Molecular Symmetry and the Reduction of the Secular Equation

A method is given for expressing a bond eigenfunction of any multiplicity in terms of a linear independent set. The independent sets for the multiplicities corresponding to one bond and to two bonds for an arbitrary number of electrons are given. A method recently given for obtaining matrix components for singlet bond eigenfunctions is generalized to include all multiplicities. Group theory is applied to the bond eigenfunctions for symmetrical molecules to reduce the secular equation and examples are worked out for all multiplicities. The possible reasons for the approximate additivity of bond energies for molecules is examined in connection with the chemist's custom of ignoring all but the strongest bonds.