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

Schile, Addison J.; Limmer, David T.

doi:10.1063/1.5106379

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

Journal Article · 03 July 2019 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5106379 · OSTI ID:1577599

Schile, Addison J. ^[1];

^[1]

Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)

Grant/Contract Number:: AC02-05CH11231; AC02- 05CH11231

OSTI ID:: 1577599

Alternate ID(s):: OSTI ID: 1530912

Journal Information:: Journal of Chemical Physics, Vol. 151, Issue 1; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 19 works

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References (64)

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method Chen, Lipeng; Gelin, Maxim F.; Chernyak, Vladimir Y. Faraday Discussions, Vol. 194 https://doi.org/10.1039/c6fd00088f	journal	January 2016
A classical analog for electronic degrees of freedom in nonadiabatic collision processes Meyera), Hans‐Dieter; Miller, William H. The Journal of Chemical Physics, Vol. 70, Issue 7 https://doi.org/10.1063/1.437910	journal	April 1979
Path Integral Calculation of Quantum Nonadiabatic Rates in Model Condensed Phase Reactions Topaler, Maria; Makri, Nancy The Journal of Physical Chemistry, Vol. 100, Issue 11 https://doi.org/10.1021/jp951673k	journal	January 1996
Tracking an electronic wave packet in the vicinity of a conical intersection Qi, Da-Long; Duan, Hong-Guang; Sun, Zhen-Rong The Journal of Chemical Physics, Vol. 147, Issue 7 https://doi.org/10.1063/1.4989462	journal	August 2017
Time-convolutionless projection operator formalism for elimination of fast variables. Applications to Brownian motion Chaturvedi, S.; Shibata, F. Zeitschrift f�r Physik B Condensed Matter and Quanta, Vol. 35, Issue 3 https://doi.org/10.1007/bf01319852	journal	September 1979
Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. II. Application to environment-induced nonadiabatic dynamics Hughes, Keith H.; Christ, Clara D.; Burghardt, Irene The Journal of Chemical Physics, Vol. 131, Issue 12 https://doi.org/10.1063/1.3226343	journal	September 2009
Extending the applicability of Redfield theories into highly non-Markovian regimes Montoya-Castillo, Andrés; Berkelbach, Timothy C.; Reichman, David R. The Journal of Chemical Physics, Vol. 143, Issue 19 https://doi.org/10.1063/1.4935443	journal	November 2015
The Diabatic Picture of Electron Transfer, Reaction Barriers, and Molecular Dynamics Van Voorhis, Troy; Kowalczyk, Tim; Kaduk, Benjamin Annual Review of Physical Chemistry, Vol. 61, Issue 1 https://doi.org/10.1146/annurev.physchem.012809.103324	journal	March 2010
Quantum dynamical simulation of ultrafast molecular processes in the condensed phase Thoss, Michael; Wang, Haobin Chemical Physics, Vol. 322, Issue 1-2 https://doi.org/10.1016/j.chemphys.2005.07.011	journal	March 2006
Role of Conical Intersections in Molecular Spectroscopy and Photoinduced Chemical Dynamics Domcke, Wolfgang; Yarkony, David R. Annual Review of Physical Chemistry, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103522	journal	May 2012
Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra Ikeda, Tatsushi; Dijkstra, Arend G.; Tanimura, Yoshitaka The Journal of Chemical Physics, Vol. 150, Issue 11 https://doi.org/10.1063/1.5086948	journal	March 2019
Dynamics at Conical Intersections Schuurman, Michael S.; Stolow, Albert Annual Review of Physical Chemistry, Vol. 69, Issue 1 https://doi.org/10.1146/annurev-physchem-052516-050721	journal	April 2018
Linear and nonlinear spectroscopy from quantum master equations Fetherolf, Jonathan H.; Berkelbach, Timothy C. The Journal of Chemical Physics, Vol. 147, Issue 24 https://doi.org/10.1063/1.5006824	journal	December 2017
