On the quasiclassical calculation of fundamental and overtone intensities

Nikitin, E. E.; Noda, Chifuru; Zare, Richard N.

doi:10.1063/1.464640

Cited by 29 publications

(26 citation statements)

References 10 publications

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“…Surprisingly, they found extreme sensitivity of the higher-overtone intensities to even minor variations of the potential: The potentials investigated had nearly the same energy levels and perfect overlaps of the wave functions, yet the intensities were drastically different. The conclusion from these studies was that the above-mentioned property was the steepness of the repulsive wall of the potential in agreement with other studies (Medvedev, 1984(Medvedev, , 1985b(Medvedev, , 1998Nikitin et al, 1993). The immediate outcome of this result was a straightforward explanation to the so-called chemical transferability of the CH higher-overtone intensities observed in rows of similar compounds [see, for example, Ahmed and Henry (1987); ; ; Lange et al (2001); Lehmann and Smith (1990); Lewerenz and Quack (1986); Phillips et al (1998); Vaida et al (2008)] and insensitivity of the intensities to electron correlations (Kjaergaard et al, 1997Schwenke and Partridge, 2000).…”

Section: Introductionsupporting

confidence: 90%

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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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Section: Introductionsupporting

confidence: 90%

“…In Sec. III B the repulsive wall in the tunneling region is specified by the corresponding segment of the displacement axis, and the effect of the repulsive wall is compared with the one considered by Lehmann and Smith (1990); Nikitin et al (1993). The tunneling exponents are calculated for some potentials in Sec.…”

Section: Introductionmentioning

confidence: 99%

Towards understanding the nature of the intensities of overtone vibrational transitions

Medvedev

2012

The Journal of Chemical Physics

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“…Still, one practical question remained: Is it still possible to get a reliable estimation of the quasiclassical matrix elements between distant states by using information on the motion of a system solely in a classically allowed region of the phase space, without making an excursion into the complex time and space domain? This is indeed possible for a certain class of interactions, and the Landau-Lifshitz matrix elements can be recovered from the Fourier transforms of the classical functions calculated along real-time trajectories (48)(49)(50). These findings applied to an earlier quasiclassical theory of vibrational predissociation (51) showed that the quasiclassical theory is extremely close to the quantum theory by Beswick & Jortner (52).…”

Section: A Story Of the Landau-teller Modelmentioning

confidence: 65%

NONADIABATICTRANSITIONS: What We Learned from Old Masters and How Much We Owe Them

Nikitin

1999

Annu. Rev. Phys. Chem.

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104

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Key Words nonadiabatic coupling, analytical continuation, quasiclassical approximation s Abstract This chapter discusses the impact of two-state models of nonadiabatic coupling by Landau, Zener, Stückelberg, Rosen, and Teller on the current theory of nonadiabatic interaction. In particular, the idea of analytical continuation of classical dynamical variables into complex-valued phase space and time is emphasized. The development of the basic models over the past 30 years has provided us with a useful means of investigating the nonadiabatic molecular dynamics; this is illustrated by the references to our earlier and most recent work.

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“…20,21 Because the ratios of the transition moments shown in Table 2 have a very small substituent dependence, even though their DMFs have a great molecular variance and their matrix elements of ΔR 2 contribute largely to their overtone transition moments (see …”

Section: Introductionmentioning

confidence: 99%

Interpretation of Semiclassical Transition Moments through Wave Function Expansion of Dipole Moment Functions with Applications to the OH Stretching Spectra of Simple Acids and Alcohols

Takahashi

Yabushita

2015

J. Phys. Chem. A

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Semiclassical description of molecular vibrations has provided us with various computational approximations and enhanced our conceptual understanding of quantum mechanics. In this study, the transition moments of the OH stretching fundamental and overtone intensities (Δv = 1-6) of some alcohols and acids are calculated by three kinds of semiclassical methods, correspondence-principle (CP) approximation, quasiclassical approximation, and uniform WKB approximation, and their respective transition moments are compared to those by the quantum theory. On the basis of the local mode picture, the one-dimensional potential energy curves and the dipole moment functions (DMFs) were obtained by density functional theory calculations and then fitted to Morse functions and sixth-order polynomials, respectively. It was shown that both the transition energies and the absorption intensities derived in the semiclassical methods reproduced their respective quantum values. In particular, the CP approximation reproduces the quantum transition moments if the formula given by Naccache is used for the action integral value. On the basis of these semiclassical results, we present a picture to understand the small variance in the overtone intensities of these acids and alcohols. Another important result is the ratios of semiclassical-to-quantum transition moment are almost independent of the applied molecules even with a great molecular variance of the DMFs, and they depend only on the nature of the semiclassical approximations and the quantum number. The difference between the semiclassical and quantum transition moments was analyzed in terms of a hitherto unrecognized concept that the Fourier expansion of the time dependent DMF in the CP treatment is a kind of the wave function expansion method using trigonometric functions as the quotient functions. For a Morse oscillator, we derive the analytic and approximate expressions of the quotient functions in terms of the bond displace coordinate in both the CP and the quantum mechanical frameworks and discuss the methodological dependence of the calculated transition moments. As a byproduct, we have found a simple derivation of the DMF expression first derived by Timm and Mecke long time ago.

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On the quasiclassical calculation of fundamental and overtone intensities

Cited by 29 publications

References 10 publications

Towards understanding the nature of the intensities of overtone vibrational transitions

Towards understanding the nature of the intensities of overtone vibrational transitions

NONADIABATICTRANSITIONS: What We Learned from Old Masters and How Much We Owe Them

Interpretation of Semiclassical Transition Moments through Wave Function Expansion of Dipole Moment Functions with Applications to the OH Stretching Spectra of Simple Acids and Alcohols

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