AXIS-SWITCHING CORRECTIONS TO THE DUSCHINSKY EFFECT

$^{1}$F. Duschinsky, Acta Physicochimica URSS, 7, 551-577 (1937). $^{2}$J. T. Hougen and J. K. G. Watson, Canad. J. Phys. 43, 298-320 (1965). $^{3}$I. ${\ddot{O}}$zkan, J. Mol. Spectrosc. 139, 137-162 (1990).""Author Institution: Department of Chemistry, Faculty of Science, Kyoto University; Molecular Physics Division, National Instiute of Standards and TechnologyEarly work on the Duschinsky $effect^{1}$ concentrated en relating vibrational modes in one electronic state to those in another by means of a simple rotation and translation in vibrational coordinate space: $$x_{1}^{\prime}=\sum a_{ik}x_{k}+C_{i}$$ where the subscripts i and j range over the 3N-6 vibrational degrees of freedom. Because of the different equilibrium geometries in the two electronic states, however, the form of the Eckart, conditions separating vibrational and rotational motion will be different. The consequences of this difference for rotational intensity distributions (assuming molecular shapes frozen at their equilibrium geometries in the two electonic states) has already been investigated (axis $switching^{2}$). In the present talk we examine the consequences for Franck-Condon overlap integrals in electronic transitions of polyatomic molecules. Our treatment differs somewhat from a related investigation of \""{O}$zkan^{3}$. We have found that in general the indices i and j above must be augmented to include the three rotatioal degrees of freedom, in addition to the 3N-6 vibratioal modes. The resulting formalism, when it is applied to condensed phases, remains almost unchanged from Duschinsky’s original treatment, a result which is not surprising, since the three ``rotational” degrees of freedom of the isolated molecule than become simply large-amplitude librational (i.e., special vibrational) modes. The resulting formalism is somewhat more difficult to apply to gas-phase high-resolution spectra since vibrational and rotational motions must be considered simultaneously. We are presently in the early stages of exploring the latter question, both algebraically and numerically, for various molecular geometries and geometry changes. The results of this investigation will be reported