An exciton–phonon (ex–ph) model based on our recently developed block interaction product basis framework is introduced to simulate the distal charge separation (CS) process in aggregated perylenediimide (PDI) trimer incorporating the quantum dynamic method, i.e., the time-dependent density matrix renormalization group. The electronic Hamiltonian in the ex–ph model is represented by nine constructed diabatic states, which include three local excited (LE) states and six charge transfer (CT) states from both the neighboring and distal chromophores. These diabatic states are automatically generated from the direct products of the leading localized neutral or ionic states of each chromophore’s reduced density matrix, which are obtained from ab initio quantum chemical calculation of the subsystem consisting of the targeted chromophore and its nearest neighbors, thus considering the interaction of the adjacent environment. In order to quantum-dynamically simulate the distal CS process with massive coupled vibrational modes in molecular aggregates, we used our recently proposed hierarchical mapping approach to renormalize these modes and truncate those vibrational modes that are not effectively coupled with electronic states accordingly. The simulation result demonstrates that the formation of the distal CS process undergoes an intermediate state of adjacent CT, i.e., starts from the LE states, passes through an adjacent CT state to generate the intermediates ( fs), and then formalizes the targeted distal CS via further charge transference ( ps). This finding agrees well with the results observed in the experiment, indicating that our scheme is capable of quantitatively investigating the CS process in a realistic aggregated PDI trimer and can also be potentially applied to exploring CS and other photoinduced processes in larger systems.
REFERENCES
1.
E.
Romero
, V. I.
Novoderezhkin
, and R.
van Grondelle
, “Quantum design of photosynthesis for bio-inspired solar-energy conversion
,” Nature
543
, 355
–365
(2017
).2.
M. H.
Vos
, F.
Rappaport
, J.-C.
Lambry
, J.
Breton
, and J.-L.
Martin
, “Visualization of coherent nuclear motion in a membrane protein by femtosecond spectroscopy
,” Nature
363
, 320
–325
(1993
).3.
A. N.
Bartynski
, M.
Gruber
, S.
Das
, S.
Rangan
, S.
Mollinger
, C.
Trinh
, S. E.
Bradforth
, K.
Vandewal
, A.
Salleo
, R. A.
Bartynski
, W.
Bruetting
, and M. E.
Thompson
, “Symmetry-breaking charge transfer in a zinc chlorodipyrrin acceptor for high open circuit voltage organic photovoltaics
,” J. Am. Chem. Soc.
137
, 5397
–5405
(2015
).4.
C. L.
Kufner
, S.
Crucilla
, D.
Ding
, P.
Stadlbauer
, J.
Šponer
, J. W.
Szostak
, D. D.
Sasselov
, and R.
Szabla
, “Photoinduced charge separation and DNA self-repair depend on sequence directionality and stacking pattern
,” Chem. Sci.
15
, 2158
(2024
).5.
N.
Pearce
, K. E. A.
Reynolds
, S.
Kayal
, X. Z.
Sun
, E. S.
Davies
, F.
Malagreca
, C. J.
Schürmann
, S.
Ito
, A.
Yamano
, S. P.
Argent
, M. W.
George
, and N. R.
Champness
, “Selective photoinduced charge separation in perylenediimide-pillar[5]arene rotaxanes
,” Nat. Commun.
13
, 415
(2022
).6.
C.
Lin
, T.
Kim
, J. D.
Schultz
, R. M.
Young
, and M. R.
Wasielewski
, “Accelerating symmetry-breaking charge separation in a perylenediimide trimer through a vibronically coherent dimer intermediate
,” Nat. Chem.
14
, 786
–793
(2022
).7.
H.-G.
Duan
, V. I.
Prokhorenko
, E.
Wientjes
, R.
Croce
, M.
Thorwart
, and R. J. D.
Miller
, “Primary charge separation in the photosystem II reaction center revealed by a global analysis of the two-dimensional electronic spectra
,” Sci. Rep.
7
, 12347
(2017
).8.
R.
Crespo-Otero
and M.
Barbatti
, “Recent advances and perspectives on nonadiabatic mixed quantum–classical dynamics
,” Chem. Rev.
118
, 7026
–7068
(2018
).9.
T. R.
Nelson
, A. J.
White
, J. A.
Bjorgaard
, A. E.
Sifain
, Y.
Zhang
, B.
Nebgen
, S.
Fernandez-Alberti
, D.
Mozyrsky
, A. E.
Roitberg
, and S.
Tretiak
, “Non-adiabatic excited-state molecular dynamics: Theory and applications for modeling photophysics in extended molecular materials
,” Chem. Rev.
120
, 2215
–2287
(2020
).10.
A.
