DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Three-state harmonic models for photoinduced charge transfer

Abstract

A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensedphase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model. We do so within the framework of nonequilibrium Fermi’s golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid–porphyrin–C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor–acceptor, donor–ground, and acceptor–ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC60/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our resultsmore » show that the photoinduced charge transfer in CPC60/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [1]
  1. New York Univ. (NYU), Shanghai (China). Division of Arts and Sciences; New York Univ. (NYU), Shanghai (China). NYU-ECNU Center for Computational Chemistry; New York Univ. (NYU), NY (United States). Department of Chemistry
  2. Kent State Univ., Kent, OH (United States). Dept. of Chemistry and Biochemistry
  3. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Chemistry
Publication Date:
Research Org.:
Kent State Univ., Kent, OH (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; National Natural Science Foundation of China (NSFC); USDOE
OSTI Identifier:
1852263
Alternate Identifier(s):
OSTI ID: 1781437
Grant/Contract Number:  
SC0016501; 21903054
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 154; Journal Issue: 17; 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; Chemistry; physics; molecular dynamics; Fermi's golden rule; organic materials; linear response; condensed phase systems; quantum effects; Marcus equation; spin-boson model; energy levels; photovoltaics

Citation Formats

Brian, Dominikus, Liu, Zengkui, Dunietz, Barry D., Geva, Eitan, and Sun, Xiang. Three-state harmonic models for photoinduced charge transfer. United States: N. p., 2021. Web. doi:10.1063/5.0050289.
Brian, Dominikus, Liu, Zengkui, Dunietz, Barry D., Geva, Eitan, & Sun, Xiang. Three-state harmonic models for photoinduced charge transfer. United States. https://doi.org/10.1063/5.0050289
Brian, Dominikus, Liu, Zengkui, Dunietz, Barry D., Geva, Eitan, and Sun, Xiang. Tue . "Three-state harmonic models for photoinduced charge transfer". United States. https://doi.org/10.1063/5.0050289. https://www.osti.gov/servlets/purl/1852263.
@article{osti_1852263,
title = {Three-state harmonic models for photoinduced charge transfer},
author = {Brian, Dominikus and Liu, Zengkui and Dunietz, Barry D. and Geva, Eitan and Sun, Xiang},
abstractNote = {A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensedphase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model. We do so within the framework of nonequilibrium Fermi’s golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid–porphyrin–C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor–acceptor, donor–ground, and acceptor–ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC60/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our results show that the photoinduced charge transfer in CPC60/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.},
doi = {10.1063/5.0050289},
journal = {Journal of Chemical Physics},
number = 17,
volume = 154,
place = {United States},
year = {Tue May 04 00:00:00 EDT 2021},
month = {Tue May 04 00:00:00 EDT 2021}
}

Works referenced in this record:

Fragment charge difference method for estimating donor–acceptor electronic coupling: Application to DNA π-stacks
journal, September 2002

  • Voityuk, Alexander A.; Rösch, Notker
  • The Journal of Chemical Physics, Vol. 117, Issue 12
  • DOI: 10.1063/1.1502255

Design of Organic Dyes and Cobalt Polypyridine Redox Mediators for High-Efficiency Dye-Sensitized Solar Cells
journal, November 2010

  • Feldt, Sandra M.; Gibson, Elizabeth A.; Gabrielsson, Erik
  • Journal of the American Chemical Society, Vol. 132, Issue 46
  • DOI: 10.1021/ja1088869

Probing the pathways of free charge generation in organic bulk heterojunction solar cells
journal, May 2018


On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. I
journal, May 1956

  • Marcus, R. A.
  • The Journal of Chemical Physics, Vol. 24, Issue 5
  • DOI: 10.1063/1.1742723

Electrostatic Free Energy and Other Properties of States Having Nonequilibrium Polarization. I
journal, May 1956

  • Marcus, R. A.
  • The Journal of Chemical Physics, Vol. 24, Issue 5
  • DOI: 10.1063/1.1742724

Nonadiabatic quantum Liouville and master equations in the adiabatic basis
journal, December 2012

  • Jang, Seogjoo
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4748142

Applicability of the Caldeira–Leggett Model to Vibrational Spectroscopy in Solution
journal, June 2015

  • Gottwald, Fabian; Ivanov, Sergei D.; Kühn, Oliver
  • The Journal of Physical Chemistry Letters, Vol. 6, Issue 14
  • DOI: 10.1021/acs.jpclett.5b00718

