This work presents the investigations of the impact of an increasing electron correlation in the hierarchy of coupled-cluster methods, i.e., CC2, CCSD, and CC3, on two-photon absorption (2PA) strengths for the lowest excited state of the minimal rhodopsin’s chromophore model—cis-penta-2,4-dieniminium cation (PSB3). For a larger chromophore’s model [4-cis-hepta-2,4,6-trieniminium cation (PSB4)], CC2 and CCSD calculations of 2PA strengths were performed. Additionally, 2PA strengths predicted by some popular density functional theory (DFT) functionals differing in HF exchange contribution were assessed against the reference CC3/CCSD data. For PSB3, the accuracy of 2PA strengths increases in the following order: CC2 < CCSD < CC3, with the CC2 deviation from both higher-level methods exceeding 10% at 6-31+G* basis sets and 2% at aug-cc-pVDZ basis set. However, for PSB4, this trend is reversed and CC2-based 2PA strength is larger than the corresponding CCSD value. Among the DFT functionals investigated, CAM-B3LYP and BHandHLYP provide 2PA strengths in best compliance with reference data, however, with the error approaching an order of magnitude.

1.
C.
Xu
,
W.
Zipfel
,
J. B.
Shear
,
R. M.
Williams
, and
W. W.
Webb
, “
Multiphoton fluorescence excitation: New spectral windows for biological nonlinear microscopy
,”
Proc. Natl. Acad. Sci. U. S. A.
93
,
10763
10768
(
1996
).
2.
W. R.
Zipfel
,
R. M.
Williams
, and
W. W.
Webb
, “
Nonlinear magic: Multiphoton microscopy in the biosciences
,”
Nat. Biotechnol.
21
,
1369
1377
(
2003
).
3.
D. A.
Parthenopoulos
and
P. M.
Rentzepis
, “
Three-dimensional optical storage memory
,”
Science
245
,
843
845
(
1989
).
4.
M.
Nakano
,
T.
Kooriya
,
T.
Kuragaito
,
C.
Egami
,
Y.
Kawata
,
M.
Tsuchimori
, and
O.
Watanabe
, “
Three-dimensional patterned media for ultrahigh-density optical memory
,”
Appl. Phys. Lett.
85
,
176
178
(
2004
).
5.
R. U.
Kulkarni
,
M.
Vandenberghe
,
M.
Thunemann
,
F.
James
,
O. A.
Andreassen
,
S.
Djurovic
,
A.
Devor
, and
E. W.
Miller
, “
In vivo two-photon voltage imaging with sulfonated rhodamine dyes
,”
ACS Cent. Sci.
4
,
1371
1378
(
2018
).
6.
G.
Palczewska
,
J.
Boguslawski
,
P.
Stremplewski
,
L.
Kornaszewski
,
J.
Zhang
,
Z.
Dong
,
X.-X.
Liang
,
E.
Gratton
,
A.
Vogel
,
M.
Wojtkowski
 et al, “
Noninvasive two-photon optical biopsy of retinal fluorophores
,”
Proc. Natl. Acad. Sci. U. S. A.
117
,
22532
22543
(
2020
).
7.
J. M.
An
,
S. H.
Kim
, and
D.
Kim
, “
Recent advances in two-photon absorbing probes based on a functionalized dipolar naphthalene platform
,”
Org. Biomol. Chem.
18
,
4288
4297
(
2020
).
8.
C. R.
Stoltzfus
,
L. M.
Barnett
,
M.
Drobizhev
,
G.
Wicks
,
A.
Mikhaylov
,
T. E.
Hughes
, and
A.
Rebane
, “
Two-photon directed evolution of green fluorescent proteins
,”
Sci. Rep.
5
,
11968
(
2015
).
9.
R. S.
Molina
,
T. M.
Tran
,
R. E.
Campbell
,
G. G.
Lambert
,
A.
Salih
,
N. C.
Shaner
,
T. E.
Hughes
, and
M.
Drobizhev
, “
Blue-shifted green fluorescent protein homologues are brighter than enhanced green fluorescent protein under two-photon excitation
,”
J. Phys. Chem. Lett.
8
,
2548
2554
(
2017
).
10.
B.
Ośmiałowski
,
E. F.
Petrusevich
,
M. A.
Antoniak
,
I.
Grela
,
M. A.
Bin Jassar
,
M.
Nyk
,
J. M.
Luis
,
B.
Jędrzejewska
,
R.
Zaleśny
,
D.
Jacquemin
 et al, “
Controlling two-photon action cross section by changing a single heteroatom position in fluorescent dyes
,”
J. Phys. Chem. Lett.
11
,
5920
5925
(
2020
).
11.
M.
Drobizhev
,
N. S.
Makarov
,
S. E.
Tillo
,
T. E.
Hughes
, and
A.
Rebane
, “
Two-photon absorption properties of fluorescent proteins
,”
Nat. Methods
8
,
393
399
(
2011
).
12.
H.
Hosoi
,
S.
Yamaguchi
,
H.
Mizuno
,
A.
Miyawaki
, and
T.
Tahara
, “
Hidden electronic excited state of enhanced green fluorescent protein
,”
J. Phys. Chem. B
112
,
2761
2763
(
2008
).
13.
M. A.
Rizzo
,
G.
Springer
,
K.
Segawa
,
W. R.
Zipfel
, and
D. W.
Piston
, “
Optimization of pairings and detection conditions for measurement of FRET between cyan and yellow fluorescent proteins
,”
Microsc. Microanal.
12
,
238
254
(
2006
).
14.
S.
Gholami
,
L.
Pedraza-González
,
X.
Yang
,
A. A.
Granovsky
,
I. N.
Ioffe
, and
M.
Olivucci
, “
Multistate multiconfiguration quantum chemical computation of the two-photon absorption spectra of bovine rhodopsin
,”
J. Phys. Chem. Lett.
10
,
6293
6300
(
2019
).
15.
J.
Kozłowska
,
M.
Chołuj
,
R.
Zaleśny
, and
W.
Bartkowiak
, “
Two-photon absorption of the spatially confined LiH molecule
,”
Phys. Chem. Chem. Phys.
19
,
7568
7575
(
2017
).
16.
M. J.
Paterson
,
O.
Christiansen
,
F.
Pawłowski
,
P.
Jørgensen
,
C.
Hättig
,
T.
Helgaker
, and
P.
Sałek
, “
Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory
,”
J. Chem. Phys.
124
,
054322
(
2006
).
17.
G.
Palczewska
,
F.
Vinberg
,
P.
Stremplewski
,
M. P.
Bircher
,
D.
Salom
,
K.
Komar
,
J.
Zhang
,
M.
Cascella
,
M.
Wojtkowski
,
V. J.
Kefalov
 et al, “
Human infrared vision is triggered by two-photon chromophore isomerization
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
E5445
(
2014
).
18.
M. T. P.
Beerepoot
,
D. H.
Friese
,
N. H.
List
,
J.
Kongsted
, and
K.
Ruud
, “
Benchmarking two-photon absorption cross sections: Performance of CC2 and CAM-B3LYP
,”
Phys. Chem. Chem. Phys.
17
,
19306
19314
(
2015
).
19.
M.
Wielgus
,
R.
Zaleśny
,
N. A.
Murugan
,
J.
Kongsted
,
H.
Ågren
,
M.
Samoc
, and
W.
Bartkowiak
, “
Two-photon solvatochromism II: Experimental and theoretical study of solvent effects on the two-photon absorption spectrum of Reichardt’s dye
,”
ChemPhysChem
14
,
3731
3739
(
2013
).
20.
A. H.
Steindal
,
J. M. H.
Olsen
,
K.
Ruud
,
L.
Frediani
, and
J.
Kongsted
, “
A combined quantum mechanics/molecular mechanics study of the one- and two-photon absorption in the green fluorescent protein
,”
Phys. Chem. Chem. Phys.
14
,
5440
(
2012
).
21.
R.
Di Remigio
,
T.
Giovannini
,
M.
Ambrosetti
,
C.
Cappelli
, and
L.
Frediani
, “
Fully polarizable QM/fluctuating charge approach to two-photon absorption of aqueous solutions
,”
J. Chem. Theory Comput.
15
,
4056
4068
(
2019
).
22.
M. A.
Salem
and
A.
Brown
, “
Two-photon absorption in fluorescent protein chromophores: TDDFT and CC2 results
,”
J. Chem. Theory Comput.
10
,
3260
3269
(
2014
).
23.
I. H.
Nayyar
,
A. E.
Masunov
, and
S.
Tretiak
, “
Comparison of TD-DFT methods for the calculation of two-photon absorption spectra of oligophenylvinylenes
,”
J. Phys. Chem. C
117
,
18170
18189
(
2013
).
24.
D.
Grabarek
and
T.
Andruniów
, “
Illuminating the origins of two-photon absorption properties in fluorescent protein chromophores
,”
Int. J. Quantum Chem.
120
,
e26086
(
2019
).
25.
K.
Sneskov
,
J. M. H.
Olsen
,
T.
Schwabe
,
C.
Hättig
,
O.
Christiansen
, and
J.
Kongsted
, “
Computational screening of one- and two-photon spectrally tuned channelrhodopsin mutants
,”
Phys. Chem. Chem. Phys.
15
,
7567
(
2013
).
26.
M.
Alaraby Salem
and
A.
Brown
, “
Two-photon absorption of fluorescent protein chromophores incorporating non-canonical amino acids: TD-DFT screening and classical dynamics
,”
Phys. Chem. Chem. Phys.
17
,
25563
25571
(
2015
).
27.
D.
Grabarek
and
T.
Andruniów
, “
Assessment of functionals for TDDFT calculations of one- and two-photon absorption properties of neutral and anionic fluorescent proteins chromophores
,”
J. Chem. Theory Comput.
15
,
490
508
(
2018
).
28.
P. J.
Walla
,
J.
Yom
,
B. P.
Krueger
, and
G. R.
Fleming
, “
Two-photon excitation spectrum of light-harvesting complex II. And fluorescence upconversion after one- and two-photon excitation of the carotenoids
,”
J. Phys. Chem. B
104
,
4799
4806
(
2000
).
29.
D. A.
Gacek
,
A.
Betke
,
J.
Nowak
,
H.
Lokstein
, and
P. J.
Walla
, “
Two-photon absorption and excitation spectroscopy of carotenoids, chlorophylls and pigment–protein complexes
,”
Phys. Chem. Chem. Phys.
23
,
8731
8738
(
2021
).
30.
M. T. P.
Beerepoot
,
D. H.
Friese
, and
K.
Ruud
, “
Intermolecular charge transfer enhances two-photon absorption in yellow fluorescent protein
,”
Phys. Chem. Chem. Phys.
16
,
5958
(
2014
).
31.
K. D.
Nanda
and
A. I.
Krylov
, “
Two-photon absorption cross sections within equation-of-motion coupled-cluster formalism using resolution-of-the-identity and Cholesky decomposition representations: Theory, implementation, and benchmarks
,”
J. Chem. Phys.
142
,
064118
(
2015
).
32.
K. D.
Nanda
and
A. I.
Krylov
, “
The effect of polarizable environment on two-photon absorption cross sections characterized by the equation-of-motion coupled-cluster singles and doubles method combined with the effective fragment potential approach
,”
J. Chem. Phys.
149
,
164109
(
2018
).
33.
P.-F.
Loos
,
F.
Lipparini
,
D. A.
Matthews
,
A.
Blondel
, and
D.
Jacquemin
, “
A mountaineering strategy to excited states: Revising reference values with EOM-CC4
,”
J. Chem. Theory Comput.
18
,
4418
4427
(
2022
).
34.
D.
Grabarek
,
E.
Walczak
, and
T.
Andruniów
, “
Assessing the accuracy of various ab initio methods for Geometries and excitation energies of retinal chromophore minimal model by comparison with CASPT3 results
,”
J. Chem. Theory Comput.
12
,
2346
2356
(
2016
).
35.
J. J.
Szymczak
,
M.
Barbatti
, and
H.
Lischka
, “
Is the photoinduced isomerization in retinal protonated Schiff bases a single- or double-torsional process?
,”
J. Phys. Chem. A
113
,
11907
11918
(
2009
).
36.
I.
Rivalta
,
A.
Nenov
, and
M.
Garavelli
, “
Modelling retinal chromophores photoisomerization: From minimal models in vacuo to ultimate bidimensional spectroscopy in rhodopsins
,”
Phys. Chem. Chem. Phys.
16
,
16865
16879
(
2014
).
37.
O.
Valsson
and
C.
Filippi
, “
Photoisomerization of model retinal chromophores: Insight from quantum Monte Carlo and multiconfigurational perturbation theory
,”
J. Chem. Theory Comput.
6
,
1275
1292
(
2010
).
38.
J. J.
Szymczak
,
M.
Barbatti
, and
H.
Lischka
, “
Mechanism of ultrafast photodecay in restricted motions in protonated Schiff bases: The pentadieniminium cation
,”
J. Chem. Theory Comput.
4
,
1189
1199
(
2008
).
39.
P.
Zhou
,
J.
Liu
,
K.
Han
, and
G.
He
, “
The photoisomerization of 11-cis-retinal protonated Schiff base in gas phase: Insight from spin-flip density functional theory
,”
J. Comput. Chem.
35
,
109
120
(
2013
).
40.
S.
Gozem
,
A. I.
Krylov
, and
M.
Olivucci
, “
Conical intersection and potential energy surface features of a model retinal chromophore: Comparison of EOM-CC and multireference methods
,”
J. Chem. Theory Comput.
9
,
284
292
(
2012
).
41.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
, “
The second-order approximate coupled cluster singles and doubles model CC2
,”
Chem. Phys. Lett.
243
,
409
418
(
1995
).
42.
G. D.
Purvis
and
R. J.
Bartlett
, “
A. Full coupled-cluster singles and doubles model: The inclusion of disconnected triples
,”
J. Chem. Phys.
76
,
1910
1918
(
1982
).
43.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
, “
Response functions in the CC3 iterative triple excitation model
,”
J. Chem. Phys.
103
,
7429
7441
(
1995
).
44.
H.
Koch
,
O.
Christiansen
,
P.
Jørgensen
,
A. M.
Sanchez de Merás
, and
T.
Helgaker
, “
The CC3 model: An iterative coupled cluster approach including connected triples
,”
J. Chem. Phys.
106
,
1808
1818
(
1997
).
45.
A. D.
Becke
, “
Density-functional exchange-energy approximation with correct asymptotic behavior
,”
Phys. Rev. A
38
,
3098
3100
(
1988
).
46.
C.
Lee
,
W.
Yang
, and
R. G.
Parr
, “
Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density
,”
Phys. Rev. B
37
,
785
789
(
1988
).
47.
A. D.
Becke
, “
Density-functional thermochemistry. III. The role of exact exchange
,”
J. Chem. Phys.
98
,
5648
5652
(
1993
).
48.
C.
Adamo
and
V.
BarOne
, “
Toward reliable adiabatic connection models free from adjustable parameters
,”
Chem. Phys. Lett.
274
,
242
250
(
1997
).
49.
A. D.
Becke
, “
New mixing of Hartree–Fock and local density-functional theories
,”
J. Chem. Phys.
98
,
1372
1377
(
1993
).
50.
T.
Yanai
,
D. P.
Tew
, and
N. C.
Handy
, “
A new hybrid exchange–correlation functional using the coulomb-attenuating method (CAM-B3LYP)
,”
Chem. Phys. Lett.
393
,
51
57
(
2004
).
51.
M.
Chołuj
,
M. M.
Alam
,
M. T. P.
Beerepoot
,
S.
Sitkiewicz
,
E.
Matito
,
K.
Ruud
, and
R.
Zaleśny
, “
Choosing bad versus worse: Predictions of two-photon-absorption strengths based on popular density functional approximations
,”
J. Chem. Theory Comput.
18
,
1046
1060
(
2022
).
52.
P.-O.
Widmark
,
P. k.
Malmqvist
, and
B. O.
Roos
, “
Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions
,”
Theor. Chim. Acta
77
,
291
306
(
1990
).
53.
P.-O.
Widmark
,
B. J.
Persson
, and
B. O.
Roos
, “
Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions
,”
Theor. Chim. Acta
79
,
419
432
(
1991
).
54.
R.
Pou-Amérigo
,
M.
Merchán
,
I.
Nebot-Gil
,
P.-O.
Widmark
, and
B. O.
Roos
, “
Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions
,”
Theor. Chim. Acta
92
,
149
181
(
1995
).
55.
I. F.
Galván
,
M.
Vacher
,
A.
Alavi
,
C.
Angeli
,
F.
Aquilante
,
J.
Autschbach
,
J. J.
Bao
,
S. I.
Bokarev
,
N. A.
Bogdanov
,
R. K.
Carlson
 et al, “
OpenMolcas: From source code to insight
,”
J. Chem. Theory Comput.
15
,
5925
5964
(
2019
).
56.
F.
Aquilante
,
J.
Autschbach
,
A.
Baiardi
,
S.
Battaglia
,
V. A.
Borin
,
L. F.
Chibotaru
,
I.
Conti
,
L.
De Vico
,
M.
Delcey
,
F. I.
Galván
 et al, “
Modern quantum chemistry with [open]MOLCAS
,”
J. Chem. Phys.
152
,
214117
(
2020
).
57.
K.
Aidas
,
C.
Angeli
,
K. L.
Bak
,
V.
Bakken
,
R.
Bast
,
L.
Boman
,
O.
Christiansen
,
R.
Cimiraglia
,
S.
Coriani
,
P.
Dahle
 et al, “
The Dalton quantum chemistry program system
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
4
,
269
284
(
2013
).
58.
See http://daltonprogram.org. for Dalton, a molecular electronic structure program release v2020.0 (
2020
).
59.
T. H.
Dunning
, “
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,”
J. Chem. Phys.
90
,
1007
1023
(
1989
).
60.
R. A.
Kendall
,
T. H.
Dunning
, and
R. J.
Harrison
, “
Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
,”
J. Chem. Phys.
96
,
6796
6806
(
1992
).
61.
R.
Ditchfield
,
W. J.
Hehre
, and
J. A.
Pople
, “
Self-Consistent molecular-orbital methods. IX. An extended Gaussian-type basis for molecular-orbital studies of organic molecules
,”
J. Chem. Phys.
54
,
724
728
(
1971
).
62.
W. J.
Hehre
,
R.
Ditchfield
, and
J. A.
Pople
, “
Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules
,”
J. Chem. Phys.
56
,
2257
2261
(
1972
).
63.
P. C.
Hariharan
and
J. A.
Pople
, “
The influence of polarization functions on molecular orbital hydrogenation energies
,”
Theor. Chim. Acta
28
,
213
222
(
1973
).
64.
T.
Clark
,
J.
Chandrasekhar
,
G. W.
Spitznagel
, and
P. V. R.
Schleyer
, “
Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21 + G. Basis set for first-row elements, Li–F
,”
J. Comput. Chem.
4
,
294
301
(
1983
).
65.
A.
Köhn
and
C.
Hättig
, “
Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation
,”
J. Chem. Phys.
119
,
5021
5036
(
2003
).
66.
P.
Jørgensen
,
H. J.
Jensen
, and
J.
Olsen
, “
Linear response calculations for large scale multiconfiguration self-consistent Field wave functions
,”
J. Chem. Phys.
89
,
3654
3661
(
1988
).
67.
O.
Christiansen
,
A.
Halkier
,
H.
Koch
,
P.
Jørgensen
, and
T.
Helgaker
, “
Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties
,”
J. Chem. Phys.
108
,
2801
2816
(
1998
).
68.
K.
Hald
,
F.
Pawłowski
,
P.
Jørgensen
, and
C.
Hättig
, “
Calculation of frequency-dependent polarizabilities using the approximate coupled-cluster triples model CC3
,”
J. Chem. Phys.
118
,
1292
1300
(
2003
).
69.
O.
Vahtras
,
H.
