Coupling molecules to the confined light modes of an optical cavity is showing great promise for manipulating chemical reactions. However, to fully exploit this principle and use cavities as a new tool for controlling chemistry, a complete understanding of the effects of strong light–matter coupling on molecular dynamics and reactivity is required. While quantum chemistry can provide atomistic insight into the reactivity of uncoupled molecules, the possibilities to also explore strongly coupled systems are still rather limited due to the challenges associated with an accurate description of the cavity in such calculations. Despite recent progress in introducing strong coupling effects into quantum chemistry calculations, applications are mostly restricted to single or simplified molecules in ideal lossless cavities that support a single light mode only. However, even if commonly used planar mirror micro-cavities are characterized by a fundamental mode with a frequency determined by the distance between the mirrors, the cavity energy also depends on the wave vector of the incident light rays. To account for this dependency, called cavity dispersion, in atomistic simulations of molecules in optical cavities, we have extended our multi-scale molecular dynamics model for strongly coupled molecular ensembles to include multiple confined light modes. To validate the new model, we have performed simulations of up to 512 Rhodamine molecules in red-detuned Fabry–Pérot cavities. The results of our simulations suggest that after resonant excitation into the upper polariton at a fixed wave vector, or incidence angle, the coupled cavity-molecule system rapidly decays into dark states that lack dispersion. Slower relaxation from the dark state manifold into both the upper and lower bright polaritons causes observable photo-luminescence from the molecule–cavity system along the two polariton dispersion branches that ultimately evolves toward the bottom of the lower polariton branch, in line with experimental observations. We anticipate that the more realistic cavity description in our approach will help to better understand and predict how cavities can modify molecular properties.

1.
J. A.
Hutchison
,
T.
Schwartz
,
C.
Genet
,
E.
Devaux
, and
T. W.
Ebbesen
, “
Modifying chemical landscapes by coupling to vacuum fields
,”
Angew. Chem., Int. Ed.
51
,
1592
1596
(
2012
).
2.
A.
Thomas
,
J.
George
,
A.
Shalabney
,
M.
Dryzhakov
,
S. J.
Varma
,
J.
Moran
,
T.
Chervy
,
X.
Zhong
,
E.
Devaux
,
C.
Genet
,
J. A.
Hutchison
, and
T. W.
Ebbesen
, “
Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field
,”
Angew. Chem., Int. Ed.
55
,
11462
11466
(
2016
).
3.
K.
Stranius
,
M.
Herzog
, and
K.
Börjesson
, “
Selective manipulation of electronically excited states through strong light-matter interactions
,”
Nat. Commun.
9
,
2273
(
2018
).
4.
B.
Munkhbat
,
M.
Wersäll
,
D. G.
Baranov
,
T. J.
Antosiewicz
, and
T.
Shegai
, “
Suppression of photo-oxidation of organic chromophores by strong coupling to plasmonic nanoantennas
,”
Sci. Adv.
4
,
eaas9552
(
2018
).
5.
A.
Thomas
,
L.
Lethuillier-Karl
,
K.
Nagarajan
,
R. M. A.
Vergauwe
,
J.
George
,
T.
Chervy
,
A.
Shalabney
,
E.
Devaux
,
J.
Moran
, and
T. W.
Ebbesen
, “
Tilting a ground-state reactivity landscape by vibrational strong coupling
,”
Science
363
,
615
619
(
2019
).
6.
J.
Lather
,
P.
Bhatt
,
A.
Thomas
,
T. W.
Ebbesen
, and
J.
George
, “
Cavity catalysis by cooperative vibrational strong coupling of reactant and solvent molecules
,”
Angew. Chem., Int. Ed.
58
,
10635
10638
(
2019
).
7.
R. M. A.
Vergauwe
,
A.
Thomas
,
K.
Nagarajan
,
A.
Shalabney
,
J.
George
,
T.
Chervy
,
M.
Seidel
,
E.
Devaux
,
V.
Torbeev
, and
T. W.
Ebbesen
, “
Cavity catalysis by cooperative vibrational strong coupling of reactant and solvent molecules
,”
Angew. Chem., Int. Ed.
58
,
15324
15328
(
2019
).
8.
H.
Mabuchi
and
A. C.
Doherty
, “
Cavity quantum electrodynamics: Coherence in context
,”
Science
298
,
1372
1377
(
2002
).
9.
P.
Törmä
and
W. L.
Barnes
, “
Strong coupling between surface plasmon polaritons and emitters: A review
,”
Rep. Prog. Phys.
78
,
013901
(
2015
).
10.
T. W.
Ebbesen
, “
Hybrid light-matter states in a molecular and material science perspective
,”
Acc. Chem. Res.
49
,
2403
2412
(
2016
).
11.
J.
Feist
,
J.
Galego
, and
F. J.
Garcia-Vidal
, “
Polaritonic chemistry with organic molecules
,”
ACS Photonics
5
,
205
216
(
2018
).
12.
A.
Armitage
,
M. S.
Skolnick
,
V. N.
Astratov
,
D. M.
Whittaker
,
G.
Panzarini
,
L. C.
Andreani
,
T. A.
Fisher
,
J. S.
Roberts
,
A. V.
Kavokin
,
M. A.
Kaliteevski
, and
M. R.
Vladimirova
, “
Optically induced splitting of bright excitonic states in coupled quantum microcavities
,”
Phys. Rev. B
57
,
14877
14881
(
1998
).
13.
J. H.
Burroughes
,
D. D. C.
Bradley
,
A. R.
Brown
,
R. N.
Marks
,
K.
Mackay
,
R. H.
Friend
,
P. L.
Burns
, and
A. B.
Holmes
, “
Light-emitting diodes based on conjugated polymers
,”
Nature
347
,
539
541
(
1990
).
14.
D. G.
Lidzey
,
D. D. C.
Bradley
,
S. J.
Martin
, and
M. A.
Pate
, “
Pixelated multicolor microcavity displays
,”
IEEE J. Sel. Top. Quantum Electron.
4
,
113
118
(
1998
).
15.
D. G.
Lidzey
,
D. D. C.
Bradley
,
M. S.
Skolnick
,
T.
Virgili
,
S.
Walker
, and
D. M.
Whittaker
, “
Strong exciton-photon coupling in an organic semiconductor microcavity
,”
Nature
395
,
53
55
(
1998
).
16.
D. G.
Lidzey
,
T.
Virgili
,
D. D. C.
Bradley
,
M. S.
Skolnick
,
S.
Walker
, and
D. M.
Whittaker
, “
Observation of strong exciton-photon coupling in semiconductor microcavities containing organic dyes and J-aggregates
,”
Opt. Mater.
12
,
243
247
(
1999
).
17.
D. G.
Lidzey
,
D. D. C.
Bradley
,
T.
Virgili
,
A.
Armitage
,
M. S.
Skolnick
, and
S.
Walker
, “
Room temperature polariton emission from strongly coupled organic semiconductor microcavities
,”
Phys. Rev. Lett.
82
,
3316
3319
(
1999
).
18.
D. G.
Lidzey
,
D.
Bradley
,
A.
Armitage
,
S.
Walker
, and
M.
Skolnick
, “
Photon-mediated hybridization of Frenkel excitons in organic semiconductor microcavities
,”
Science
288
,
1620
1623
(
2000
).
19.
D.
Lidzey
,
A.
Fox
,
M.
Rahn
,
M.
Skolnick
,
V.
Agranovich
, and
S.
Walker
, “
Experimental study of light emission from strongly coupled organic semiconductor microcavities following nonresonant laser excitation
,”
Phys. Rev. B
65
,
195312-1
195312-10
(
2002
).
20.
J.-H.
Song
,
Y.
He
,
A.
Nurmikko
,
J.
Tischler
, and
V.
Bulovic
, “
Exciton-polariton dynamics in a transparent organic semiconductor microcavity
,”
Phys. Rev. B
69
,
235330
(
2004
).
21.
G.
Lodden
and
R.
Holmes
, “
Electrical excitation of microcavity polaritons by radiative pumping from a weakly coupled organic semiconductor
,”
Phys. Rev. B
82
,
125317
(
2010
).
22.
D. M.
Coles
,
P.
Michetti
,
C.
Clark
,
W. C.
Tsoi
,
A. M.
Adawi
,
J.-S.
Kim
, and
D. G.
Lidzey
, “
Vibrationally assisted polariton-relaxation processes in strongly coupled organic-semiconductor microcavities
,”
Adv. Funct. Mater.
21
,
3691
3696
(
2011
).
23.
V. M.
Agranovich
,
M.
Litinskaia
, and
D. G.
Lidzey
, “
Cavity polaritons in microcavities containing disordered organic semiconductors
,”
Phys. Rev. B
67
,
085311
(
2003
).
24.
V. M.
Agranovich
and
G. C.
La Rocca
, “
Electronic excitations in organic microcavities with strong light-matter coupling
,”
Solid State Commun.
135
,
544
553
(
2005
).
25.
V.
Agranovich
and
Y.
Gartstein
, “
Nature and dynamics of low-energy exciton polaritons in semiconductor microcavities
,”
Phys. Rev. B
75
,
075302
(
2007
).
26.
M.
Litinskaya
, “
Propagation and localization of polaritons in disordered organic microcavities
,”
Phys. Lett. A
372
,
3898
3903
(
2008
).
27.
D. M.
Coles
,
P.
Michetti
,
C.
Clark
,
A. M.
Adawi
, and
D. G.
Lidzey
, “
Temperature dependence of the upper-branch polariton population in an organic semiconductor microcavity
,”
Phys. Rev. B
84
,
205214
(
2011
).
28.
M.
Litinskaya
,
P.
Reineker
, and
V. M.
Agranovich
, “
Fast polariton relaxation in strongly coupled organic microcavities
,”
J. Lumin.
110
,
364
372
(
2004
).
29.
P.
Michetti
and
G. C.
La Rocca
, “
Polariton states in disordered organic microcavities
,”
Phys. Rev. B
71
,
115320
(
2005
).
30.
P.
Michetti
and
G. C.
La Rocca
, “
Simulation of J-aggregate microcavity photoluminescence
,”
Phys. Rev. B
77
,
195301
(
2008
).
31.
P.
Michetti
and
G. C.
La Rocca
, “
Exciton-phonon scattering and photoexcitation dynamics in J-aggregate microcavities
,”
Phys. Rev. B
79
,
35325
(
2009
).
32.
P.
Michetti
and
G. C.
La Rocca
, “
Polariton-polariton scattering in organic microcavities at high excitation densities
,”
Phys. Rev. B
82
,
115327
(
2010
).
33.
M.
Litinskaya
and
P.
Reineker
, “
Balance between incoming and outgoing cavity polaritons in a disordered organic microcavity
,”
J. Lumin.
122-123
,
418
420
(
2007
).
34.
J. d.
Pino
,
J.
Feist
, and
F. J.
Garcia-Vidal
, “
Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode
,”
New J. Phys.
17
,
053040
(
2015
).
35.
K. B.
Arnardottir
,
A. J.
Moilanen
,
A.
Strashko
,
P.
Törmä
, and
J.
Keeling
, “
Multimode organic polariton lasing
,”
Phys. Rev. Lett.
125
,
233603
(
2020
).
36.
H. L.
Luk
,
J.
Feist
,
J. J.
Toppari
, and
G.
Groenhof
, “
Multiscale molecular dynamics simulations of polaritonic chemistry
,”
J. Chem. Theory Comput.
13
,
4324
4335
(
2017
).
37.
J.
del Pino
,
F. A. Y. N.
Schröder
,
A. W.
Chin
,
J.
Feist
, and
F. J.
Garcia-Vidal
, “
Tensor network simulation of non-Markovian dynamics in organic polaritons
,”
Phys. Rev. Lett.
121
,
227401
(
2018
).
38.
G.
Groenhof
,
C.
Climent
,
J.
Feist
,
D.
Morozov
, and
J. J.
Toppari
, “
Tracking polariton relaxation with multiscale molecular dynamics simulations
,”
J. Chem. Phys. Lett.
10
,
5476
5483
(
2019
).
39.
O.
Vendrell
, “
Collective Jahn-Teller interactions through light-matter coupling in a cavity
,”
Phys. Rev. Lett.
121
,
253001
(
2018
).
40.
F.
Herrera
and
F. C.
Spano
, “
Dark vibronic polaritons and the spectroscopy of organic microcavities
,”
Phys. Rev. Lett.
118
,
223601
(
2017
).
41.
F.
Herrera
and
F. C.
Spano
, “
Absorption and photoluminescence in organic cavity QED
,”
Phys. Rev. A
95
,
053867
(
2017
).
42.
A.
Warshel
and
M.
Levitt
, “
Theoretical studies of enzymatic reactions: Dielectric, electrostatic and steric stabilization of carbonium ion in the reaction of lysozyme
,”
J. Mol. Biol.
103
,
227
249
(
1976
).
43.
E. T.
Jaynes
and
F. W.
Cummings
, “
Comparison of quantum and semiclassical radiation theories with to the beam maser
,”
Proc. IEEE
51
,
89
109
(
1963
).
44.
M.
Tavis
and
F. W.
Cummings
, “
Approximate solutions for an N-molecule radiation-field Hamiltonian
,”
Phys. Rev.