Charge Transfer Dynamics from Photoexcited Semiconductor Quantum Dots
journal, May 2016


Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions
journal, July 2011

  • Tao, Guohua; Miller, William H.
  • The Journal of Chemical Physics, Vol. 135, Issue 2
  • DOI: 10.1063/1.3600656

EPR Investigation of Photoinduced Radical Pair Formation and Decay to a Triplet State in a Carotene−Porphyrin−Fullerene Triad
journal, May 1998

  • Carbonera, Donatella; Di Valentin, Marilena; Corvaja, Carlo
  • Journal of the American Chemical Society, Vol. 120, Issue 18
  • DOI: 10.1021/ja9712074

Stochastic description of quantum Brownian dynamics
journal, May 2016


A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation
journal, January 2019

  • Mulvihill, Ellen; Schubert, Alexander; Sun, Xiang
  • The Journal of Chemical Physics, Vol. 150, Issue 3
  • DOI: 10.1063/1.5055756

Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model
journal, March 1999

  • Georgievskii, Yuri; Hsu, Chao-Ping; Marcus, R. A.
  • The Journal of Chemical Physics, Vol. 110, Issue 11
  • DOI: 10.1063/1.478425

Photoexcitation of a Light-Harvesting Supramolecular Triad: A Time-Dependent DFT Study
journal, April 2009

  • Spallanzani, N.; Rozzi, C. A.; Varsano, D.
  • The Journal of Physical Chemistry B, Vol. 113, Issue 16
  • DOI: 10.1021/jp900820q

Understanding the Surface Hopping View of Electronic Transitions and Decoherence
journal, May 2016


Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
journal, July 2020

  • Tanimura, Yoshitaka
  • The Journal of Chemical Physics, Vol. 153, Issue 2
  • DOI: 10.1063/5.0011599

A new method to improve the numerical stability of the hierarchical equations of motion for discrete harmonic oscillator modes
journal, November 2020

  • Yan, Yaming; Xing, Tao; Shi, Qiang
  • The Journal of Chemical Physics, Vol. 153, Issue 20
  • DOI: 10.1063/5.0027962

Charge transfer in organic molecules for solar cells: theoretical perspective
journal, January 2012


Molecular Understanding of Organic Solar Cells: The Challenges
journal, November 2009

  • Brédas, Jean-Luc; Norton, Joseph E.; Cornil, Jérôme
  • Accounts of Chemical Research, Vol. 42, Issue 11
  • DOI: 10.1021/ar900099h

Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence
journal, December 2013

  • Subotnik, Joseph E.; Ouyang, Wenjun; Landry, Brian R.
  • The Journal of Chemical Physics, Vol. 139, Issue 21
  • DOI: 10.1063/1.4829856

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
journal, September 2014


Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics
journal, August 2017

  • Greene, Samuel M.; Batista, Victor S.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 9
  • DOI: 10.1021/acs.jctc.7b00608

A semiclassical generalized quantum master equation for an arbitrary system-bath coupling
journal, June 2004

  • Shi, Qiang; Geva, Eitan
  • The Journal of Chemical Physics, Vol. 120, Issue 22
  • DOI: 10.1063/1.1738109

Photoinduced Electron Transfer in Carotenoporphyrin−Fullerene Triads:  Temperature and Solvent Effects
journal, May 2000

  • Kuciauskas, Darius; Liddell, Paul A.; Lin, Su
  • The Journal of Physical Chemistry B, Vol. 104, Issue 18
  • DOI: 10.1021/jp9935135

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

Molecular dynamics simulation of rigid molecules
journal, September 1986


Contemporary Issues in Electron Transfer Research
journal, January 1996

  • Barbara, Paul F.; Meyer, Thomas J.; Ratner, Mark A.
  • The Journal of Physical Chemistry, Vol. 100, Issue 31
  • DOI: 10.1021/jp9605663

Nonequilibrium photoinduced electron transfer
journal, July 1995

  • Cho, Minhaeng; Silbey, Robert J.
  • The Journal of Chemical Physics, Vol. 103, Issue 2
  • DOI: 10.1063/1.470094

Intramolecular vibrational excitations accompanying solvent‐controlled electron transfer reactions
journal, January 1988

  • Jortner, Joshua; Bixon, Mordechai
  • The Journal of Chemical Physics, Vol. 88, Issue 1
  • DOI: 10.1063/1.454632

Multiscale Simulation of the Ground and Photo-Induced Charge-Separated States of a Molecular Triad in Polar Organic Solvent: Exploring the Conformations, Fluctuations, and Free Energy Landscapes
journal, October 2013

