skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on July 3, 2020

Title: Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations

Abstract

We introduce a framework for simulating relaxation dynamics through a conical intersection of an open quantum system that combines methods to approximate the motion of degrees of freedom with disparate time and energy scales. In the vicinity of a conical intersection, a few degrees of freedom render the nuclear dynamics nonadiabatic with respect to the electronic degrees of freedom. We treat these strongly coupled modes by evolving their wavepacket dynamics in the absence of additional coupling exactly. The remaining weakly coupled nuclear degrees of freedom are partitioned into modes that are fast relative to the nonadiabatic coupling and those that are slow. The fast degrees of freedom can be traced out and treated with second-order perturbation theory in the form of the time-convolutionless master equation. The slow degrees of freedom are assumed to be frozen over the ultrafast relaxation and treated as sources of static disorder. Similarly, we adopt the recently developed frozen-mode extension to second-order quantum master equations. We benchmark this approach to numerically exact results in models of pyrazine internal conversion and rhodopsin photoisomerization. We use this framework to study the dependence of the quantum yield on the reorganization energy and the characteristic time scale of the bathmore » in a two-mode model of photoisomerization. We believe that the yield is monotonically increasing with reorganization energy for a Markovian bath but monotonically decreasing with reorganization energy for a non-Markovian bath. This reflects the subtle interplay between dissipation and decoherence in conical intersection dynamics in the condensed phase.« less

Authors:
 [1]; ORCiD logo [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), Advanced Scientific Computing Research (ASCR) (SC-21). Scientific Discovery through Advanced Computing (SciDAC)
OSTI Identifier:
1577599
Alternate Identifier(s):
OSTI ID: 1530912
Grant/Contract Number:  
AC02-05CH11231; AC02- 05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 1; 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

Citation Formats

Schile, Addison J., and Limmer, David T. Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations. United States: N. p., 2019. Web. doi:10.1063/1.5106379.
Schile, Addison J., & Limmer, David T. Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations. United States. doi:10.1063/1.5106379.
Schile, Addison J., and Limmer, David T. Wed . "Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations". United States. doi:10.1063/1.5106379.
@article{osti_1577599,
title = {Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations},
author = {Schile, Addison J. and Limmer, David T.},
abstractNote = {We introduce a framework for simulating relaxation dynamics through a conical intersection of an open quantum system that combines methods to approximate the motion of degrees of freedom with disparate time and energy scales. In the vicinity of a conical intersection, a few degrees of freedom render the nuclear dynamics nonadiabatic with respect to the electronic degrees of freedom. We treat these strongly coupled modes by evolving their wavepacket dynamics in the absence of additional coupling exactly. The remaining weakly coupled nuclear degrees of freedom are partitioned into modes that are fast relative to the nonadiabatic coupling and those that are slow. The fast degrees of freedom can be traced out and treated with second-order perturbation theory in the form of the time-convolutionless master equation. The slow degrees of freedom are assumed to be frozen over the ultrafast relaxation and treated as sources of static disorder. Similarly, we adopt the recently developed frozen-mode extension to second-order quantum master equations. We benchmark this approach to numerically exact results in models of pyrazine internal conversion and rhodopsin photoisomerization. We use this framework to study the dependence of the quantum yield on the reorganization energy and the characteristic time scale of the bath in a two-mode model of photoisomerization. We believe that the yield is monotonically increasing with reorganization energy for a Markovian bath but monotonically decreasing with reorganization energy for a non-Markovian bath. This reflects the subtle interplay between dissipation and decoherence in conical intersection dynamics in the condensed phase.},
doi = {10.1063/1.5106379},
journal = {Journal of Chemical Physics},
number = 1,
volume = 151,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on July 3, 2020
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method
journal, January 2016

  • Chen, Lipeng; Gelin, Maxim F.; Chernyak, Vladimir Y.
  • Faraday Discussions, Vol. 194
  • DOI: 10.1039/c6fd00088f

