On the rapid evaluation of cofactors in the calculation of nonorthogonal matrix elements

The calculation of matrix elements involving nonorthogonal orbitals is speeded up by recognizing the orthogonalities between orbitals, leading to generalized Slater rules. The block structure present in the overlap matrix makes an efficient evaluation of its cofactors possible. These cofactors are calculated per subblock, each with its own parity sign. An adjustment parity sign has to be evaluated, which is added to the combined local signs, to give the correct total sign for the matrix element. An algorithm for the evaluation of this adjustment sign has been developed, making an easy and correct evaluation possible. The current scheme is shown to be very efficient, but possibilities for further improvement remain.