Isomerization Through Conical Intersections Levine, Benjamin G.; Martínez, Todd J. Annual Review of Physical Chemistry, Vol. 58, Issue 1 https://doi.org/10.1146/annurev.physchem.57.032905.104612	journal	May 2007
Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics Hughes, Keith H.; Christ, Clara D.; Burghardt, Irene The Journal of Chemical Physics, Vol. 131, Issue 2 https://doi.org/10.1063/1.3159671	journal	July 2009
Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and non-adiabatic quantum dynamics Berkelbach, Timothy C.; Reichman, David R.; Markland, Thomas E. The Journal of Chemical Physics, Vol. 136, Issue 3 https://doi.org/10.1063/1.3671372	journal	January 2012
Impact of Vibrational Coherence on the Quantum Yield at a Conical Intersection Duan, Hong-Guang; Miller, R. J. Dwayne; Thorwart, Michael The Journal of Physical Chemistry Letters, Vol. 7, Issue 17 https://doi.org/10.1021/acs.jpclett.6b01551	journal	August 2016
Perspective: Nonadiabatic dynamics theory Tully, John C. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4757762	journal	December 2012
Signatures of conical intersections in two-dimensional electronic spectra Krčmář, Jindřich; Gelin, Maxim F.; Egorova, Dassia Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 47, Issue 12 https://doi.org/10.1088/0953-4075/47/12/124019	journal	June 2014
Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories Schile, Addison J.; Limmer, David T. The Journal of Chemical Physics, Vol. 149, Issue 21 https://doi.org/10.1063/1.5058281	journal	December 2018
Vibronic exciton theory of singlet fission. III. How vibronic coupling and thermodynamics promote rapid triplet generation in pentacene crystals Tempelaar, Roel; Reichman, David R. The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5031778	journal	June 2018
Non-Adiabatic Effects on Excited States of Vinylidene Observed with Slow Photoelectron Velocity-Map Imaging DeVine, Jessalyn A.; Weichman, Marissa L.; Zhou, Xueyao Journal of the American Chemical Society, Vol. 138, Issue 50 https://doi.org/10.1021/jacs.6b10233	journal	December 2016
Slow Electron Velocity-Map Imaging of Negative Ions: Applications to Spectroscopy and Dynamics ^† Neumark, Daniel M. The Journal of Physical Chemistry A, Vol. 112, Issue 51 https://doi.org/10.1021/jp807182q	journal	December 2008
On the Theory of Relaxation Processes Redfield, A. G. IBM Journal of Research and Development, Vol. 1, Issue 1 https://doi.org/10.1147/rd.11.0019	journal	January 1957
Gaussian Field Model of Dielectric Solvation Dynamics Song, Xueyu; Chandler, David; Marcus, R. A. The Journal of Physical Chemistry, Vol. 100, Issue 29 https://doi.org/10.1021/jp960887e	journal	January 1996
The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets Beck, M. Physics Reports, Vol. 324, Issue 1 https://doi.org/10.1016/S0370-1573(99)00047-2	journal	January 2000
Action-spectroscopy studies of positively charge-tagged azobenzene in solution and in the gas-phase Gruber, Elisabeth; Strauss, Marcel A.; Wegner, Hermann A. The Journal of Chemical Physics, Vol. 150, Issue 8 https://doi.org/10.1063/1.5085743	journal	February 2019
Signature of the geometric phase in the wave packet dynamics on hypersurfaces Duan, Hong-Guang; Qi, Da-Long; Sun, Zhen-Rong Chemical Physics, Vol. 515 https://doi.org/10.1016/j.chemphys.2018.09.016	journal	November 2018
Correlating the motion of electrons and nuclei with two-dimensional electronic-vibrational spectroscopy Oliver, T. A. A.; Lewis, N. H. C.; Fleming, G. R. Proceedings of the National Academy of Sciences, Vol. 111, Issue 28 https://doi.org/10.1073/pnas.1409207111	journal	June 2014
Quasi-adiabatic propagator path integral methods. Exact quantum rate constants for condensed phase reactions Topaler, Maria; Makri, Nancy Chemical Physics Letters, Vol. 210, Issue 1-3 https://doi.org/10.1016/0009-2614(93)89135-5	journal	July 1993