188
,
692
695
(
1969
).
45.
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
).
46.
J. C.
Tully
, “
Molecular dynamics with electronic transitions
,”
J. Chem. Phys.
93
,
1061
1071
(
1990
).
47.
R.
Crespo-Otero
and
M.
Barbatti
, “
Recent advances and perspectives on nonadiabatic mixed quantum-classical dynamics
,”
Chem. Rev.
118
,
7026
7068
(
2018
).
48.
G.
Groenhof
and
J. J.
Toppari
, “
Coherent light harvesting through strong coupling to confined light
,”
J. Phys. Chem. Lett.
9
,
4848
4851
(
2018
).
49.
P.
Ehrenfest
, “
Bemerkung über die angenäherte gültigkeit der klassischen mechanik innerhalb der quantenmechanik
,”
Z. Phys.
45
,
445
457
(
1927
).
50.
G.
Granucci
,
M.
Persico
, and
A.
Toniolo
, “
Direct semiclassical simulation of photochemical processes with semiempirical wave functions
,”
J. Chem. Phys.
114
,
10608
10615
(
2001
).
51.
K. J.
Vahala
, “
Optical microcavities
,”
Nature
424
,
839
846
(
2003
).
52.
T.
Schwartz
,
J. A.
Hutchison
,
J.
Léonard
,
C.
Genet
,
S.
Haacke
, and
T. W.
Ebbesen
, “
Polariton dynamics under strong light-molecule coupling
,”
ChemPhysChem
14
,
125
131
(
2013
).
53.
J.
George
,
S.
Wang
,
T.
Chervy
,
A.
Canaguier-Durand
,
G.
Schaeffer
,
J.-M.
Lehn
,
J. A.
Hutchison
,
C.
Genet
, and
T. W.
Ebbesen
, “
Ultra-strong coupling of molecular materials: Spectroscopy and dynamics
,”
Faraday Discuss.
178
,
281
294
(
2015
).
54.
Y.
Duan
,
C.
Wu
,
S.
Chowdhury
,
M. C.
Lee
,
G.
Xiong
,
W.
Zhang
,
R.
Yang
,
P.
Cieplak
,
R.
Luo
,
T.
Lee
,
J.
Caldwell
,
J.
Wang
, and
P.
Kollman
, “
A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations
,”
J. Comput. Chem.
24
,
1999
2012
(
2003
).
55.
W. L.
Jorgensen
,
J.
Chandrasekhar
,
J. D.
Madura
,
R. W.
Impey
, and
M. L.
Klein
, “
Comparison of simple potential functions for simulation liquid water
,”
J. Chem. Phys.
79
,
926
935
(
1983
).
56.
H. J. C.
Berendsen
,
J. P. M.
Postma
,
W. F.
van Gunsteren
,
A.
DiNola
, and
J. R.
Haak
, “
Molecular dynamics with coupling to an external bath
,”
J. Chem. Phys.
81
,
3684
3690
(
1984
).
57.
B.
Hess
,
H.
Bekker
,
H. J. C.
Berendsen
, and
J. G. E. M.
Fraaije
, “
LINCS: A linear constraint solver for molecular simulations
,”
J. Comput. Chem.
18
,
1463
1472
(
1997
).
58.
S.
Miyamoto
and
P. A.
Kollman
, “
SETTLE: An analytical version of the SHAKE and RATTLE algorithms for rigid water molecules
,”
J. Comput. Chem.
13
,
952
962
(
1992
).
59.
U.
Essmann
,
L.
Perera
,
M. L.
Berkowitz
,
T.
Darden
,
H.
Lee
, and
L. G.
Pedersen
, “
A smooth particle mesh Ewald potential
,”
J. Chem. Phys.
103
,
8577
8592
(
1995
).
60.
E.
Runge
and
E. K. U.
Gross
, “
Density-functional theory for time-dependent systems
,”
Phys. Rev. Lett.
52
,
997
1000
(
1984
).
61.
B. O.
Roos
, “
Theoretical studies of electronically excited states of molecular systems using multiconfigurational perturbation theory
,”
Acc. Chem. Res.
32
,
137
144
(
1999
).
62.
A. A.
Granovsky
, “
Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory
,”
J. Chem. Phys.
134
,
214113
(
2011
).
63.
B.
Hess
,
C.
Kutzner
,
D.
van der Spoel
, and
E.
Lindahl
, “
GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation
,”
J. Chem. Theory Comput.
4
,
435
447
(
2008
).
64.
