The photoinduced charge separation in a symmetric donor–acceptor–donor (D–A–D) triad is studied quantum mechanically using a realistic diabatic vibronic coupling model. The model includes a locally excited DA*D state and two charge-transfer states D+A−D and DA−D+ and is constructed according to a procedure generally applicable to semirigid D–A–D structures and based on energies, forces, and force constants obtained by quantum chemical calculations. In this case, the electronic structure is described by time-dependent density functional theory, and the corrected linear response is used in conjunction with the polarizable continuum model to account for state-specific solvent effects. The multimode dynamics following the photoexcitation to the locally excited state are simulated by the hybrid Gaussian-multiconfigurational time-dependent Hartree method, and temperature effects are included using thermo field theory. The dynamics are connected to the transient absorption spectrum obtained in recent experiments, which is simulated and fully assigned from first principles. It is found that the charge separation is mediated by symmetry-breaking vibrations of relatively low frequency, which implies that temperature should be accounted for to obtain reliable estimates of the charge transfer rate.
REFERENCES
1.
V.
May
and O.
Kühn
, Charge and Energy Transfer Dynamics in Molecular Systems
(John Wiley & Sons
, 2011
).2.
H. J.
Wörner
, C. A.
Arrell
, N.
Banerji
, A.
Cannizzo
, M.
Chergui
, A. K.
Das
, P.
Hamm
, U.
Keller
, P. M.
Kraus
, E.
Liberatore
, P.
Lopez-Tarifa
, M.
Lucchini
, M.
Meuwly
, C.
Milne
, J.-E.
Moser
, U.
Rothlisberger
, G.
Smolentsev
, J.
Teuscher
, J. A.
van Bokhoven
, and O.
Wenger
, “Charge migration and charge transfer in molecular systems
,” Struct. Dyn.
4
, 061508
(2017
).3.
Y.
Tamaki
, K.
Watanabe
, K.
Koike
, H.
Inoue
, T.
Morimoto
, and O.
Ishitani
, “Development of highly efficient supramolecular CO2 reduction photocatalysts with high turnover frequency and durability
,” Faraday Discuss.
155
, 115
(2012
).4.
S.
Kuhri
, V.
Engelhardt
, R.
Faust
, and D. M.
Guldi
, “En route towards panchromatic light harvesting: Photophysical and electrochemical properties of Bodipy–porphyrazine conjugates
,” Chem. Sci.
5
, 2580
(2014
).5.
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
(2015
).6.
M.
Viard
, J.
Gallay
, M.
Vincent
, and M.
Paternostre
, “Origin of laurdan sensitivity to the vesicle-to-micelle transition of phospholipid-octylglucoside system: A time-resolved fluorescence study
,” Biophys. J.
80
, 347
(2001
).7.
M.
Kellogg
, A.
Akil
, D. S.
Muthiah Ravinson
, L.
Estergreen
, S. E.
Bradforth
, and M. E.
Thompson
, “Symmetry breaking charge transfer as a means to study electron transfer with no driving force
,” Faraday Discuss.
216
, 379
(2019
).8.
J. T.
Buck
, R. W.
Wilson
, and T.
Mani
, “Intramolecular long-range charge-transfer emission in donor–bridge–acceptor systems
,” J. Phys. Chem. Lett.
10
, 3080
(2019
).9.
B.
Dereka
, D.
Svechkarev
, A.
Rosspeintner
, A.
Aster
, M.
Lunzer
, R.
Liska
, A. M.
Mohs
, and E.
Vauthey
, “Solvent tuning of photochemistry upon excited-state symmetry breaking
,” Nat. Commun.
11
, 1925
(2020
).10.
A. A.
Bakulin
, A.
Rao
, V. G.
Pavelyev
, P. H. M.
van Loosdrecht
, M. S.
Pshenichnikov
, D.
Niedzialek
, J.
Cornil
, D.
Beljonne
, and R. H.
Friend
, “The role of driving energy and delocalized states for charge separation in organic semiconductors
,” Science
335
, 1340
(2012
).11.
B. T.
Phelan
, J. D.
Schultz
, J.
Zhang
, G.-J.
Huang
, R. M.
Young
, and M. R.
Wasielewski
, “Quantum coherence in ultrafast photo-driven charge separation
,” Faraday Discuss.
216
, 319
(2019
).12.
S.
Rafiq
and G. D.
Scholes
, “From fundamental theories to quantum coherences in electron transfer
,” J. Am. Chem. Soc.
141
, 708
(2019
).13.
B.
Carlotti
, E.
Benassi
, A.
Spalletti
, C. G.
Fortuna
, F.
Elisei
, and V.
Barone
, “Photoinduced symmetry-breaking intramolecular charge transfer in a quadrupolar pyridinium derivative
,” Phys. Chem. Chem. Phys.
