For the rational design of new fluorophores, reliable predictions of fluorescence quantum yields from first principles would be of great help. However, efficient computational approaches for predicting transition rates usually assume that the vibrational structure is harmonic. While the harmonic approximation has been used successfully to predict vibrationally resolved spectra and radiative rates, its reliability for non-radiative rates is much more questionable. Since non-adiabatic transitions convert large amounts of electronic energy into vibrational energy, the highly excited final vibrational states deviate greatly from harmonic oscillator eigenfunctions. We employ a time-dependent formalism to compute radiative and non-radiative rates for transitions and study the dependence on model parameters. For several coumarin dyes, we compare different adiabatic and vertical harmonic models (AS, ASF, AH, VG, VGF, and VH), in order to dissect the importance of displacements, frequency changes, and Duschinsky rotations. In addition, we analyze the effect of different broadening functions (Gaussian, Lorentzian, or Voigt). Moreover, to assess the qualitative influence of anharmonicity on the internal conversion rate, we develop a simplified anharmonic model. We address the reliability of these models considering the potential errors introduced by the harmonic approximation and the phenomenological width of the broadening function.

1.
J.
Batchelder
,
A.
Zewai
, and
T.
Cole
,
Appl. Opt.
18
,
3090
(
1979
).
2.
J. V.
Frangioni
,
Curr. Opin. Chem. Biol.
7
,
626
(
2003
).
3.
Y.
Niu
,
W.
Li
,
Q.
Peng
,
H.
Geng
,
Y.
Yi
,
L.
Wang
,
G.
Nan
,
D.
Wang
, and
Z.
Shuai
,
Mol. Phys.
116
,
1078
(
2018
).
4.
F.
Santoro
and
J.
Cerezo
, FCclasses3, a code to simulate electronic spectra, version FCclasses3-0.1,
2019
, see http://www.pi.iccom.cnr.it/fcclasses.
5.
S.
Banerjee
,
A.
Baiardi
,
J.
Bloino
, and
V.
Barone
,
J. Chem. Theory Comput.
12
,
774
(
2016
).
6.
R. R.
Valiev
,
V. N.
Cherepanov
,
R. T.
Nasibullin
,
D.
Sundholm
, and
T.
Kurten
,
Phys. Chem. Chem. Phys.
21
,
18495
(
2019
).
7.
B.
de Souza
,
G.
Farias
,
F.
Neese
, and
R.
Izsák
,
J. Chem. Theory Comput.
15
,
1896
(
2019
).
8.
R. R.
Valiev
,
V. N.
Cherepanov
,
G. V.
Baryshnikov
, and
D.
Sundholm
,
Phys. Chem. Chem. Phys.
20
,
6121
(
2018
).
9.
Q.
Peng
,
Y.
Yi
,
Z.
Shuai
, and
J.
Shao
,
J. Am. Chem. Soc.
129
,
9333
(
2007
).
10.
A. W.
Kohn
,
Z.
Lin
, and
T.
Van Voorhis
,
J. Phys. Chem. C
123
,
15394
(
2019
).
11.
J.
Hoche
,
A.
Schulz
,
L. M.
Dietrich
,
A.
Humeniuk
,
M.
Stolte
,
D.
Schmidt
,
T.
Brixner
,
F.
Würthner
, and
R.
Mitrić
,
Chem. Sci.
10
,
11013
(
2019
).
12.
S.
Lin
,
C.
Chang
,
K.
Liang
,
R.
Chang
,
J.
Zhang
,
T.
Yang
,
M.
Hayashi
,
Y.
Shiu
, and
F.
Hsu
,
Adv. Chem. Phys.
121
,
1
(
2002
).
13.
Q.
Peng
,
Y.
Niu
,
C.
Deng
, and
Z.
Shuai
,
Chem. Phys.
370
,
215
(
2010
).
14.
F. J.
Avila Ferrer
and
F.
Santoro
,
Phys. Chem. Chem. Phys.
14
,
13549
(
2012
).
15.

The effect of anharmonicity on the absorption and fluorescence spectra has been studied in C. Zhu et al., Chem. Phys.358, 137 (2009) also employing the displaced oscillator model (AS) and the Morse potential.

