The Use of Free Electron Model Wave Functions in the Derivation and Representation of LCAO MO Wave Functions of Conjugated Molecules

Abstract

A simple relation between free electron model and LCAO molecular orbital wave functions is derived for linear and cyclic conjugated molecules involving no branching of the π-electron system. On the basis of this relation LCAO MO wave functions and their energies can be calculated without solution of secular equations or extensive numerical computations, and simple analytic expressions for the wave functions and energies can be derived. The method assumes equal resonance and Coulomb integrals in the conjugated system but does not require neglect of overlap integrals. The types of molecules for which the method is most appropriate are discussed. For other molecules the LCAO MO WF's derived from FEM WF's may be improved by perturbation calculations. The relations are also shown to hold for molecules containing heteroatoms and branched π-electron systems if the FEM WF's are replaced by the FEM-like WF's derived. Finally, a simple method of graphic representation of LCAO WF's is proposed and illustrated.