Machine learning (ML) continues to revolutionize computational chemistry for accelerating predictions and simulations by training on experimental or accurate but expensive quantum mechanical (QM) calculations. Photodynamics simulations require hundreds of trajectories coupled with multiconfigurational QM calculations of excited-state potential energies surfaces that contribute to the prohibitive computational cost at long timescales and complex organic molecules. ML accelerates photodynamics simulations by combining nonadiabatic photodynamics simulations with an ML model trained with high-fidelity QM calculations of energies, forces, and non-adiabatic couplings. This approach has provided time-dependent molecular structural information for understanding photochemical reaction mechanisms of organic reactions in vacuum and complex environments (i.e., explicit solvation). This review focuses on the fundamentals of QM calculations and ML techniques. We, then, discuss the strategies to balance adequate training data and the computational cost of generating these training data. Finally, we demonstrate the power of applying these ML-photodynamics simulations to understand the origin of reactivities and selectivities of organic photochemical reactions, such as cis–trans isomerization, [2 + 2]-cycloaddition, 4π-electrostatic ring-closing, and hydrogen roaming mechanism.

1.
A.
de Meijere
,
S.
Redlich
,
D.
Frank
,
J.
Magull
,
A.
Hofmeister
,
H.
Menzel
,
B.
Konig
, and
J.
Svoboda
, “
Octacyclopropylcubane and some of its isomers
,”
Angew. Chem. Int. Ed. Engl.
46
(
24
),
4574
4576
(
2007
).
2.
S.
Poplata
,
A.
Troster
,
Y. Q.
Zou
, and
T.
Bach
, “
Recent advances in the synthesis of cyclobutanes by olefin [2 + 2] photocycloaddition reactions
,”
Chem. Rev.
116
(
17
),
9748
9815
(
2016
).
3.
J.
Ma
,
S.
Chen
,
P.
Bellotti
,
R.
Guo
,
F.
Schafer
,
A.
Heusler
,
X.
Zhang
,
C.
Daniliuc
,
M. K.
Brown
,
K. N.
Houk
et al, “
Photochemical intermolecular dearomative cycloaddition of bicyclic azaarenes with alkenes
,”
Science
371
(
6536
),
1338
1345
(
2021
).
4.
M. D.
Karkas
,
J. A.
Porco
, Jr.
, and
C. R.
Stephenson
, “
Photochemical approaches to complex chemotypes: Applications in natural product synthesis
,”
Chem. Rev.
116
(
17
),
9683
9747
(
2016
).
5.
S. P.
Pitre
and
L. E.
Overman
, “
Strategic use of visible-light photoredox catalysis in natural product synthesis
,”
Chem. Rev.
122
(
2
),
1717
1751
(
2022
).
6.
C. S.
Gravatt
,
L.
Melecio-Zambrano
, and
T. P.
Yoon
, “
Olefin-supported cationic copper catalysts for photochemical synthesis of structurally complex cyclobutanes
,”
Angew. Chem. Int. Ed. Engl.
60
(
8
),
3989
3993
(
2021
).
7.
J.
Xie
,
X.
Zhang
,
C.
Shi
,
L.
Pan
,
F.
Hou
,
G.
Nie
,
J.
Xie
,
Q.
Liu
, and
J.-J.
Zou
, “
Self-photosensitized [2 + 2] cycloaddition for synthesis of high-energy-density fuels
,”
Sustainable Energy Fuels
4
(
2
),
911
920
(
2020
).
8.
Y.
Liu
,
Y.
Chen
,
S.
Ma
,
X.
Liu
,
X.
Zhang
,
J.-J.
Zou
, and
L.
Pan
, “
Synthesis of advanced fuel with density higher than 1 g/mL by photoinduced [2 + 2] cycloaddition of norbornene
,”
Fuel
318
,
123629
(
2022
).
9.
K. F.
Biegasiewicz
,
J. R.
Griffiths
,
G. P.
Savage
,
J.
Tsanaktsidis
, and
R.
Priefer
, “
Cubane: 50 years later
,”
Chem. Rev.
115
(
14
),
6719
6745
(
2015
).
10.
L.
Dong
,
Y.
Feng
,
L.
Wang
, and
W.
Feng
, “
Azobenzene-based solar thermal fuels: Design, properties, and applications
,”
Chem. Soc. Rev.
