Cluster expansion of the wave function. Valence and Rydberg excitations and ionizations of benzene

Abstract

The SAC (symmetry-adapted cluster) expansion and the SAC-CI theory are applied to the calculations of the valence and Rydberg excitations and the ionizations of benzene. The active space consists of 80 MO’s including both π and σ spaces; viz., 35π+45σ for the valence excitations and ionizations and 29π+51σ for the Rydberg excitations. For the lower six valence excited states, 3B1u(T1), 3E1u(T2), 1B2u(S1), 3B2u(T3), 1B1u(S2), and 1E1u(S3), generated from the π(e1g)→π*(e2u) transitions, the excitation energies are reproduced to within 0.5 eV of the experimental values with the average discrepancy being 0.34 eV. The first three states are explainable within the π electron space. For the other three states, the σ-reorganization effect is very important; viz., 0.6, 0.7, and 0.8 eV for the T3, S2, and S3 states, respectively. The polarization d π function also works to lower the T3 and S2 states by 0.3 and 0.4 eV, respectively. The total lowerings from the SDT π-CI of Hay and Shavitt to the 35π+45σ SAC-CI are about 1 eV for these three states. With including the σ-reorganization effect, the diffuse nature of the S3 state, a typical V state, decrease from 〈x2〉=62 (π SAC-CI) to 41 (π+σ SAC-CI) a.u., in comparison with the ground state value of 30 a.u. Accordingly, the oscillator strength changes from 0.61 (π SAC-CI) to 1.03 (π+σ SAC-CI). The first systematic theoretical study is given for the Rydberg excitations including both π and σ states. With the aid of the recent experimental studies due to the MPI (multiphoton ionization) spectroscopy, the lower Rydberg excited states are almost completely identified. The SAC-CI results agree with the experimental values to within 0.3 eV for all the Rydberg states studied here. The σ-reorganization effect on the Rydberg transitions is about 0.3 eV. The SAC-CI calculation further gives satisfactory results for the outer and inner valence ionizations and their satellite peaks. The theoretical ionization spectrum well reproduces the general trends of the observed ESCA spectrum.