16
, 13984
(2014
).14.
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
(2015
).15.
T.
Kim
, J.
Kim
, H.
Mori
, S.
Park
, M.
Lim
, A.
Osuka
, and D.
Kim
, “Symmetry-breaking charge transfer in the excited state of directly linked push–pull porphyrin arrays
,” Phys. Chem. Chem. Phys.
19
, 13970
(2017
).16.
R. E.
Cook
, B. T.
Phelan
, R. J.
Kamire
, M. B.
Majewski
, R. M.
Young
, and M. R.
Wasielewski
, “Excimer formation and symmetry-breaking charge transfer in cofacial perylene dimers
,” J. Phys. Chem. A
121
, 1607
(2017
).17.
B.
Dereka
, M.
Koch
, and E.
Vauthey
, “Looking at photoinduced charge transfer processes in the IR: Answers to several long-standing questions
,” Acc. Chem. Res.
50
, 426
(2017
).18.
H.
Phillips
, E.
Geva
, and B. D.
Dunietz
, “Calculating off-site excitations in symmetric donor–acceptor systems via time-dependent density functional theory with range-separated density functionals
,” J. Chem. Theory Comput.
8
, 2661
(2012
).19.
M.
Renz
, M.
Kess
, M.
Diedenhofen
, A.
Klamt
, and M.
Kaupp
, “Reliable quantum chemical prediction of the localized/delocalized character of organic mixed-valence radical anions. From continuum solvent models to direct-COSMO-RS
,” J. Chem. Theory Comput.
8
, 4189
(2012
).20.
A.
Solovyeva
, M.
Pavanello
, and J.
Neugebauer
, “Describing long-range charge-separation processes with subsystem density-functional theory
,” J. Chem. Phys.
140
, 164103
(2014
).21.
A. I.
Ivanov
, B.
Dereka
, and E.
Vauthey
, “A simple model of solvent-induced symmetry-breaking charge transfer in excited quadrupolar molecules
,” J. Chem. Phys.
146
, 164306
(2017
).22.
A. I.
Ivanov
and V. G.
Tkachev
, “Exact solution of three-level model of excited state electron transfer symmetry breaking in quadrupolar molecules
,” J. Chem. Phys.
151
, 124309
(2019
).23.
C.
Lee
, C. H.
Choi
, and T.
Joo
, “A solvent–solute cooperative mechanism for symmetry-breaking charge transfer
,” Phys. Chem. Chem. Phys.
22
, 1115
(2020
).24.
M.
Beck
, A.
Jäckle
, G.
Worth
, and H.-D.
Meyer
, “The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propagating wavepackets
,” Phys. Rep.
324
, 1
(2000
).25.
H.-D.
Meyer
, “Studying molecular quantum dynamics with the multiconfiguration time-dependent Hartree method
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 351
(2012
).26.
A.
Aster
, A.-B.
Bornhof
, N.
Sakai
, S.
Matile
, and E.
Vauthey
, “Lifetime broadening and impulsive generation of vibrational coherence triggered by ultrafast electron transfer
,” J. Phys. Chem. Lett.
12
, 1052
(2021
).27.
A.
Aster
, C.
Rumble
, A.-B.
Bornhof
, H.-H.
Huang
, N.
Sakai
, T.
Šolomek
, S.
Matile
, and E.
Vauthey
, “Long-lived triplet charge-separated state in naphthalenediimide based donor–acceptor systems
,” Chem. Sci.
12
, 4908
(2021
).28.
I.
Burghardt
, H.-D.
Meyer
, and L. S.
Cederbaum
, “Approaches to the approximate treatment of complex molecular systems by the multiconfiguration time-dependent Hartree method
,” J. Chem. Phys.
111
, 2927
–2939
(1999
).29.
D.
Picconi
and I.
Burghardt
, “Time-resolved spectra of I2 in a krypton crystal by G-MCTDH simulations: Nonadiabatic dynamics, dissipation and environment driven decoherence
,” Faraday Discuss.
221
, 30
(2020
).30.
D.
Picconi
, “Nonadiabatic quantum dynamics of the coherent excited state intramolecular proton transfer of 10-hydroxybenzo[h]quinoline
,” Photochem. Photobiol. Sci.
20
, 1455
(2021
).31.
W. D.
Tuttle
, A. M.
Gardner
, K. B.
O’Regan
, W.
Malewicz
, and T. G.
Wright
, “Vibrational and vibrational-torsional interactions in the 0–600 cm−1 region of the S1 ← S0 spectrum of p-xylene investigated with resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy
,” J. Chem. Phys.
146
, 124309
(2017
).32.
The full molecular symmetry group of DM-NDI, accounting for the para methyl rotations, is of order 72.
33.
R.
Cammi
and B.
