Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion

Mangaud, Etienne; Lasorne, Benjamin; Atabek, Osman; Desouter-Lecomte, Michèle

doi:10.1063/1.5128852

Article (Scientific journals)

Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion

Mangaud, Etienne; Lasorne, Benjamin; Atabek, Osman et al.

2019 • In Journal of Chemical Physics

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https://hdl.handle.net/2268/242499

DOI
10.1063/1.5128852

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31893912

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Keywords :

conical intersection; dissipative dynamics; HEOM

Abstract :

[en] We investigate the possibility of extracting the probability distribution of the effective environmental tuning and coupling modes during the nonadiabatic relaxation through a conical intersection. Dynamics are dealt with an open quantum system master equation by partitioning a multistate electronic subsystem out of all the nuclear vibrators. This is an alternative to the more usual partition retaining the tuning and coupling modes of a conical intersection in the active subsystem coupled to a residual bath. The minimal partition of the electronic system generally leads to highly structured spectral densities for both vibrational baths and requires a strongly nonperturbative non-Markovian master equation, treated here by the hierarchical equations of motion (HEOMs). We extend—for a two-bath situation—the procedure proposed by Shi et al. [J. Chem. Phys. 140, 134106 (2014)], whereby the information contained in the auxiliary HEOM matrices is exploited in order to derive the nuclear dissipative wave packet, i.e., the statistical distribution of the displacement of the two tuning and coupling collective coordinates in each electronic state and the coherence. This allows us to visualize the distribution, all along the nonadiabatic decay. We explore a large parameter space for a symmetrical conical intersection model and a symmetrical initial Franck-Condon preparation. Some parameters could be controlled by external fields, while others are molecule dependent and could be designed by molecular engineering. We illustrate the relation between the strongly coupled electronic and bath dynamics together with a geometric measure of non-Markovianity.

Disciplines :

Chemistry

Author, co-author :

Mangaud, Etienne

Lasorne, Benjamin

Atabek, Osman

Desouter-Lecomte, Michèle ; Université de Liège - ULiège > Département de chimie (sciences) > Département de chimie (sciences)

Language :

English

Title :

Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion

Publication date :

2019

Journal title :

Journal of Chemical Physics

ISSN :

0021-9606

eISSN :

1089-7690

Publisher :