Sisto
, D. R.
Glowacki
, and T. J.
Martinez
, “Ab initio nonadiabatic dynamics of multichromophore complexes: A scalable graphical-processing-unit-accelerated exciton framework
,” Acc. Chem. Res.
47
, 2857
–2866
(2014
).11.
D. R.
Yarkony
, “Nonadiabatic quantum chemistry—Past, present, and future
,” Chem. Rev.
112
, 481
–498
(2012
).12.
T.
Yonehara
, K.
Hanasaki
, and K.
Takatsuka
, “Fundamental approaches to nonadiabaticity: Toward a chemical theory beyond the Born–Oppenheimer paradigm
,” Chem. Rev.
112
, 499
–542
(2012
).13.
P.
Ehrenfest
, “Bemerkung über die angenäherte gültigkeit der klassischen mechanik innerhalb der quantenmechanik
,” Z. Phys.
45
, 455
–457
(1927
).14.
S.-I.
Sawada
, A.
Nitzan
, and H.
Metiu
, “Mean-trajectory approximation for charge- and energy-transfer processes at surfaces
,” Phys. Rev. B
32
, 851
–867
(1985
).15.
J. C.
Tully
, “Molecular dynamics with electronic transitions
,” J. Chem. Phys.
93
, 1061
–1071
(1990
).16.
J. C.
Tully
and R. K.
Preston
, “Trajectory surface hopping approach to nonadiabatic molecular collisions: The reaction of H+ with D2
,” J. Chem. Phys.
55
, 562
–572
(1971
).17.
A. V.
Akimov
and O. V.
Prezhdo
, “Nonadiabatic dynamics of charge transfer and singlet fission at the pentacene/C60 interface
,” J. Am. Chem. Soc.
136
, 1599
–1608
(2014
).18.
X.-Y.
Liu
, Z.-W.
Li
, W.-H.
Fang
, and G.
Cui
, “Nonadiabatic exciton and charge separation dynamics at interfaces of zinc phthalocyanine and fullerene: Orientation does matter
,” J. Phys. Chem. A
124
, 7388
–7398
(2020
).19.
D.
Mao
, X.-R.
Chen
, D.-H.
Li
, X.-Y.
Liu
, G.
Cui
, and L.
Li
, “Ultrafast charge transfer in a nonfullerene all-small-molecule organic solar cell: A nonadiabatic dynamics simulation with optimally tuned range-separated functional
,” Phys. Chem. Chem. Phys.
24
, 27173
–27183
(2022
).20.
X.-Y.
Xie
, X.-Y.
Liu
, W.-H.
Fang
, and G.
Cui
, “Insights into photoinduced carrier dynamics and hydrogen evolution reaction of organic PM6/PCBM heterojunctions
,” J. Mater. Chem. A
10
, 24529
–24537
(2022
).21.
D.
Mester
and M.
Kállay
, “Reduced-scaling approach for configuration interaction singles and time-dependent density functional theory calculations using hybrid functionals
,” J. Chem. Theory Comput.
15
, 1690
–1704
(2019
).22.
K.
Wang
, G.
Shao
, S.
Peng
, X.
You
, X.
Chen
, J.
Xu
, H.
Huang
, H.
Wang
, D.
Wu
, and J.
Xia
, “Achieving symmetry-breaking charge separation in perylenediimide trimers: The effect of bridge resonance
,” J. Phys. Chem. B
126
, 3758
–3767
(2022
).23.
Y.
Wu
, R. M.
Young
, M.
Frasconi
, S. T.
Schneebeli
, P.
Spenst
, D. M.
Gardner
, K. E.
Brown
, F.
Würthner
, J. F.
Stoddart
, and M. R.
Wasielewski
, “Ultrafast photoinduced symmetry-breaking charge separation and electron sharing in perylenediimide molecular triangles
,” J. Am. Chem. Soc.
137
, 13236
–13239
(2015
).24.
M. H.
Beck
, A.
Jäckle
, G. A.
Worth
, and H. D.
Meyer
, “The multiconfiguration time-dependent hartree (MCTDH) method: A highly efficient algorithm for propagating wavepackets
,” Phys. Rep.
324
, 1
–105
(2000
).25.
A.
Raab
, I.
Burghardt
, and H.-D.
Meyer
, “The multiconfiguration time-dependent Hartree method generalized to the propagation of density operators
,” J. Chem. Phys.
111
, 8759
–8772
(1999
).26.
S.
Paeckel
, T.
Köhler
, A.
Swoboda
, S. R.
Manmana
, U.
Schollwöck
, and C.
Hubig
, “Time-evolution methods for matrix-product states
,” Ann. Phys.