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

  • Meyera), Hans‐Dieter; Miller, William H.
  • The Journal of Chemical Physics, Vol. 70, Issue 7
  • DOI: 10.1063/1.437910

Path Integral Calculation of Quantum Nonadiabatic Rates in Model Condensed Phase Reactions
journal, January 1996

  • Topaler, Maria; Makri, Nancy
  • The Journal of Physical Chemistry, Vol. 100, Issue 11
  • DOI: 10.1021/jp951673k

Tracking an electronic wave packet in the vicinity of a conical intersection
journal, August 2017

  • Qi, Da-Long; Duan, Hong-Guang; Sun, Zhen-Rong
  • The Journal of Chemical Physics, Vol. 147, Issue 7
  • DOI: 10.1063/1.4989462

Time-convolutionless projection operator formalism for elimination of fast variables. Applications to Brownian motion
journal, September 1979

  • Chaturvedi, S.; Shibata, F.
  • Zeitschrift f�r Physik B Condensed Matter and Quanta, Vol. 35, Issue 3
  • DOI: 10.1007/bf01319852

Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. II. Application to environment-induced nonadiabatic dynamics
journal, September 2009

  • Hughes, Keith H.; Christ, Clara D.; Burghardt, Irene
  • The Journal of Chemical Physics, Vol. 131, Issue 12
  • DOI: 10.1063/1.3226343

Extending the applicability of Redfield theories into highly non-Markovian regimes
journal, November 2015

  • Montoya-Castillo, Andrés; Berkelbach, Timothy C.; Reichman, David R.
  • The Journal of Chemical Physics, Vol. 143, Issue 19
  • DOI: 10.1063/1.4935443

The Diabatic Picture of Electron Transfer, Reaction Barriers, and Molecular Dynamics
journal, March 2010


Quantum dynamical simulation of ultrafast molecular processes in the condensed phase
journal, March 2006


Role of Conical Intersections in Molecular Spectroscopy and Photoinduced Chemical Dynamics
journal, May 2012


Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra
journal, March 2019

  • Ikeda, Tatsushi; Dijkstra, Arend G.; Tanimura, Yoshitaka
  • The Journal of Chemical Physics, Vol. 150, Issue 11
  • DOI: 10.1063/1.5086948

Dynamics at Conical Intersections
journal, April 2018


Linear and nonlinear spectroscopy from quantum master equations
journal, December 2017

  • Fetherolf, Jonathan H.; Berkelbach, Timothy C.
  • The Journal of Chemical Physics, Vol. 147, Issue 24
  • DOI: 10.1063/1.5006824

Isomerization Through Conical Intersections
journal, May 2007


Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics
journal, July 2009

  • Hughes, Keith H.; Christ, Clara D.; Burghardt, Irene
  • The Journal of Chemical Physics, Vol. 131, Issue 2
  • DOI: 10.1063/1.3159671

Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and non-adiabatic quantum dynamics
journal, January 2012

  • Berkelbach, Timothy C.; Reichman, David R.; Markland, Thomas E.
  • The Journal of Chemical Physics, Vol. 136, Issue 3
  • DOI: 10.1063/1.3671372

Impact of Vibrational Coherence on the Quantum Yield at a Conical Intersection
journal, August 2016

  • Duan, Hong-Guang; Miller, R. J. Dwayne; Thorwart, Michael
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 17
  • DOI: 10.1021/acs.jpclett.6b01551

Perspective: Nonadiabatic dynamics theory
journal, December 2012

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4757762

Signatures of conical intersections in two-dimensional electronic spectra
journal, June 2014

  • Krčmář, Jindřich; Gelin, Maxim F.; Egorova, Dassia
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 47, Issue 12
  • DOI: 10.1088/0953-4075/47/12/124019

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

Vibronic exciton theory of singlet fission. III. How vibronic coupling and thermodynamics promote rapid triplet generation in pentacene crystals
journal, June 2018

