Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

Abstract

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. As a result, we present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

Authors:
 [1];  [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Division of Chemistry and Chemical Engineering
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1498059
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 10; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Tao, Xuecheng, Shushkov, Philip, and Miller, III, Thomas F. Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics. United States: N. p., 2017. Web. doi:10.1063/1.5005544.
Copy to clipboard
Tao, Xuecheng, Shushkov, Philip, & Miller, III, Thomas F. Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics. United States. https://doi.org/10.1063/1.5005544
Copy to clipboard
Tao, Xuecheng, Shushkov, Philip, and Miller, III, Thomas F. Tue . "Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics". United States. https://doi.org/10.1063/1.5005544. https://www.osti.gov/servlets/purl/1498059.
Copy to clipboard
@article{osti_1498059,
title = {Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics},
author = {Tao, Xuecheng and Shushkov, Philip and Miller, III, Thomas F.},
abstractNote = {We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. As a result, we present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.},
doi = {10.1063/1.5005544},
journal = {Journal of Chemical Physics},
number = 10,
volume = 148,
place = {United States},
year = {Tue Dec 12 00:00:00 EST 2017},
month = {Tue Dec 12 00:00:00 EST 2017}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5005544
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 45 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Tryptophan-Accelerated Electron Flow Through Proteins
journal, June 2008

Dynamics and dissipation in enzyme catalysis
journal, September 2011

  • Boekelheide, N.; Salomon-Ferrer, R.; Miller, T. F.
  • Proceedings of the National Academy of Sciences, Vol. 108, Issue 39
  • DOI: 10.1073/pnas.1106397108

A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables
journal, August 1999

  • Jang, Seogjoo; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 111, Issue 6
  • DOI: 10.1063/1.479515

Surface hopping, transition state theory, and decoherence. II. Thermal rate constants and detailed balance
journal, October 2015

  • Jain, Amber; Subotnik, Joseph E.
  • The Journal of Chemical Physics, Vol. 143, Issue 13
  • DOI: 10.1063/1.4930549

The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties
journal, April 1994

  • Cao, Jianshu; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 100, Issue 7
  • DOI: 10.1063/1.467176

Mapping variable ring polymer molecular dynamics: A path-integral based method for nonadiabatic processes
journal, September 2013

  • Ananth, Nandini
  • The Journal of Chemical Physics, Vol. 139, Issue 12
  • DOI: 10.1063/1.4821590

Quantum diffusion in liquid water from ring polymer molecular dynamics
journal, October 2005

  • Miller, Thomas F.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 123, Issue 15
  • DOI: 10.1063/1.2074967

Surface-hopping dynamics of a spin-boson system
journal, February 2002

  • Mac Kernan, Donal; Ciccotti, Giovanni; Kapral, Raymond
  • The Journal of Chemical Physics, Vol. 116, Issue 6
  • DOI: 10.1063/1.1433502

Proton transfer in solution: Molecular dynamics with quantum transitions
journal, September 1994

  • Hammes‐Schiffer, Sharon; Tully, John C.
  • The Journal of Chemical Physics, Vol. 101, Issue 6
  • DOI: 10.1063/1.467455

Communication: Predictive partial linearized path integral simulation of condensed phase electron transfer dynamics
journal, October 2013

  • Huo, Pengfei; Miller, Thomas F.; Coker, David F.
  • The Journal of Chemical Physics, Vol. 139, Issue 15
  • DOI: 10.1063/1.4826163

Quantum diffusion in liquid para -hydrogen from ring-polymer molecular dynamics
journal, May 2005

  • Miller, Thomas F.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 122, Issue 18
  • DOI: 10.1063/1.1893956

Ring polymer molecular dynamics with surface hopping
journal, December 2012

  • Shushkov, Philip; Li, Richard; Tully, John C.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4766449

Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids
journal, April 1981

  • Chandler, David; Wolynes, Peter G.
  • The Journal of Chemical Physics, Vol. 74, Issue 7
  • DOI: 10.1063/1.441588

Direct simulation of proton-coupled electron transfer across multiple regimes
journal, April 2013

  • Kretchmer, Joshua S.; Miller, Thomas F.
  • The Journal of Chemical Physics, Vol. 138, Issue 13
  • DOI: 10.1063/1.4797462

Proton-Coupled Electron Transfer
journal, November 2007

  • Huynh, My Hang V.; Meyer, Thomas J.
  • Chemical Reviews, Vol. 107, Issue 11
  • DOI: 10.1021/cr0500030

Isomerization Through Conical Intersections
journal, May 2007

Exact quantum statistics for electronically nonadiabatic systems using continuous path variables
journal, December 2010