411
, 167998
(2019
).27.
J.
Ren
, W.
Li
, T.
Jiang
, Y.
Wang
, and Z.
Shuai
, “Time-dependent density matrix renormalization group method for quantum dynamics in complex systems
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
12
, e1614
(2022
).28.
S. R.
White
and A. E.
Feiguin
, “Real-time evolution using the density matrix renormalization group
,” Phys. Rev. Lett.
93
, 076401
(2004
).29.
Y.
Xu
, Y.
Cheng
, Y.
Song
, and H.
Ma
, “New density matrix renormalization group approaches for strongly correlated systems coupled with large environments
,” J. Chem. Theory Comput.
19
, 4781
–4795
(2023
).30.
X.
Chang
, M.
Balooch Qarai
, and F. C.
Spano
, “Absorption and photoluminescence in π-stacks of donor–acceptor–donor chromophores: Effective Frenkel–Holstein Hamiltonian approach
,” Chem. Mater.
35
, 10018
–10029
(2023
).31.
S. M.
Janke
, M. B.
Qarai
, V.
Blum
, and F. C.
Spano
, “Frenkel–Holstein Hamiltonian applied to absorption spectra of quaterthiophene-based 2D hybrid organic–inorganic perovskites
,” J. Chem. Phys.
152
, 144702
(2020
).32.
S.
Feng
, Y.-C.
Wang
, Y.
Ke
, W.
Liang
, and Y.
Zhao
, “Effect of charge-transfer states on the vibrationally resolved absorption spectra and exciton dynamics in ZnPc aggregates: Simulations from a non-Makovian stochastic Schrödinger equation
,” J. Chem. Phys.
153
, 034116
(2020
).33.
S.
Feng
, Y.
Zhao
, and W.
Liang
, “Substituent effect on vibrationally resolved absorption spectra and exciton dynamics of dipyrrolonaphthyridinedione aggregates
,” J. Phys. Chem. A
126
, 6395
–6406
(2022
).34.
H.
Zang
, Y.
Zhao
, and W.
Liang
, “Quantum interference in singlet fission: J- and H-aggregate behavior
,” J. Phys. Chem. Lett.
8
, 5105
–5112
(2017
).35.
B.
Zhang
, Y.
Zhao
, and W.
Liang
, “Joint effects of exciton–exciton and exciton–photon couplings on the singlet fission dynamics in organic aggregates
,” J. Phys. Chem. C
125
, 1654
–1664
(2021
).36.
J.
Aragó
and A.
Troisi
, “Dynamics of the excitonic coupling in organic crystals
,” Phys. Rev. Lett.
114
, 026402
(2015
).37.
T.
Nematiaram
, D.
Padula
, and A.
Troisi
, “Bright Frenkel excitons in molecular crystals: A survey
,” Chem. Mater.
33
, 3368
–3378
(2021
).38.
X.
Xie
, A.
Santana-Bonilla
, W.
Fang
, C.
Liu
, A.
Troisi
, and H.
Ma
, “Exciton–phonon interaction model for singlet fission in prototypical molecular crystals
,” J. Chem. Theory Comput.
15
, 3721
–3729
(2019
).39.
S.
Jiang
, Y.
Xie
, and Z.
Lan
, “The role of the charge-transfer states in the ultrafast excitonic dynamics of the DTDCTB dimers embedded in a crystal environment
,” Chem. Phys.
515
, 603
–613
(2018
), part of the Special Issue: Ultrafast Photoinduced Processes in Polyatomic Molecules: Electronic Structure, Dynamics and Spectroscopy (Dedicated to Wolfgang Domcke on the Occasion of his 70th Birthday).40.
N. J.
Hestand
and F. C.
Spano
, “Expanded theory of H- and J-molecular aggregates: The effects of vibronic coupling and intermolecular charge transfer
,” Chem. Rev.
118
, 7069
–7163
(2018
).41.
F. C.
Spano
, “Symmetry-breaking charge separation and null aggregates
,” J. Phys. Chem. C
128
, 248
–260
(2024
).42.
Y.
Xie
, H.
Sun
, Q.
Zheng
, J.
Zhao
, H.
Ren
, and Z.
Lan
, “Diabatic Hamiltonian construction in van der Waals heterostructure complexes
,” J. Mater. Chem. A
7
, 27484
–27492
(2019
).43.
Y.
Yao
, K.-W.
Sun
, Z.
Luo
, and H.
Ma
, “Full quantum dynamics simulation of a realistic molecular system using the adaptive time-dependent density matrix renormalization group method
,” J. Phys. Chem. Lett.
9
, 413
–419
(2018
).44.
Y.
Yao
, X.
Xie
, and H.
