A vectorial model of photon–molecule interactions and the development of an Octupole Rule of vibrational excitation

Abstract

An alternative approach to the assignment of molecular vibrations is suggested in which both the molecule and the photon are taken as coincident quantum mechanical entities at the instant of impulse. This model permits the description of the excitation in a simple vectorial form. Using subduction techniques, complete and orthonormal basis vectors for both particles can be defined and the probabilities of excitation are directly related to the overlap of these basis vectors at the instant of space and time coincidence. The model obeys fully the requirements of the 3n – 6 degrees of freedom rule and is found to express the motions of atoms in terms of their overlap with available multipole fields of the photon. To first order the photon–molecule interaction is taken as the Coulomb potential between the electric fields of the photon and those of the shielded atomic nuclei. The relatively low valence electron density is ignored but becomes important in second order. With this assumption, molecular translational motion correlates to, and exhausts, the dipolar photon field, rotation corresponds to three of the five components of the photon quadrupole and ungerade internal modes are first permitted by overlap with the photon octupole. Some of the consequences of this Octupole Rule are discussed with particular reference to octahedral molecules from which molecules of lower symmetry can be algebraically subduced.