American Institute of Physics, United States - New York

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 23 December 2019

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Bibliography

G. Herzberg and H. C. Longuet-Higgins, "Intersection of potential energy surfaces in polyatomic molecules," Discuss. Faraday Soc. 35 (0), 77-82 (1963). 10.1039/df9633500077
J. Michl and V. Bonacićic-Koutecký, Electronic Aspects of Organic Photochemistry (Wiley, New York, 1990).
M. Klessinger and J. Michl, Excited States and Photochemistry of Organic Molecules (Cambridge VCH, New York, 1995).
D. R. Yarkony, "Diabolical conical intersections," Rev. Mod. Phys. 68, 985-1013 (1996). 10.1103/revmodphys.68.985
W. Domcke, D. Yarkony, and H. Koppel, Conical Intersection, Electronic Structure, Dynamics and Spectroscopy (World Scientific Publishing Co Pte Ltd., 2004).
G. A. Worth and L. S. Cederbaum, "Beyond Born-Oppenheimer: Molecular dynamics through a conical intersection," Annu. Rev. Phys. Chem. 55 (1), 127-158 (2004). 10.1146/annurev.physchem.55.091602.094335
I. Bersuker, The Jahn-Teller Effect (Cambridge University Press, Cambridge, 2006).
M. Baer and N. J. Hoboken, Beyond Born-Oppenheimer: Electronic Nonadiabatic Couling Terms and Conical Intersections (Wiley, 2006).
S. Matsika and P. Krause, "Nonadiabatic events and conical intersections," Annu. Rev. Phys. Chem. 62 (1), 621-643 (2011). 10.1146/annurev-physchem-032210-103450
W. Domcke, D. Yarkony, H. Koppel, and N. J. Hackensack, Conical Intersection: Theory, Computation and Experiment (World Scientific, 2011).
J. von Neuman and E. Wigner, "Uber merkwürdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen," Phys. Z. 30, 467-470 (1929); in The Collected Works of Eugene Paul Wigner. Part A: The Scientific Papers, edited by A. S. Wightman (Springer, Berlin, Heidelberg, 1993), pp. 294-297. 10.1007/978-3-662-02781-3_20
M. Kowalewski, B. P. Fingerhut, K. E. Dorfman, K. Bennett, and S. Mukamel, "Simulating coherent multidimensional spectroscopy of nonadiabatic molecular processes: From the infrared to the X-ray regime," Chem. Rev. 117 (19), 12165-12226 (2017). 10.1021/acs.chemrev.7b00081
M. S. Schuurman and A. Stolow, "Dynamics at conical intersections," Annu. Rev. Phys. Chem. 69 (1), 427-450 (2018). 10.1146/annurev-physchem-052516-050721
E. C. Wu, Q. Ge, E. A. Arsenault, N. H. C. Lewis, N. L. Gruenke, M. J. Head-Gordon, and G. R. Fleming, "Two-dimensional electronic-vibrational spectroscopic study of conical intersection dynamics: An experimental and electronic structure study," Phys. Chem. Chem. Phys. 21 (26), 14153-14163 (2019). 10.1039/c8cp05264f
E. Palacino-González, M. F. Gelin, and W. Domcke, "Analysis of transient-absorption pump-probe signals of nonadiabatic dissipative systems: "Ideal" and "real" spectra," J. Chem. Phys. 150 (20), 204102 (2019). 10.1063/1.5094485
M. Garavelli, F. Bernardi, M. Olivucci, T. Vreven, S. Klein, P. Celani, and M. A. Robb, "Potential-energy surfaces for ultrafast photochemistry static and dynamic aspects," Faraday Discuss. 110 (0), 51-70 (1998). 10.1039/a802270d
M. A. Robb, M. Garavelli, M. Olivucci, and F. Bernardi, "A computational strategy for organic photochemistry," in Reviews in Computational Chemistry (John Wiley & Sons, Ltd., 2007), pp. 87-146.
M. Olivucci, Computational Potochemistry (Elsevier, Amsterdam, 2005).
G. A. Worth, H.-D. Meyer, H. Köppel, L. S. Cederbaum, and I. Burghardt, "Using the MCTDH wavepacket propagation method to describe multimode non-adiabatic dynamics," Int. Rev. Phys. Chem. 27 (3), 569-606 (2008). 10.1080/01442350802137656
B. Lasorne, G. A. Worth, and M. A. Robb, "Excited-state dynamics," Wiley Interdiscip. Rev.: Comput. Mol. Sci. 1 (3), 460-475 (2011). 10.1002/wcms.26
