Towards understanding the nature of the intensities of overtone vibrational transitions
Authors: Medvedev Emile S. 
Published: November 2012

The overtone vibrational transitions, i.e., transitions between states separated by more than one vibrational quantum play important role in many fields of physics and chemistry. The overtone transition is a purely quantum process associated with the so-called dynamical tunneling [Heller, E. J., “The many faces of tunneling,” J. Phys. Chem. A 103(49), 10433–10444 (1999)10.1021/jp9924171] whose probability is small as compared to the fundamental transition. The transition probability is proportional to the Landau-Lifshitz tunneling factor similar to the Gamov factor in nuclear physics. However, as opposed to the Gamov tunneling, the Landau-Lifshitz tunneling lacks any barrier to tunnel through: Its probability looks as if the system were forced to “dive” under the barrier up to a point where the transition can be performed without any change in momentum, hence with a high probability, and then to “emerge back” in a new state. It follows that the transition probability is associated with the shape of the potential in the classically forbidden region in the same sense as the transition energy is associated with the shape of the potential in the classically allowed region, as implied by the Bohr-Sommerfeld quantization rule, and in the same sense as the probability of the Gamov tunneling is associated with the shape of the potential within the barrier region. As soon as the tunneling character of the transition is recognized, the well-known extreme sensitivity of the overtone intensities to small variations of the fitting function representing the molecular potential [Lehmann, K. K. and Smith, A. M., “Where does overtone intensity come from?” J. Chem. Phys. 93(9), 6140–6147 (1990)10.1063/1.458985] becomes fully understood: Small variations of the potential in the classical region, which do not affect the energy levels significantly, cause large variations in the forbidden region and hence do affect the tunneling factor. This dictates a clear strategy of constructing the potential energy and dipole moment functions (PEF and DMF) capable of explaining the data of vibrational spectroscopy and possessing a predictive power. In this paper, we will show that, for stretching vibrations, knowledge of the inner wall of the PEF is necessary to perform this task. Incorrect behavior of the PEF at extremely small interatomic separations corresponding to energies well above the dissociation limit results in an incorrect rate of the intensity falloff, hence a rapid increase of discrepancies between the calculated and observed intensities with overtone number. Analysis of experimental data on some di- and polyatomic molecules and their interpretations is presented, which shows that neglecting the tunneling nature of overtone transitions does not permit making predictions of the intensities with a known uncertainty. A new approach has to be developed. First of all, an ab initio PEF giving correct energy levels and having correct behavior of the repulsive wall must be constructed; thereafter, an ab initio DMF is invoked to explain the experimental data for lower (observed) transitions and to predict the intensities of higher (not yet observed) transitions with approximately the same accuracy as that for lower overtones. These ideas also apply to radiationless deactivation of rare-earth and transition-metal ions in laser media, which proceeds via overtone absorption of electronic energy by medium local vibrations.