Theory of Projectors and Its Application to Molecular Symmetry

Abstract

Projector theory can serve as a powerful tool to perform the symmetric computation of molecular systems. The work of William Harter has long demonstrated the effectiveness of this theory in molecular spectroscopy; however, it seems its usefulness has not been realized by many in the field. We have described this methodology and have considered the D3 symmetry system and the tetrahedral symmetry of methane molecules as concrete examples where the computed rotation tensors and vibrational wavefunction were derived for some symmetry states.