Mennucci
, “Linear response theory for the polarizable continuum model
,” J. Chem. Phys.
110
, 9877
(1999
).34.
M.
Cossi
and V.
Barone
, “Time-dependent density functional theory for molecules in liquid solutions
,” J. Chem. Phys.
115
, 4708
(2001
).35.
R.
Cammi
, S.
Corni
, B.
Mennucci
, and J.
Tomasi
, “Electronic excitation energies of molecules in solution: State specific and linear response methods for nonequilibrium continuum solvation models
,” J. Chem. Phys.
122
, 104513
(2005
).36.
R.
Improta
, V.
Barone
, G.
Scalmani
, and M. J.
Frisch
, “A state-specific polarizable continuum model time dependent density functional theory method for excited state calculations in solution
,” J. Chem. Phys.
125
, 054103
(2006
).37.
C. A.
Guido
, D.
Jacquemin
, C.
Adamo
, and B.
Mennucci
, “Electronic excitations in solution: The interplay between state specific approaches and a time-dependent density functional theory description
,” J. Chem. Theory Comput.
11
, 5782
(2015
).38.
M.
Caricato
, B.
Mennucci
, J.
Tomasi
, F.
Ingrosso
, R.
Cammi
, S.
Corni
, and G.
Scalmani
, “Formation and relaxation of excited states in solution: A new time dependent polarizable continuum model based on time dependent density functional theory
,” J. Chem. Phys.
124
, 124520
(2006
).39.
S.
Chibani
, A. D.
Laurent
, A.
Blondel
, B.
Mennucci
, and D.
Jacquemin
, “Excited-state geometries of solvated molecules: Going beyond the linear-response polarizable continuum model
,” J. Chem. Theory Comput.
10
, 1848
(2014
).40.
H.
Köppel
, W.
Domcke
, and L. S.
Cederbaum
, “The multi-mode vibronic coupling approach
,” in Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
, edited by H.
Köppel
, W.
Domcke
, and L. S.
Cederbaum
(World Scientific
, Singapore
, 2004
), p. 323
.41.
The dimensionless normal modes Qi are related to the mass-weighted normal modes qi by the relation .
42.
H.
Köppel
, W.
Domcke
, and L. S.
Cederbaum
, “Multimode molecular dynamics beyond the Born-Oppenheimer approximation
,” Adv. Chem. Phys.
57
, 59
(1984
).43.
D.
Picconi
, F. J.
Avila Ferrer
, R.
Improta
, A.
Lami
, and F.
Santoro
, “Quantum-classical effective-modes dynamics of the ππ* → nπ* decay in 9H-adenine. A quadratic vibronic coupling model
,” Faraday Discuss.
163
, 223
(2013
).44.
R. J.
Cave
and J. F.
Stanton
, “A simple quasi-diabatization scheme suitable for spectroscopic problems based on one-electron properties of interacting states
,” J. Chem. Phys.
144
, 054110
(2016
).45.
G. R.
Medders
, E. C.
Alguire
, A.
Jain
, and J. E.
Subotnik
, “Ultrafast electronic relaxation through a conical intersection: Nonadiabatic dynamics disentangled through an oscillator strength-based diabatization framework
,” J. Phys. Chem. A
121
, 1425
(2017
).46.
W.
Popp
, D.
Brey
, R.
Binder
, and I.
Burghardt
, “Quantum dynamics of exciton transport and dissociation in multichromophoric systems
,” Annu. Rev. Phys. Chem.
72
, 591
(2021
).47.
J. A.
Green
, M.
Yaghoubi Jouybari
, H.
Asha
, F.
Santoro
, and R.
Improta
, “Fragment diabatization linear vibronic coupling model for quantum dynamics of multichromophoric systems: Population of the charge-transfer state in the photoexcited guanine–cytosine pair
,” J. Chem. Theory Comput.
17
, 4660
(2021
).48.
G. M.
Sando
, K. G.
Spears
, J. T.
Hupp
, and P. T.
Ruhoff
, “Large electron transfer rate effects from the Duschinsky mixing of vibrations
,” J. Phys. Chem. A
105
, 5317
(2001
).49.
J.
Tang
, M. T.
Lee
, and S. H.
Lin
, “Effects of the Duschinsky mode-mixing mechanism on temperature dependence of electron transfer processes
,” J. Chem. Phys.
119
, 7188
(2003
).50.
M.
Caricato
, F.
Ingrosso
, B.
Mennucci
, and J.
Tomasi
, “A time-dependent polarizable continuum model: Theory and application
,” J. Chem. Phys.
122
, 154501
(2005
).51.
E.
Gindensperger
, H.
Köppel
, and L. S.
Cederbaum
, “Hierarchy of effective modes for the dynamics through conical intersections in macrosystems
,” J. Chem. Phys.