M. A. Robb, "Chapter three-In this molecule there must be a conical intersection," Adv. Phys. Org. Chem. 48, 189-228 (2014). 10.1016/b978-0-12-800256-8.00003-5
F. Gatti, B. Lasorne, H.-D. Meyer, and A. Nauts, Applications of Quantum Dynamics in Chemistry (Springer International Publishing, Cham, 2017).
Y. Guan, H. Guo, and D. R. Yarkony, "Neural network based quasi-diabatic Hamiltonians with symmetry adaptation and a correct description of conical intersections," J. Chem. Phys. 150 (21), 214101 (2019). 10.1063/1.5099106
M. Desouter-Lecomte, C. Galloy, J. C. Lorquet, and M. V. Pires, "Nonadiabatic interactions in unimolecular decay. V. Conical and Jahn-Teller intersections," J. Chem. Phys. 71 (9), 3661-3672 (1979). 10.1063/1.438810
T. Van Voorhis, T. Kowalczyk, B. Kaduk, L.-P. Wang, C.-L. Cheng, and Q. Wu, "The diabatic picture of electron transfer, reaction barriers, and molecular dynamics," Annu. Rev. Phys. Chem. 61 (1), 149-170 (2010). 10.1146/annurev.physchem.012809.103324
C. A. Mead and D. G. Truhlar, "Conditions for the definition of a strictly diabatic electronic basis for molecular systems," J. Chem. Phys. 77 (12), 6090-6098 (1982). 10.1063/1.443853
A. Thiel and H. Köppel, "Proposal and numerical test of a simple diabatization scheme," J. Chem. Phys. 110 (19), 9371-9383 (1999). 10.1063/1.478902
E. R. Davidson, "Global topology of triatomic potential surfaces," J. Am. Chem. Soc. 99 (2), 397-402 (1977). 10.1021/ja00444a015
M. Desouter-Lecomte, D. Dehareng, B. Leyh-Nihant, M. T. Praet, A. J. Lorquet, and J. C. Lorquet, "Nonadiabatic unimolecular reactions of polyatomic molecules," J. Phys. Chem. 89 (2), 214-222 (1985). 10.1021/j100248a006
G. J. Atchity, S. S. Xantheas, and K. Ruedenberg, "Potential energy surfaces near intersections," J. Chem. Phys. 95 (3), 1862-1876 (1991). 10.1063/1.461036
B. Gonon, B. Lasorne, G. Karras, L. Joubert-Doriol, D. Lauvergnat, F. Billard, B. Lavorel, O. Faucher, S. Guérin, E. Hertz, and F. Gatti, "A generalized vibronic-coupling Hamiltonian for molecules without symmetry: Application to the photoisomerization of benzopyran," J. Chem. Phys. 150 (12), 124109 (2019). 10.1063/1.5085059
H. Wang and H.-D. Meyer, "On regularizing the ML-MCTDH equations of motion," J. Chem. Phys. 149 (4), 044119 (2018). 10.1063/1.5042776
M. Ben-Nun and T. J. Martínez, "Ab initio quantum molecular dynamics," in Advances in Chemical Physics (John Wiley & Sons, Ltd., 2002), pp. 439-512.
B. G. Levine and T. J. Martínez, "Isomerization through conical intersections," Annu. Rev. Phys. Chem. 58 (1), 613-634 (2007). 10.1146/annurev.physchem.57.032905.104612
G. Richings, I. Polyak, K. Spinlove, G. Worth, I. Burghardt, and B. Lasorne, "Quantum dynamics simulations using Gaussian wavepackets: The vMCG method," Int. Rev. Phys. Chem. 34 (2), 269-308 (2015). 10.1080/0144235x.2015.1051354
F. A. Schroder, D. H. Turban, A. J. Musser, N. D. Hine, and A. W. Chin, "Tensor network simulation of multi-environmental open quantum dynamics via machine learning and entanglement renormalisation," Nat. Commun. 10 (1), 1062 (2019). 10.1038/s41467-019-09039-7
T. Schaupp and V. Engel, "A classical ride through a conical intersection," J. Chem. Phys. 150 (3), 034301 (2019). 10.1063/1.5080399
J. C. Tully, "Mixed quantum-classical dynamics," Faraday Discuss. 110 (0), 407-419 (1998). 10.1039/a801824c
W. Xie, M. Sapunar, N. Došlić, M. Sala, and W. Domcke, "Assessing the performance of trajectory surface hopping methods: Ultrafast internal conversion in pyrazine," J. Chem. Phys. 150 (15), 154119 (2019). 10.1063/1.5084961
