The accuracy of the quasiclassical Landau–Lifshitz formula for matrix elements and its application to the analysis of the intensities of vibrational overtone transitions

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Abstract
Intensities of vibrational overtone transitions have been analyzed on the basis of the quasiclassical Landau–Lifshitz formula including the pre-exponential factor derived previously. The accuracy of this formula is shown to be very high, on the order of a few percent. An unusual feature of the Landau–Lifshitz formula is the prediction that the overall rapid decrease in intensity with overtone number is highly sensitive to the behavior of the analytical continuation of the molecular potential into regions where the amplitudes of the wave functions are negligible. The dipole moment enters the slowly varying prefactor, which in general superimposes only small modulations on the above steep intensity falloff. However, this prefactor may go through zero, in which case the intensities of one or two transitions nearest the prefactor’s zero are anomalously low. These results imply that knowledge of the analytical continuation of the potential is crucial for extracting meaningful information about the dipole moment from overtone intensities.