  • Ananth, Nandini; Miller, Thomas F.
  • The Journal of Chemical Physics, Vol. 133, Issue 23
  • DOI: 10.1063/1.3511700

Communication: Nonadiabatic ring-polymer molecular dynamics
journal, July 2013

  • Richardson, Jeremy O.; Thoss, Michael
  • The Journal of Chemical Physics, Vol. 139, Issue 3
  • DOI: 10.1063/1.4816124

i-PI: A Python interface for ab initio path integral molecular dynamics simulations
journal, March 2014

  • Ceriotti, Michele; More, Joshua; Manolopoulos, David E.
  • Computer Physics Communications, Vol. 185, Issue 3
  • DOI: 10.1016/j.cpc.2013.10.027

Tipping the Balance between Concerted versus Sequential Proton-Coupled Electron Transfer
journal, October 2015

The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions
journal, September 1989

  • Marston, C. Clay; Balint‐Kurti, Gabriel G.
  • The Journal of Chemical Physics, Vol. 91, Issue 6
  • DOI: 10.1063/1.456888

Mixed quantum-classical surface hopping dynamics
journal, April 2000

  • Nielsen, Steve; Kapral, Raymond; Ciccotti, Giovanni
  • The Journal of Chemical Physics, Vol. 112, Issue 15
  • DOI: 10.1063/1.481225

Theory of Coupled Electron and Proton Transfer Reactions
journal, December 2010

  • Hammes-Schiffer, Sharon; Stuchebrukhov, Alexei A.
  • Chemical Reviews, Vol. 110, Issue 12
  • DOI: 10.1021/cr1001436

Ring Polymer Surface Hopping: Incorporating Nuclear Quantum Effects into Nonadiabatic Molecular Dynamics Simulations
journal, June 2017

Dynamic molecular oxygen production in cometary comae
journal, May 2017

  • Yao, Yunxi; Giapis, Konstantinos P.
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms15298

Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space
journal, April 2013

Comparison of path integral molecular dynamics methods for the infrared absorption spectrum of liquid water
journal, August 2008

  • Habershon, Scott; Fanourgakis, George S.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 129, Issue 7
  • DOI: 10.1063/1.2968555

A Centroid Molecular Dynamics Approach for Nonadiabatic Dynamical Processes in Condensed Phases:  the Spin-Boson Case †
journal, August 2002

  • Liao, Jie-Lou; Voth, Gregory A.
  • The Journal of Physical Chemistry B, Vol. 106, Issue 33
  • DOI: 10.1021/jp020978d

An efficient ring polymer contraction scheme for imaginary time path integral simulations
journal, July 2008

  • Markland, Thomas E.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 129, Issue 2
  • DOI: 10.1063/1.2953308

Mixed quantum-classical dynamics
journal, May 1999

  • Kapral, Raymond; Ciccotti, Giovanni
  • The Journal of Chemical Physics, Vol. 110, Issue 18
  • DOI: 10.1063/1.478811

The semiclassical calculation of nonadiabatic tunneling rates
journal, January 1998

  • Schwieters, Charles D.; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 108, Issue 3
  • DOI: 10.1063/1.475467

Semiclassical description of electronically nonadiabatic dynamics via the initial value representation
journal, August 2007

  • Ananth, Nandini; Venkataraman, Charulatha; Miller, William H.
  • The Journal of Chemical Physics, Vol. 127, Issue 8
  • DOI: 10.1063/1.2759932

Inverse Velocity Dependence of Vibrationally Promoted Electron Emission from a Metal Surface
journal, August 2008

Mean field ring polymer molecular dynamics for electronically nonadiabatic reaction rates
journal, January 2016

  • Duke, Jessica Ryan; Ananth, Nandini
  • Faraday Discussions, Vol. 195
  • DOI: 10.1039/c6fd00123h

Mixed quantum-classical equilibrium: Surface hopping
journal, July 2008

  • Schmidt, J. R.; Parandekar, Priya V.; Tully, John C.
  • The Journal of Chemical Physics, Vol. 129, Issue 4
  • DOI: 10.1063/1.2955564

Path-integral simulations beyond the adiabatic approximation
journal, September 2007

  • Schmidt, J. R.; Tully, John C.
  • The Journal of Chemical Physics, Vol. 127, Issue 9
  • DOI: 10.1063/1.2757170

Solution of the Schrödinger equation by a spectral method
journal, September 1982

Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: Connection with semiclassical instanton theory
journal, December 2009

  • Richardson, Jeremy O.; Althorpe, Stuart C.
  • The Journal of Chemical Physics, Vol. 131, Issue 21
  • DOI: 10.1063/1.3267318