I. de Vega and D. Alonso, "Dynamics of non-Markovian open quantum systems," Rev. Mod. Phys. 89, 015001 (2017). 10.1103/revmodphys.89.015001
Y. Ke and Y. Zhao, "Hierarchy of stochastic Schrödinger equation towards the calculation of absorption and circular dichroism spectra," J. Chem. Phys. 146 (17), 174105 (2017). 10.1063/1.4982230
Y.-C. Wang, Y. Ke, and Y. Zhao, "The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials," Wiley Interdiscip. Rev.: Comput. Mol. Sci. 9 (1), e1375 (2019). 10.1002/wcms.1407
K. Nakamura and Y. Tanimura, "Hierarchical Schrödinger equations of motion for open quantum dynamics," Phys. Rev. A 98, 012109 (2018). 10.1103/physreva.98.012109
T. Ikeda and Y. Tanimura, "Probing photoisomerization processes by means of multi-dimensional electronic spectroscopy: The multi-state quantum hierarchical Fokker-Planck equation approach," J. Chem. Phys. 147 (1), 014102 (2017). 10.1063/1.4989537
T. Ikeda and Y. Tanimura, "Phase-space wavepacket dynamics of internal conversion via conical intersection: Multi-state quantum Fokker-Planck equation approach," Chem. Phys. 515, 203-213 (2018), part of Special Issue on Ultrafast Photoinduced Processes in Polyatomic Molecules: Electronic Structure, Dynamics and Spectroscopy (Dedicated to Wolfgang Domcke on the occasion of his 70th birthday). 10.1016/j.chemphys.2018.07.013
T. Ikeda and Y. Tanimura, "Low-temperature quantum Fokker-Planck and Smoluchowski equations and their extension to multistate systems," J. Chem. Theory Comput. 15 (4), 2517-2534 (2019). 10.1021/acs.jctc.8b01195
T. Ikeda, A. G. Dijkstra, and Y. Tanimura, "Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra," J. Chem. Phys. 150 (11), 114103 (2019). 10.1063/1.5086948
Y. Tanimura and R. Kubo, "Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath," J. Phys. Soc. Jpn. 58, 101-114 (1989). 10.1143/jpsj.58.101
Y. Tanimura, "Stochastic Liouville, Langevin, Fokker-Planck, and master equation approaches to quantum dissipative systems," J. Phys. Soc. Jpn. 75 (8), 082001 (2006). 10.1143/jpsj.75.082001
A. M. Levine, M. Shapiro, and E. Pollak, "Hamiltonian theory for vibrational dephasing rates of small molecules in liquids," J. Chem. Phys. 88 (3), 1959-1966 (1988). 10.1063/1.454718
L. S. Cederbaum, E. Gindensperger, and I. Burghardt, "Short-time dynamics through conical intersections in macrosystems," Phys. Rev. Lett. 94, 113003 (2005). 10.1103/physrevlett.94.113003
E. Gindensperger, I. Burghardt, and L. S. Cederbaum, "Short-time dynamics through conical intersections in macrosystems. I. Theory: Effective-mode formulation," J. Chem. Phys. 124 (14), 144103 (2006). 10.1063/1.2183304
K. H. Hughes, C. D. Christ, and I. Burghardt, "Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. II. Application to environment-induced nonadiabatic dynamics," J. Chem. Phys. 131 (12), 124108 (2009). 10.1063/1.3226343
A. Pereverzev, E. R. Bittner, and I. Burghardt, "Energy and charge-transfer dynamics using projected modes," J. Chem. Phys. 131 (3), 034104 (2009). 10.1063/1.3174447
R. Martinazzo, K. H. Hughes, and I. Burghardt, "Unraveling a Brownian particle's memory with effective mode chains," Phys. Rev. E 84, 030102 (2011). 10.1103/physreve.84.030102
J. Roden, W. T. Strunz, K. B. Whaley, and A. Eisfeld, "Accounting for intra-molecular vibrational modes in open quantum system description of molecular systems," J. Chem. Phys. 137 (20), 204110 (2012). 10.1063/1.4765329
A. Garg, J. N. Onuchic, and V. Ambegaokar, "Effect of friction on electron transfer in biomolecules," J. Chem. Phys. 83 (9), 4491-4503 (1985). 10.1063/1.449017
Y. Tanimura and S. Mukamel, "Optical Stark spectroscopy of a Brownian oscillator in intense fields," J. Phys. Soc. Jpn. 63 (1), 66-77 (1994). 10.1143/jpsj.63.66
