Boltzmann wavepacket dynamics of tunnelling of molecules through symmetric and asymmetric energy barriers on non-periodic potential functions

Hughes, Keith H.; Macdonald, John N.

doi:10.1039/b002675l

Cited by 8 publications

(16 citation statements)

References 11 publications

(7 reference statements)

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“…Eigenfunctions (4) and energies of the corresponding time-independent states are determined by diagonalization of the Hamiltonian matrix (2).…”

Section: Methodsmentioning

confidence: 99%

“…It has a significant influence on the structure of molecular spectra [1]. A dynamic description of the tunneling process is more complete than the traditional solution of the steady-state Schrödinger equation because it can follow in detail the evolution of fragments of the molecular system and its coupling with the variable electromagnetic field of a light wave.The dynamics of wavepackets tunneling through potential barriers, their coupling with external fields, and the effect of asymmetry in the potential function on the formation and structure of vibrational spectra have recently been widely studied [2][3][4][5][6][7][8][9]. However, most of these studies [2, 4, 6-9] are dedicated to tunneling in a non-periodic potential, a typical example of which is the inversion potential of ammonia.…”

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confidence: 99%

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Dynamics of wavepacket tunneling in a periodic double-well potential

Shundalov

Romanov

2008

J Appl Spectrosc

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539.194 Temporal evolution of wavepacket tunneling in a periodic double-well torsional potential has been studied numerically. Peculiarities of wavepacket tunneling dynamics under conditions of asymmetric distortion of the periodic potential function have been analyzed. Introduction.Tunneling through potential barriers that separate potential-energy minima is a very common quantum-mechanical phenomenon in molecular systems. It has a significant influence on the structure of molecular spectra [1]. A dynamic description of the tunneling process is more complete than the traditional solution of the steady-state Schrödinger equation because it can follow in detail the evolution of fragments of the molecular system and its coupling with the variable electromagnetic field of a light wave.The dynamics of wavepackets tunneling through potential barriers, their coupling with external fields, and the effect of asymmetry in the potential function on the formation and structure of vibrational spectra have recently been widely studied [2][3][4][5][6][7][8][9]. However, most of these studies [2, 4, 6-9] are dedicated to tunneling in a non-periodic potential, a typical example of which is the inversion potential of ammonia. A wavepacket initially localized in one of the minima of such a non-periodic double-well potential then moves in a definite direction, tunneling into the neighboring minimum because its propagation in the opposite direction is limited by a quadratically increasing potential wall. The shape of the wavepacket determined by the potential-energy power function will be described approximately by a Gaussian function.Tunneling in a periodic potential, a typical manifestation of which is internal rotation in non-rigid molecules, has a specific peculiarity associated with identification of the boundary points of the potential function. According to quantum-mechanical principles, a particle initially localized in one of the minima of a symmetric double-well periodic potential tunnels simultaneously in two directions corresponding to the two possible directions of rotation of the molecular fragment. The probabilities of tunneling through the right and left barrier are obviously identical if their heights are equal and different if the barrier heights are different. The shape of the wavepacket determined by the periodic potential function may differ significantly from Gaussian. These essential details of the tunneling process in a periodic potential have not been considered in studies of the dynamics of tunneling transitions.Another important and influential effect on tunneling dynamics is asymmetric distortion of the shape of the potential function that causes the minima to be nonequivalent. Coherent tunneling conditions are destroyed if the potential wells are nonequivalent. This has a substantial effect on the stability of various molecular conformations. A transition into another potential minimum can be made only through incoherent tunneling [7], i.e., coupling with external fields or other degrees of freedom o...

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“…Eigenfunctions (4) and energies of the corresponding time-independent states are determined by diagonalization of the Hamiltonian matrix (2).…”

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Dynamics of wavepacket tunneling in a periodic double-well potential

Shundalov

Romanov

2008

J Appl Spectrosc

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“…6 Results and discussion Fig.1 shows that the parameters of the potential (2) can be chosen to provide good description of the energy levels structure for a set of specific experimental data. In Fig.1 the energy levels for the inversion of the ammonia molecule NH 3 (experimental data determined with help of microwave and IR spectroscopy are taken from [7], [32]) are presented. The energy levels for the inversion mode of NH 3 form a pair of doublets within the wells.…”

Section: Symmetric Potentialmentioning

confidence: 99%

“…The energy levels for the inversion mode of NH 3 form a pair of doublets within the wells. For the ground-state splitting the values E 1 − E 0 = 0.66 ÷ 0.8 cm −1 are given in the literature [32], [7], [8]. To be specific we choose the value E 1 − E 0 = 0.76 cm −1 .…”

Section: Symmetric Potentialmentioning

confidence: 99%

“…For these reason we do not pretend to provide a very precise description of NH 3 with the help of spheroidal functions. The The parameters of the potential are chosen to describe the energy levels for the inversion vibrational mode in ammonia molecule N H 3 (experimental data are taken from [7], [32]). The splitting of the ground state ǫ 1 − ǫ 0 = 0.26 corresponds to 0.76 cm −1 in dimensional units.…”

Section: Symmetric Potentialmentioning

confidence: 99%

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Analytic description of inversion vibrational mode for ammonia molecule

Sitnitsky

2017

Vibrational Spectroscopy

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The one-dimensional Schrödinger equation with symmetric trigonometric doublewell potential is exactly solved via angular prolate spheroidal function. Although it is inferior compared with multidimensional counterparts and its limitations are obvious nevertheless its solution is shown to be analytic rather than commonly used numerical or approximate semiclassical (WKB) one. This comprises the novelty and the merit of the present work. Our exact analytic description of the ground state splitting can well be a referee point for comparison of the accuracy of numerous WKB formulas suggested in the literature. The approach reasonably well suits for the inversion mode in the ammonia molecule N H 3 and thus yields a new theoretical tool for its description. The results obtained provide good quantitative description of relevant experimental data on microwave and IR spectroscopy of N H 3 .

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Analytic calculation of ground state splitting in symmetric double well potential

Sitnitsky

2018

Computational and Theoretical Chemistry

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The exact solution of the one-dimensional Schrödinger equation with symmetric trigonometric double-well potential (DWP) is obtained via angular oblate spheroidal function. The results of stringent analytic calculation for the ground state splitting of ring-puckering vibration in the 1,3-dioxole (as an example of the case when the ground state tunneling doublet is well below the potential barrier top) and 2,3dihydrofuran (as an example of the case when the ground state tunneling doublet is close to the potential barrier top) are compared with several variants of approximate semiclassical (WKB) ones. This enables us to verify the accuracy of various WKB formulas suggested in the literature: 1. ordinary WKB, i.e., the formula from the Landau and Lifshitz textbook; 2. Garg's formula; 3. instanton approach. We show that for the former case all three variants of WKB provide good accuracy while for the latter one they are very inaccurate. The results obtained provide a new theoretical tool for describing relevant experimental data on IR spectroscopy of ring-puckering vibrations.

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Boltzmann wavepacket dynamics of tunnelling of molecules through symmetric and asymmetric energy barriers on non-periodic potential functions

Cited by 8 publications

References 11 publications

Dynamics of wavepacket tunneling in a periodic double-well potential

Dynamics of wavepacket tunneling in a periodic double-well potential

Analytic description of inversion vibrational mode for ammonia molecule

Analytic calculation of ground state splitting in symmetric double well potential

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