Theory of Shifts of Vibration—Rotation Lines of Diatomic Molecules in Noble-Gas Matrices. Intermolecular Forces in Crystals

Abstract

It is shown that the observed shift of infrared lines of diatomic molecules trapped in noble-gas crystals can be considered to be made up of a ``vibrational'' shift of the band center with a superimposed ``rotational'' shift dependent on the rotational quantum number J. These shifts were studied by means of a detailed analysis of the molecular motion. Application of the Born—Oppenheimer method shows that the intermolecular potential energy, which governs the rotational and translational motions of a system of electronically unexcited molecules, depends on v, the intramolecular vibrational state. This dependence is analyzed using an extension of the principle of corresponding states, thus introducing v-dependent Lennard-Jones force constants ε and σ. Explicit values of the variation with v of ε and σ have been calculated taking into account dispersion, induction, and repulsion forces. In this way vibrational shifts of HCl, DCl, HBr, and CO in Ar, Kr, and Xe matrices were obtained. Rotational shifts are interpreted by assuming that the trapped molecule is free to rotate about a point which does not coincide with the molecular center of mass. The resulting coupling between the rotational motion of the molecule and its constrained translational motion in the lattice is treated as a perturbation. The relation between this theory and the crystal-field theory is discussed.