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. doi: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. doi: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:
Works referenced in this record:
New semiclassical treatments of rotational and vibrational transitions in heavy‐particle collisions. I. H–H _{2} and He–H _{2} collisions
journal, December 1975
 McCann, K. J.; Flannery, M. R.
 The Journal of Chemical Physics, Vol. 63, Issue 11
A novel mixed quantum/classical method for the dynamics of molecules in a gas environment with an application to femtosecond timeresolved spectroscopy
journal, March 1999
 Ermoshin, V. A.; Kazansky, A. K.; Engel, V.
 Chemical Physics Letters, Vol. 302, Issue 12
Dynamics of metal electron excitation in atomsurface collisions: A quantum wave packet approach
journal, February 1984
 Kirson, Z.; Gerber, R. B.; Nitzan, A.
 Surface Science, Vol. 137, Issue 23
Quantum simulation of reaction dynamics by density matrix evolution
journal, December 1993
 Berendsen, Herman J. C.; Mavri, Janez
 The Journal of Physical Chemistry, Vol. 97, Issue 51
A quantumclassical study of the OH + H 2 reactive and inelastic collisions
journal, April 2017
 Martí, Carles; Pacifici, Leonardo; Laganà, Antonio
 Chemical Physics Letters, Vol. 674
Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in spacefixed and bodyfixed reference frames
journal, November 2013
 Semenov, Alexander; Babikov, Dmitri
 The Journal of Chemical Physics, Vol. 139, Issue 17
Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H _{2} + H _{2}
journal, May 2016
 Semenov, Alexander; Babikov, Dmitri
 The Journal of Physical Chemistry A, Vol. 120, Issue 22
A multistate semiclassical orbital treatment of heavyparticle collisions with application to HH2 rotational transitions
journal, August 1975
 McCann, K. J.; Flannery, M. R.
 Chemical Physics Letters, Vol. 35, Issue 1
Integral cross sections and rate constants for the reaction OH+H _{2} →H _{2} O+H: A semiclassical wave packet approach
journal, August 1994
 Balakrishnan, N.; Billing, G. D.
 The Journal of Chemical Physics, Vol. 101, Issue 4
Semiclassical coupled wave packet study of the nonadiabatic collisions Ar ^{+} ( J )+H _{2} : Zero angular momentum case
journal, March 1996
 Aguillon, F.; Sizun, M.; Sidis, V.
 The Journal of Chemical Physics, Vol. 104, Issue 12
A self‐consistent eikonal treatment of electronic transitions in molecular collisions
journal, June 1983
 Micha, D. A.
 The Journal of Chemical Physics, Vol. 78, Issue 12
Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory
journal, December 2013
 Semenov, Alexander; Babikov, Dmitri
 The Journal of Physical Chemistry Letters, Vol. 5, Issue 2
Molecular dynamics with electronic frictions
journal, December 1995
 Head‐Gordon, Martin; Tully, John C.
 The Journal of Chemical Physics, Vol. 103, Issue 23
Quantumclassical calculation of cross sections and rate constants for the H2+CN→HCN+H reaction
journal, December 2000
 Coletti, Cecilia; Billing, Gert D.
 The Journal of Chemical Physics, Vol. 113, Issue 24
Rovibrational quenching of CO ( v = 1) by He impact in a broad range of temperatures: A benchmark study using mixed quantum/classical inelastic scattering theory
journal, August 2013
 Semenov, Alexander; Ivanov, Mikhail; Babikov, Dmitri
 The Journal of Chemical Physics, Vol. 139, Issue 7
Mixed Quantum/Classical Approach for Description of Molecular Collisions in Astrophysical Environments
journal, May 2015
 Semenov, Alexander; Babikov, Dmitri
 The Journal of Physical Chemistry Letters, Vol. 6, Issue 10
Collisional stabilization of van der Waals states of ozone
journal, May 2011
 Ivanov, Mikhail V.; Babikov, Dmitri
 The Journal of Chemical Physics, Vol. 134, Issue 17
A mixed quantal/classical study of the reaction OH + H2 → H2O + H
journal, February 1995
 Balakrishnan, N.; Billing, G. D.
 Chemical Physics Letters, Vol. 233, Issue 12
Fragmentation of ${\mathrm{Na}}_{2}^{+}$ dimer ions in kiloelectronvolt collisions with He: A coupled wavepacket study
journal, January 1999
 Babikov, D.; Aguillon, F.; Sizun, M.