Ma
, “Ultrafast long-range charge separation in organic photovoltaics: Promotion by off-diagonal vibronic couplings and entropy increase
,” J. Phys. Chem. Lett.
7
, 4830
–4835
(2016
).45.
H.
Ma
and A.
Troisi
, “Direct optical generation of long-range charge-transfer states in organic photovoltaics
,” Adv. Mater.
26
, 6163
–6167
(2014
).46.
K.
Wang
, J.
Ma
, and H.
Ma
, “Characterizing the excited states of large photoactive systems by exciton models
,” J. Chin. Chem. Soc.
70
, 253
–268
(2023
).47.
W.
Barford
, “Exciton transfer integrals between polymer chains
,” J. Chem. Phys.
126
, 134905
(2007
).48.
N. J.
Hestand
and F. C.
Spano
, “Molecular aggregate photophysics beyond the Kasha model: Novel design principles for organic materials
,” Acc. Chem. Res.
50
, 341
–350
(2017
).49.
N. J.
Hestand
and F. C.
Spano
, “Interference between coulombic and CT-mediated couplings in molecular aggregates: H- to J-aggregate transformation in perylene-based π-stacks
,” J. Chem. Phys.
143
, 244707
(2015
).50.
K.
Wang
, Z.
Xie
, Z.
Luo
, and H.
Ma
, “Low-scaling excited state calculation using the block interaction product state
,” J. Phys. Chem. Lett.
13
, 462
–470
(2022
).51.
Y.
Xu
, C.
Liu
, and H.
Ma
, “Hierarchical mapping for efficient simulation of strong system-environment interactions
,” J. Chem. Theory Comput.
19
, 426
–435
(2023
).52.
J.
Haegeman
, J. I.
Cirac
, T. J.
Osborne
, I.
Pižorn
, H.
Verschelde
, and F.
Verstraete
, “Time-dependent variational principle for quantum lattices
,” Phys. Rev. Lett.
107
, 070601
(2011
).53.
J.
Haegeman
, C.
Lubich
, I.
Oseledets
, B.
Vandereycken
, and F.
Verstraete
, “Unifying time evolution and optimization with matrix product states
,” Phys. Rev. B
94
, 165116
(2016
).54.
N.
Lyu
, E.
Mulvihill
, M. B.
Soley
, E.
Geva
, and V. S.
Batista
, “Tensor-train thermo-field memory kernels for generalized quantum master equations
,” J. Chem. Theory Comput.
19
, 1111
–1129
(2023
).55.
H.
Sun
, Z.
Jin
, C.
Yang
, R. L. C.
Akkermans
, S. H.
Robertson
, N. A.
Spenley
, S.
Miller
, and S. M.
Todd
, “Compass II: Extended coverage for polymer and drug-like molecule databases
,” J. Mol. Model.
22
, 47
(2016
).56.
F. C.
Module
, Materials studio v 7.0, Accelrys, Inc.
, 2013
.57.
Q.
Sun
, T. C.
Berkelbach
, N. S.
Blunt
, G. H.
Booth
, S.
Guo
, Z.
Li
, J.
Liu
, J. D.
McClain
, E. R.
Sayfutyarova
, S.
Sharma
, S.
Wouters
, and G. K.-L.
Chan
, “PySCF: The python-based simulations of chemistry framework
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
, e1340
(2018
).58.
Q.
Sun
, X.
Zhang
, S.
Banerjee
, P.
Bao
, M.
Barbry
, N. S.
Blunt
, N. A.
Bogdanov
, G. H.
Booth
, J.
Chen
, Z.-H.
Cui
, J. J.
Eriksen
, Y.
Gao
, S.
Guo
, J.
Hermann
, M. R.
Hermes
, K.
Koh
, P.
Koval
, S.
Lehtola
, Z.
Li
, J.
Liu
, N.
Mardirossian
, J. D.
McClain
, M.
Motta
, B.
Mussard
, H. Q.
Pham
, A.
Pulkin
, W.
Purwanto
, P. J.
Robinson
, E.
Ronca
, E. R.
Sayfutyarova
, M.
Scheurer
, H. F.
Schurkus
, J. E. T.
Smith
, C.
Sun
, S.-N.
Sun
, S.
Upadhyay
, L. K.
Wagner
, X.
Wang
, A.
White
, J. D.
Whitfield
, M. J.
Williamson
, S.
Wouters
, J.
Yang
, J. M.
Yu
, T.
Zhu
, T. C.
Berkelbach
, S.
Sharma
, A. Y.
Sokolov
, and G. K.-L.
Chan
, “Recent developments in the PySCF program package
,” J. Chem. Phys.
153
, 024109
(2020
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
