogonalization. Such an outcome calls for a weighted orthogonalization. One instance for this task occurs for the construction of quasi-atomic orbitals. At the present time, the algorithm of Carlson and Keller is the only method that accomplishes this objective. A numerical weakness of the Carlson–Keller weighted orthogonalization method is identified: the method breaks down when the spread in the weights becomes too large. An alternative algorithm is presented that accomplishes the same weighted orthogonalization and eliminates these numerical problems. The benefits of the new algorithm over the Carlson–Keller method are exemplified by constructing ordered correlating quasi-atomic orbitals for HNO and CO using large basis sets.