Vibrational Interactions in Pariser—Parr Theory. I. Bandwidths and Transition Intensities

Abstract

It is shown that bandwidths of some transitions can be calculated with good accuracy in the Pariser—Parr theory. For these calculations the critical point is a knowledge of the variation of the bond resonance integral β with respect to distance, which is given by $\mathrm{\kappa =-d}\ln {\text{(−β)/dR=2.0\hspace{0.17em}Å}}^{\text{−1}}$ . Calculations are carried out for the bandwidths of the N–V transition of ethylene and the ¹A_1g→¹E_1u, ¹E_2g transitions of benzene and the intensities of the ¹A_1g→¹B_2u, ¹B_1u transitions of benzene. Satisfactory agreement with experiment is obtained; the neglect of electronic repulsion terms is demonstrated to have a relatively small effect. Selection rules are established for the strength of vibrational coupling in alternant hydrocarbons.