Molecular Motion and the Moment Analysis of Molecular Spectra in Condensed Phases. I. Dipole-Allowed Spectra

Abstract

Molecular absorption and emission spectra (of a vibrational transition or of a single vibrational component of an electronic transition) are analyzed in terms of moments of their intensity distributions. The results are valid for an arbirtary intermolecular potential energy. The first-moment formula allows one to identify, in an experimental spectrum, the shifted band origin. The second moment is found to have additive contributions from dynamical terms and from fluctuations in the environmental frequency shift. The dynamical terms depend on the average molecular rotational kinetic energy, the principal moments of inertia of the molecule, and the direction of the transition moment relative to the principal axes of inertia. In the classical limit, the average rotational kinetic energy is determined by the temperature, and the dynamical terms of the second moment are then independent of the intermolecular potential energy. If general, the measurement of a second moment gives an upper limit to the average rotational kinetic energy. If the shift fluctuation effect is small, the second moment measures the rotational kinetic energy. The third and higher moments depend on averages of angular derivatives of the intermolecular potential energy, as well as on the rotational kinetic energy and shift-fluctuation-type terms found in the second moment. For example, one of the contributions to the fourth moment of a linear molecule is the mean squared torque on the molecule.