Theoretical Study of Optical Absorption Curves of Molecules. III: Force Constant and Bond-Bond Interaction in Conjugated Molecules

Theory for the calculation of force constants and of bond-bond interaction constants of carbon-carbon conjugated molecules is made by means of the NMO method. That is, we develop an earlier work of Coulson and Longuet-Higgins by improving the forms of an adiabatic potential of single-bond and of the resonance integral of π-electrons as a function of bond length. Analysing our results, we find that an increase of the force constant with bond order is entirely due to anharmonic terms of single-bond, and that π-electrons contribute to decrease the force constant very much. The bond-bond interaction which comes from a delocalizable property of π-electrons is rather small in the ground state but becomes considerably large in the excited state. It is found that the sign of the bond-bond interaction constant changes alternatively as the distance between the two bonds becomes large. Therefore, vibrational frequency of the top-mode whose vibrational motion corresponds to increase or decrease of the bond alternation is expected to be lowered very much when the bond-bond interaction is large. Our theory is applied to some polyenes, and the results are rather satisfactory. But it is found that the degree of bond alternation is small compared with experimental values for large conjugated molecules.