Correlation effects in the spectra of polyenes

A Hamiltonian of the Pariser-Parr-Pople form is employed to investigate the effect of correlation on the π-electron spectrum of polyenes. Two limiting cases for the electron-electron interaction (short- and long-range limit) are considered, and it is shown that they yield descriptions corresponding to the standard valence-bond (Dirac-Heisenberg) and molecular-orbital models, respectively. The intermediate, chemically most interesting, range is examined in detail by means of a full configuration-interaction treatment with an exponential model potential that includes a variable effective range parameter. It is shown that correlation effects become more important as the effective range of the interaction decreases. The states of polyenes are classified as covalent or noncovalent, and it is found that the former are much more sensitive to correlation than the latter. Configuration interaction through double excitations yields a qualitatively correct ordering for all states in the chemical range, but triple and quadruple excitations are required for quantitative results. Applications to butadiene, hexatriene, and benzene demonstrate that correlation effects in these molecules lead to an important lowering in energy of the manifold of covalent states relative to that of the noncovalent states; most important, the first covalent (¹A _g^-) state of the polyenes is found to be near degenerate with the strongly allowed noncovalent (¹B_u⁺) state. Density correlation functions and the fluctuation potential are obtained for the polyenes and used to clarify the nature of the correlation correction. Configuration interaction including double excitations is performed for polyenes through C₁₂H₁₄ to exhibit the length dependence of the correlation effects. It is shown that with increasing chain length, an increasing number of covalent states appears in the energy range of the two usually observed excited ¹B_u⁺ and ¹A_g⁺ (cis peak) states.