Molecular symmetry and closed‐shell SCF calculations. I

For efficient integral evaluation, orbital basis functions are grouped into shells and integrals into blocks in the recently developed SCF program Hondo. This shell structure is ideally suited to the scheme of Dacre and Elder for using point group symmetry. An entire block of two‐electron integrals is eliminated if it is symmetrically equivalent to another block with a higher index (four label). Using the “petite list” of blocks of integrals, a skeleton Fock matrix is formed from which the true Fock matrix is generated by “symmetrization.” We prove two theorems which provide a clear and rigorous justification for this version of the Dacre–Elder procedure. We compare SCF calculations on the phosphorus molecule using T_d symmetry with those using various subgroups of T_d. The number of integrals computed is found to be approximately inversely proportional to the order of the group. Integral evaluation time and SCF iteration time are each linear functions of the number of integrals. The computer spends a negligible amount of time in executing symmetry‐related code, and the human effort involved is little more than picking the appropriate Schönflies symbol for the molecule.