Quantum Mechanics of Mobile Electrons in Conjugated Bond Systems. I. General Analysis in the Tight-Binding Formulation

Abstract

The quantum-mechanical treatment is carried through for a set of electrons in a homonuclear conjugated bond system of arbitrary size, including electronic interaction and including all overlap effects between neighbors. All framework contributions are obtained by explicit integration over the framework Hamiltonian, including the effect of nonconjugated neighbor atoms and differentiating between different types of conjugated atoms (joint, nonjoints, etc.). Expressions are given for the ground-state energy, ionization potential, electron affinity, electronegativity, and for the configuration interaction matrix for the calculation of excited states, assuming singly excited configurations. The results take simple forms permitting instructive interpretations. The partial additivity of one-electron binding-energy contributions, obtained as eigenvalues of topological molecular orbitals, and the approximate validity of the ``neglect of differential overlap'' is proved.