Computer Generation of Molecular Symmetry Orbitals

Abstract

We show how molecular symmetry adapted linear combinations of atomic orbitals can be produced by carrying out standard manipulations on the matrices that represent values for each of two rotationally invariant operators evaluated over the atomic orbitals of interest. Attention is given to obtaining final orbitals that have not only the desired transformation properties but that are also ``beautiful'' in the sense that they have simple atomic orbital coefficients like the symmetry orbitals that are traditionally discussed in the literature and generated by inspection. Our implementation of this method in Fortran on a CDC 3600 requires a time for symmetry adaptation that increases as the symmetry of the molecule becomes greater. In several calculations that we have done on small (5–12 atoms), reasonably symmetrical (D2h–Oh) molecules, the adaptation required times comparable to those required for calculating the overlap and kinetic energy matrix elements used in the symmetry adaptation.