On the use of spatial symmetry in atomic‐integral calculations: An efficient permutational approach

The minimal number of independent nonzero atomic integrals that occur over arbitrarily oriented basis orbitals of the form ℛ( r ) · Y lm (Ω) is theoretically derived. The corresponding method can be easily applied to any point group, including the molecular continuous groups C ∞ v and D ∞ h . On the basis of this (theoretical) lower bound, the efficiency of the permutational approach in generating sets of independent integrals is discussed. It is proved that lobe orbitals are always more efficient than the familiar Cartesian Gaussians, in the sense that GLO s provide the shortest integral lists. Moreover, it appears that the new axial GLO s often lead to a number of integrals, which is the theoretical lower bound previously defined. With AGLO s, the numbers of two‐electron integrals to be computed, stored, and processed are divided by factors 2.9 (NH 3 ), 4.2 (C 5 H 5 ), and 3.6 (C 6 H 6 ) with reference to the corresponding CGTO s calculations. Remembering that in the permutational approach, atomic integrals are directly computed without any four‐indice transformation, it appears that its utilization in connection with AGLO s provides one of the most powerful tools for treating symmetrical species.