Femtosecond Dynamics of Pyridine in the Condensed Phase: Valence Isomerization by Conical Intersections Chachisvilis, Mirianas; Zewail, Ahmed H. International Conference on Ultrafast Phenomena https://doi.org/10.1364/up.2000.tuf15	conference	January 2000
A generalized stochastic liouville equation. Non-Markovian versus memoryless master equations Shibata, Fumiaki; Takahashi, Yoshinori; Hashitsume, Natsuki Journal of Statistical Physics, Vol. 17, Issue 4 https://doi.org/10.1007/bf01040100	journal	October 1977
Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics Kelly, Aaron; Markland, Thomas E. The Journal of Chemical Physics, Vol. 139, Issue 1 https://doi.org/10.1063/1.4812355	journal	July 2013
Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density Thoss, Michael; Wang, Haobin; Miller, William H. The Journal of Chemical Physics, Vol. 115, Issue 7 https://doi.org/10.1063/1.1385562	journal	August 2001
Multilevel Redfield description of the dissipative dynamics at conical intersections Kühl, Axel; Domcke, Wolfgang The Journal of Chemical Physics, Vol. 116, Issue 1 https://doi.org/10.1063/1.1423326	journal	January 2002
Short-time dynamics through conical intersections in macrosystems. I. Theory: Effective-mode formulation Gindensperger, Etienne; Burghardt, Irene; Cederbaum, Lorenz S. The Journal of Chemical Physics, Vol. 124, Issue 14 https://doi.org/10.1063/1.2183304	journal	April 2006
Short-time dynamics through conical intersections in macrosystems. II. Applications Gindensperger, Etienne; Burghardt, Irene; Cederbaum, Lorenz S. The Journal of Chemical Physics, Vol. 124, Issue 14 https://doi.org/10.1063/1.2183305	journal	April 2006
Reduced density matrix hybrid approach: Application to electronic energy transfer Berkelbach, Timothy C.; Markland, Thomas E.; Reichman, David R. The Journal of Chemical Physics, Vol. 136, Issue 8 https://doi.org/10.1063/1.3687342	journal	February 2012
Ensemble Method in the Theory of Irreversibility Zwanzig, Robert The Journal of Chemical Physics, Vol. 33, Issue 5 https://doi.org/10.1063/1.1731409	journal	November 1960
Stochastic unraveling of time-local quantum master equations beyond the Lindblad class Kleinekathöfer, Ulrich; Kondov, Ivan; Schreiber, Michael Physical Review E, Vol. 66, Issue 3 https://doi.org/10.1103/physreve.66.037701	journal	September 2002
Compact MCTDH Wave Functions for High-Dimensional System-Bath Quantum Dynamics Bonfanti, M.; Tantardini, G. F.; Hughes, K. H. The Journal of Physical Chemistry A, Vol. 116, Issue 46 https://doi.org/10.1021/jp3064504	journal	September 2012
Activated barrier crossing: Comparison of experiment and theory Fleming, Graham R.; Courtney, Scott H.; Balk, Michael W. Journal of Statistical Physics, Vol. 42, Issue 1-2 https://doi.org/10.1007/bf01010842	journal	January 1986
Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem Ben-Nun, M.; Martı́nez, Todd J. The Journal of Chemical Physics, Vol. 108, Issue 17 https://doi.org/10.1063/1.476142	journal	May 1998
Quantum‐mechanical derivation of the Bloch equations: Beyond the weak‐coupling limit Laird, Brian B.; Budimir, Jane; Skinner, James L. The Journal of Chemical Physics, Vol. 94, Issue 6 https://doi.org/10.1063/1.460626	journal	March 1991
Completely positive dynamical semigroups of N-level systems Gorini, Vittorio Journal of Mathematical Physics, Vol. 17, Issue 5 https://doi.org/10.1063/1.522979	journal	January 1976
BEYOND BORN-OPPENHEIMER: Molecular Dynamics Through a Conical Intersection Worth, Graham A.; Cederbaum, Lorenz S. Annual Review of Physical Chemistry, Vol. 55, Issue 1 https://doi.org/10.1146/annurev.physchem.55.091602.094335	journal	June 2004
Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation Köuppel, H.; Domcke, W.; Cederbaum, L. S. Advances in Chemical Physics https://doi.org/10.1002/9780470142813.ch2	book	January 2007