V. Chernyak and S. Mukamel, "Collective coordinates for nuclear spectral densities in energy transfer and femtosecond spectroscopy of molecular aggregates," J. Chem. Phys. 105 (11), 4565-4583 (1996). 10.1063/1.472302
J. Cao, "A phase-space study of Bloch-Redfield theory," J. Chem. Phys. 107 (8), 3204-3209 (1997). 10.1063/1.474670
J. Cao and G. A. Voth, "A unified framework for quantum activated rate processes. II. The nonadiabatic limit," J. Chem. Phys. 106 (5), 1769-1779 (1997). 10.1063/1.474123
M. Thoss, H. Wang, and W. H. Miller, "Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density," J. Chem. Phys. 115 (7), 2991-3005 (2001). 10.1063/1.1385562
M. Tanaka and Y. Tanimura, "Quantum dissipative dynamics of electron transfer reaction system: Nonperturbative hierarchy equations approach," J. Phys. Soc. Jpn. 78 (7), 073802 (2009). 10.1143/jpsj.78.073802
M. Tanaka and Y. Tanimura, "Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach," J. Chem. Phys. 132 (21), 214502 (2010). 10.1063/1.3428674
A. Chenel, E. Mangaud, I. Burghardt, C. Meier, and M. Desouter-Lecomte, "Exciton dissociation at donor-acceptor heterojunctions: Dynamics using the collective effective mode representation of the spin-boson model," J. Chem. Phys. 140 (4), 044104 (2014). 10.1063/1.4861853
J. Iles-Smith, N. Lambert, and A. Nazir, "Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems," Phys. Rev. A 90, 032114 (2014). 10.1103/physreva.90.032114
J. Iles-Smith, A. G. Dijkstra, N. Lambert, and A. Nazir, "Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations," J. Chem. Phys. 144 (4), 044110 (2016). 10.1063/1.4940218
M. Wertnik, A. Chin, F. Nori, and N. Lambert, "Optimizing co-operative multi-environment dynamics in a dark-state-enhanced photosynthetic heat engine," J. Chem. Phys. 149 (8), 084112 (2018). 10.1063/1.5040898
A. Kühl and W. Domcke, "Multilevel Redfield description of the dissipative dynamics at conical intersections," J. Chem. Phys. 116 (1), 263-274 (2002). 10.1063/1.1423326
D.-L. Qi, H.-G. Duan, Z.-R. Sun, R. J. D. Miller, and M. Thorwart, "Tracking an electronic wave packet in the vicinity of a conical intersection," J. Chem. Phys. 147 (7), 074101 (2017). 10.1063/1.4989462
A. J. Schile and D. T. Limmer, "Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations," J. Chem. Phys. 151 (1), 014106 (2019). 10.1063/1.5106379
L. Chen, M. F. Gelin, V. Y. Chernyak, W. Domcke, and Y. Zhao, "Dissipative dynamics at conical intersections: Simulations with the hierarchy equations of motion method," Faraday Discuss. 194 (0), 61-80 (2016). 10.1039/c6fd00088f
L. Chen, M. F. Gelin, Y. Zhao, and W. Domcke, "Mapping of wave packet dynamics at conical intersections by time-and frequency-resolved fluorescence spectroscopy: A computational study," J. Phys. Chem. Lett. 10 (19), 5873-5880 (2019). 10.1021/acs.jpclett.9b02208
H.-G. Duan and M. Thorwart, "Quantum mechanical wave packet dynamics at a conical intersection with strong vibrational dissipation," J. Phys. Chem. Lett. 7 (3), 382-386 (2016). 10.1021/acs.jpclett.5b02793
A. G. Dijkstra and V. I. Prokhorenko, "Simulation of photo-excited adenine in water with a hierarchy of equations of motion approach," J. Chem. Phys. 147 (6), 064102 (2017). 10.1063/1.4997433
L. Zhu, H. Liu, W. Xie, and Q. Shi, "Explicit system-bath correlation calculated using the hierarchical equations of motion method," J. Chem. Phys. 137 (19), 194106 (2012). 10.1063/1.4766358
H. Liu, L. Zhu, S. Bai, and Q. Shi, "Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes," J. Chem. Phys. 140 (13), 134106 (2014). 10.1063/1.4870035
