Irreducible Representations of Molecular Orbitals

Each M.O. is subjected to the operation

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

from which the expectation value

$\begin{displaymath}\chi=<\psi'\vert\psi> \end{displaymath}$

can readily be calculated.

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

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

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.