 Physical Review A, Vol. 59, Issue 1
Mixed quantum/classical theory for inelastic scattering of asymmetrictoprotor + atom in the bodyfixed reference frame and application to the H _{2} O + He system
journal, September 2014
 Semenov, Alexander; Dubernet, MarieLise; Babikov, Dmitri
 The Journal of Chemical Physics, Vol. 141, Issue 11
Meantrajectory approximation for charge and energytransfer processes at surfaces
journal, July 1985
 Sawada, ShinIchi; Nitzan, Abraham; Metiu, Horia
 Physical Review B, Vol. 32, Issue 2
Quantum/classical timedependent selfconsistent field treatment of Ar+HCO inelastic and dissociative scattering
journal, March 1999
 Whittier, Gregory S.; Light, John C.
 The Journal of Chemical Physics, Vol. 110, Issue 9
Efficient quantumclassical method for computing thermal rate constant of recombination: Application to ozone formation
journal, May 2012
 Ivanov, Mikhail V.; Babikov, Dmitri
 The Journal of Chemical Physics, Vol. 136, Issue 18
Semiclassical calculation of collisional dissociation cross sections for N+N2
journal, October 2002
 Tully, Catherine; Johnson, Robert E.
 The Journal of Chemical Physics, Vol. 117, Issue 14
Mixed quantum/classical calculations of total and differential elastic and rotationally inelastic scattering cross sections for light and heavy reduced masses in a broad range of collision energies
journal, January 2014
 Semenov, Alexander; Babikov, Dmitri
 The Journal of Chemical Physics, Vol. 140, Issue 4
On molecular origin of massindependent fractionation of oxygen isotopes in the ozone forming recombination reaction
journal, February 2013
 Ivanov, M. V.; Babikov, D.
 Proceedings of the National Academy of Sciences, Vol. 110, Issue 44
MultipleConfiguration Quantum/Classical Studies of the Photodissociation Dynamics of H _{2} O ^{†}
journal, September 2003
 Chen, Feng; McCoy, Anne B.
 The Journal of Physical Chemistry A, Vol. 107, Issue 37
Extended HellmannFeynman theorem for nonstationary states and its application in quantumclassical molecular dynamics simulations
journal, March 1994
 Bala, P.; Lesyng, B.; McCammon, J. A.
 Chemical Physics Letters, Vol. 219, Issue 34
Equivalence of the Ehrenfest theorem and the fluidrotor model for mixed quantum/classical theory of collisional energy transfer
journal, April 2013
 Semenov, Alexander; Babikov, Dmitri
 The Journal of Chemical Physics, Vol. 138, Issue 16
CO Dimer: New Potential Energy Surface and Rovibrational Calculations
journal, June 2013
 Dawes, Richard; Wang, XiaoGang; Carrington, Tucker
 The Journal of Physical Chemistry A, Vol. 117, Issue 32
Recent Advances in Development and Applications of the Mixed Quantum/Classical Theory for Inelastic Scattering
journal, December 2015
 Babikov, Dmitri; Semenov, Alexander
 The Journal of Physical Chemistry A, Vol. 120, Issue 3
The semiclassical treatment of molecular roto/vibrational energy transfer
journal, June 1984
 Billing, G. D.
 Computer Physics Reports, Vol. 1, Issue 5
Classical path method in inelastic and reactive scattering
journal, September 1994
 Billing, Gert. D.
 International Reviews in Physical Chemistry, Vol. 13, Issue 2
Mixed Quantum/Classical Theory for Molecule–Molecule Inelastic Scattering: Derivations of Equations and Application to N _{2} + H _{2} System
journal, September 2015
 Semenov, Alexander; Babikov, Dmitri
 The Journal of Physical Chemistry A, Vol. 119, Issue 50
Theoretical investigation of the Ar+(J) + H2 → ArH+ + H reaction: semiclassical coupled wavepacket treatment
journal, September 1996
 Sizun, M.; Aguillon, F.; Sidis, V.
 Chemical Physics, Vol. 209, Issue 23
Wavepacket dynamics: new physics and chemistry in femtotime
journal, April 1995
 Garraway, B. M.; Suominen, K. A
 Reports on Progress in Physics, Vol. 58, Issue 4
Analysis and extension of some recently proposed classical models for electronic degrees of freedom
journal, February 1980
 Meyer, Hans‐Dieter; Miller, William H.
 The Journal of Chemical Physics, Vol. 72, Issue 4
Rotational Excitations in CO–CO Collisions at Low Temperature: TimeIndependent and Multiconfigurational TimeDependent Hartree Calculations
journal, February 2015
 Ndengué, Steve A.; Dawes, Richard; Gatti, Fabien
 The Journal of Physical Chemistry A, Vol. 119, Issue 28
A variational solution of the timedependent Schrodinger equation
journal, January 1964
 McLachlan, A. D.
 Molecular Physics, Vol. 8, Issue 1
Works referencing / citing this record:
Semiclassical initial value theory of rotationally inelastic scattering: Some remarks on the phase index in the interaction picture
journal, May 2018
 Bonnet, L.
 The Journal of Chemical Physics, Vol. 148, Issue 19
Figures / Tables found in this record: