Pi-Electron Forces between Conjugated Double Bond Molecules

Abstract

The long-range forces between large conjugated double bond molecules are highly directional and anomalously strong. This is the result of pi electrons moving freely from one end of the conjugated double bond system to the other, making the molecule behave like an extended oscillator. All three types of dispersion forces: σσ, σπ, and ππ are calculated for ethylene, acetylene, and the higher polyenes. In addition the ππ interaction energy is calculated for benzene. The free electron molecular orbitals are used for the π electrons and products of these orbitals are approximated by ``transition monopoles.'' Our treatment of the σ electrons and the use of the transition monopoles were suggested by London. The resulting energies are easy to calculate and easy to interpret. The ππ energy is proportional to the square of the energy of interaction of two real transition dipoles (real in the sense of the monopoles being separated by a finite distance). Previously, Coulson and Davies calculated the ππ interaction energy using LCAO orbitals and evaluating all integrals accurately; however, because of the complicated nature of their calculations it was not possible for them to obtain a simple understanding of the variation of the energy with the orientations of the molecules. The values we obtain for the ππ energy agree with those of Coulson and Davies except for a scale factor, our results being uniformly 35 smaller. Such a scale factor corresponds to an adjustable parameter in either the Coulson and Davies treatment or ours. The σπ interaction energy has never previously been considered. For long polyenes, for which a simplified treatment is given, the ππ energy is larger than the σπ which is larger than that of the σσ. In the appendix, the free-electron model is used to calculate the pi-electron contribution to the polarizability and excellent agreement is obtained with the LCAO calculations of Davies.