H. Choi, W.-J. Son, S. Shin, B. Y. Chang, and I. R. Sola, "Selective photodissociation in diatomic molecules by dynamical Stark-shift control," J. Chem. Phys. 128 (10), 104315 (2008). 10.1063/1.2838911
S. Scheit, Y. Arasaki, and K. Takatsuka, "Control scheme of nonadiabatic transitions with the dynamical shift of potential curve crossing," J. Chem. Phys. 140 (24), 244115 (2014). 10.1063/1.4884784
M. Saab, M. Sala, B. Lasorne, F. Gatti, and S. Guérin, "Full-dimensional control of the radiationless decay in pyrazine using the dynamic Stark effect," J. Chem. Phys. 141 (13), 134114 (2014). 10.1063/1.4896938
M. Richter, F. Bouakline, J. González-Vázquez, L. Martínez-Fernández, I. Corral, S. Patchkovskii, F. Morales, M. Ivanov, F. Martín, and O. Smirnova, "Sub-laser-cycle control of coupled electron-nuclear dynamics at a conical intersection," New J. Phys. 17, 113023 (2015). 10.1088/1367-2630/17/11/113023
B. G. Levine, M. P. Esch, B. S. Fales, D. T. Hardwick, W.-T. Peng, and Y. Shu, "Conical intersections at the nanoscale: Molecular ideas for materials," Annu. Rev. Phys. Chem. 70 (1), 21-43 (2019). 10.1146/annurev-physchem-042018-052425
E. Pollak, "Theory of activated rate processes: A new derivation of Kramers' expression," J. Chem. Phys. 85 (2), 865-867 (1986). 10.1063/1.451294
Y. Tanimura, "Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy," J. Chem. Phys. 137 (22), 22A550 (2012). 10.1063/1.4766931
R. Martinazzo, K. H. Hughes, F. Martelli, and I. Burghardt, "Effective spectral densities for system-environment dynamics at conical intersections: S2-S1 conical intersection in pyrazine," Chem. Phys. 377 (1), 21-29 (2010). 10.1016/j.chemphys.2010.08.010
H. Tamura, R. Martinazzo, M. Ruckenbauer, and I. Burghardt, "Quantum dynamics of ultrafast charge transfer at an oligothiophene-fullerene heterojunction," J. Chem. Phys. 137 (22), 22A540 (2012). 10.1063/1.4751486
S. Valleau, A. Eisfeld, and A. Aspuru-Guzik, "On the alternatives for bath correlators and spectral densities from mixed quantum-classical simulations," J. Chem. Phys. 137 (22), 224103 (2012). 10.1063/1.4769079
M. Aghtar, J. Strümpfer, C. Olbrich, K. Schulten, and U. Kleinekathöfer, "Different types of vibrations interacting with electronic excitations in phycoerythrin 545 and Fenna-Matthews-Olson antenna systems," J. Phys. Chem. Lett. 5 (18), 3131-3137 (2014). 10.1021/jz501351p
H. Wang, M. Thoss, and W. H. Miller, "Systematic convergence in the dynamical hybrid approach for complex systems: A numerically exact methodology," J. Chem. Phys. 115 (7), 2979-2990 (2001). 10.1063/1.1385561
C. Meier and D. J. Tannor, "Non-Markovian evolution of the density operator in the presence of strong laser fields," J. Chem. Phys. 111 (8), 3365-3376 (1999). 10.1063/1.479669
R. Martinazzo, B. Vacchini, K. H. Hughes, and I. Burghardt, "Communication: Universal Markovian reduction of Brownian particle dynamics," J. Chem. Phys. 134 (1), 011101 (2011). 10.1063/1.3532408
A. Pomyalov, C. Meier, and D. J. Tannor, "The importance of initial correlations in rate dynamics: A consistent non-Markovian master equation approach," Chem. Phys. 370, 98-108 (2010). 10.1016/j.chemphys.2010.02.017
R. Kubo, "Stochastic Liouville equations," J. Math. Phys. 4 (2), 174 (1963). 10.1063/1.1703941
A. Ishizaki and Y. Tanimura, "Quantum dynamics of system strongly coupled to low-temperature colored noise bath: Reduced hierarchy equations approach," J. Phys. Soc. Jpn. 74, 3131-3134 (2005). 10.1143/jpsj.74.3131
Q. Shi, L. Chen, G. Nan, R.-X. Xu, and Y. Yan, "Efficient hierarchical Liouville space propagator to quantum dissipative dynamics," J. Chem. Phys. 130 (8), 084105 (2009). 10.1063/1.3077918
J. Jin, S. Welack, J. Luo, X.-Q. Li, P. Cui, R.-X. Xu, and Y. Yan, "Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach," J. Chem. Phys. 126 (13), 134113 (2007). 10.1063/1.2713104
