Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them
Abstract
In order to identify the origin of possible errors in the mixed quantum/classical approach to inelastic scattering [A. Semenov and D. Babikov, J. Chem. Phys. 140, 044306 (2014) and A. Semenov, M.L. Dubernet, and D. Babikov, J. Chem. Phys. 141, 114304 (2014)], a simplified model is considered that consists of one intermolecular degree of freedom and two intramolecular states, coupled by a simple potential. For this system, analytic derivations are carried out to determine (i) the exact quantum mechanical solution of the inelastic scattering problem, (ii) a simplified version of it with all oscillatory terms neglected, and (iii) the Ehrenfest solution in which the translational motion is described by the meanfield trajectory while the internal molecular motion is treated by the timedependent Schrodinger equation. It is shown that the appropriate choice of velocity for the meanfield trajectory permits to enforce microscopic reversibility and gives results in excellent agreement with fullquantum results. The average velocity method of Billing is rigorously derived as a limiting case (of this more general approach), when reversibility is enforced locally, at the initial moment of time only. It is demonstrated that errors of statetostate transition probabilities in the Ehrenfest approach occur at lower values of totalmore »
 Authors:

 Marquette Univ., Milwaukee, WI (United States). Dept. of Chemistry
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1497844
 Grant/Contract Number:
 AC025CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 146; Journal Issue: 22; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Semenov, Alexander, and Babikov, Dmitri. Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them. United States: N. p., 2017.
Web. doi:10.1063/1.4985074.
Semenov, Alexander, & Babikov, Dmitri. Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them. United States. https://doi.org/10.1063/1.4985074
Semenov, Alexander, and Babikov, Dmitri. Mon .
"Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them". United States. https://doi.org/10.1063/1.4985074. https://www.osti.gov/servlets/purl/1497844.
@article{osti_1497844,
title = {Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them},
author = {Semenov, Alexander and Babikov, Dmitri},
abstractNote = {In order to identify the origin of possible errors in the mixed quantum/classical approach to inelastic scattering [A. Semenov and D. Babikov, J. Chem. Phys. 140, 044306 (2014) and A. Semenov, M.L. Dubernet, and D. Babikov, J. Chem. Phys. 141, 114304 (2014)], a simplified model is considered that consists of one intermolecular degree of freedom and two intramolecular states, coupled by a simple potential. For this system, analytic derivations are carried out to determine (i) the exact quantum mechanical solution of the inelastic scattering problem, (ii) a simplified version of it with all oscillatory terms neglected, and (iii) the Ehrenfest solution in which the translational motion is described by the meanfield trajectory while the internal molecular motion is treated by the timedependent Schrodinger equation. It is shown that the appropriate choice of velocity for the meanfield trajectory permits to enforce microscopic reversibility and gives results in excellent agreement with fullquantum results. The average velocity method of Billing is rigorously derived as a limiting case (of this more general approach), when reversibility is enforced locally, at the initial moment of time only. It is demonstrated that errors of statetostate transition probabilities in the Ehrenfest approach occur at lower values of total energy E if the magnitudes of excitation energy ΔE, potential energy difference between the two states ΔV, and coupling of two states V12 are large. Possible ways of applying this concept to rotational transitions in real molecules are explored, using examples from CO + CO inelastic scattering.},
doi = {10.1063/1.4985074},
journal = {Journal of Chemical Physics},
number = 22,
volume = 146,
place = {United States},
year = {2017},
month = {6}
}
Web of Science
Figures / Tables:
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