Statistical mechanics of quantum-classical systems
journal, October 2001

  • Nielsen, Steve; Kapral, Raymond; Ciccotti, Giovanni
  • The Journal of Chemical Physics, Vol. 115, Issue 13
  • DOI: 10.1063/1.1400129

A new approach to decoherence and momentum rescaling in the surface hopping algorithm
journal, January 2011

  • Subotnik, Joseph E.; Shenvi, Neil
  • The Journal of Chemical Physics, Vol. 134, Issue 2
  • DOI: 10.1063/1.3506779

Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics
journal, August 2004

  • Craig, Ian R.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 121, Issue 8
  • DOI: 10.1063/1.1777575

Mimicking Protein−Protein Electron Transfer:  Voltammetry of Pseudomonas aeruginosa Azurin and the Thermus thermophilus Cu A Domain at ω-Derivatized Self-Assembled-Monolayer Gold Electrodes
journal, November 2004

  • Fujita, Kyoko; Nakamura, Nobufumi; Ohno, Hiroyuki
  • Journal of the American Chemical Society, Vol. 126, Issue 43
  • DOI: 10.1021/ja047875o

A Modification of Path Integral Quantum Transition State Theory for Asymmetric and Metastable Potentials
journal, October 1999

  • Jang, Seogjoo; Schwieters, Charles D.; Voth, Gregory A.
  • The Journal of Physical Chemistry A, Vol. 103, Issue 47
  • DOI: 10.1021/jp992190+

Iterative linearized density matrix propagation for modeling coherent excitation energy transfer in photosynthetic light harvesting
journal, November 2010

  • Huo, P.; Coker, D. F.
  • The Journal of Chemical Physics, Vol. 133, Issue 18
  • DOI: 10.1063/1.3498901

Biochemistry and Theory of Proton-Coupled Electron Transfer
journal, January 2014

  • Migliore, Agostino; Polizzi, Nicholas F.; Therien, Michael J.
  • Chemical Reviews, Vol. 114, Issue 7
  • DOI: 10.1021/cr4006654

A Simple, Exact Density-Functional-Theory Embedding Scheme
journal, July 2012

  • Manby, Frederick R.; Stella, Martina; Goodpaster, Jason D.
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 8
  • DOI: 10.1021/ct300544e

Nonadiabatic Tunneling in Photodissociation of Phenol
journal, June 2016

  • Xie, Changjian; Ma, Jianyi; Zhu, Xiaolei
  • Journal of the American Chemical Society, Vol. 138, Issue 25
  • DOI: 10.1021/jacs.6b03288

How to remove the spurious resonances from ring polymer molecular dynamics
journal, June 2014

  • Rossi, Mariana; Ceriotti, Michele; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 140, Issue 23
  • DOI: 10.1063/1.4883861

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory
journal, February 2016

  • Marsalek, Ondrej; Markland, Thomas E.
  • The Journal of Chemical Physics, Vol. 144, Issue 5
  • DOI: 10.1063/1.4941093

Extension of path integral quantum transition state theory to the case of nonadiabatic activated dynamics
journal, August 1999

  • Schwieters, Charles D.; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 111, Issue 7
  • DOI: 10.1063/1.479569

A novel discrete variable representation for quantum mechanical reactive scattering via the S ‐matrix Kohn method
journal, February 1992

  • Colbert, Daniel T.; Miller, William H.
  • The Journal of Chemical Physics, Vol. 96, Issue 3
  • DOI: 10.1063/1.462100

Book reviews
journal, January 1996

  • Voth, D.; Resch, K. D. M.; Nopf, Nikolai
  • Neurosurgical Review, Vol. 19, Issue 2
  • DOI: 10.1007/bf00418086

Photodissociation Dynamics of Phenol: Multistate Trajectory Simulations including Tunneling
journal, November 2014

  • Xu, Xuefei; Zheng, Jingjing; Yang, Ke R.
  • Journal of the American Chemical Society, Vol. 136, Issue 46
  • DOI: 10.1021/ja509016a

Semiclassical initial value representation for electronically nonadiabatic molecular dynamics
journal, April 1997

  • Sun, Xiong; Miller, William H.
  • The Journal of Chemical Physics, Vol. 106, Issue 15
  • DOI: 10.1063/1.473624

The computation of electron transfer rates: The nonadiabatic instanton solution
journal, July 1995

  • Cao, Jianshu; Minichino, Camilla; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 103, Issue 4
  • DOI: 10.1063/1.469762

Nonadiabatic instanton calculation of multistate electron transfer reaction rate: Interference effects in three and four states systems
journal, June 2001