J. Hu, M. Luo, F. Jiang, R.-X. Xu, and Y. Yan, "Padé spectrum decompositions of quantum distribution functions and optimal hierarchical equations of motion construction for quantum open systems," J. Chem. Phys. 134 (24), 244106 (2011). 10.1063/1.3602466
L. Cui, H.-D. Zhang, X. Zheng, R.-X. Xu, and Y. Yan, "Highly efficient and accurate sum-over-poles expansion of Fermi and Bose functions at near zero temperatures: Fano spectrum decomposition scheme," J. Chem. Phys. 151 (2), 024110 (2019). 10.1063/1.5096945
H. Rahman and U. Kleinekathöfer, "Chebyshev hierarchical equations of motion for systems with arbitrary spectral densities and temperatures," J. Chem. Phys. 150 (24), 244104 (2019). 10.1063/1.5100102
A. Ishizaki and G. R. Fleming, "On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer," J. Chem. Phys. 130, 234110 (2009). 10.1063/1.3155214
A. Ishizaki, T. R. Calhoun, G. S. Schlau-Cohen, and G. R. Fleming, "Quantum coherence and its interplay with protein environments in photosynthetic electronic energy transfer," Phys. Chem. Chem. Phys. 12, 7319-7337 (2010). 10.1039/c003389h
J. Strümpfer and K. Schulten, "Excited state dynamics in photosynthetic reaction center and light harvesting complex 1," J. Chem. Phys. 137 (6), 065101 (2012). 10.1063/1.4738953
S.-H. Yeh, J. Zhu, and S. Kais, "Population and coherence dynamics in light harvesting complex II (LH2)," J. Chem. Phys. 137 (8), 084110 (2012). 10.1063/1.4747622
L. Chen, R. Zheng, Y. Jing, and Q. Shi, "Simulation of the two-dimensional electronic spectra of the Fenna-Matthews-Olson complex using the hierarchical equations of motion method," J. Chem. Phys. 134 (19), 194508 (2011). 10.1063/1.3589982
L. Song and Q. Shi, "Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach," J. Chem. Phys. 143 (19), 194106 (2015). 10.1063/1.4935799
E. Mangaud, C. Meier, and M. Desouter-Lecomte, "Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction," Chem. Phys. 494, 90-102 (2017). 10.1016/j.chemphys.2017.07.011
J.-J. Ding, R.-X. Xu, and Y. Yan, "Optimizing hierarchical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum transfer mechanisms," J. Chem. Phys. 136 (22), 224103 (2012). 10.1063/1.4724193
L. Song and Q. Shi, "Hierarchical equations of motion method applied to nonequilibrium heat transport in model molecular junctions: Transient heat current and high-order moments of the current operator," Phys. Rev. B 95, 064308 (2017). 10.1103/physrevb.95.064308
Y. Yan, L. Song, and Q. Shi, "Understanding the free energy barrier and multiple timescale dynamics of charge separation in organic photovoltaic cells," J. Chem. Phys. 148 (8), 084109 (2018). 10.1063/1.5017866
A. G. Dijkstra and Y. Tanimura, "Non-Markovian entanglement dynamics in the presence of system-bath coherence," Phys. Rev. Lett. 104, 250401 (2010). 10.1103/physrevlett.104.250401
Y. Tanimura, "Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities," J. Chem. Phys. 141 (4), 044114 (2014). 10.1063/1.4890441
A. Chin, E. Mangaud, V. Chevet, O. Atabek, and M. Desouter-Lecomte, "Visualising the role of non-perturbative environment dynamics in the dissipative generation of coherent electronic motion," Chem. Phys. 525, 110392 (2019). 10.1016/j.chemphys.2019.110392
Q. Shi, L. Chen, G. Nan, R. Xu, and Y. Yan, "Electron transfer dynamics: Zusman equation versus exact theory," J. Chem. Phys. 130 (16), 164518 (2009). 10.1063/1.3125003
Á. Rivas, S. F. Huelga, and M. B. Plenio, "Quantum non-Markovianity: Characterization, quantification and detection," Rep. Prog. Phys. 77, 094001 (2014). 10.1088/0034-4885/77/9/094001
