Spectral moments of vibrationally excited components of continuous vibronic spectra

The spectral absorption coefficient of a continuous vibronic system is a composite of contributions which change according to the population of the vibrational levels of the lower electronic state. These components have distinctive shapes related to the shape of the vibrational wave function for a particular mode of the lower state. In addition, the component from each level of the lower electronic state is characterized by an average spectral frequency, or first spectral moment, observed as a shift from the position of the spectrum of molecules which are not vibrationally excited. The spectral moments can be calculated from sum rules. The present paper compares the spectral shifts observed in thermally excited spectra of Cl2, OCS, and O3 with those calculated using different approximations to the sum rules to examine the relative importance of: (a) the relative frequencies of the upper and lower states; (b) changes in the electronic transition moment with vibrational excitation; (c) anharmonicity; or (d) anharmonic mode coupling. It is found that each of these effects can be important, or even dominant, in individual cases.