1
|
Braver Y, Valkunas L, Gelzinis A. Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications. J Chem Theory Comput 2021; 17:7157-7168. [PMID: 34618457 PMCID: PMC8719324 DOI: 10.1021/acs.jctc.1c00777] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2021] [Indexed: 01/20/2023]
Abstract
Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum-classical theory─it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum-classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum-classical Liouville equation, namely, the forward-backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna-Matthews-Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [Gelzinis, A.; J. Chem. Phys. 2020, 152, 051103] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.
Collapse
Affiliation(s)
- Yakov Braver
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
| | - Leonas Valkunas
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
| | - Andrius Gelzinis
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
| |
Collapse
|
2
|
Janković V, Mančal T. Exact description of excitonic dynamics in molecular aggregates weakly driven by light. J Chem Phys 2020; 153:244122. [PMID: 33380075 DOI: 10.1063/5.0029914] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a rigorous theoretical description of excitonic dynamics in molecular light-harvesting aggregates photoexcited by weak-intensity radiation of arbitrary properties. While the interaction with light is included up to the second order, the treatment of the excitation-environment coupling is exact and results in an exact expression for the reduced excitonic density matrix that is manifestly related to the spectroscopic picture of the photoexcitation process. This expression takes fully into account the environmental reorganization processes triggered by the two interactions with light. This is particularly important for slow environments and/or strong excitation-environment coupling. Within the exponential decomposition scheme, we demonstrate how our result can be recast as the hierarchy of equations of motion (HEOM) that explicitly and consistently includes the photoexcitation step. We analytically describe the environmental reorganization dynamics triggered by a delta-like excitation of a single chromophore and demonstrate how our HEOM, in appropriate limits, reduces to the Redfield equations comprising a pulsed photoexcitation and the nonequilibrium Förster theory. We also discuss the relation of our formalism to the combined Born-Markov-HEOM approaches in the case of excitation by thermal light.
Collapse
Affiliation(s)
- Veljko Janković
- Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic
| | - Tomáš Mančal
- Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic
| |
Collapse
|
3
|
Braver Y, Valkunas L, Gelzinis A. Benchmarking the forward–backward trajectory solution of the quantum-classical Liouville equation. J Chem Phys 2020; 152:214116. [DOI: 10.1063/5.0006538] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yakov Braver
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania
- Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
| | - Leonas Valkunas
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania
- Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
| | - Andrius Gelzinis
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania
- Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
| |
Collapse
|
4
|
|
5
|
|
6
|
Fetherolf JH, Berkelbach TC. Linear and nonlinear spectroscopy from quantum master equations. J Chem Phys 2018; 147:244109. [PMID: 29289132 DOI: 10.1063/1.5006824] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.
Collapse
Affiliation(s)
- Jonathan H Fetherolf
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Timothy C Berkelbach
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
7
|
Perlík V, Šanda F. Vibrational relaxation beyond the linear damping limit in two-dimensional optical spectra of molecular aggregates. J Chem Phys 2017; 147:084104. [DOI: 10.1063/1.4999680] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Václav Perlík
- Institute of Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, Prague 121 16, Czech Republic
| | - František Šanda
- Institute of Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, Prague 121 16, Czech Republic
| |
Collapse
|
8
|
Lim J, Ing DJ, Rosskopf J, Jeske J, Cole JH, Huelga SF, Plenio MB. Signatures of spatially correlated noise and non-secular effects in two-dimensional electronic spectroscopy. J Chem Phys 2017; 146:024109. [DOI: 10.1063/1.4973975] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
9
|
Chorošajev V, Gelzinis A, Valkunas L, Abramavicius D. Benchmarking the stochastic time-dependent variational approach for excitation dynamics in molecular aggregates. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.06.014] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
10
|
Malý P, Gruber JM, van Grondelle R, Mančal T. Single Molecule Spectroscopy of Monomeric LHCII: Experiment and Theory. Sci Rep 2016; 6:26230. [PMID: 27189196 PMCID: PMC4870570 DOI: 10.1038/srep26230] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Accepted: 04/26/2016] [Indexed: 01/16/2023] Open
Abstract
We derive approximate equations of motion for excited state dynamics of a multilevel open quantum system weakly interacting with light to describe fluorescence-detected single molecule spectra. Based on the Frenkel exciton theory, we construct a model for the chlorophyll part of the LHCII complex of higher plants and its interaction with previously proposed excitation quencher in the form of the lutein molecule Lut 1. The resulting description is valid over a broad range of timescales relevant for single molecule spectroscopy, i.e. from ps to minutes. Validity of these equations is demonstrated by comparing simulations of ensemble and single-molecule spectra of monomeric LHCII with experiments. Using a conformational change of the LHCII protein as a switching mechanism, the intensity and spectral time traces of individual LHCII complexes are simulated, and the experimental statistical distributions are reproduced. Based on our model, it is shown that with reasonable assumptions about its interaction with chlorophylls, Lut 1 can act as an efficient fluorescence quencher in LHCII.
Collapse
Affiliation(s)
- Pavel Malý
- Department of Physics and Astronomy, Faculty of Sciences, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
- Institute of Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, CZ-121 16 Prague 2, Czech Republic
| | - J. Michael Gruber
- Department of Physics and Astronomy, Faculty of Sciences, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Rienk van Grondelle
- Department of Physics and Astronomy, Faculty of Sciences, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
| | - Tomáš Mančal
- Department of Physics and Astronomy, Faculty of Sciences, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
- Institute of Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, CZ-121 16 Prague 2, Czech Republic
| |
Collapse
|
11
|
Olšina J, Kramer T, Kreisbeck C, Mančal T. Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion. J Chem Phys 2014; 141:164109. [DOI: 10.1063/1.4898354] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jan Olšina
- Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, CZ-121 16 Prague 2, Czech Republic
| | - Tobias Kramer
- Mads Clausen Insitute, University of Southern Denmark, 6400 Sønderborg, Denmark
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Christoph Kreisbeck
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Tomáš Mančal
- Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, CZ-121 16 Prague 2, Czech Republic
| |
Collapse
|
12
|
|