Ågren
,
P.
Jørgensen
,
H. J. A.
Jensen
,
T.
Helgaker
, and
J.
Olsen
, “
Multiconfigurational quadratic response functions for singlet and triplet perturbations: The phosphorescence lifetime of formaldehyde
,”
J. Chem. Phys.
97
,
9178
9187
(
1992
).
70.
H.
Hettema
,
H. J. A.
Jensen
,
P.
Jørgensen
, and
J.
Olsen
, “
Quadratic response functions for a multiconfigurational self-consistent Field wave function
,”
J. Chem. Phys.
97
,
1174
1190
(
1992
).
71.
H.
Ågren
,
O.
Vahtras
,
H.
Koch
,
P.
Jørgensen
, and
T.
Helgaker
, “
Direct atomic orbital based self-consistent-field calculations of nonlinear molecular properties. Application to the frequency dependent hyperpolarizability of para-nitroaniline
,”
J. Chem. Phys.
98
,
6417
6423
(
1993
).
72.
C.
Hättig
,
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
, “
Frequency-dependent first hyperpolarizabilities using coupled cluster quadratic response theory
,”
Chem. Phys. Lett.
269
,
428
434
(
1997
).
73.
P.
Sałek
,
O.
Vahtras
,
T.
Helgaker
, and
H.
Ågren
, “
Density-functional theory of linear and nonlinear time-dependent molecular properties
,”
J. Chem. Phys.
117
,
9630
9645
(
2002
).
74.
T. D.
Crawford
and
H. F.
Schaefer
, “
An introduction to coupled cluster theory for computational chemists
,”
Rev. Comput. Chem.
14
,
33
136
(
2007
).
75.
P.
Cronstrand
,
Y.
Luo
, and
H.
Ågren
, “
Generalized few-state models for two-photon absorption of conjugated molecules
,”
Chem. Phys. Lett.
352
,
262
269
(
2002
).
76.
J. J.
Eriksen
,
S. P. A.
Sauer
,
K. V.
Mikkelsen
,
O.
Christiansen
,
H. J. A.
Jensen
, and
J.
Kongsted
, “
Failures of TDDFT in describing the lowest intramolecular charge-transfer excitation in para-nitroaniline
,”
Mol. Phys.
111
,
1235
1248
(
2013
).
77.
M.
Broser
,
A.
Spreen
,
P. E.
Konold
,
E.
Peter
,
S.
Adam
,
V.
Borin
,
I.
Schapiro
,
R.
Seifert
,
J. T. M.
Kennis
,
Y. A.
Bernal Sierra
, and
P.
Hegemann
, “
NeoR, A near-infrared absorbing rhodopsin
,”
Nat. Commun.
11
,
5682
(
2020
).
78.
M.
Caricato
,
G. W.
Trucks
,
M. J.
Frisch
, and
K. B.
Wiberg
, “
Oscillator strength: How does TDDFT compare to EOM-CCSD?
,”
J. Chem. Theory Comput.
7
,
456
466
(
2011
).
79.
D.
Robinson
, “
Comparison of the transition dipole moments calculated by TDDFT with high level wave function theory
,”
J. Chem. Theory Comput.
14
,
5303
5309
(
2018
).
80.
D.
Grabarek
and
T.
Andruniów
, “
The role of hydrogen bonds and electrostatic interactions in enhancing two-photon absorption in green and yellow fluorescent proteins
,”
ChemPhysChem
23
,
e202200003
(
2022
).
81.
D.
Grabarek
and
T.
Andruniów
, “
Quantum chemistry study of the multiphoton absorption in enhanced green fluorescent protein at the single amino acid residue level
,”
ChemPhysChem
23
,
e202200335
(
2022
).
82.
R.
Palombo
,
L.
Barneschi
,
L.
Pedraza-González
,
D.
Padula
,
I.
Schapiro
, and
M.
Olivucci
, “
Retinal chromophore charge delocalization and confinement explain the extreme photophysics of neorhodopsin
,”
Nat. Commun.
13
,
6652
(
2022
).

Supplementary Material

You do not currently have access to this content.