Calculation of the Landau quasiclassical exponent from the Fourier components of classical functions

Ee, Nikitin; Lp, Pitaevskii

doi:10.1103/physreva.49.695

Cited by 30 publications

(11 citation statements)

References 23 publications

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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: 62%

“…Because the quasiclassical theory is simple, it was possible to go beyond first-order perturbation theory (53). Yet another implication of the connection between Landau matrix elements and the Fourier components of classical functions was a relation between the so-called energy gap and momentum gap laws in the energy-transfer in VT and vibrational predissociation events (49).…”

Section: A Story Of the Landau-teller Modelmentioning

confidence: 99%

See 1 more Smart Citation

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

Nikitin

1999

Annu. Rev. Phys. Chem.

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105

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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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Section: A Story Of the Landau-teller Modelmentioning

confidence: 62%

Section: A Story Of the Landau-teller Modelmentioning

confidence: 99%

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

Nikitin

1999

Annu. Rev. Phys. Chem.

Self Cite

105

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“…(9), expresses a well-known intimate relation between various parts of an analytical function. [Nikitin and Pitaevskii (1994) have shown that this relation permits recovering the tunneling exponent using classical trajectories of the system within the allowed region. They characterise the Landau-Lifshitz method as calculation of quantum matrix elements without the use of wave functions.]…”

Section: B Effect Of the Repulsive Wallmentioning

confidence: 96%

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 fact that the transition probability can be calculated accurately by using the semiclassical formula ͑3.2͒ with the modified Landau exponent, Eqs. ͑4.10͒ and ͑4.11͒, provides an indication that the so-called improved semiclassical approximation suggested recently 33,34 for weak coupling cases works also for the strong coupling. This needs further investigation.…”

Section: Discussionmentioning

confidence: 63%

Semiclassical analysis of resonance states induced by a conical intersection

Zhu

Nikitin

Nakamura

1996

The Journal of Chemical Physics

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The resonance states induced by nonadiabatic coupling in the conical intersection problem are analyzed semiclassically. Not only the general framework but also the explicit analytical expressions of resonance positions and widths are presented. Interestingly, the nonadiabatic transition schemes are found to be quite different in the two representations employed, i.e., the adiabatic and generalized adiabatic ͑or dynamical state, or postadiabatic͒ representations. In the former case the transition is assigned to be of the Landau-Zener ͑LZ͒ type, and the latter case is analyzed by a mixture of LZ-and Rosen-Zener ͑RZ͒-type in the case of mу3/2 and by the nonadiabatic tunneling ͑NT͒ type in the case of mϭ1/2, where m is the angular momentum quantum number. Both of these semiclassical results agree well not only with each other in spite of the very different schemes, but also with the exact numerical results in a wide range of energy and angular momentum.

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Calculation of the Landau quasiclassical exponent from the Fourier components of classical functions

Cited by 30 publications

References 23 publications

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

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

Towards understanding the nature of the intensities of overtone vibrational transitions

Semiclassical analysis of resonance states induced by a conical intersection

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