Correlation effects in the low-lying excited states of the PPP models of alternant hydrocarbons. II. State correlation diagrams

Abstract

It is shown how to construct highly realistic state correlation diagrams for alternant hydrocarbons in the π-electron approximation based on the Pariser-Parr-Pople (PPP) Hamiltonian. These diagrams display the dependence of the N-electron eigenenergies of the PPP Hamiltonian on the coupling constant, which is chosen conveniently as the reciprocal value of the resonance integral β. These diagrams are easily constructed, using a minimum of calculations, since (a) the exact eigenstates and energies of the PPP Hamiltonian are easily found in both fully correlated and uncorrelated limits, (b) the states in both limits may be interrelated using the spin, space, and alternancy symmetry classification as well as the assumption of the noncrossing rule, and (c) the slopes of the eigenenergy dependence on the coupling constant is easily available in both limits. The resulting correlation diagrams give a good approximation to the low-lying exact eigenvalues of the PPP Hamiltonian for the whole range of the coupling constant and yield the correct sequences of the low-lying excited states for physically plausible values of the resonance integral.