Vibronic Calculations in Benzene

A group-theoretical reduction incorporating normal-coordinate parameters is applied to obtain expressions for the oscillator strengths of forbidden B2u, B1u, and E2g transitions in benzene in terms of the minimum number of electronic integrals. The simplification obtained encourages the testing of wave functions within the Herzberg-Teller framework as well as empirical evaluation of the theory. An investigation is made of the possible effect of isotopic substitution on forbidden intensities. The group-theoretical reduction is carried out for 1,4 dideuterobenzene, sym-benzene-d3, 2,3,5,6-tetradeuterobenzene, benzene-d6, and a hypothetical molecule p-di-X-benzene (where (X) = 20 and C—X = 1.40 A). It is observed that the B2u and B1u transitions are very insensitive to mass effects independent of the nature of the electronic functions. On the other hand, E2g transitions may or may not show a significant sensitivity depending on the details of the wave functions. By way of illustration, oscillator strengths are calculated for all compounds for B2u, B1u, and two E2g transitions using conventional benzene ASMO functions and published integrals. The distribution of oscillator strengths among all active normal modes is given for benzene, benzene-d6, and p-di-X-benzene. It is found that especially for the E2g transitions the distribution among normal modes is considerably more sensitive to mass effects than is the total oscillator strength. A general expression is given for the temperature dependence of ``forbidden'' transition probabilities.