  • Balamurugan, D.; Aquino, Adelia J. A.; de Dios, Francis
  • The Journal of Physical Chemistry B, Vol. 117, Issue 40
  • DOI: 10.1021/jp4026927

Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems
journal, June 1993

  • Darden, Tom; York, Darrin; Pedersen, Lee
  • The Journal of Chemical Physics, Vol. 98, Issue 12
  • DOI: 10.1063/1.464397

Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Electronically Nonadiabatic Molecular Dynamics
journal, March 2020

  • Gao, Xing; Saller, Maximilian A. C.; Liu, Yudan
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 5
  • DOI: 10.1021/acs.jctc.9b01267

Efficient Charge Generation via Hole Transfer in Dilute Organic Donor–Fullerene Blends
journal, February 2020

  • Song, Yin; Schubert, Alexander; Liu, Xiao
  • The Journal of Physical Chemistry Letters, Vol. 11, Issue 6
  • DOI: 10.1021/acs.jpclett.0c00058

Non-Condon nonequilibrium Fermi’s golden rule rates from the linearized semiclassical method
journal, August 2016

  • Sun, Xiang; Geva, Eitan
  • The Journal of Chemical Physics, Vol. 145, Issue 6
  • DOI: 10.1063/1.4960337

Quantum coherence controls the charge separation in a prototypical artificial light-harvesting system
journal, March 2013

  • Andrea Rozzi, Carlo; Maria Falke, Sarah; Spallanzani, Nicola
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms2603

The Linear Response Approximation and Its Lowest Order Corrections:  An Influence Functional Approach
journal, April 1999

  • Makri, Nancy
  • The Journal of Physical Chemistry B, Vol. 103, Issue 15
  • DOI: 10.1021/jp9847540

Multiscale Simulation on a Light-Harvesting Molecular Triad
journal, February 2012

  • Su, Guoxiong; Czader, Arkadiusz; Homouz, Dirar
  • The Journal of Physical Chemistry B, Vol. 116, Issue 29
  • DOI: 10.1021/jp212273n

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

Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics
journal, May 2016

  • Montoya-Castillo, Andrés; Reichman, David R.
  • The Journal of Chemical Physics, Vol. 144, Issue 18
  • DOI: 10.1063/1.4948408

Density Functional Theory with Correct Long-Range Asymptotic Behavior
journal, February 2005


Accurate Long-Time Mixed Quantum-Classical Liouville Dynamics via the Transfer Tensor Method
journal, November 2016

  • Kananenka, Alexei A.; Hsieh, Chang-Yu; Cao, Jianshu
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 23
  • DOI: 10.1021/acs.jpclett.6b02389

Induced polarization restricts the conformational distribution of a light-harvesting molecular triad in the ground state
journal, January 2017

  • Starovoytov, Oleg N.; Zhang, Pengzhi; Cieplak, Piotr
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 34
  • DOI: 10.1039/c7cp03177g

Modified Ehrenfest Formalism for Efficient Large-Scale ab initio Molecular Dynamics
journal, March 2009

  • Andrade, Xavier; Castro, Alberto; Zueco, David
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 4
  • DOI: 10.1021/ct800518j

Non-Condon equilibrium Fermi’s golden rule electronic transition rate constants via the linearized semiclassical method
journal, June 2016

  • Sun, Xiang; Geva, Eitan
  • The Journal of Chemical Physics, Vol. 144, Issue 24
  • DOI: 10.1063/1.4954509

An extension of stochastic hierarchy equations of motion for the equilibrium correlation functions
journal, June 2017

  • Ke, Yaling; Zhao, Yi
  • The Journal of Chemical Physics, Vol. 146, Issue 21
  • DOI: 10.1063/1.4984260

Trotter-Based Simulation of Quantum-Classical Dynamics
journal, January 2008

  • Mac Kernan, Dónal; Ciccotti, Giovanni; Kapral, Raymond
  • The Journal of Physical Chemistry B, Vol. 112, Issue 2
  • DOI: 10.1021/jp0761416

Nonequilibrium Fermi’s Golden Rule Charge Transfer Rates via the Linearized Semiclassical Method
journal, May 2016


Linear-Response and Nonlinear-Response Formulations of the Instantaneous Marcus Theory for Nonequilibrium Photoinduced Charge Transfer
journal, March 2021

  • Brian, Dominikus; Sun, Xiang
  • Journal of Chemical Theory and Computation, Vol. 17, Issue 4
  • DOI: 10.1021/acs.jctc.0c01250

