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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]
  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (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) (SC-22). Chemical Sciences, Geosciences & Biosciences Division; USDOE
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.
Cotton, Stephen J., Liang, Ruibin, & Miller, William H. On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics. United States. doi:10.1063/1.4995301.
Cotton, Stephen J., Liang, Ruibin, and Miller, William H. Fri . "On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics". United States. doi:10.1063/1.4995301. https://www.osti.gov/servlets/purl/1543838.
@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 = {2017},
month = {8}
}

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