The restricted active space spin–flip (RAS-SF) formalism is a particular form of single-reference configuration interaction that can describe some forms of strong correlation at a relatively low cost and which has recently been formulated for the description of charge-transfer excited states. Here, we introduce both equilibrium and nonequilibrium versions of a state-specific solvation correction for vertical transition energies computed using RAS-SF wave functions, based on the framework of a polarizable continuum model (PCM). Ground-state polarization is described using the solvent’s static dielectric constant and in the nonequilibrium solvation approach that polarization is modified upon vertical excitation using the solvent’s optical dielectric constant. Benchmark calculations are reported for well-studied models of photo-induced charge transfer, including naphthalene dimer, C2H4⋯C2F4, pentacene dimer, and perylene diimide (PDI) dimer, several of which are important in organic photovoltaic applications. For the PDI dimer, we demonstrate that the charge-transfer character of the excited states is enhanced in the presence of a low-dielectric medium (static dielectric constant ɛ0 = 3) as compared to a gas-phase calculation (ɛ0 = 1). This stabilizes mechanistic traps for singlet fission and helps to explain experimental singlet fission rates. We also examine the effects of nonequilibrium solvation on charge-separated states in an intramolecular singlet fission chromophore, where we demonstrate that the energetic ordering of the states changes as a function of solvent polarity. The RAS-SF + PCM methodology that is reported here provides a framework to study charge-separated states in solution and in photovoltaic materials.
REFERENCES
1.
P. G.
Szalay
, T.
Müller
, G.
Gidofalvi
, H.
Lischka
, and R.
Shepard
, “Multiconfiguration self-consistent field and multireference configuration interaction methods and applications
,” Chem. Rev.
112
, 108
–181
(2012
).2.
H.
Lischka
, D.
Nachtigallová
, A. J. A.
Aquino
, P. G.
Szalay
, F.
Plasser
, F. B. C.
Machado
, and M.
Barbatti
, “Multireference approaches for excited states of molecules
,” Chem. Rev.
118
, 7293
–7361
(2018
).3.
J. W.
Park
, R.
Al-Saadon
, M. K.
MacLeod
, T.
Shiozaki
, and B.
Vlaisavljevich
, “Multireference electron correlation methods: Journeys along potential energy surfaces
,” Chem. Rev.
120
, 5878
–5909
(2020
).4.
D.
Casanova
and M.
Head-Gordon
, “Restricted active space spin-flip configuration interaction approach: Theory, implementation and examples
,” Phys. Chem. Chem. Phys.
11
, 9779
–9790
(2009
).5.
P. M.
Zimmerman
, F.
Bell
, M.
Goldey
, A. T.
Bell
, and M.
Head-Gordon
, “Restricted active space spin-flip configuration interaction: Theory and examples for multiple spin flips with odd numbers of electrons
,” J. Chem. Phys.
137
, 164110
(2012
).6.
F.
Bell
, P. M.
Zimmerman
, D.
Casanova
, M.
Goldey
, and M.
Head-Gordon
, “Restricted active space spin-flip (RAS-SF) with arbitrary number of spin-flips
,” Phys. Chem. Chem. Phys.
15
, 358
–366
(2013
).7.
D.
Casanova
, “Restricted active space configuration interaction methods for strong correlation: Recent developments
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
12
, e1561
(2021
).8.
D.
Casanova
and A. I.
Krylov
, “Spin-flip methods in quantum chemistry
,” Phys. Chem. Chem. Phys.
22
, 4326
–4342
(2020
).9.
J. M.
Herbert
and A.
Mandal
, “Spin-flip TDDFT for photochemistry
,” in Time-Dependent Density-Functional Theory: Nonadiabatic Molecular Dynamics
, edited by C.
Zhu
(Jenny Stanford
, 2022
).10.
A. D.
Chien
and P. M.
Zimmerman
, “Recovering dynamic correlation in spin flip configuration interaction through a difference dedicated approach
,” J. Chem. Phys.
146
, 014103
(2017
).11.
H.
Jiang
and P. M.
Zimmerman
, “Charge transfer via spin flip configuration interaction: Benchmarks and application to singlet fission
,” J. Chem. Phys.
153
, 064109
(2020
).12.
A. W.
Lange
, M. A.
Rohrdanz
, and J. M.
Herbert
, “Charge-transfer excited states in a π-stacked adenine dimer, as predicted using long-range-corrected time-dependent density functional theory
,” J. Phys. Chem. B
112
, 6304
–6308
(2008
);
[PubMed]
13.
S.
Zheng
, E.
Geva
, and B. D.
Dunietz
, “Solvated charge transfer states of functionalized anthracene and tetracyanoethylene dimers: A computational study based on a range separated hybrid functional and charge constrained self-consistent field with switching Gaussian polarized continuum models
,” J. Chem. Theory Comput.
9
, 1125
–1131
(2013
).14.
S.
Bhandari
and B. D.
Dunietz
, “Quantitative accuracy in calculating charge transfer state energies in solvated molecular complexes using a screened range separated hybrid functional within a polarized continuum model
,” J. Chem. Theory Comput.
15
, 4305
–4311
(2019
).15.
B.
Alam
, A. F.
Morrison
, and J. M.
Herbert
, “Charge separation and charge transfer in the low-lying excited states of pentacene
,” J. Phys. Chem. C
124
, 24653
–24666
(2020
).16.
J. M.
Herbert
, “Dielectric continuum methods for quantum chemistry
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
11
, e1519
(2021
).17.
B.
Mennucci
, “Polarizable continuum model
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 386
–404
(2012
).18.
J. M.
Herbert
and A. W.
Lange
, “Polarizable continuum models for (bio)molecular electrostatics: Basic theory and recent developments for macromolecules and simulations
,” in Many-Body Effects and Electrostatics in Biomolecules
, edited by Q.
Cui
, P.
Ren
, and M.
Meuwly
(CRC Press
, Boca Raton
, 2016
), Chap. 11, pp. 363
–416
.19.
B.
Mennucci
, “Continuum models for excited states
,” in Continuum Solvation Models in Chemical Physics
, edited by B.
Mennucci
and R.
Cammi
(Wiley
, Chichester, UK
, 2007
), pp. 110
–123
.20.
J.-M.
Mewes
, Z.-Q.
You
, M.
Wormit
, T.
Kriesche
, J. M.
Herbert
, and A.
Dreuw
, “Experimental benchmark data and systematic evaluation of two a posteriori, polarizable-continuum corrections for vertical excitation energies in solution
,” J. Phys. Chem. A
119
, 5446
–5464
(2015
).21.
Z. Q.
You
, J. M.
Mewes
, A.
Dreuw
, and J. M.
Herbert
, “Comparison of the Marcus and Pekar partitions in the context of non-equilibrium, polarizable-continuum reaction-field solvation models
,” J. Chem. Phys.
143
, 204104
(2015
).22.
J.-M.
Mewes
, J. M.
Herbert
, and A.
Dreuw
, “On the accuracy of the general, state-specific polarizable-continuum model for the description of correlated ground- and excited states in solution
,” Phys. Chem. Chem. Phys.
19
, 1644
–1654
(2017
).23.
M. P.
Coons
, Z.-Q.
You
, and J. M.
Herbert
, “The hydrated electron at the surface of neat liquid water appears to be indistinguishable from the bulk species
,” J. Am. Chem. Soc.
138
, 10879
–10886
(2016
).24.
M. P.
Coons
and J. M.
Herbert
, “Quantum chemistry in arbitrary dielectric environments: Theory and implementation of nonequilibrium Poisson boundary conditions and application to compute vertical ionization energies at the air/water interface
,” J. Chem. Phys.
148
, 222834 (2018
);25.
A. W.
Lange
and J. M.
Herbert
, “A smooth, nonsingular, and faithful discretization scheme for polarizable continuum models: The switching/Gaussian approach
,” J. Chem. Phys.
133
, 244111
(2010
).26.
L. D.
Jacobson
and J. M.
Herbert
, “A simple algorithm for determining orthogonal, self-consistent excited-state wave functions for a state-specific Hamiltonian: Application to the optical spectrum of the aqueous electron
,” J. Chem. Theory Comput.
7
, 2085
–2093
(2011
).27.
C. J. F.
Böttcher
and P.
Bordewijk
, Theory of Electric Polarization
(Elsevier
, Amsterdam
, 1978
), Vol. 2.28.
R.
Improta
, V.
Barone
, G.
Scalmani
, and M. J.
Frisch
, “A state-specific polarizable continuum model time dependent density functional method for excited state calculations in solution
,” J. Chem. Phys.
125
, 054103
(2006
).29.
R.
Improta
, G.
Scalmani
, M. J.
Frisch
, and V.
Barone
, “Toward effective and reliable fluorescence energies in solution by a new state specific polarizable continuum model time dependent density functional theory approach
,” J. Chem. Phys.
127
, 074504
(2007
).30.
F.
Lipparini
, G.
Scalmani
, and B.
Mennucci
, “Non covalent interactions in RNA and DNA base pairs: A quantum-mechanical study of the coupling between solvent and electronic density
,” Phys. Chem. Chem. Phys.
11
, 11617
–11623
(2009
).31.
F.
Lipparini
and B.
Mennucci
, “Perspective: Polarizable continuum models for quantum-mechanical descriptions
,” J. Chem. Phys.
144
, 160901
(2016
).32.
M.
Caricato
, “CCSD-PCM excited state energy gradients with the linear response singles approximation to study the photochemistry of molecules in solution
,” ChemPhotoChem
3
, 747
–754
(2019
).33.
M.
Caricato
, “Coupled cluster theory in the condensed phase within the singles-T density scheme for the environment response
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
10
, e1463
(2020
).34.
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
).35.
E.
Epifanovsky
, A. T. B.
Gilbert
, X.
Feng
, J.
Lee
, Y.
Mao
, N.
Mardirossian
, P.
Pokhilko
, A. F.
White
, M. P.
Coons
, A. L.
Dempwolff
, Z.
Gan
, D.
Hait
, P. R.
Horn
, L. D.
Jacobson
, I.
Kaliman
, J.
Kussmann
, A. W.
Lange
, K. U.
Lao
, D. S.
Levine
, J.
Liu
, S. C.
McKenzie
, A. F.
Morrison
, K. D.
Nanda
, F.
Plasser
, D. R.
Rehn
, M. L.
Vidal
, Z.-Q.
You
, Y.
Zhu
, B.
Alam
, B. J.
Albrecht
, A.
Aldossary
, E.
Alguire
, J. H.
Andersen
, V.
Athavale
, D.
Barton
, K.
Begam
, A.
Behn
, N.
Bellonzi
, Y. A.
Bernard
, E. J.
Berquist
, H. G. A.
Burton
, A.
Carreras
, K.
Carter-Fenk
, R.
Chakraborty
, A. D.
Chien
, K. D.
Closser
, V.
Cofer-Shabica
, S.
Dasgupta
, M.
de Wergifosse
, J.
Deng
, M.
Diedenhofen
, H.
Do
, S.
Ehlert
, P.-T.
Fang
, S.
Fatehi
, Q.
Feng
, T.
Friedhoff
, J.
Gayvert
, Q.
Ge
, G.
Gidofalvi
, M.
Goldey
, J.
Gomes
, C. E.
González-Espinoza
, S.
Gulania
, A. O.
Gunina
, M. W. D.
Hanson-Heine
, P. H. P.
Harbach
, A.
Hauser
, M. F.
Herbst
, M.
Hernández Vera
, M.
Hodecker
, Z. C.
