Dynamics of wavepacket tunneling in a periodic double-well potential

Abstract

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...

Probing Nuclear Dynamics in Momentum Space: A New Interpretation of (e, 2e) Electron Impact Ionization Experiments on Ethanol

“…It is, in our opinion, extremely unlikely that such scenarios will quantitatively improve our understanding of EMS experiments on ethanol. Indeed, according to results by Shundalov et al, tunneling wavepacket dynamics in π-periodic potentials, which are very much comparable to that describing the hydroxyl rotation in ethanol, occurs within a time scale on the order of 333 ps, to compare with thermal conversion rates on the order of 5.6 transitions per picoseconds at 298 K, according to an application of elementary transition-state theory onto barriers on the order of 1.15 kcal/mol. Tunneling occurs thus at a much too slow pace to have really some significance.…”