Modeling physical systems by effective harmonic oscillators: The optimized quadratic approximation
journal, February 1995

  • Cao, Jianshu; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 102, Issue 8
  • DOI: 10.1063/1.469207

Coherent ultrafast charge transfer in an organic photovoltaic blend
journal, May 2014


Semiclassical-limit molecular dynamics on multiple electronic surfaces
journal, March 1997

  • Martens, Craig C.; Fang, Jian-Yun
  • The Journal of Chemical Physics, Vol. 106, Issue 12
  • DOI: 10.1063/1.473541

VMD: Visual molecular dynamics
journal, February 1996


Three-centered model of ultrafast photoinduced charge transfer: Continuum dielectric approach
journal, March 2006

  • Khohlova, Svetlana S.; Mikhailova, Valentina A.; Ivanov, Anatoly I.
  • The Journal of Chemical Physics, Vol. 124, Issue 11
  • DOI: 10.1063/1.2178810

Covalent and Noncovalent Phthalocyanine−Carbon Nanostructure Systems: Synthesis, Photoinduced Electron Transfer, and Application to Molecular Photovoltaics
journal, November 2010

  • Bottari, Giovanni; de la Torre, Gema; Guldi, Dirk M.
  • Chemical Reviews, Vol. 110, Issue 11
  • DOI: 10.1021/cr900254z

Direct determination of discrete harmonic bath parameters from molecular dynamics simulations
journal, November 2016

  • Walters, Peter L.; Allen, Thomas C.; Makri, Nancy
  • Journal of Computational Chemistry, Vol. 38, Issue 2
  • DOI: 10.1002/jcc.24527

Photonic Switching of Photoinduced Electron Transfer in a Dithienylethene−Porphyrin−Fullerene Triad Molecule
journal, July 2002

  • Liddell, Paul A.; Kodis, Gerdenis; Moore, Ana L.
  • Journal of the American Chemical Society, Vol. 124, Issue 26
  • DOI: 10.1021/ja026327c

Organic Redox Couples and Organic Counter Electrode for Efficient Organic Dye-Sensitized Solar Cells
journal, June 2011

  • Tian, Haining; Yu, Ze; Hagfeldt, Anders
  • Journal of the American Chemical Society, Vol. 133, Issue 24
  • DOI: 10.1021/ja2030933

Calculating Two-Dimensional Spectra with the Mixed Quantum-Classical Ehrenfest Method
journal, February 2013

  • van der Vegte, C. P.; Dijkstra, A. G.; Knoester, J.
  • The Journal of Physical Chemistry A, Vol. 117, Issue 29
  • DOI: 10.1021/jp311668r

Electronic Dynamics through Conical Intersections via Quasiclassical Mapping Hamiltonian Methods
journal, May 2020

  • Liu, Yudan; Gao, Xing; Lai, Yifan
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 7
  • DOI: 10.1021/acs.jctc.0c00177

Nonadiabatic Excited-State Molecular Dynamics Modeling of Photoinduced Dynamics in Conjugated Molecules
journal, May 2011

  • Nelson, Tammie; Fernandez-Alberti, Sebastian; Chernyak, Vladimir
  • The Journal of Physical Chemistry B, Vol. 115, Issue 18
  • DOI: 10.1021/jp109522g

Thermal electron transfer reactions in polar solvents
journal, October 1974

  • Kestner, Neil R.; Logan, Jean; Jortner, Joshua
  • The Journal of Physical Chemistry, Vol. 78, Issue 21
  • DOI: 10.1021/j100614a017

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
journal, June 2008

  • Jin, Jinshuang; Zheng, Xiao; Yan, YiJing
  • The Journal of Chemical Physics, Vol. 128, Issue 23
  • DOI: 10.1063/1.2938087

Nonequilibrium Fermi golden rule for electronic transitions through conical intersections
journal, December 2011

  • Izmaylov, Artur F.; Mendive–Tapia, David; Bearpark, Michael J.
  • The Journal of Chemical Physics, Vol. 135, Issue 23
  • DOI: 10.1063/1.3667203

Photoinduced Charge Transfer Dynamics in the Carotenoid–Porphyrin–C 60 Triad via the Linearized Semiclassical Nonequilibrium Fermi’s Golden Rule
journal, October 2020

  • Hu, Zhubin; Tong, Zhengqing; Cheung, Margaret S.
  • The Journal of Physical Chemistry B, Vol. 124, Issue 43
  • DOI: 10.1021/acs.jpcb.0c06306