Holden
, S.
Houck
, X.
Huang
, K.
Hui
, B. C.
Huynh
, M.
Ivanov
, Á.
Jász
, H.
Ji
, H.
Jiang
, B.
Kaduk
, S.
Kähler
, K.
Khistyaev
, J.
Kim
, G.
Kis
, P.
Klunzinger
, Z.
Koczor-Benda
, J. H.
Koh
, D.
Kosenkov
, L.
Koulias
, T.
Kowalczyk
, C. M.
Krauter
, K.
Kue
, A.
Kunitsa
, T.
Kus
, I.
Ladjánszki
, A.
Landau
, K. V.
Lawler
, D.
Lefrancois
, S.
Lehtola
, R. R.
Li
, Y.-P.
Li
, J.
Liang
, M.
Liebenthal
, H.-H.
Lin
, Y.-S.
Lin
, F.
Liu
, K.-Y.
Liu
, M.
Loipersberger
, A.
Luenser
, A.
Manjanath
, P.
Manohar
, E.
Mansoor
, S. F.
Manzer
, S.-P.
Mao
, A. V.
Marenich
, T.
Markovich
, S.
Mason
, S. A.
Maurer
, P. F.
McLaughlin
, M. F. S. J.
Menger
, J.-M.
Mewes
, S. A.
Mewes
, P.
Morgante
, J. W.
Mullinax
, K. J.
Oosterbaan
, G.
Paran
, A. C.
Paul
, S. K.
Paul
, F.
Pavošević
, Z.
Pei
, S.
Prager
, E. I.
Proynov
, Á.
Rák
, E.
Ramos-Cordoba
, B.
Rana
, A. E.
Rask
, A.
Rettig
, R. M.
Richard
, F.
Rob
, E.
Rossomme
, T.
Scheele
, M.
Scheurer
, M.
Schneider
, N.
Sergueev
, S. M.
Sharada
, W.
Skomorowski
, D. W.
Small
, C. J.
Stein
, Y.-C.
Su
, E. J.
Sundstrom
, Z.
Tao
, J.
Thirman
, G. J.
Tornai
, T.
Tsuchimochi
, N. M.
Tubman
, S. P.
Veccham
, O.
Vydrov
, J.
Wenzel
, J.
Witte
, A.
Yamada
, K.
Yao
, S.
Yeganeh
, S. R.
Yost
, A.
Zech
, I. Y.
Zhang
, X.
Zhang
, Y.
Zhang
, D.
Zuev
, A.
Aspuru-Guzik
, A. T.
Bell
, N. A.
Besley
, K. B.
Bravaya
, B. R.
Brooks
, D.
Casanova
, J.-D.
Chai
, S.
Coriani
, C. J.
Cramer
, G.
Cserey
, A. E.
DePrince
III, R. A.
DiStasio
, Jr., A.
Dreuw
, B. D.
Dunietz
, T. R.
Furlani
, W. A.
Goddard
III, S.
Hammes-Schiffer
, T.
Head-Gordon
, W. J.
Hehre
, C.-P.
Hsu
, T.-C.
Jagau
, Y.
Jung
, A.
Klamt
, J.
Kong
, D. S.
Lambrecht
, W.
Liang
, N. J.
Mayhall
, C. W.
McCurdy
, J. B.
Neaton
, C.
Ochsenfeld
, J. A.
Parkhill
, R.
Peverati
, V. A.
Rassolov
, Y.
Shao
, L. V.
Slipchenko
, T.
Stauch
, R. P.
Steele
, J. E.
Subotnik
, A. J. W.
Thom
, A.
Tkatchenko
, D. G.
Truhlar
, T.
Van Voorhis
, T. A.
Wesolowski
, K. B.
Whaley
, H. L.
Woodcock
III, P. M.
Zimmerman
, S.
Faraji
, P. M. W.
Gill
, M.
Head-Gordon
, J. M.
Herbert
, and A. I.
Krylov
, “Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package
,” J. Chem. Phys.
155
, 084801
(2021
).36.
J.
Pipek
and P. G.
Mezey
, “A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions
,” J. Chem. Phys.
90
, 4916
–4926
(1989
).37.
D. E.
Bernholdt
and R. J.
Harrison
, “Fitting basis set for the RI-MP2 approximate second-order many-body perturbation theory method
,” J. Chem. Phys.
109
, 1593
–1600
(1998
).38.
F.
Weigend
, M.
Häser
, H.
Patzelt
, and R.
Ahlrichs
, “RI-MP2: Optimized auxiliary basis sets and demonstration of efficiency
,” Chem. Phys. Lett.
294
, 143
–152
(1998
).39.
V.
Barone
and M.
Cossi
, “Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent model
,” J. Phys. Chem. A
102
, 1995
–2001
(1998
).40.
J.
Tomasi
, B.
Mennucci
, and E.
Cancès
, “The IEF version of the PCM solvation method: An overview of a new method addressed to study molecular solutes at the QM ab initio level
,” J. Mol. Struct.: THEOCHEM
464
, 211
–226
(1999
).41.
D. M.
Chipman
, “Simulation of volume polarization in reaction field theory
,” J. Chem. Phys.
110
, 8012
–8018
(1999
).42.
E.
Cancès
and B.
Mennucci
, “Comment on ‘Reaction field treatment of charge penetration’ [J. Chem. Phys. 112, 5558 (2000)]
,” J. Chem. Phys.
114
, 4744
–4745
(2001
).43.
D. M.
Chipman
, “Comparison of solvent reaction field representations
,” Theor. Chem. Acc.
107
, 80
–89
(2002
).44.
A. W.
Lange
and J. M.
Herbert
, “A simple polarizable continuum solvation model for electrolyte solutions
,” J. Chem. Phys.
134
, 204110
(2011
).45.
A. V.
Marenich
, C. J.
Cramer
, and D. G.
Truhlar
, “Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions
,” J. Phys. Chem. B
113
, 6378
–6396
(2009
).46.
A.
Klamt
, C.
Moya
, and J.
Palomar
, “A comprehensive comparison of the IEFPCM and SS(V)PE continuum solvation methods with the COSMO approach
,” J. Chem. Theory Comput.
11
, 4220
–4225
(2015
).47.
D. M.
Chipman
, “Charge penetration in dielectric models of solvation
,” J. Chem. Phys.
106
, 10194
–10206
(1997
).48.
A. W.
Lange
and J. M.
Herbert
, “Symmetric versus asymmetric discretization of the integral equations in polarizable continuum solvation models
,” Chem. Phys. Lett.
509
, 77
–87
(2011
).49.
A. W.
Lange
, J. M.
Herbert
, B. J.
Albrecht
, and Z.-Q.
You
, “Intrinsically smooth discretization of Connolly’s solvent-excluded molecular surface
,” Mol. Phys.
118
, e1644384
(2020
).50.
R. S.
Rowland
and R.
Taylor
, “Intermolecular nonbonded contact distances in organic crystal structures: Comparison with distances expected from van der Waals radii
,” J. Phys. Chem.
100
, 7384
–7391
(1996
).51.
A. W.
Lange
and J. M.
Herbert
, “Polarizable continuum reaction-field solvation models affording smooth potential energy surfaces
,” J. Phys. Chem. Lett.
1
, 556
–561
(2010
).52.
B.
Kaduk
, T.
Kowalczyk
, and T.
Van Voorhis
, “Constrained density functional theory
,” Chem. Rev.
112
, 321
–370
(2012
).53.
J. M.
Herbert
and K.
Carter-Fenk
, “Electrostatics, charge transfer, and the nature of the halide–water hydrogen bond
,” J. Phys. Chem. A
125
, 1243
–1256
(2021
).54.
J. M.
Herbert
and S. K.