126
, 034106
(2007
).52.
D.
Picconi
, A.
Lami
, and F.
Santoro
, “Hierarchical transformation of Hamiltonians with linear and quadratic couplings for nonadiabatic quantum dynamics: Application to the ππ*/nπ* internal conversion in thymine
,” J. Chem. Phys.
136
, 244104
(2012
).53.
M. J.
Frisch
, G. W.
Trucks
, H. B.
Schlegel
, G. E.
Scuseria
, M. A.
Robb
, J. R.
Cheeseman
, G.
Scalmani
, V.
Barone
, G. A.
Petersson
, H.
Nakatsuji
, X.
Li
, M.
Caricato
, A. V.
Marenich
, J.
Bloino
, B. G.
Janesko
, R.
Gomperts
, B.
Mennucci
, H. P.
Hratchian
, J. V.
Ortiz
, A. F.
Izmaylov
, J. L.
Sonnenberg
, D.
Williams-Young
, F.
Ding
, F.
Lipparini
, F.
Egidi
, J.
Goings
, B.
Peng
, A.
Petrone
, T.
Henderson
, D.
Ranasinghe
, V. G.
Zakrzewski
, J.
Gao
, N.
Rega
, G.
Zheng
, W.
Liang
, M.
Hada
, M.
Ehara
, K.
Toyota
, R.
Fukuda
, J.
Hasegawa
, M.
Ishida
, T.
Nakajima
, Y.
Honda
, O.
Kitao
, H.
Nakai
, T.
Vreven
, K.
Throssell
, J. A.
Montgomery
, Jr., J. E.
Peralta
, F.
Ogliaro
, M. J.
Bearpark
, J. J.
Heyd
, E. N.
Brothers
, K. N.
Kudin
, V. N.
Staroverov
, T. A.
Keith
, R.
Kobayashi
, J.
Normand
, K.
Raghavachari
, A. P.
Rendell
, J. C.
Burant
, S. S.
Iyengar
, J.
Tomasi
, M.
Cossi
, J. M.
Millam
, M.
Klene
, C.
Adamo
, R.
Cammi
, J. W.
Ochterski
, R. L.
Martin
, K.
Morokuma
, O.
Farkas
, J. B.
Foresman
, and D. J.
Fox
, Gaussian 16, Revision C.01, Gaussian, Inc.
, Wallingford, CT
, 2016
.54.
J.
Tomasi
, B.
Mennucci
, and R.
Cammi
, “Quantum mechanical continuum solvation models
,” Chem. Rev.
105
, 2999
(2005
).55.
G. W.
Richings
, I.
Polyak
, K. E.
Spinlove
, G. A.
Worth
, I.
Burghardt
, and B.
Lasorne
, “Quantum dynamics simulations using Gaussian wavepackets: The vMCG method
,” Int. Rev. Phys. Chem.
34
, 269
(2015
).56.
I.
Burghardt
, K.
Giri
, and G. A.
Worth
, “Multimode quantum dynamics using Gaussian wavepackets: The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method applied to the absorption spectrum of pyrazine
,” J. Chem. Phys.
129
, 174104
(2008
).57.
Y.
Takahashi
and H.
Umezawa
, “Thermo field dynamics
,” Int. J. Mod. Phys. B
10
, 1755
(1996
).58.
G.
Ritschel
, D.
Suess
, S.
Möbius
, W. T.
Strunz
, and A.
Eisfeld
, “Non-Markovian Quantum State Diffusion for temperature-dependent linear spectra of light harvesting aggregates
,” J. Chem. Phys.
142
, 034115
(2015
).59.
E. W.
Fischer
and P.
Saalfrank
, “A thermofield-based multilayer multiconfigurational time-dependent Hartree approach to non-adiabatic quantum dynamics at finite temperature
,” J. Chem. Phys.
155
, 134109
(2021
).60.
K. K.
Liang
, A. M.
Mebel
, S. H.
Lin
, M.
Hayashi
, H. L.
Selzle
, E. W.
Schlag
, and M.
Tachiya
, “Influence of distortion and Duschinsky effects on Marcus-type theories of electron transfer rate
,” Phys. Chem. Chem. Phys.
5
, 4656
(2003
).61.
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
, 204102
(2019
).62.
A. T. B.
Gilbert
, N. A.
Besley
, and P. M. W.
Gill
, “Self-consistent field calculations of excited states using the maximum overlap method (MOM)
,” J. Phys. Chem. A
112
, 13164
(2008
).63.
D. A.
Fedotov
, A. C.
Paul
, H.
Koch
, F.
Santoro
, S.
Coriani
, and R.
Improta
, “Excited state absorption of DNA bases in the gas phase and in chloroform solution: A comparative quantum mechanical study
,” Phys. Chem. Chem. Phys.
24
, 4987
(2022
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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