47
(
19
),
7339
7368
(
2018
).
11.
J.
Orrego-Hernandez
,
A.
Dreos
, and
K.
Moth-Poulsen
, “
Engineering of norbornadiene/quadricyclane photoswitches for molecular solar thermal energy storage applications
,”
Acc. Chem. Res.
53
(
8
),
1478
1487
(
2020
).
12.
A.
Lennartson
,
A.
Roffey
, and
K.
Moth-Poulsen
, “
Designing photoswitches for molecular solar thermal energy storage
,”
Tetrahedron Lett.
56
(
12
),
1457
1465
(
2015
).
13.
Z.
Wang
,
P.
Erhart
,
T.
Li
,
Z.-Y.
Zhang
,
D.
Sampedro
,
Z.
Hu
,
H. A.
Wegner
,
O.
Brummel
,
J.
Libuda
,
M. B.
Nielsen
et al, “
Storing energy with molecular photoisomers
,”
Joule
5
(
12
),
3116
3136
(
2021
).
14.
X.
Xu
and
G.
Wang
, “
Molecular solar thermal systems towards phase change and visible light photon energy storage
,”
Small
18
(
16
),
e2107473
(
2022
).
15.
A. K.
Saydjari
,
P.
Weis
, and
S.
Wu
, “
Spanning the solar spectrum: Azopolymer solar thermal fuels for simultaneous UV and visible light storage
,”
Adv. Energy Mater.
7
(
3
),
1601622
(
2017
).
16.
A. U.
Petersen
,
A. I.
Hofmann
,
M.
Fillols
,
M.
Manso
,
M.
Jevric
,
Z.
Wang
,
C. J.
Sumby
,
C.
Muller
, and
K.
Moth-Poulsen
, “
Solar energy storage by molecular norbornadiene-quadricyclane photoswitches: Polymer film devices
,”
Adv. Sci.
6
(
12
),
1900367
(
2019
).
17.
K.
Hull
,
J.
Morstein
, and
D.
Trauner
, “
In vivo photopharmacology
,”
Chem. Rev.
118
(
21
),
10710
10747
(
2018
).
18.
B.
Cox
,
K. I.
Booker-Milburn
,
L. D.
Elliott
,
M.
Robertson-Ralph
, and
V.
Zdorichenko
, “
Escaping from flatland: [2 + 2] photocycloaddition; conformationally constrained sp(3)-rich Scaffolds for lead generation
,”
ACS Med. Chem. Lett.
10
(
11
),
1512
1517
(
2019
).
19.
P. M.
Stanley
,
J.
Haimerl
,
N. B.
Shustova
,
R. A.
Fischer
, and
J.
Warnan
, “
Merging molecular catalysts and metal-organic frameworks for photocatalytic fuel production
,”
Nat. Chem.
14
,
1342
1356
(
2022
).
20.
S. M.
Oburn
,
S.
Huss
,
J.
Cox
,
M. C.
Gerthoffer
,
S.
Wu
,
A.
Biswas
,
M.
Murphy
,
V. H.
Crespi
,
J. V.
Badding
,
S. A.
Lopez
et al, “
Photochemically mediated polymerization of molecular furan and pyridine: Synthesis of nanothreads at reduced pressures
,”
J. Am. Chem. Soc.
144
(
48
),
22026
22034
(
2022
).
21.
M.
Kowalewski
,
K.
Bennett
,
K. E.
Dorfman
, and
S.
Mukamel
, “
Catching conical intersections in the act: Monitoring transient electronic coherences by attosecond stimulated x-ray Raman signals
,”
Phys. Rev. Lett.
115
(
19
),
193003
(
2015
).
22.
I. C. D.
Merritt
,
D.
Jacquemin
, and
M.
Vacher
, “
Attochemistry: Is controlling electrons the future of photochemistry?
,”
J. Phys. Chem. Lett.
12
(
34
),
8404
8415
(
2021
).
23.
T.
Gruhl
,
T.
Weinert
,
M. J.
Rodrigues
,
C. J.
Milne
,
G.
Ortolani
,
K.
Nass
,
E.
Nango
,
S.
Sen
,
P. J. M.
Johnson
,
C.
Cirelli
et al, “
Ultrafast structural changes direct the first molecular events of vision
,”
Nature
615
(
7954
),
939
944
(
2023
).
24.
Y.
Boeije
and
M.
Olivucci
, “
From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions
,”
Chem. Soc. Rev.
52
(
8
),
2643
2687
(
2023
).
25.
J. P.
Zobel
and
L.
González
, “
The quest to simulate excited-state dynamics of transition metal complexes
,”
JACS Au
1
,
1116
1140
(
2021
).
26.
R.
Crespo-Otero
and
M.
Barbatti
, “
Recent advances and perspectives on nonadiabatic mixed quantum-classical dynamics
,”
Chem. Rev.
118
(
15
),
7026
7068
(
2018
).
27.
W.
Weber
and
W.
Thiel
, “
Orthogonalization corrections for semiempirical methods
,”
Theor. Chem. Acc.
103
(
6
),
495
506
(
2000
).
28.
A.
Koslowski
,
M. E.
Beck
, and
W.
Thiel
, “
Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach
,”
J. Comput. Chem.
24
(
6
),
714
726
(
2003
).
29.
J. J.
Kranz
,
M.
Elstner
,
B.
Aradi
,
T.
Frauenheim
,
V.
Lutsker
,
A. D.
Garcia
, and
T. A.
Niehaus
, “
Time-dependent extension of the long-range corrected density functional based tight-binding method
,”
J. Chem. Theory Comput.
13
(
4
),
1737
1747
(
2017
).
30.
J. P.
Zobel
,
M.
Heindl
,
F.
Plasser
,
S.
Mai
, and
L.
Gonzalez
, “
Surface hopping dynamics on vibronic coupling models
,”
Acc. Chem. Res.
54
(
20
),
3760
3771
(
2021
).
31.
F.
Plasser
,
S.
Gomez
,
M.
Menger
,
S.
Mai
, and
L.
Gonzalez
, “
Highly efficient surface hopping dynamics using a linear vibronic coupling model
,”
Phys. Chem. Chem. Phys.
21
(
1
),
57
69
(
2018
).
32.
S.
Seritan
,
C.
Bannwarth
,
B. S.
Fales
,
E. G.
Hohenstein
,
C. M.
Isborn
,
S. I. L.
Kokkila‐Schumacher
,
X.
Li
,
F.
Liu
,
N.
Luehr
,
J. W.
Snyder
et al, “
TeraChem: A graphical processing unit‐accelerated electronic structure package for large‐scale ab initio molecular dynamics
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
11
(
2
),
e1494
(
2020
).
33.
A.
Nandy
,
C.
Duan
,
M. G.
Taylor
,
F.
Liu
,
A. H.
Steeves
, and
H. J.
Kulik
, “
Computational discovery of transition-metal complexes: From high-throughput screening to machine learning
,”
Chem. Rev.
121
(
16
),
9927
10000
(
2021
).
34.
P.
Friederich
,
F.
Hase
,
J.
Proppe
, and
A.
Aspuru-Guzik
, “
Machine-learned potentials for next-generation matter simulations
,”
Nat. Mater.
20
(
6
),
750
761
(
2021
).
35.
S.
Jiang
,
G.
Malkomes
,
B.
Moseley
, and
R.
Garnett
, “
Efficient nonmyopic active search with applications in drug and materials discovery
,” arXiv:1811.08871 (
2018
).
36.
S.
Jiang
,
G.
Malkomes
,
G.
Converse
,
A.
Shofner
,
B.
Moseley
, and
R.
Garnett
, “
Efficient nonmyopic active search
,” in
Proceedings of the 34th International Conference on Machine Learning Research
(
2017
).
37.
T.
Lewis‐Atwell
,
P. A.
Townsend
, and
M. N.
Grayson
, “
Machine learning activation energies of chemical reactions
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
12
,
e1593
(
2021
).
38.
A. A.
Peterson
, “
Acceleration of saddle-point searches with machine learning
,”
J. Chem. Phys.
145
(
7
),
074106
(
2016
).
39.
Z. D.
Pozun
,
K.
Hansen
,
D.
Sheppard
,
M.
Rupp
,
K. R.
Muller
, and
G.
Henkelman
, “
Optimizing transition states via kernel-based machine learning
,”
J. Chem. Phys.
136
(
17
),
174101
(
2012
).
40.
S.
Choi
, “
Prediction of transition state structures of gas-phase chemical reactions via machine learning
,”
Nat. Commun.
14
(
1
),
1168
(
2023
).
