Knowledge Bank

The vibrational and rotational coordinates of a polyatomic molecule in one electronic state are, in general, quite different from those in another state, because of the different equilibrium geometries in different electronic states. The difference of the coordinates between the two states influences the vibronic or rovibronic transition intensity distribution. The first consideration of this was done by Duschinsky in 1937, and he pointed out the linear relation between the vibrational coordinates of two electronic states with 3N-6 vibrational degrees of freedom $(‘‘Duschinskyeffect”).1$ On the other hand, Hougen and Watson showed the importance of the ""axis switching effect"" for rotational line intensities because of the fact that each electronic state has its own molecule-fixed axis $system.2$ In the present talk we extend the idea of the axis switching effect to apply to general problems where vibrational motion as well as rotational motion occurs. We examine the consequence for the vibronic and rovibronic intensities of polyatomic molecules in the gas phase, in which the rotational motion should be described by the Euler angles ($\chi$, $\theta$, $\varphi$). Since the axis switching angle is a function only of the instantenious displacement vectors of one state. $B,2$ it can be shown that the rotational coordinates ($\chi A$, $\theta A$, $\varphi A$) of a second state A are a function of both the rotational coordinates ($\chi B$, $\theta B$, $\Pi B$) of state B and the vibrational coordinates ($QB)$, while the vibrational normal coordinates ($QA)$ of state A are still only a function of $QB$. The relation between $QA$ and $QB$, however, is no longer linear as was discussed by ""{o}zkan.$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ The consequences of the above arguments have been investigated to reveal the following effects on the transition intensities: 1) the nonlinear relation between $QA$ and $QB$ affects the Franck-Condon integrals, and 2) the vibrational dependence of the axis switching angle plays an additional role in the anomalous rotational and vibrational selection rules of rovibronic transitions. Neither of the above effects has been extensively considered before. In addition to the algebraic equations, some numerical examples of the effects will be reported.