I. S.
Ufimtsev
and
T. J.
Martínez
, “
Quantum chemistry on graphical processing units. 3. Analytical energy gradients and first principles molecular dynamics
,”
J. Chem. Theory Comput.
5
,
2619
2628
(
2009
).
65.
A. V.
Titov
,
I. S.
Ufimtsev
,
N.
Luehr
, and
T. J.
Martínez
, “
Generating efficient quantum chemistry codes for novel architectures
,”
J. Chem. Theory Comput.
9
,
213
221
(
2013
).
66.
G.
Zengin
,
M.
Wersäll
,
S.
Nilsson
,
T. J.
Antosiewicz
,
M.
Käll
, and
T.
Shegai
, “
Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions
,”
Phys. Rev. Lett.
114
,
157401
(
2015
).
67.
D.
Melnikau
,
R.
Esteban
,
D.
Savateeva
,
A.
Sánchez-Iglesias
,
M.
Grzelczak
,
M. K.
Schmidt
,
L. M.
Liz-Marzán
,
J.
Aizpurua
, and
Y. P.
Rakovich
, “
Rabi splitting in photoluminescence spectra of hybrid systems of gold nanorods and J-aggregates
,”
J. Phys. Chem. Lett.
7
,
354
362
(
2016
).
68.
C. A.
Delpo
,
B.
Kudisch
,
K. H.
Park
,
S.-U.-Z.
Khan
,
F.
Fassioli
,
D.
Fausti
,
B. P.
Rand
, and
G. D.
Scholes
, “
Polariton transitions in femtosecond transient absorption studies of ultrastrong light-molecule coupling
,”
J. Phys. Chem. Lett.
11
,
2667
2674
(
2020
).
69.
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
.
70.
Mathematica, Version 11.3,
Wolfram Research, Inc.
,
Champaign, IL
,
2018
.
71.
P.
Forn-Díaz
,
L.
Lamata
,
E.
Rico
,
J.
Kono
, and
E.
Solano
, “
Ultrastrong coupling regimes of light-matter interaction
,”
Rev. Mod. Phys.
91
,
025005
(
2019
).
72.
J.
Flick
,
H.
Appel
,
M.
Ruggenthaler
, and
A.
Rubio
, “
Cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon systems
,”
J. Chem. Theory Comput.
13
,
1616
1625
(
2017
).
73.
J.
Flick
,
M.
Ruggenthaler
,
H.
Appel
, and
A.
Rubio
, “
Atoms and molecules in cavities: From weak to strong coupling in QED chemistry
,”
Proc. Natl. Acad. Sci. U. S. A.
114
,
3026
3034
(
2017
).
74.
D. M.
Coles
,
R.
Grant
,
D. G.
Lidzey
,
C.
Clark
, and
P. G.
Lagoudakis
, “
Imaging the polariton relaxation bottleneck in strongly coupled organic semiconductor microcavities
,”
Phys. Rev. B
88
,
121303
(
2013
).
75.
K.
Georgiou
,
R.
Jayaprakash
,
A.
Askitopoulos
,
D. M.
Coles
,
P. G.
Lagoudakis
, and
D. G.
Lidzey
, “
Generation of anti-Stokes fluorescence in a strongly coupled organic semiconductor microcavity
,”
ACS Photonics
5
,
4343
4351
(
2018
).
76.
S.
Takahashi
and
K.
Watanabe
, “
Decoupling from a thermal bath via molecular polariton formation
,”
J. Phys. Chem. Lett.
11
,
1349
1356
(
2020
).
77.
V.
Agranovich
,
H.
Benisty
, and
C.
Weisbuch
, “
Organic and inorganic quantum wells in a microcavity: Frenkel-Wannier-Mott excitons hybridization and energy transformation
,”
Solid State Commun.
102
,
631
636
(
1997
).
78.
S.
Kéna-Cohen
and
S. R.
Forrest
, “
Room-temperature polariton lasing in an organic single-crystal microcavity
,”
Nat. Photonics
4
,
371
375
(
2010
).
79.
K. S.
Daskalakis
,
S. A.
Maier
,
R.
Murray
, and
S.
Kéna-Cohen
, “
Nonlinear interactions in an organic polariton condensate
,”
Nat. Mater.
13
,
271
275
(
2014
).
80.
J.
Keeling
and
S.
Kéna-Cohen
, “
Bose-Einstein condensation of exciton-polaritons in organic microcavities
,”
Annu. Rev. Phys. Chem.
71
,
435
459
(
2020
).

Supplementary Material

You do not currently have access to this content.