Two-dimensional Fourier transform electronic spectroscopy at a conical intersection Kitney-Hayes, Katherine A.; Ferro, Allison A.; Tiwari, Vivek The Journal of Chemical Physics, Vol. 140, Issue 12 https://doi.org/10.1063/1.4867996	journal	March 2014
How to recover Marcus theory with fewest switches surface hopping: Add just a touch of decoherence Landry, Brian R.; Subotnik, Joseph E. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4733675	journal	December 2012
Multilayer formulation of the multiconfiguration time-dependent Hartree theory Wang, Haobin; Thoss, Michael The Journal of Chemical Physics, Vol. 119, Issue 3 https://doi.org/10.1063/1.1580111	journal	July 2003
Solution of the Redfield equation for the dissipative quantum dynamics of multilevel systems Pollard, W. Thomas; Friesner, Richard A. The Journal of Chemical Physics, Vol. 100, Issue 7 https://doi.org/10.1063/1.467222	journal	April 1994
Stochastic Bloch-Redfield theory: Quantum jumps in a solid-state environment Vogt, Nicolas; Jeske, Jan; Cole, Jared H. Physical Review B, Vol. 88, Issue 17 https://doi.org/10.1103/physrevb.88.174514	journal	November 2013
Femtosecond Dynamics of Pyridine in the Condensed Phase: Valence Isomerization by Conical Intersections Chachisvilis, Mirianas; Zewail, Ahmed H. The Journal of Physical Chemistry A, Vol. 103, Issue 37 https://doi.org/10.1021/jp991821x	journal	September 1999
Dynamics on potential energy surfaces with a conical intersection: Adiabatic, intermediate, and diabatic behavior Manthe, U.; Köppel, H. The Journal of Chemical Physics, Vol. 93, Issue 3 https://doi.org/10.1063/1.459094	journal	August 1990
Molecular dynamics with electronic transitions Tully, John C. The Journal of Chemical Physics, Vol. 93, Issue 2 https://doi.org/10.1063/1.459170	journal	July 1990
Progress in the Theory of Mixed Quantum-Classical Dynamics Kapral, Raymond Annual Review of Physical Chemistry, Vol. 57, Issue 1 https://doi.org/10.1146/annurev.physchem.57.032905.104702	journal	May 2006
Two-dimensional electronic-vibrational spectroscopic study of conical intersection dynamics: an experimental and electronic structure study Wu, Eric C.; Ge, Qinghui; Arsenault, Eric A. Physical Chemistry Chemical Physics, Vol. 21, Issue 26 https://doi.org/10.1039/C8CP05264F	journal	January 2019
Effect of a dissipative environment on the dynamics at a conical intersection Kühl, Axel; Domcke, Wolfgang Chemical Physics, Vol. 259, Issue 2-3 https://doi.org/10.1016/s0301-0104(00)00199-3	journal	September 2000
Reduced density matrix hybrid approach: An efficient and accurate method for adiabatic and non-adiabatic quantum dynamics Berkelbach, Timothy C.; Reichman, David R.; Markland, Thomas E. arXiv https://doi.org/10.48550/arxiv.1110.0490	text	January 2011
Extending the applicability of Redfield theories into highly non-Markovian regimes Montoya-Castillo, Andrés; Berkelbach, Timothy C.; Reichman, David R. arXiv https://doi.org/10.48550/arxiv.1507.02755	text	January 2015
Linear and nonlinear spectroscopy from quantum master equations Fetherolf, Jonathan H.; Berkelbach, Timothy C. arXiv https://doi.org/10.48550/arxiv.1709.04075	text	January 2017
Vibronic exciton theory of singlet fission. III. How vibronic coupling and thermodynamics promote rapid triplet generation in pentacene crystals Tempelaar, Roel; Reichman, David R. arXiv https://doi.org/10.48550/arxiv.1803.10216	text	January 2018
Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories Schile, Addison J.; Limmer, David T. arXiv https://doi.org/10.48550/arxiv.1809.03501	text	January 2018
Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra Ikeda, Tatsushi; Dijkstra, Arend G.; Tanimura, Yoshitaka arXiv https://doi.org/10.48550/arxiv.1902.07400	text	January 2019

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