Linear scaling computation of the Fock matrix. III. Formation of the exchange matrix with permutational symmetry

A direct comparison is made between two recently proposed methods for linea r scaling computation of the Hartree-Fock exchange matrix to investigate th e importance of exploiting two-electron integral permutational symmetry. Ca lculations on three-dimensional water clusters and graphitic sheets with di fferent basis sets and levels of accuracy are presented to identify specifi c cases where permutational symmetry may or may not be useful. We conclude that a reduction in integrals via permutational symmetry does not necessari ly translate into a reduction in computation times. For large insulating sy stems and weakly contracted basis sets the advantage of permutational symme try is found to be negligible, while for noninsulating systems and highly c ontracted basis sets a fourfold speedup is approached.