Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them
- Marquette Univ., Milwaukee, WI (United States). Dept. of Chemistry
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 mean-field trajectory while the internal molecular motion is treated by the time-dependent Schrodinger equation. It is shown that the appropriate choice of velocity for the mean-field trajectory permits to enforce microscopic reversibility and gives results in excellent agreement with full-quantum 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 state-to-state 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.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- AC02-5CH11231
- OSTI ID:
- 1497844
- Journal Information:
- Journal of Chemical Physics, Vol. 146, Issue 22; ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Semiclassical initial value theory of rotationally inelastic scattering: Some remarks on the phase index in the interaction picture
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journal | May 2018 |
| Semiclassical initial value theory of rotationally inelastic scattering: Some remarks on the phase index in the interaction picture | text | January 2018 |
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