Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics

Pfalzgraff, William C.; Montoya-Castillo, Andrés; Kelly, Aaron; Markland, Thomas E.

doi:10.1063/1.5095715

Title: Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics

Journal Article · 25 June 2019 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5095715 · OSTI ID:1577593

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Stanford Univ., CA (United States); Chatham University, Pittsburgh, PA (United States)
Stanford Univ., CA (United States)
Dalhousie Univ., Halifax, NS (Canada)

Techniques derived from the generalized quantum master equation (GQME) framework have provided the basis for elucidating energy and charge transfer in systems ranging from molecular solids to photosynthetic complexes. Recently, the nonperturbative combination of the GQME with quantum-classical methods has resulted in approaches whose accuracy and efficiency exceed those of the original quantumclassical schemes while offering significant accuracy improvements over perturbative expansions of the GQME. In this work, we show that, while the non-Markovian memory kernel required to propagate the GQME scales quartically with the number of subsystem states, the number of trajectories required scales at most quadratically when using quantum-classical methods to construct the kernel. We then present an algorithm that allows further acceleration of the quantum-classical GQME by offering a way to selectively sample the kernel matrix elements that are most important to the process of interest. We demonstrate the utility of these advances by applying the combination of Ehrenfest mean field theory with the GQME (MF-GQME) to models of the Fenna-Matthews-Olson (FMO) complex and the light harvesting complex II (LHCII), with 7 and 14 states, respectively. This allows us to show that the MF-GQME is able to accurately capture all the relevant dynamical time scales in LHCII: the initial nonequilibrium population transfer on the femtosecond time scale, the steady state-type trapping on the picosecond time scale, and the long time population relaxation. Remarkably, all of these physical effects spanning tens of picoseconds can be encoded in a memory kernel that decays only after ~65 fs.

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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); Univ. of California, Merced, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-05CH11231; SC0014437

OSTI ID:: 1577593

Alternate ID(s):: OSTI ID: 1529414

Journal Information:: Journal of Chemical Physics, Vol. 150, Issue 24; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

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Cited by: 28 works

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References (66)

