Irreducible Representations of  Molecular Orbitals

Each M.O. is subjected to the operation

\begin{displaymath}\psi' = \vert R\vert\psi>

from which the expectation value


can readily be calculated.

All χ's within a given degenerate manifold are summed:

\begin{displaymath}\chi_i = \sum_j\chi_j^{(i)}

where j runs over all components of the degenerate manifold i.

This results in a set of characters which can be compared to those stored in the character tables.

Since molecular orbitals involve single electrons, the irreducible representations are rendered into lower case before printing.