Modeling Electronic-Nuclear Interactions for Excitation Energy Transfer Processes in Light-Harvesting Complexes
journal, August 2016


Metal-Free Organic Dyes for Dye-Sensitized Solar Cells: From Structure: Property Relationships to Design Rules
journal, March 2009

  • Mishra, Amaresh; Fischer, Markus K. R.; Bäuerle, Peter
  • Angewandte Chemie International Edition, Vol. 48, Issue 14
  • DOI: 10.1002/anie.200804709

Calculation from First Principles of Intramolecular Golden-Rule Rate Constants for Photo-Induced Electron Transfer in Molecular Donor–Acceptor Systems
journal, October 2013

  • Lee, Myeong H.; Dunietz, Barry D.; Geva, Eitan
  • The Journal of Physical Chemistry C, Vol. 117, Issue 44
  • DOI: 10.1021/jp4081417

A well-tempered density functional theory of electrons in molecules
journal, January 2007

  • Livshits, Ester; Baer, Roi
  • Physical Chemistry Chemical Physics, Vol. 9, Issue 23
  • DOI: 10.1039/b617919c

Exact solution of three-level model of excited state electron transfer symmetry breaking in quadrupolar molecules
journal, September 2019

  • Ivanov, Anatoly I.; Tkachev, Vladimir G.
  • The Journal of Chemical Physics, Vol. 151, Issue 12
  • DOI: 10.1063/1.5116015

Coherence penalty functional: A simple method for adding decoherence in Ehrenfest dynamics
journal, May 2014

  • Akimov, Alexey V.; Long, Run; Prezhdo, Oleg V.
  • The Journal of Chemical Physics, Vol. 140, Issue 19
  • DOI: 10.1063/1.4875702

Quantum Dissipative Systems
book, March 2012


Unraveling the Mechanism of Photoinduced Charge Transfer in Carotenoid–Porphyrin–C 60 Molecular Triad
journal, March 2015

  • Manna, Arun K.; Balamurugan, D.; Cheung, Margaret S.
  • The Journal of Physical Chemistry Letters, Vol. 6, Issue 7
  • DOI: 10.1021/acs.jpclett.5b00074

Entropic Changes Control the Charge Separation Process in Triads Mimicking Photosynthetic Charge Separation
journal, May 2008

  • Rizzi, Alberto C.; van Gastel, Maurice; Liddell, Paul A.
  • The Journal of Physical Chemistry A, Vol. 112, Issue 18
  • DOI: 10.1021/jp712008b

Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model
journal, December 2015

  • Kidon, Lyran; Wilner, Eli Y.; Rabani, Eran
  • The Journal of Chemical Physics, Vol. 143, Issue 23
  • DOI: 10.1063/1.4937396

Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation
journal, July 2006

  • Zhang, Ming-Liang; Ka, Being J.; Geva, Eitan
  • The Journal of Chemical Physics, Vol. 125, Issue 4
  • DOI: 10.1063/1.2218342

A nonequilibrium golden rule formula for electronic state populations in nonadiabatically coupled systems
journal, July 1994

  • Coalson, Rob D.; Evans, Deborah G.; Nitzan, Abraham
  • The Journal of Chemical Physics, Vol. 101, Issue 1
  • DOI: 10.1063/1.468153

A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling
journal, December 2003

  • Shi, Qiang; Geva, Eitan
  • The Journal of Chemical Physics, Vol. 119, Issue 23
  • DOI: 10.1063/1.1624830

A comparative study of different methods for calculating electronic transition rates
journal, March 2018

  • Kananenka, Alexei A.; Sun, Xiang; Schubert, Alexander
  • The Journal of Chemical Physics, Vol. 148, Issue 10
  • DOI: 10.1063/1.4989509

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

Mimicking Photosynthetic Solar Energy Transduction
journal, January 2001

  • Gust, Devens; Moore, Thomas A.; Moore, Ana L.
  • Accounts of Chemical Research, Vol. 34, Issue 1
  • DOI: 10.1021/ar9801301

Photoinduced Charge Separation and Charge Recombination to a Triplet State in a Carotene−Porphyrin−Fullerene Triad
journal, February 1997

  • Liddell, Paul A.; Kuciauskas, Darius; Sumida, John P.
  • Journal of the American Chemical Society, Vol. 119, Issue 6
  • DOI: 10.1021/ja9631054

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

Semiclassical Path Integral Dynamics: Photosynthetic Energy Transfer with Realistic Environment Interactions
journal, May 2016