  • Jang, Seogjoo; Cao, Jianshu
  • The Journal of Chemical Physics, Vol. 114, Issue 22
  • DOI: 10.1063/1.1371262

Molecular dynamics with electronic transitions
journal, July 1990

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 93, Issue 2
  • DOI: 10.1063/1.459170

Study of an F center in molten KCl
journal, January 1984

  • Parrinello, M.; Rahman, A.
  • The Journal of Chemical Physics, Vol. 80, Issue 2
  • DOI: 10.1063/1.446740

Kinetically constrained ring-polymer molecular dynamics for non-adiabatic chemical reactions
journal, February 2014

  • Menzeleev, Artur R.; Bell, Franziska; Miller, Thomas F.
  • The Journal of Chemical Physics, Vol. 140, Issue 6
  • DOI: 10.1063/1.4863919

Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation
journal, November 1998

  • Sun, Xiong; Wang, Haobin; Miller, William H.
  • The Journal of Chemical Physics, Vol. 109, Issue 17
  • DOI: 10.1063/1.477389

Proton-Coupled Electron Transfer
text, January 2007

  • J., Meyer, Thomas; V., Huynh, My Hang
  • The University of North Carolina at Chapel Hill University Libraries
  • DOI: 10.17615/cywa-5d70

Proton-Coupled Electron Transfer
journal, October 1998

Kinetically Constrained Ring-Polymer Molecular Dynamics for Non-adiabatic Chemical Reactions
text, January 2014

i-PI: A Python interface for ab initio path integral molecular dynamics simulations
text, January 2014

How to remove the spurious resonances from ring polymer molecular dynamics
text, January 2014

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Preface: Special Topic on Nuclear Quantum Effects
    journal, March 2018

    • Tuckerman, Mark; Ceperley, David
    • The Journal of Chemical Physics, Vol. 148, Issue 10
    • DOI: 10.1063/1.5026714

    Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories
    journal, December 2018

    • Schile, Addison J.; Limmer, David T.
    • The Journal of Chemical Physics, Vol. 149, Issue 21
    • DOI: 10.1063/1.5058281

    Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems
    journal, March 2019

    • Thapa, Manish J.; Fang, Wei; Richardson, Jeremy O.
    • The Journal of Chemical Physics, Vol. 150, Issue 10
    • DOI: 10.1063/1.5081108

    On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics
    journal, February 2019

    • Saller, Maximilian A. C.; Kelly, Aaron; Richardson, Jeremy O.
    • The Journal of Chemical Physics, Vol. 150, Issue 7
    • DOI: 10.1063/1.5082596

    Probing photodissociation dynamics using ring polymer molecular dynamics
    journal, March 2019

    • Kaur, Rajwant; Welsch, Ralph
    • The Journal of Chemical Physics, Vol. 150, Issue 11
    • DOI: 10.1063/1.5086218

    State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics
    journal, June 2019

    • Chowdhury, Sutirtha N.; Huo, Pengfei
    • The Journal of Chemical Physics, Vol. 150, Issue 24
    • DOI: 10.1063/1.5096276

    Spin-mapping approach for nonadiabatic molecular dynamics
    journal, July 2019

    • Runeson, Johan E.; Richardson, Jeremy O.
    • The Journal of Chemical Physics, Vol. 151, Issue 4
    • DOI: 10.1063/1.5100506

    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

    On the calculation of quantum mechanical electron transfer rates
    journal, September 2019

    • Lawrence, Joseph E.; Fletcher, Theo; Lindoy, Lachlan P.
    • The Journal of Chemical Physics, Vol. 151, Issue 11
    • DOI: 10.1063/1.5116800

    An analysis of isomorphic RPMD in the golden rule limit
    journal, December 2019

    • Lawrence, Joseph E.; Manolopoulos, David E.
    • The Journal of Chemical Physics, Vol. 151, Issue 24
    • DOI: 10.1063/1.5138913

    Nuclear quantum effects in state-selective scattering from ring polymer molecular dynamics
    journal, May 2020

    • Marjollet, Adrien; Welsch, Ralph
    • The Journal of Chemical Physics, Vol. 152, Issue 19
    • DOI: 10.1063/5.0004179

    Probing photodissociation dynamics using ring polymer molecular dynamics
    text, January 2019

    On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics
    text, January 2019

    Spin-mapping approach for nonadiabatic molecular dynamics
    text, January 2019

    Nuclear quantum effects in state-selective scattering from ring polymer molecular dynamics
    text, January 2020

    An analysis of isomorphic RPMD in the golden rule limit
    text, January 2019

      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: