Theoretical and experimental studies since the 1980s have pointed to the existence of organic molecules that violate Hund's rule of maximum multiplicity, with the lowest singlet excited state having lower energy than the lowest triplet excited state. With the rising prevalence of organic light-emitting diodes (OLEDs) in display technology, these types of molecules are being investigated as a new class of organic emitters. The singlet–triplet inversion implies that thermal activation is not necessary to achieve fast triplet harvesting, providing potential benefits over conventional thermally activated delayed fluorescence emitters. Here, we overview prominent studies regarding inverted singlet and triplet excited states in the context of OLEDs.
REFERENCES
1.
C. W.
Tang
and
S. A.
VanSlyke
, “
Organic electroluminescent diodes
,” Appl. Phys. Lett.
51
, 913
–915
(1987
).2.
M. A.
Baldo
et al, “
Highly efficient phosphorescent emission from organic electroluminescent devices
,” Nature
395
, 151
–154
(1998
).3.
M. A.
Baldo
,
S.
Lamansky
,
P.
Burrows
,
M. E.
Thompson
, and
S. R.
Forrest
, “
Very high-efficiency green organic light-emitting devices based on electrophosphorescence
,” Appl. Phys. Lett.
75
, 4
–6
(1999
).4.
A.
Endo
et al, “
Efficient up-conversion of triplet excitons into a singlet state and its application for organic light emitting diodes
,” Appl. Phys. Lett.
98
, 083302
(2011
).5.
H.
Uoyama
,
K.
Goushi
,
K.
Shizu
,
H.
Nomura
, and
C.
Adachi
, “
Highly efficient organic light-emitting diodes from delayed fluorescence
,” Nature
492
, 234
–238
(2012
).6.
Z.
Yang
et al, “
Recent advances in organic thermally activated delayed fluorescence materials
,” Chem. Soc. Rev.
46
, 915
–1016
(2017
).7.
J. C.
Slater
, “
The theory of complex spectra
,” Phys. Rev.
34
, 1293
(1929
).8.
M.
Moral
,
L.
Muccioli
,
W.-J.
Son
,
Y.
Olivier
, and
J. C.
Sancho-García
, “
Theoretical rationalization of the singlet–triplet gap in OLEDs materials: Impact of charge-transfer character
,” J. Chem. Theory Comput.
11
, 168
–177
(2015
).9.
T.
Hatakeyama
,
K.
Shiren
,
K.
Nakajima
,
S.
Nomura
,
S.
Nakatsuka
,
K.
Kinoshita
,
J.
Ni
,
Y.
Ono
, and
T.
Ikuta
, “
Ultrapure blue thermally activated delayed fluorescence molecules: Efficient HOMO–LUMO separation by the multiple resonance effect
,” Adv. Mater.
28
, 2777
–2891
(2016
).10.
M. A.
Baldo
,
C.
Adachi
, and
S. R.
Forrest
, “
Transient analysis of organic electrophosphorescence. II. Transient analysis of triplet–triplet annihilation
,” Phys. Rev. B
62
, 10967
(2000
).11.
C.
Murawski
,
K.
Leo
, and
M. C.
Gather
, “
Efficiency roll-off in organic light-emitting diodes
,” Adv. Mater.
25
, 6801
–6827
(2013
).12.
S.
Schmidbauer
,
A.
Hohenleutner
, and
B.
König
, “
Chemical degradation in organic light-emitting devices: Mechanisms and implications for the design of new materials
,” Adv. Mater.
25
, 2114
–2129
(2013
).13.
J.
Ehrmaier
et al, “
Singlet–triplet inversion in heptazine and in polymeric carbon nitrides
,” J. Phys. Chem. A
123
, 8099
–8108
(2019
).14.
P.
de Silva
, “
Inverted singlet–triplet gaps and their relevance to thermally activated delayed fluorescence
,” J. Phys. Chem. Lett.
10
, 5674
–5679
(2019
).15.
J.
Sanz-Rodrigo
,
G.
Ricci
,
Y.
Olivier
, and
J. C.
Sancho-García
, “
Negative singlet–triplet excitation energy gap in triangle-shaped molecular emitters for efficient triplet harvesting
,” J. Phys. Chem. A
125
, 513
–522
(2021
).16.
S.
Pios
,
X.
Huang
,
A. L.
Sobolewski
, and
W.
Domcke
, “
Triangular boron carbon nitrides: An unexplored family of chromophores with unique properties for photocatalysis and optoelectronics
,” Phys. Chem. Chem. Phys.
23
, 12968
–12975
(2021
).17.
R.
Pollice
,
P.
Friederich
,
C.
Lavigne
,
G. d P.
Gomes
, and
A.
Aspuru-Guzik
, “
Organic molecules with inverted gaps between first excited singlet and triplet states and appreciable fluorescence rates
,” Matter
4
, 1654
–1682
(2021
).18.
A. L.
Sobolewski
and
W.
Domcke
, “
Are heptazine-based organic light-emitting diode chromophores thermally activated delayed fluorescence or inverted singlet–triplet systems?
,” J. Phys. Chem. Lett.
12
, 6852
–6860
(2021
).19.
F.
Dinkelbach
,
M.
Bracker
,
M.
Kleinschmidt
, and
C. M.
Marian
, “
Large inverted singlet–triplet energy gaps are not always favorable for triplet harvesting: Vibronic Coupling drives the (reverse) intersystem crossing in heptazine derivatives
,” J. Phys. Chem. A
125
, 10044
–10051
(2021
).20.
J. C.
Sancho-García
,
E.
Brémond
,
G.
Ricci
,
A. J.
Pérez-Jiménez
,
Y.
Olivier
, and
C.
Adamo
, “
Violation of Hund's rule in molecules: Predicting the excited-state energy inversion by TD-DFT with double-hybrid methods
,” J. Chem. Phys.
156
, 034105
(2022
).21.
S.
Ghosh
and
K.
Bhattacharyya
, “
Origin of the failure of density functional theories in predicting inverted singlet–triplet gaps
,” J. Phys. Chem. A
126
, 1378
–1385
(2022
).22.
N.
Aizawa
et al, “
Delayed fluorescence from inverted singlet and triplet excited states
,” Nature
609
, 502
–506
(2022
).23.
W.
Leupin
and
J.
Wirz
, “
Low-lying electronically excited states of cycl [3.3.3]azine, a bridged 12π-perimeter
,” J. Am. Chem. Soc.
102
, 6068
–6075
(1980
).24.
W.
Leupin
,
D.
Magde
,
G.
Persy
, and
J.
Wirz
, “
1,4,7-triazacycl [3.3.3]azine: Basicity, photoelectron spectrum, photophysical properties
,” J. Am. Chem. Soc.
108
, 17
–22
(1986
).25.
M.
Shahbaz
,
S.
Urano
,
P. R.
LeBreton
,
M. A.
Rossman
,
R. S.
Hosmane
, and
N. J.
Leonard
, “
Tri-j-triazine: Synthesis, chemical behavior, and spectroscopic and theoretical probes of valence orbital structure
,” J. Am. Chem. Soc.
106
, 2805
–2811
(1984
).26.
P.
Audebert
,
E.
Kroke
,
C.
Posern
, and
S.-H.
Lee
, “
State of the art in the preparation and properties of molecular monomeric s‐heptazines: Syntheses, characteristics, and functional applications
,” Chem. Rev.
121
, 2515
–2544
(2021
).27.
L.
Galmiche
,
C.
Allain
,
T.
Le
,
R.
Guillot
, and
P.
Audebert
, “
Renewing accessible heptazine chemistry: 2,5,8-tris(3,5-diethyl-pyrazolyl)-heptazine, a new highly soluble heptazine
,” Chem. Sci.
10
, 5513
(2019
).28.
T.
Le
,
L.
Galmiche
,
G.
Masson
,
C.
Allain
, and
P.
Audebert
, “
A straightforward synthesis of a new family of molecules: 2,5,8-trialkoxyheptazines. Application to photoredox catalyzed transformations
,” Chem. Commun.
56
, 10742
–10745
(2020
).29.
J.
Li
et al, “
Highly efficient organic light-emitting diode based on a hidden thermally activated delayed fluorescence channel in a heptazine derivative
,” Adv. Mater.
25
, 3319
–3323
(2013
).30.
J.
Li
,
Q.
Zhang
,
H.
Nomura
,
H.
Miyazaki
, and
C.
Adachi
, “
Thermally activated delayed fluorescence from 3nπ* to 1nπ* up-conversion and its application to organic light-emitting diodes
,” Appl. Phys. Lett.
105
, 013301
(2014
).31.
F. Z.
Hund
, “
Deutung verwickelter spektren, insbesondere der elemente scandium bis nickel
,” Z. Phys.
33
, 345
–371
(1925
).32.
W. T.
Borden
, “
Can a square or effectively square singlet be the ground state of cyclobutadiene
,” J. Am. Chem. Soc.
97
, 5968
–5970
(1975
).33.
H.
Kollmar
and
V.
Staemmler
, “
Violation of Hund's rule by spin polarization in molecules
,” Theor. Chim. Acta
48
, 223
–239
(1978
).34.
S.
Koseki
,
T.
Nakajima
, and
A.
Toyota
, “
Violation of Hund's multiplicity rule in the electronically excited states of conjugated hydrocarbons
,” Can. J. Chem.
63
, 1572
–1579
(1985
).35.
A.
Toyota
, “
Violation of Hund's rule in the lowest excited singlet-triplet pairs of dicyclohepta [cd,gh]pentalene and dicyclopenta[ef,ki]heptalene,” Theor
. Chim. Acta
74
, 209
–217
(1988
).36.
A.
Toyota
and
T.
Nakajima
, “
Violation of Hund's multiplicity rule in the lowest excited singlet-triplet pairs of cyclic bicalicene and its higher homologues
,” J. Chem. Soc. Perkin Trans. II
2
, 1731
–1734
(1986
).37.
S.
Difley
,
D.
Beljonne
, and
T. V.
Voorhis
, “
On the singlet−triplet splitting of geminate electron−hole pairs in organic semiconductors
,” J. Am. Chem. Soc.
130
, 3420
–3427
(2008
).38.
A.
Pershin
,
D.
Hall
,
V.
Lemaur
,
J.-C.
Sancho-Garcia
,
L.
Muccioli
,
E.
Zysman-Colman
,
D.
Beljonne
, and
Y.
Olivier
, “
Highly emissive excitons with reduced exchange energy in thermally activated delayed fluorescent molecules
,” Nat. Commun.
10
, 597
(2019
).39.
E. U.
Condon
, “
The theory of complex spectra
,” Phys. Rev.
36
, 1121
–1133
(1930
).40.
S.
Hirata
and
M.
Head-Gordon
, “
Time-dependent density functional theory within the Tamm–Dancoff approximation
,” Chem. Phys. Lett.
314
, 291
–299
(1999
).41.
P.
Elliott
,
S.
Goldson
,
C.
Canahui
, and
N. T.
Maitra
, “
Perspectives on double-excitations in TDDFT
,” Chem. Phys.
391
, 110
–119
(2011
).42.
G.
Mazur
and
R.
Włodarczyk
, “
Application of the dressed time-dependent density functional theory for the excited states of linear polyenes
,” J. Comput. Chem.
30
, 811
–817
(2009
).43.
S.
Grimme
and
F.
Neese
, “
Double-hybrid density functional theory for excited electronic states of molecules
,” J. Chem. Phys.
127
, 154116
(2007
).44.
Y.
Shao
,
M.
Head-Gordon
, and
A. I.
Krylov
, “
The spin–flip approach within time-dependent density functional theory: Theory and applications to diradicals
,” J. Chem. Phys.
118
, 4807
–4818
(2003
).45.
Q.
Wu
and
T. V.
Voorhis
, “
Direct optimization method to study constrained systems within density-functional theory
,” Phys. Rev. A
72
, 024502
(2005
).46.
M. E.
Sandoval-Salinas
,
A.
Carreras
, and
D.
Casanova
, “
Triangular graphene nanofragments: Open-shell character and doping
,” Phys. Chem. Chem. Phys.
21
, 9069
–9076
(2019
).47.
J. T.
Blaskovits
,
M. H.
Garner
, and
C.
Corminboeuf
, “
Symmetry-induced singlet-triplet inversions in non-alternant hydrocarbons
,” Angew. Chem., Int. Ed.
62
, e202218156
(2023
).48.
G.
Ricci
,
J. C.
Sancho-García
, and
Y.
Olivier
, “
Establishing design strategies for emissive materials with an inverted singlet–triplet energy gap (INVEST): A computational perspective on how symmetry rules the interplay between triplet harvesting and light emission
,” J. Mater. Chem. C
10
, 12680
–12698
(2022
).49.
L.
Tučková
,
M.
Straka
,
R. R.
Valiev
, and
D.
Sundholm
, “
On the origin of the inverted singlet–triplet gap of the 5th generation light-emitting molecules
,” Phys. Chem. Chem. Phys.
24
, 18713
–18721
(2022
).50.
D.
Blasco
,
R. T.
Nasibullin
,
R. R.
Valiev
, and
D.
Sundholm
, “
Gold(I)-containing light-emitting molecules with an inverted singlet–triplet gap
,” Chem. Sci.
14
, 3873
–3880
(2023
).51.
N.
Aizawa
,
Y.
Harabuchi
,
S.
Maeda
, and
Y.-J.
Pu
, “
Kinetic prediction of reverse intersystem crossing in organic donor–acceptor molecules
,” Nat. Commun.
11
, 3909
(2020
).52.
C.
Parker
and
C.
Hatchard
, “
Triplet-singlet emission in fluid solutions. Phosphorescence of eosin
,” Trans. Faraday Soc.
57
, 1894
–1904
(1961
).53.
C.
Parker
, “
Sensitized p-type delayed fluorescence
,” Proc. R. Soc. London, Ser. A
276
, 125
–135
(1963
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
