Multireference perturbation theory with complete active space self-consistent field ͑CASSCF͒ reference functions was applied to the study of the valence →* excited states of benzene and naphthalene. The eigenvectors and eigenvalues of CASSCF with valence active orbitals satisfy pairing properties for the alternant hydrocarbons to a good approximation. The excited states of polyacenes are classified into the covalent minus states and ionic plus states with the use of the alternancy symmetry. The present theory satisfactorily describes the ordering of low-lying valence →* excited states. The overall accuracy of the present approach is surprisingly high. We were able to predict the valence excitation energies with an accuracy of 0.27 eV for singlet u states and of 0.52 eV or better for singlet g states of naphthalene. Our predicted triplet states spectrum provides a consistent assignment of the triplet-triplet absorption spectrum of naphthalene. For benzene we were able to predict the valence excitation energy with an accuracy of about 0.29 eV. The covalent minus states and ionic plus states exhibit different behavior as far as the electron correlation is concerned. The ionic plus states are dominated by the single excitations but covalent minus states include a large fraction of doubly excited configurations. The covalent minus states always give lower energy than the corresponding ionic plus states. This is true for triplet states. The dynamicpolarization effects introduced by perturbation theory are significant for the ionic plus states while those on covalent excited states are usually of the same order as in the covalent ground state. The enlargement of the active space of the reference functions represents a great improvement of the description of the ionic states. The present approach with the pairing properties has proved to be of great value in understanding and predicting the experimental data of the alternant hydrocarbons.

The multireference Møller-Plesset perturbation (MRMP) theory with complete active space self-consistent field (CASSCF) reference functions is applied to the study of the Q and B bands of free-base, magnesium, and zinc porphyrins and their derivatives. The Q band of free-base porphyrin is so weak because the transition is pseudoparity-forbidden because of the alternancy symmetry. The Q band in the visible region can be intensified if the pairing property is broken. This is achieved by various chemical modifications to the basic structure of free-base porphyrin such as external substituents, changes in conjugation pathway, and change in central substituent. The intensity and color of the Q band as well as the macrocyclic porphyrin skeleton are perturbed to a greater or lesser extent by various chemical modifications. Insertion of aza groups in meso position leads to the shrinking of the size of the central hole, whereas hydrogenation to the exo double bond of pyrrole rings expands the central hole. Substitution of nitrogen atoms for meso carbon atoms significantly intensifies the oscillator strength of the higher energy side transition of the Q band with the peak position unchanged. Ring reduction widens the splitting of two peaks of the Q band, giving rise to the characteristically strong far-red band and the weaker visible band. Changes from metal-free to metalloporphyrins have a less dramatic effect on the spectra.

The valence p ® p* excited states of anthracene and naphthacene are studied with multireference perturbation theory with complete active space selfconsistent ®eld reference functions. The predicted spectra provide a consistent assignment of all one-and twophoton spectra and T-T spectra of low-lying valence p ® p* excited states of anthracene and naphthacene. The present theory predicts the valence p ® p* excitation energies with an accuracy of 0.15 eV for anthracene and of 0.25 eV or better for naphthacene. The excited states of anthracene and naphthacene are compared with those of benzene and naphthalene studied previously. The present calculations predict that, going from anthracene to naphthacene, there is a symmetry reversal of the two lowest singlet state transitions, but not for the triplet, just as indicated by the experimental data. Some general trends of polyacene excited states are discussed based on the calculated results for benzene to naphthacene. Conclusive results obtained for anthracene and naphthacene can be used as a model for understanding the excited states of larger polyacenes.

Multireference perturbation theory with complete active space self-consistent field ͑CASSCF͒ reference functions was applied to the study of the valence and Rydberg excited states in the range of 5-8 eV of five-membered ring compounds, cyclopentadiene, furan, and pyrrole. The spectra of these molecules have been studied extensively for many years but characterization is far from complete. The present approach can describe all kinds of excited states with the same accuracy. The calculated transition energies are in good agreement with corresponding experimental data. We were able to predict the valence and Rydberg excited states with an accuracy of 0.27 eV or better except for the B 2 ϩ of pyrrole. The valence excited states of five-membered ring compounds were interpreted in terms of the covalent minus states and ionic plus states of the alternate symmetry. The unobserved 1A 1 →A 1 Ϫ transition with very weak intensity, which is hidden under the strong 1A 1 →B 2 ϩ transition, is also discussed. Overall, the present theory supports the assignments recently made by Serrano-Andres et al. based on the CASSCF plus second-order perturbation results. However, there remain some discrepancies in the assignment of the spectrum of pyrrole.

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