Paul
, “Interaction energy analysis of monovalent inorganic anions in bulk water versus air/water interface
,” Molecules
26
, 6719
(2021
).55.
A.
Dreuw
, J. L.
Weisman
, and M.
Head-Gordon
, “Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange
,” J. Chem. Phys.
119
, 2943
–2946
(2003
).56.
R.
Peverati
and D. G.
Truhlar
, “Improving the accuracy of hybrid meta-GGA density functionals by range separation
,” J. Phys. Chem. Lett.
2
, 2810
–2817
(2011
).57.
A.
Solovyeva
, M.
Pavanello
, and J.
Neugebauer
, “Describing long-range charge-separation processes with subsystem density-functional theory
,” J. Chem. Phys.
140
, 164103
(2014
).58.
A. L. L.
East
and E. C.
Lim
, “Naphthalene dimer: Electronic states, excimers, and triplet decay
,” J. Chem. Phys.
113
, 8981
–8994
(2000
).59.
F.
Plasser
and H.
Lischka
, “Analysis of excitonic and charge transfer interactions from quantum chemical calculations
,” J. Chem. Theory Comput.
8
, 2777
–2789
(2012
).60.
N. O.
Dubinets
, A. A.
Safonov
, and A. A.
Bagaturyants
, “Structures and binding energies of the naphthalene dimer in its ground and excited states
,” J. Phys. Chem. A
120
, 2779
–2782
(2016
).61.
A.
Benny
, R.
Ramakrishnan
, and M.
Hariharan
, “Mutually exclusive hole and electron transfer coupling in cross stacked acenes
,” Chem. Sci.
12
, 5064
–5072
(2021
).62.
M. B.
Smith
and J.
Michl
, “Recent advances in singlet fission
,” Annu. Rev. Phys. Chem.
64
, 361
–386
(2013
).63.
S. W.
Eaton
, L. E.
Shoer
, S. D.
Karlen
, S. M.
Dyar
, E. A.
Margulies
, B. S.
Veldkamp
, C.
Ramanan
, D. A.
Hartzler
, S.
Savikhin
, T. J.
Marks
, and M. R.
Wasielewski
, “Singlet exciton fission in polycrystalline thin films of a slip-stacked perylenediimide
,” J. Am. Chem. Soc.
135
, 14701
–14712
(2013
).64.
M. J. Y.
Tayebjee
, D. R.
McCamey
, and T. W.
Schmidt
, “Beyond Shockley–Queisser: Molecular approaches to high-efficiency photovoltaics
,” J. Phys. Chem. Lett.
6
, 2367
–2378
(2015
).65.
A. K.
Le
, J. A.
Bender
, and S. T.
Roberts
, “Slow singlet fission observed in a polycrystalline perylenediimide thin film
,” J. Phys. Chem. Lett.
7
, 4922
–4928
(2016
).66.
A. M.
Alvertis
, S.
Lukman
, T. J. H.
Hele
, E. G.
Fuemmeler
, J.
Feng
, J.
Wu
, N. C.
Greenham
, A. W.
Chin
, and A. J.
Musser
, “Switching between coherent and incoherent singlet fission via solvent-induced symmetry breaking
,” J. Am. Chem. Soc.
141
, 17558
–17570
(2019
).67.
I.
Papadopoulos
, M. J.
Álvaro‐Martins
, D.
Molina
, P. M.
McCosker
, P. A.
Keller
, T.
Clark
, Á.
Sastre‐Santos
, and D. M.
Guldi
, “Solvent-dependent singlet fission in diketopyrrolopyrrole dimers: A mediating charge transfer versus a trapping symmetry-breaking charge separation
,” Adv. Energy Mater.
10
, 2001496
(2020
).68.
E. A.
Margulies
, C. E.
Miller
, Y.
Wu
, L.
Ma
, G. C.
Schatz
, R. M.
Young
, and M. R.
Wasielewski
, “Enabling singlet fission by controlling intramolecular charge transfer in π-stacked covalent terrylenediimide dimers
,” Nat. Chem.