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
Statistical Mechanics of Nonequilibrium Liquids Evans, Denis J.; Morriss, Gary P. ANU Press https://doi.org/10.22459/SMNL.08.2007	book	January 2007
Communication: Partial linearized density matrix dynamics for dissipative, non-adiabatic quantum evolution Huo, Pengfei; Coker, David F. The Journal of Chemical Physics, Vol. 135, Issue 20 https://doi.org/10.1063/1.3664763	journal	November 2011
Mapping variable ring polymer molecular dynamics: A path-integral based method for nonadiabatic processes Ananth, Nandini The Journal of Chemical Physics, Vol. 139, Issue 12 https://doi.org/10.1063/1.4821590	journal	September 2013
Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature Ishizaki, A.; Fleming, G. R. Proceedings of the National Academy of Sciences, Vol. 106, Issue 41 https://doi.org/10.1073/pnas.0908989106	journal	October 2009
A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation Mulvihill, Ellen; Schubert, Alexander; Sun, Xiang The Journal of Chemical Physics, Vol. 150, Issue 3 https://doi.org/10.1063/1.5055756	journal	January 2019
Non-Markovian population and phase relaxation and absorption lineshape for a two-level system strongly coupled to a harmonic quantum bath Chang, T. -M.; Skinner, J. L. Physica A: Statistical Mechanics and its Applications, Vol. 193, Issue 3-4 https://doi.org/10.1016/0378-4371(93)90489-q	journal	April 1993
A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters Swope, William C.; Andersen, Hans C.; Berens, Peter H. The Journal of Chemical Physics, Vol. 76, Issue 1 https://doi.org/10.1063/1.442716	journal	January 1982
Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equation approach Ishizaki, Akihito; Fleming, Graham R. The Journal of Chemical Physics, Vol. 130, Issue 23 https://doi.org/10.1063/1.3155372	journal	June 2009
Exact quantum statistics for electronically nonadiabatic systems using continuous path variables Ananth, Nandini; Miller, Thomas F. The Journal of Chemical Physics, Vol. 133, Issue 23 https://doi.org/10.1063/1.3511700	journal	December 2010
Theory of multichromophoric coherent resonance energy transfer: A polaronic quantum master equation approach Jang, Seogjoo The Journal of Chemical Physics, Vol. 135, Issue 3 https://doi.org/10.1063/1.3608914	journal	July 2011
How Proteins Trigger Excitation Energy Transfer in the FMO Complex of Green Sulfur Bacteria Adolphs, Julia; Renger, Thomas Biophysical Journal, Vol. 91, Issue 8 https://doi.org/10.1529/biophysj.105.079483	journal	October 2006
Excitation Dynamics in the LHCII Complex of Higher Plants: Modeling Based on the 2.72 Å Crystal Structure Novoderezhkin, Vladimir I.; Palacios, Miguel A.; van Amerongen, Herbert The Journal of Physical Chemistry B, Vol. 109, Issue 20 https://doi.org/10.1021/jp044082f	journal	May 2005
Communication: Nonadiabatic ring-polymer molecular dynamics Richardson, Jeremy O.; Thoss, Michael The Journal of Chemical Physics, Vol. 139, Issue 3 https://doi.org/10.1063/1.4816124	journal	July 2013
The role of vibronic modes in formation of red antenna states of cyanobacterial PSI Pishchalnikov, Roman Y.; Shubin, Vladimir. V.; Razjivin, Andrei. P. Photosynthesis Research, Vol. 146, Issue 1-3 https://doi.org/10.1007/s11120-020-00779-y	journal	August 2020
Nonadiabatic dynamics in open quantum-classical systems: Forward-backward trajectory solution Hsieh, Chang-Yu; Kapral, Raymond The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4736841	journal	December 2012
Coupled forward-backward trajectory approach for nonequilibrium electron-ion dynamics Sato, Shunsuke A.; Kelly, Aaron; Rubio, Angel Physical Review B, Vol. 97, Issue 13 https://doi.org/10.1103/physrevb.97.134308	journal	April 2018
Chemical Dynamics in Condensed Phases Nitzan, Abraham Oxford University Press https://doi.org/10.1093/oso/9780198529798.001.0001	book	April 2006
Distribution functions in physics: Fundamentals Hillery, M.; O'Connell, R. F.; Scully, M. O. Physics Reports, Vol. 106, Issue 3 https://doi.org/10.1016/0370-1573(84)90160-1	journal	April 1984
Mixed Quantum-Classical Description of Excitation Energy Transfer in a Model Fenna−Matthews−Olsen Complex Kelly, Aaron; Rhee, Young Min The Journal of Physical Chemistry Letters, Vol. 2, Issue 7 https://doi.org/10.1021/jz200059t	journal	March 2011
A semiclassical generalized quantum master equation for an arbitrary system-bath coupling Shi, Qiang; Geva, Eitan The Journal of Chemical Physics, Vol. 120, Issue 22 https://doi.org/10.1063/1.1738109	journal	June 2004
A Centroid Molecular Dynamics Approach for Nonadiabatic Dynamical Processes in Condensed Phases: the Spin-Boson Case ^† Liao, Jie-Lou; Voth, Gregory A. The Journal of Physical Chemistry B, Vol. 106, Issue 33 https://doi.org/10.1021/jp020978d	journal	August 2002
Charge and Energy Transfer Dynamics in Molecular Systems May, Volkhard; Kühn, Oliver Wiley-VCH Verlag GmbH & Co. KGaA https://doi.org/10.1002/9783527633791	book	February 2011
Scalable High-Performance Algorithm for the Simulation of Exciton Dynamics. Application to the Light-Harvesting Complex II in the Presence of Resonant Vibrational Modes Kreisbeck, Christoph; Kramer, Tobias; Aspuru-Guzik, Alán Journal of Chemical Theory and Computation, Vol. 10, Issue 9 https://doi.org/10.1021/ct500629s	journal	August 2014
Theory of coherent resonance energy transfer Jang, Seogjoo; Cheng, Yuan-Chung; Reichman, David R. The Journal of Chemical Physics, Vol. 129, Issue 10 https://doi.org/10.1063/1.2977974	journal	September 2008
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
Generalized quantum master equations in and out of equilibrium: When can one win? Kelly, Aaron; Montoya-Castillo, Andrés; Wang, Lu The Journal of Chemical Physics, Vol. 144, Issue 18 https://doi.org/10.1063/1.4948612	journal	May 2016
A variational solution of the time-dependent Schrodinger equation McLachlan, A. D. Molecular Physics, Vol. 8, Issue 1 https://doi.org/10.1080/00268976400100041	journal	January 1964
Intra- and inter-monomeric transfers in the light harvesting LHCII complex: the Redfield–Förster picture Novoderezhkin, Vladimir; Marin, Alessandro; van Grondelle, Rienk Physical Chemistry Chemical Physics, Vol. 13, Issue 38 https://doi.org/10.1039/c1cp21079c	journal	January 2011
Semiclassical Description of Electronic Excitation Population Transfer in a Model Photosynthetic System Tao, Guohua; Miller, William H. The Journal of Physical Chemistry Letters, Vol. 1, Issue 6 https://doi.org/10.1021/jz1000825	journal	February 2010
Applicability of transfer tensor method for open quantum system dynamics Gelzinis, Andrius; Rybakovas, Edvardas; Valkunas, Leonas The Journal of Chemical Physics, Vol. 147, Issue 23 https://doi.org/10.1063/1.5009086	journal	December 2017
Wigner Method in Quantum Statistical Mechanics İmre, Kaya; Özizmir, Ercüment; Rosenbaum, Marcos Journal of Mathematical Physics, Vol. 8, Issue 5 https://doi.org/10.1063/1.1705323	journal	May 1967
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
A semiclassical self‐consistent‐field approach to dissipative dynamics: The spin–boson problem Stock, Gerhard The Journal of Chemical Physics, Vol. 103, Issue 4 https://doi.org/10.1063/1.469778	journal	July 1995
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
Correlation-Dependent Coherent to Incoherent Transitions in Resonant Energy Transfer Dynamics Nazir, Ahsan Physical Review Letters, Vol. 103, Issue 14 https://doi.org/10.1103/physrevlett.103.146404	journal	October 2009
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics Montoya-Castillo, Andrés; Reichman, David R. The Journal of Chemical Physics, Vol. 144, Issue 18 https://doi.org/10.1063/1.4948408	journal	May 2016
Detailed Balance in Ehrenfest Mixed Quantum-Classical Dynamics Parandekar, Priya V.; Tully, John C. Journal of Chemical Theory and Computation, Vol. 2, Issue 2 https://doi.org/10.1021/ct050213k	journal	January 2006
Noninteracting-blip approximation for a two-level system coupled to a heat bath Dekker, H. Physical Review A, Vol. 35, Issue 3 https://doi.org/10.1103/physreva.35.1436	journal	February 1987
Nonadiabatic Dynamics in Atomistic Environments: Harnessing Quantum-Classical Theory with Generalized Quantum Master Equations Pfalzgraff, William C.; Kelly, Aaron; Markland, Thomas E. The Journal of Physical Chemistry Letters, Vol. 6, Issue 23 https://doi.org/10.1021/acs.jpclett.5b02131	journal	November 2015
Multiconfigurational molecular dynamics with quantum transitions: Multiple proton transfer reactions Hammes‐Schiffer, Sharon The Journal of Chemical Physics, Vol. 105, Issue 6 https://doi.org/10.1063/1.472093	journal	August 1996
Delocalized excitons in natural light-harvesting complexes Jang, Seogjoo J.; Mennucci, Benedetta Reviews of Modern Physics, Vol. 90, Issue 3 https://doi.org/10.1103/revmodphys.90.035003	journal	August 2018
Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model Kidon, Lyran; Wilner, Eli Y.; Rabani, Eran The Journal of Chemical Physics, Vol. 143, Issue 23 https://doi.org/10.1063/1.4937396	journal	December 2015
Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions Montoya-Castillo, Andrés; Reichman, David R. The Journal of Chemical Physics, Vol. 146, Issue 8 https://doi.org/10.1063/1.4975388	journal	February 2017
Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation Zhang, Ming-Liang; Ka, Being J.; Geva, Eitan The Journal of Chemical Physics, Vol. 125, Issue 4 https://doi.org/10.1063/1.2218342	journal	July 2006
Energy transfer in photosynthesis: experimental insights and quantitative models van Grondelle, Rienk; Novoderezhkin, Vladimir I. Phys. Chem. Chem. Phys., Vol. 8, Issue 7 https://doi.org/10.1039/b514032c	journal	January 2006
Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations Kelly, Aaron; Brackbill, Nora; Markland, Thomas E. The Journal of Chemical Physics, Vol. 142, Issue 9 https://doi.org/10.1063/1.4913686	journal	March 2015
Coherent and incoherent dynamics in excitonic energy transfer: Correlated fluctuations and off-resonance effects McCutcheon, Dara P. S.; Nazir, Ahsan Physical Review B, Vol. 83, Issue 16 https://doi.org/10.1103/physrevb.83.165101	journal	April 2011
A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling Shi, Qiang; Geva, Eitan The Journal of Chemical Physics, Vol. 119, Issue 23 https://doi.org/10.1063/1.1624830	journal	December 2003
Theory of Spin Resonance and Relaxation Argyres, P. N.; Kelley, P. L. Physical Review, Vol. 134, Issue 1A https://doi.org/10.1103/physrev.134.a98	journal	April 1964
Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H ⁺ with D ₂ Tully, John C.; Preston, Richard K. The Journal of Chemical Physics, Vol. 55, Issue 2 https://doi.org/10.1063/1.1675788	journal	July 1971
Transfer Mechanisms of Electronic Excitation Energy Förster, Th.; Forster, Th. Radiation Research Supplement, Vol. 2 https://doi.org/10.2307/3583604	journal	January 1960
The Theory of Open Quantum Systems Breuer, Heinz-Peter; Petruccione, Francesco Oxford University Press https://doi.org/10.1093/acprof:oso/9780199213900.001.0001	book	January 2007
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
Exciton-migration and three-pulse femtosecond optical spectroscopies of photosynthetic antenna complexes Zhang, Wei Min; Meier, Torsten; Chernyak, Vladimir The Journal of Chemical Physics, Vol. 108, Issue 18 https://doi.org/10.1063/1.476212	journal	May 1998
Charge and Energy Transfer Dynamics in Molecular Systems May, Volkhard; Kuhn, Oliver WILEY‐VCH Verlag GmbH & Co. KGaA https://doi.org/10.1002/9783527602575	book	January 2003
An Introduction to Numerical Analysis Süli, Endre; Mayers, David F. Cambridge University Press https://doi.org/10.1017/CBO9780511801181	book	January 2012
Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation Sun, Xiong; Wang, Haobin; Miller, William H. The Journal of Chemical Physics, Vol. 109, Issue 17 https://doi.org/10.1063/1.477389	journal	November 1998
An Introduction to Numerical Analysis S., F.; Atkinson, Kendall E. Mathematics of Computation, Vol. 54, Issue 190 https://doi.org/10.2307/2008519	journal	April 1990
Correlation-dependent coherent to incoherent transitions in resonant energy transfer dynamics Nazir, Ahsan arXiv https://doi.org/10.48550/arxiv.0906.0592	text	January 2009
Mapping Variable Ring Polymer Molecular Dynamics: A Path-Integral Based Method for Nonadiabatic Processes Ananth, Nandini arXiv https://doi.org/10.48550/arxiv.1309.4476	text	January 2013
Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations Kelly, Aaron; Brackbill, Nora; Markland, Thomas E. arXiv https://doi.org/10.48550/arxiv.1501.03147	text	January 2015
Exact Calculation of the Time Convolutionless Master Equation Generator: Application to the Nonequilibrium Resonant Level Model Kidon, Lyran; Wilner, Eli Y.; Rabani, Eran arXiv https://doi.org/10.48550/arxiv.1510.04369	text	January 2015
Approximate but accurate quantum dynamics from the Mori formalism: II. Equilibrium correlation functions Montoya-Castillo, Andrés; Reichman, David R. arXiv https://doi.org/10.48550/arxiv.1610.04242	text	January 2016
Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics Sato, Shunsuke A.; Kelly, Aaron; Rubio, Angel arXiv https://doi.org/10.48550/arxiv.1711.08197	text	January 2017
Delocalized excitons in natural light harvesting complexes Jang, Seogjoo J.; Mennucci, Benedetta arXiv https://doi.org/10.48550/arxiv.1804.09711	text	January 2018

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