  • Tempelaar, Roel; Reichman, David R.
  • The Journal of Chemical Physics, Vol. 148, Issue 24
  • DOI: 10.1063/1.5031778

Non-Adiabatic Effects on Excited States of Vinylidene Observed with Slow Photoelectron Velocity-Map Imaging
journal, December 2016

  • DeVine, Jessalyn A.; Weichman, Marissa L.; Zhou, Xueyao
  • Journal of the American Chemical Society, Vol. 138, Issue 50
  • DOI: 10.1021/jacs.6b10233

Slow Electron Velocity-Map Imaging of Negative Ions: Applications to Spectroscopy and Dynamics
journal, December 2008

  • Neumark, Daniel M.
  • The Journal of Physical Chemistry A, Vol. 112, Issue 51
  • DOI: 10.1021/jp807182q

On the Theory of Relaxation Processes
journal, January 1957

  • Redfield, A. G.
  • IBM Journal of Research and Development, Vol. 1, Issue 1
  • DOI: 10.1147/rd.11.0019

Gaussian Field Model of Dielectric Solvation Dynamics
journal, January 1996

  • Song, Xueyu; Chandler, David; Marcus, R. A.
  • The Journal of Physical Chemistry, Vol. 100, Issue 29
  • DOI: 10.1021/jp960887e

Action-spectroscopy studies of positively charge-tagged azobenzene in solution and in the gas-phase
journal, February 2019

  • Gruber, Elisabeth; Strauss, Marcel A.; Wegner, Hermann A.
  • The Journal of Chemical Physics, Vol. 150, Issue 8
  • DOI: 10.1063/1.5085743

Signature of the geometric phase in the wave packet dynamics on hypersurfaces
journal, November 2018


Correlating the motion of electrons and nuclei with two-dimensional electronic-vibrational spectroscopy
journal, June 2014

  • Oliver, T. A. A.; Lewis, N. H. C.; Fleming, G. R.
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 28
  • DOI: 10.1073/pnas.1409207111

Quasi-adiabatic propagator path integral methods. Exact quantum rate constants for condensed phase reactions
journal, July 1993


A generalized stochastic liouville equation. Non-Markovian versus memoryless master equations
journal, October 1977

  • Shibata, Fumiaki; Takahashi, Yoshinori; Hashitsume, Natsuki
  • Journal of Statistical Physics, Vol. 17, Issue 4
  • DOI: 10.1007/bf01040100

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics
journal, July 2013

  • Kelly, Aaron; Markland, Thomas E.
  • The Journal of Chemical Physics, Vol. 139, Issue 1
  • DOI: 10.1063/1.4812355

Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density
journal, August 2001

  • Thoss, Michael; Wang, Haobin; Miller, William H.
  • The Journal of Chemical Physics, Vol. 115, Issue 7
  • DOI: 10.1063/1.1385562

Multilevel Redfield description of the dissipative dynamics at conical intersections
journal, January 2002

  • Kühl, Axel; Domcke, Wolfgang
  • The Journal of Chemical Physics, Vol. 116, Issue 1
  • DOI: 10.1063/1.1423326

Short-time dynamics through conical intersections in macrosystems. I. Theory: Effective-mode formulation
journal, April 2006

  • Gindensperger, Etienne; Burghardt, Irene; Cederbaum, Lorenz S.
  • The Journal of Chemical Physics, Vol. 124, Issue 14
  • DOI: 10.1063/1.2183304

Short-time dynamics through conical intersections in macrosystems. II. Applications
journal, April 2006

  • Gindensperger, Etienne; Burghardt, Irene; Cederbaum, Lorenz S.
  • The Journal of Chemical Physics, Vol. 124, Issue 14
  • DOI: 10.1063/1.2183305

Reduced density matrix hybrid approach: Application to electronic energy transfer
journal, February 2012

  • Berkelbach, Timothy C.; Markland, Thomas E.; Reichman, David R.
  • The Journal of Chemical Physics, Vol. 136, Issue 8
  • DOI: 10.1063/1.3687342