41.
J.
Hermann
,
Z.
Schatzle
, and
F.
Noe
, “
Deep-neural-network solution of the electronic Schrodinger equation
,”
Nat. Chem.
12
(
10
),
891
897
(
2020
).
42.
J.
Han
,
L.
Zhang
, and
W.
E
, “
Solving many-electron Schrödinger equation using deep neural networks
,”
J. Comput. Phys.
399
,
108929
(
2019
).
43.
K. T.
Schutt
,
M.
Gastegger
,
A.
Tkatchenko
,
K. R.
Muller
, and
R. J.
Maurer
, “
Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions
,”
Nat. Commun.
10
(
1
),
5024
(
2019
).
44.
M.
Gastegger
,
A.
McSloy
,
M.
Luya
,
K. T.
Schutt
, and
R. J.
Maurer
, “
A deep neural network for molecular wave functions in quasi-atomic minimal basis representation
,”
J. Chem. Phys.
153
(
4
),
044123
(
2020
).
45.
Y.
Zhou
,
J.
Wu
,
S.
Chen
, and
G.
Chen
, “
Toward the exact exchange-correlation potential: A three-dimensional convolutional neural network construct
,”
J. Phys. Chem. Lett.
10
(
22
),
7264
7269
(
2019
).
46.
S.
Dick
and
M.
Fernandez-Serra
, “
Machine learning accurate exchange and correlation functionals of the electronic density
,”
Nat. Commun.
11
(
1
),
3509
(
2020
).
47.
M.
Gastegger
,
J.
Behler
, and
P.
Marquetand
, “
Machine learning molecular dynamics for the simulation of infrared spectra
,”
Chem. Sci.
8
(
10
),
6924
6935
(
2017
).
48.
J.
Westermayr
and
P.
Marquetand
, “
Deep learning for UV absorption spectra with SchNarc: First steps toward transferability in chemical compound space
,”
J. Chem. Phys.
153
(
15
),
154112
(
2020
).
49.
J.
Westermayr
and
R. J.
Maurer
, “
Physically inspired deep learning of molecular excitations and photoemission spectra
,”
Chem. Sci.
12
(
32
),
10755
10764
(
2021
).
50.
P.
Gao
,
J.
Zhang
,
Q.
Peng
,
J.
Zhang
, and
V. A.
Glezakou
, “
General protocol for the accurate prediction of molecular (13)C/(1)H NMR chemical shifts via machine learning augmented DFT
,”
J. Chem. Inf. Model.
60
(
8
),
3746
3754
(
2020
).
51.
J.
Westermayr
and
P.
Marquetand
, “
Machine learning for electronically excited states of molecules
,”
Chem. Rev.
121
(
16
),
9873
9926
(
2021
).
52.
P. O.
Dral
and
M.
Barbatti
, “
Molecular excited states through a machine learning lens
,”
Nat. Rev. Chem.
5
(
6
),
388
405
(
2021
).
53.
J.
Behler
, “
Four generations of high-dimensional neural network potentials
,”
Chem. Rev.
121
(
16
),
10037
10072
(
2021
).
54.
K. T.
Schutt
,
F.
Arbabzadah
,
S.
Chmiela
,
K. R.
Muller
, and
A.
Tkatchenko
, “
Quantum-chemical insights from deep tensor neural networks
,”
Nat. Commun.
8
,
13890
(
2017
).
55.
O. T.
Unke
and
M.
Meuwly
, “
PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges
,”
J. Chem. Theory Comput.
15
(
6
),
3678
3693
(
2019
).
56.
J. S.
Smith
,
O.
Isayev
, and
A. E.
Roitberg
, “
ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
,”
Chem. Sci.
8
(
4
),
3192
3203
(
2017
).
57.
X.
Gao
,
F.
Ramezanghorbani
,
O.
Isayev
,
J. S.
Smith
, and
A. E.
Roitberg
, “
TorchANI: A free and open source PyTorch-based deep learning implementation of the ANI neural network potentials
,”
J. Chem. Inf. Model.
60
(
7
),
3408
3415
(
2020
).
58.
L.
Zhang
,
J.
Han
,
H.
Wang
,
W. A.
Saidi
,
R.
Car
, and
E.
Weinan
, “
End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems
,” in
Proceedings of the 32nd International Conference on Neural Information Processing Systems
,
Montréal, Canada
(
2018
).
