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Title: On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics

Abstract

The Meyer-Miller (MM) classical vibronic (electronic + nuclear) Hamiltonian for electronically non-adiabatic dynamics—as used, for example, with the recently developed symmetrical quasiclassical (SQC) windowing model—can be written in either a diabatic or an adiabatic representation of the electronic degrees of freedom, the two being a canonical transformation of each other, thus giving the same dynamics. Although most recent applications of this SQC/MM approach have been carried out in the diabatic representation—because most of the benchmark model problems that have exact quantum results available for comparison are typically defined in a diabatic representation—it will typically be much more convenient to work in the adiabatic representation, e.g., when using Born-Oppenheimer potential energy surfaces (PESs) and derivative couplings that come from electronic structure calculations. The canonical equations of motion (EOMs) (i.e., Hamilton’s equations) that come from the adiabatic MM Hamiltonian, however, in addition to the common first-derivative couplings, also involve second-derivative non-adiabatic coupling terms (as does the quantum Schrödinger equation), and the latter are considerably more difficult to calculate. This paper thus revisits the adiabatic version of the MM Hamiltonian and describes a modification of the classical adiabatic EOMs that are entirely equivalent to Hamilton’s equations but that do not involve the second-derivativemore » couplings. The second-derivative coupling terms have not been neglected; they simply do not appear in these modified adiabatic EOMs. This means that SQC/MM calculations can be carried out in the adiabatic representation, without approximation, needing only the PESs and the first-derivative coupling elements. Here, the results of example SQC/MM calculations are presented, which illustrate this point, and also the fact that simply neglecting the second-derivative couplings in Hamilton’s equations (and presumably also in the Schrödinger equation) can cause very significant errors.« less

Authors:
 [1]; ORCiD logo [1];  [1]
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  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
OSTI Identifier:
1543838
Alternate Identifier(s):
OSTI ID: 1374780
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 6; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Chemistry; Physics

Citation Formats

Cotton, Stephen J., Liang, Ruibin, and Miller, William H. On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics. United States: N. p., 2017. Web. doi:10.1063/1.4995301.
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Cotton, Stephen J., Liang, Ruibin, & Miller, William H. On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics. United States. https://doi.org/10.1063/1.4995301
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Cotton, Stephen J., Liang, Ruibin, and Miller, William H. Fri . "On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics". United States. https://doi.org/10.1063/1.4995301. https://www.osti.gov/servlets/purl/1543838.
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@article{osti_1543838,
title = {On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics},
author = {Cotton, Stephen J. and Liang, Ruibin and Miller, William H.},
abstractNote = {The Meyer-Miller (MM) classical vibronic (electronic + nuclear) Hamiltonian for electronically non-adiabatic dynamics—as used, for example, with the recently developed symmetrical quasiclassical (SQC) windowing model—can be written in either a diabatic or an adiabatic representation of the electronic degrees of freedom, the two being a canonical transformation of each other, thus giving the same dynamics. Although most recent applications of this SQC/MM approach have been carried out in the diabatic representation—because most of the benchmark model problems that have exact quantum results available for comparison are typically defined in a diabatic representation—it will typically be much more convenient to work in the adiabatic representation, e.g., when using Born-Oppenheimer potential energy surfaces (PESs) and derivative couplings that come from electronic structure calculations. The canonical equations of motion (EOMs) (i.e., Hamilton’s equations) that come from the adiabatic MM Hamiltonian, however, in addition to the common first-derivative couplings, also involve second-derivative non-adiabatic coupling terms (as does the quantum Schrödinger equation), and the latter are considerably more difficult to calculate. This paper thus revisits the adiabatic version of the MM Hamiltonian and describes a modification of the classical adiabatic EOMs that are entirely equivalent to Hamilton’s equations but that do not involve the second-derivative couplings. The second-derivative coupling terms have not been neglected; they simply do not appear in these modified adiabatic EOMs. This means that SQC/MM calculations can be carried out in the adiabatic representation, without approximation, needing only the PESs and the first-derivative coupling elements. Here, the results of example SQC/MM calculations are presented, which illustrate this point, and also the fact that simply neglecting the second-derivative couplings in Hamilton’s equations (and presumably also in the Schrödinger equation) can cause very significant errors.},
doi = {10.1063/1.4995301},
journal = {Journal of Chemical Physics},
number = 6,
volume = 147,
place = {United States},
year = {Fri Aug 11 00:00:00 EDT 2017},
month = {Fri Aug 11 00:00:00 EDT 2017}
}
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https://doi.org/10.1063/1.4995301
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Works referenced in this record:

Forward–backward solution of quantum-classical Liouville equation in the adiabatic mapping basis
journal, December 2013

A classical analog for electronic degrees of freedom in nonadiabatic collision processes
journal, April 1979

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journal, August 2015

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Iterative quantum-classical path integral with dynamically consistent state hopping
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The Symmetrical Quasi-Classical Model for Electronically Non-Adiabatic Processes Applied to Energy Transfer Dynamics in Site-Exciton Models of Light-Harvesting Complexes
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journal, October 2016

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Semiclassical approximations for the calculation of thermal rate constants for chemical reactions in complex molecular systems
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Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation
journal, November 1998

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On the semiclassical description of quantum coherence in thermal rate constants
journal, September 1998

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    Works referencing / citing this record:

    Combining Meyer–Miller Hamiltonian with electronic structure methods for on-the-fly nonadiabatic dynamics simulations: implementation and application
    journal, January 2019

    • Tang, Diandong; Fang, Wei-Hai; Shen, Lin
    • Physical Chemistry Chemical Physics, Vol. 21, Issue 31
    • DOI: 10.1039/c9cp02682g

    Initial sampling in symmetrical quasiclassical dynamics based on Li–Miller mapping Hamiltonian
    journal, January 2019

    • Zheng, Jie; Xie, Yu; Jiang, Shengshi
    • Physical Chemistry Chemical Physics, Vol. 21, Issue 48
    • DOI: 10.1039/c9cp03975a

    The symmetrical quasi-classical approach to electronically nonadiabatic dynamics applied to ultrafast exciton migration processes in semiconducting polymers
    journal, July 2018

    • Liang, Ruibin; Cotton, Stephen J.; Binder, Robert
    • The Journal of Chemical Physics, Vol. 149, Issue 4
    • DOI: 10.1063/1.5037815

    Performance evaluation of the symmetrical quasi-classical dynamics method based on Meyer-Miller mapping Hamiltonian in the treatment of site-exciton models
    journal, November 2018

    • Xie, Yu; Zheng, Jie; Lan, Zhenggang
    • The Journal of Chemical Physics, Vol. 149, Issue 17
    • DOI: 10.1063/1.5047002

    A symmetrical quasi-classical windowing model for the molecular dynamics treatment of non-adiabatic processes involving many electronic states
    journal, March 2019

    • Cotton, Stephen J.; Miller, William H.
    • The Journal of Chemical Physics, Vol. 150, Issue 10
    • DOI: 10.1063/1.5087160

    A new perspective for nonadiabatic dynamics with phase space mapping models
    journal, July 2019

    • He, Xin; Liu, Jian
    • The Journal of Chemical Physics, Vol. 151, Issue 2
    • DOI: 10.1063/1.5108736
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