8
, 1120
–1125
(2016
).69.
J.-K.
Park
, R. H.
Kim
, P.
Prabhakaran
, S.
Kim
, and K.-S.
Lee
, “Highly biocompatible amphiphilic perylenediimide derivative for bioimaging
,” Opt. Mater. Express
6
, 1420
(2016
).70.
A. K.
Le
, J. A.
Bender
, D. H.
Arias
, D. E.
Cotton
, J. C.
Johnson
, and S. T.
Roberts
, “Singlet fission involves an interplay between energetic driving force and electronic coupling in perylenediimide films
,” J. Am. Chem. Soc.
140
, 814
–826
(2018
).71.
M. H.
Farag
and A. I.
Krylov
, “Singlet fission in perylenediimide dimers
,” J. Phys. Chem. C
122
, 25753
–25763
(2018
).72.
A. F.
Morrison
and J. M.
Herbert
, “Evidence for singlet fission driven by vibronic coherence in crystalline tetracene
,” J. Phys. Chem. Lett.
8
, 1442
–1448
(2017
).73.
H.
Kim
and P. M.
Zimmerman
, “Coupled double triplet state in singlet fission
,” Phys. Chem. Chem. Phys.
20
, 30083
–30094
(2018
).74.
C. M.
Mauck
, P. E.
Hartnett
, E. A.
Margulies
, L.
Ma
, C. E.
Miller
, G. C.
Schatz
, T. J.
Marks
, and M. R.
Wasielewski
, “Singlet fission via an excimer-like intermediate in 3,6-bis(thiophen-2-yl)diketopyrrolopyrrole derivatives
,” J. Am. Chem. Soc.
138
, 11749
–11761
(2016
).75.
B. S.
Basel
, J.
Zirzlmeier
, C.
Hetzer
, S. R.
Reddy
, B. T.
Phelan
, M. D.
Krzyaniak
, M. K.
Volland
, P. B.
Coto
, R. M.
Young
, T.
Clark
, M.
Thoss
, R. R.
Tykwinski
, M. R.
Wasielewski
, and D. M.
Guldi
, “Evidence for charge-transfer mediation in the primary events of singlet fission in a weakly coupled pentacene dimer
,” Chem
4
, 1092
–1111
(2018
).76.
P. M.
Zimmerman
, F.
Bell
, D.
Casanova
, and M.
Head-Gordon
, “Mechanism for singlet fission in pentacene and tetracene: From single exciton to two triplets
,” J. Am. Chem. Soc.
133
, 19944
–19952
(2011
).77.
T. C.
Berkelbach
, M. S.
Hybertsen
, and D. R.
Reichman
, “Microscopic theory of singlet exciton fission. II. Application to pentacene dimers and the role of superexchange
,” J. Chem. Phys.
138
, 114103
(2013
).78.
T. C.
Berkelbach
, M. S.
Hybertsen
, and D. R.
Reichman
, “Microscopic theory of singlet exciton fission. III. Crystalline pentacene
,” J. Chem. Phys.
141
, 074705
(2014
).79.
C. J.
Cramer
and D. G.
Truhlar
, “A universal approach to solvation modeling
,” Acc. Chem. Res.
41
, 760
–768
(2008
).80.
C. J.
Cramer
and D. G.
Truhlar
, “Implicit solvation models: Equilibria, structure, spectra, and dynamics
,” Chem. Rev.
99
, 2161
–2200
(1999
).81.
S.
Paul
and V.
Karunakaran
, “Excimer formation inhibits the intramolecular singlet fission dynamics: Systematic tilting of pentacene dimers by linking positions
,” J. Phys. Chem. B
126
, 1054
–1062
(2022
).82.
M. A.
Aguilar
, “Separation of the electric polarization into fast and slow components: A comparison of two partition schemes
,” J. Phys. Chem. A
105
, 10393
–10396
(2001
).83.
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