Renormalized configuration interaction method for electron correlation in the excited states of polyenes

Abstract

Extensive configuration interaction (CI) is needed to achieve satisfactory descriptions of the optical spectra and photochemical properties of the π-electron systems of polyenes. Although a basis of single and double excitations with respect to the SCF ground state yields a qualitatively correct energy level scheme, such a treatment introduces an imbalance in the ground state correlation (well described) relative to that of the excited states (poorly described). The result is a divergence in the excitation energies with increasing size of the π-electron system. A renormalized configuration interaction method is developed to account correctly for the excited state correlation. The method is based on the finding that the main contribution to the correlation energy in the excited states is from the electrons not directly involved in the excitation, so that the correlation correction closely resembles that in the ground state. A detailed analysis of the excited state energy permits one to isolate the dominant ground-state correlation term and to determine the smaller, but not negligible, rearrangement correction. The former does not contribute to the excitation energy. The fact that the latter is approximately constant, independent of chain length, provides an explanation for the success achieved by appropriately parametrized single excitation calculations in the assignment of the optically allowed states of polyenes. To implement the renormalized CI method a localized SCF orbital set is employed and the basis functions used for the CI expansion are expressed in terms of single and double excitations with respect to the correlated ground state. It is demonstrated that for the 1B+u, 3Bu+, and 3Ag+ states, which can be characterized in terms of ’’elementary’’ single excitations, this approach gives excellent agreement with the results of more extended CI calculations. Further, it is shown that the correlation energy of the excited state can be estimated using the results of a single-excitation calculation and the ground-state double excitation coefficients.