The hydroxyl bands in the nightglow

“…(2), (18),.- (20), and (35); they are shown as curve 3 in Fig. 1. [Again, Q was chosen to fit the 1 +--0 transition intensity; we remind the reader that in this tunneling estimates approach, Q is regarded as an arbitrary constant, since only the behavior of the exponent in Eq.…”

Section: Resultsmentioning

confidence: 99%

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

Medvedev

1994

The Journal of Chemical Physics

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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.~here wm,n~ are the frequencies of the classical vibrations of levels m,n and C m,n are close to unities; e.g., 7192 J. Chern. Phys. 100 (10). 15

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“…is independent of n provided that y is large enough for both m = m 1 and m 2 (Ferguson and Parkinson, 1963). Similarly, absorption intensities measured in experiments with two-or three-photon excitation (Császár et al, 2010;Grechko et al, 2009) should also satisfy this relation for transitions from a common lower level n to different upper levels m 1 and m 2 .…”

Section: Empirical Rules For Overtone Intensities Of Stretching Vmentioning

confidence: 87%

“…Numerical calculations for various PEFs and DMFs (Child and Halonen, 1984;Ferguson and Parkinson, 1963;Lehmann and Smith, 1990;Medvedev, 1984Medvedev, , 1994Medvedev, , 1998Nikitin et al, 1993) revealed the following empirical rules for overtone transitions of stretching vibrations.…”

Section: Empirical Rules For Overtone Intensities Of Stretching Vmentioning

confidence: 95%

“…The central idea that the transition matrix element can be factorized into "quick" and "slow" parts, with the quick part being dependent on the potential alone, was first advanced for the Morse potential by Timm and Mecke (1936), Ferguson and Parkinson (1963), Child and Halonen (1984), and verified for the CH local vibrations in (CF 3 ) 3 CH by Amrein et al (1984).…”

Section: Empirical Rules For Overtone Intensities Of Stretching Vmentioning

confidence: 99%

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Towards understanding the nature of the intensities of overtone vibrational transitions

Medvedev

2012

The Journal of Chemical Physics

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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)] 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)] 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 (obs...

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The hydroxyl bands in the nightglow

Cited by 39 publications

References 10 publications

Comment on “Anharmonic properties of the vibrational quantum computer” [J. Chem. Phys. 126, 204102 (2007)]

Comment on “Anharmonic properties of the vibrational quantum computer” [J. Chem. Phys. 126, 204102 (2007)]

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

Towards understanding the nature of the intensities of overtone vibrational transitions

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