Ensemble Method in the Theory of Irreversibility
journal, November 1960

  • Zwanzig, Robert
  • The Journal of Chemical Physics, Vol. 33, Issue 5
  • DOI: 10.1063/1.1731409

Stochastic unraveling of time-local quantum master equations beyond the Lindblad class
journal, September 2002


Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics
journal, September 2012

  • Bonfanti, M.; Tantardini, G. F.; Hughes, K. H.
  • The Journal of Physical Chemistry A, Vol. 116, Issue 46
  • DOI: 10.1021/jp3064504

Activated barrier crossing: Comparison of experiment and theory
journal, January 1986

  • Fleming, Graham R.; Courtney, Scott H.; Balk, Michael W.
  • Journal of Statistical Physics, Vol. 42, Issue 1-2
  • DOI: 10.1007/bf01010842

Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem
journal, May 1998

  • Ben-Nun, M.; Martı́nez, Todd J.
  • The Journal of Chemical Physics, Vol. 108, Issue 17
  • DOI: 10.1063/1.476142

Quantum‐mechanical derivation of the Bloch equations: Beyond the weak‐coupling limit
journal, March 1991

  • Laird, Brian B.; Budimir, Jane; Skinner, James L.
  • The Journal of Chemical Physics, Vol. 94, Issue 6
  • DOI: 10.1063/1.460626

Completely positive dynamical semigroups of N-level systems
journal, January 1976

  • Gorini, Vittorio
  • Journal of Mathematical Physics, Vol. 17, Issue 5
  • DOI: 10.1063/1.522979

BEYOND BORN-OPPENHEIMER: Molecular Dynamics Through a Conical Intersection
journal, June 2004


Two-dimensional Fourier transform electronic spectroscopy at a conical intersection
journal, March 2014

  • Kitney-Hayes, Katherine A.; Ferro, Allison A.; Tiwari, Vivek
  • The Journal of Chemical Physics, Vol. 140, Issue 12
  • DOI: 10.1063/1.4867996

How to recover Marcus theory with fewest switches surface hopping: Add just a touch of decoherence
journal, December 2012

  • Landry, Brian R.; Subotnik, Joseph E.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4733675

Multilayer formulation of the multiconfiguration time-dependent Hartree theory
journal, July 2003

  • Wang, Haobin; Thoss, Michael
  • The Journal of Chemical Physics, Vol. 119, Issue 3
  • DOI: 10.1063/1.1580111

Solution of the Redfield equation for the dissipative quantum dynamics of multilevel systems
journal, April 1994

  • Pollard, W. Thomas; Friesner, Richard A.
  • The Journal of Chemical Physics, Vol. 100, Issue 7
  • DOI: 10.1063/1.467222

Stochastic Bloch-Redfield theory: Quantum jumps in a solid-state environment
journal, November 2013


Femtosecond Dynamics of Pyridine in the Condensed Phase:  Valence Isomerization by Conical Intersections
journal, September 1999

  • Chachisvilis, Mirianas; Zewail, Ahmed H.
  • The Journal of Physical Chemistry A, Vol. 103, Issue 37
  • DOI: 10.1021/jp991821x

Dynamics on potential energy surfaces with a conical intersection: Adiabatic, intermediate, and diabatic behavior
journal, August 1990

  • Manthe, U.; Köppel, H.
  • The Journal of Chemical Physics, Vol. 93, Issue 3
  • DOI: 10.1063/1.459094

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

Progress in the Theory of Mixed Quantum-Classical Dynamics
journal, May 2006


Two-dimensional electronic-vibrational spectroscopic study of conical intersection dynamics: an experimental and electronic structure study
journal, January 2019

  • Wu, Eric C.; Ge, Qinghui; Arsenault, Eric A.
  • Physical Chemistry Chemical Physics, Vol. 21, Issue 26
  • DOI: 10.1039/C8CP05264F

Effect of a dissipative environment on the dynamics at a conical intersection
journal, September 2000