Semiempirical Calculation on the Lower Electronic States of the Benzene Molecule

Abstract

Within the semiempirical ASP—LCAO—MO—CI framework proposed by Pariser and Parr, the lower excited levels of the benzene molecule are calculated by considering CI up to and including doubly excited configurations. This calculation has three purposes: (i) a check on the value of the core resonance integral βCC, (ii) the symmetry assignment of the controversial absorption system around 2000 Å and (iii) the elucidation of the change of the ring-breathing vibrational frequency due to electronic excitation. From the condition that the calculated value of the lowest 1 B2u−1 A1g transition energy agree with experiment, the core integral βCC is found to be −2.7217 eV, which is to be compared with −2.39 eV suggested originally by Pariser and Parr without considering CI. By using this new value of βCC, CI calculations for the lower singlet levels are carried out. The theoretical energy levels are compared with the experimental data as well as the calculated values with nonempirical and the other semiempirical methods. The present calculation favors the 1 B1u←1 A1g assignment for the 2000-Å absorption system. The wavefunctions as approximated by linear combinations among the ground and the singly and doubly excited configurational functions are, also, obtained for the ground 1 A1g and the lowest-excited 1 B1u, 1 B2u and 1 E2g states. From these wavefunctions the bond orders of the CC bonds in these states are obtained. By using the values of the CC bond order, the changes in the CC bond length and the ring-breathing frequency are estimated for the 1 B1u←1 A1g, 1 B2u←1 A1g and 1 E2g←1 A1g transitions and compared with the available experimental values.