16.
Y.
Niu
,
Q.
Peng
, and
Z.
Shuai
,
Sci. China, Ser. B: Chem.
51
,
1153
(
2008
).
17.
Q.
Peng
,
Y.
Niu
,
Q.
Shi
,
X.
Gao
, and
Z.
Shuai
,
J. Chem. Theory Comput.
9
,
1132
(
2013
).
18.
19.
J. P.
Dahl
and
M.
Springborg
,
J. Chem. Phys.
88
,
4535
(
1988
).
20.
C.
Adamo
and
V.
Barone
,
J. Chem. Phys.
110
,
6158
(
1999
).
21.
M.
Ernzerhof
and
G. E.
Scuseria
,
J. Chem. Phys.
110
,
5029
(
1999
).
22.
A. D.
Becke
,
J. Chem. Phys.
98
,
1372
(
1993
).
23.
F.
Weigend
,
Phys. Chem. Chem. Phys.
8
,
1057
(
2006
).
24.
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 A.03,
Gaussian, Inc.
,
Wallingford, CT
,
2016
.
25.
F. J. A.
Ferrer
,
J.
Cerezo
,
J.
Soto
,
R.
Improta
, and
F.
Santoro
,
Comput. Theor. Chem.
1040-1041
,
328
(
2014
).
26.
V.
Barone
,
M.
Biczysko
,
J.
Bloino
,
L.
Carta
, and
A.
Pedone
,
Comput. Theor. Chem.
1040-1041
,
144
(
2014
).
27.
J.
Tomasi
,
B.
Mennucci
, and
R.
Cammi
,
Chem. Rev.
105
,
2999
(
2005
).
28.
M.
Taniguchi
and
J. S.
Lindsey
,
Photochem. Photobiol.
94
,
290
(
2018
).
29.
G.
Jones
 II
,
W. R.
Jackson
,
C. Y.
Choi
, and
W. R.
Bergmark
,
J. Phys. Chem.
89
,
294
(
1985
).
30.
S.
Mondal
,
R.
Halder
,
B.
Biswas
,
B.
Jana
, and
P. C.
Singh
,
J. Chem. Phys.
144
,
184504
(
2016
).
31.
K.
Rurack
and
M.
Spieles
,
Anal. Chem.
83
,
1232
(
2011
).
32.
V. A.
Lapina
,
T. A.
Pavich
,
P. P.
Pershukevich
,
A. V.
Trofimov
,
N. N.
Trofimova
,
Y. B.
Tsaplev
, and
P. P.
Zak
,
J. Phys. Org. Chem.
30
,
e3731
(
2017
).
33.
J. S.
Seixas de Melo
,
R. S.
Becker
, and
A. L.
Maqanita
,
J. Phys. Chem.
98
,
6054
(
1994
).
34.
G.
Reynolds
and
K. H.
Drexhage
,
Opt. Commun.
13
,
222
(
1975
).
35.
J.
Cerezo
,
F. J. A.
Ferrer
, and
F.
Santoro
,
Phys. Chem. Chem. Phys.
17
,
11401
(
2015
).
36.
C. M.
Krauter
,
J.
Möhring
,
T.
Buckup
,
M.
Pernpointner
, and
M.
Motzkus
,
Phys. Chem. Chem. Phys.
15
,
17846
(
2013
).
37.
R.
Marcus
,
J. Chem. Phys.
43
,
1261
(
1965
).
38.
F. J. A.
Ferrer
,
R.
Improta
,
F.
Santoro
, and
V.
Barone
,
Phys. Chem. Chem. Phys.
13
,
17007
(
2011
).
39.
J.
Cerezo
,
F. J. A.
Ferrer
,
G.
Prampolini
, and
F.
Santoro
,
J. Chem. Theory Comput.
11
,
5810
(
2015
).
40.
I.
Kim
,
W.-J.
Son
,
Y.-S.
Choi
,
A.
Osipov
,
D.
Lee
,
H.
Lee
,
Y.
Jung
,
J.
Son
,
H.
Choi
,
W.
Sotoyama
 et al,
J. Chem. Phys. C
123
,
11140
(
2019
).
41.
R.
Englman
and
J.
Jortner
,
Mol. Phys.
18
,
145
(
1970
).
42.
A. P.
Scott
and
L.
Radom
,
J. Phys. Chem.
100
,
16502
(
1996
).
43.
H.
Du
,
R.-C. A.
Fuh
,
J.
Li
,
L. A.
Corkan
, and
J. S.
Lindsey
,
Photochem. Photobiol.
68
,
141
(
1998
).
44.
S.
Nad
and
H.
Pal
,
J. Photochem. Photobiol., A
134
,
9
(
2000
).
45.
P. J.
Stephens
,
F. J.
Devlin
,
C. F.
Chabalowski
, and
M. J.
Frisch
,
J. Phys. Chem.
98
,
11623
(
1994
).

Supplementary Material

You do not currently have access to this content.