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

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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 dπ 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.