H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, "Colloquium: Non-Markovian dynamics in open quantum systems," Rev. Mod. Phys. 88, 021002 (2016). 10.1103/revmodphys.88.021002
H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2002).
S. Lorenzo, F. Plastina, and M. Paternostro, "Role of environmental correlations in the non-Markovian dynamics of a spin system," Phys. Rev. A 84, 032124 (2011). 10.1103/physreva.84.032124
M. J. W. Hall, J. D. Cresser, L. Li, and E. Andersson, "Canonical form of master equations and characterization of non-Markovianity," Phys. Rev. A 89, 042120 (2014). 10.1103/physreva.89.042120
G. Kimura, "The Bloch vector for N-level systems," Phys. Lett. A 314 (5), 339-349 (2003). 10.1016/s0375-9601(03)00941-1
D. Aerts and M. S. de Bianchi, "The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem," Ann. Phys. 351, 975-1025 (2014). 10.1016/j.aop.2014.09.020
H.-S. Zeng, N. Tang, Y.-P. Zheng, and G.-Y. Wang, "Equivalence of the measures of non-Markovianity for open two-level systems," Phys. Rev. A 84, 032118 (2011). 10.1103/physreva.84.032118
G. Guarnieri, A. Smirne, and B. Vacchini, "Quantum regression theorem and non-Markovianity of quantum dynamics," Phys. Rev. A 90, 022110 (2014). 10.1103/physreva.90.022110
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, The Art of Scientific Computing (Cambridge University Press, 1992).
J. Alvarellos and H. Metiu, "The evolution of the wave function in a curve crossing problem computed by a fast Fourier transform method," J. Chem. Phys. 88 (8), 4957-4966 (1988). 10.1063/1.454707
P. Nalbach, S. Javanbakht, C. Stahl, and M. Thorwart, "Stueckelberg oscillations in a two-state two-path model of a conical intersection," Ann. Phys. 529 (9), 1600147 (2017). 10.1002/andp.201600147
C. Kreisbeck, T. Kramer, and A. Aspuru-Guzik, "Scalable high-performance algorithm for the simulation of exciton dynamics. application to the light-harvesting complex II in the presence of resonant vibrational modes," J. Chem. Theory Comput. 10 (9), 4045-4054 (2014). 10.1021/ct500629s
P. Rebentrost and A. Aspuru-Guzik, "Communication: Exciton-phonon information flow in the energy transfer process of photosynthetic complexes," J. Chem. Phys. 134 (10), 101103 (2011). 10.1063/1.3563617
R. Kosloff, "Quantum thermodynamics and open-systems modeling," J. Chem. Phys. 150 (20), 204105 (2019). 10.1063/1.5096173
P. Strasberg, G. Schaller, N. Lambert, and T. Brandes, "Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping," New J. Phys. 18, 073007 (2016). 10.1088/1367-2630/18/7/073007
P. V. Demekhin and L. S. Cederbaum, "Light-induced conical intersections in polyatomic molecules: General theory, strategies of exploitation, and application," J. Chem. Phys. 139 (15), 154314 (2013). 10.1063/1.4826172
T. Szidarovszky, G. J. Halász, A. G. Császár, L. S. Cederbaum, and Á. Vibók, "Conical intersections induced by quantum light: Field-dressed spectra from the weak to the ultrastrong coupling regimes," J. Phys. Chem. Lett. 9 (21), 6215-6223 (2018). 10.1021/acs.jpclett.8b02609
E. Mangaud, R. Puthumpally-Joseph, D. Sugny, C. Meier, O. Atabek, and M. Desouter-Lecomte, "Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion," New J. Phys. 20, 043050 (2018). 10.1088/1367-2630/aab651
A. Ishizaki and G. R. Fleming, "Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equation approach," J. Chem. Phys. 130 (23), 234111 (2009). 10.1063/1.3155372
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, 1992).
T. Takagahara, E. Hanamura, and R. Kubo, "Stochastic models of intermediate state interaction in second order optical processes-stationary response. II," J. Phys. Soc. Jpn. 43, 811-816 (1977). 10.1143/jpsj.43.811