59.
S.
Chmiela
,
H. E.
Sauceda
,
K. R.
Muller
, and
A.
Tkatchenko
, “
Towards exact molecular dynamics simulations with machine-learned force fields
,”
Nat. Commun.
9
(
1
),
3887
(
2018
).
60.
P. O.
Dral
,
F.
Ge
,
B. X.
Xue
,
Y. F.
Hou
,
M.
Pinheiro
, Jr.
,
J.
Huang
, and
M.
Barbatti
, “
MLatom 2: An integrative platform for atomistic machine learning
,”
Top. Curr. Chem.
379
(
4
),
27
(
2021
).
61.
D.
Koner
and
M.
Meuwly
, “
Permutationally invariant, reproducing Kernel-based potential energy surfaces for polyatomic molecules: From formaldehyde to acetone
,”
J. Chem. Theory Comput.
16
(
9
),
5474
5484
(
2020
).
62.
A. P.
Bartok
,
M. C.
Payne
,
R.
Kondor
, and
G.
Csanyi
, “
Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons
,”
Phys. Rev. Lett.
104
(
13
),
136403
(
2010
).
63.
S.
Batzner
,
A.
Musaelian
,
L.
Sun
,
M.
Geiger
,
J. P.
Mailoa
,
M.
Kornbluth
,
N.
Molinari
,
T. E.
Smidt
, and
B.
Kozinsky
, “
E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
,”
Nat. Commun.
13
(
1
),
2453
(
2022
).
64.
A.
Musaelian
,
S.
Batzner
,
A.
Johansson
,
L.
Sun
,
C. J.
Owen
,
M.
Kornbluth
, and
B.
Kozinsky
, “
Learning local equivariant representations for large-scale atomistic dynamics
,”
Nat. Commun.
14
(
1
),
579
(
2023
).
65.
P. O.
Dral
, “
MLatom: A program package for quantum chemical research assisted by machine learning
,”
J. Comput. Chem.
40
(
26
),
2339
2347
(
2019
).
66.
Y.
Xie
,
J.
Vandermause
,
L.
Sun
,
A.
Cepellotti
, and
B.
Kozinsky
, “
Bayesian force fields from active learning for simulation of inter-dimensional transformation of stanene
,”
npj Comput. Mater.
7
(
1
),
40
(
2021
).
67.
J.
Westermayr
,
F. A.
Faber
,
A. S.
Christensen
,
O. A.
von Lilienfeld
, and
P.
Marquetand
, “
Neural networks and kernel ridge regression for excited states dynamics of CH2NH2+: From single-state to multi-state representations and multi-property machine learning models
,”
Mach. Learn.: Sci. Technol.
1
(
2
),
025009
(
2020
).
68.
M.
Pinheiro
, Jr.
,
F.
Ge
,
N.
Ferre
,
P. O.
Dral
, and
M.
Barbatti
, “
Choosing the right molecular machine learning potential
,”
Chem. Sci.
12
(
43
),
14396
14413
(
2021
).
69.
L. E. H.
Rodríguez
,
A.
Ullah
,
K. J. R.
Espinosa
,
P. O.
Dral
, and
A. A.
Kananenka
, “
A comparative study of different machine learning methods for dissipative quantum dynamics
,”
Mach. Learn.: Sci. Technol.
3
(
4
),
045016
(
2022
).
70.
M.
Rupp
,
A.
Tkatchenko
,
K. R.
Muller
, and
O. A.
von Lilienfeld
, “
Fast and accurate modeling of molecular atomization energies with machine learning
,”
Phys. Rev. Lett.
108
(
5
),
058301
(
2012
).
71.
J.
Westermayr
,
M.
Gastegger
,
M.
Menger
,
S.
Mai
,
L.
Gonzalez
, and
P.
Marquetand
, “
Machine learning enables long time scale molecular photodynamics simulations
,”
Chem. Sci.
10
(
35
),
8100
8107
(
2019
).
72.
K.
Hansen
,
F.
Biegler
,
R.
Ramakrishnan
,
W.
Pronobis
,
O. A.
von Lilienfeld
,
K. R.
Muller
, and
A.
Tkatchenko
, “
Machine learning predictions of molecular properties: Accurate many-body potentials and nonlocality in chemical space
,”
J. Phys. Chem. Lett.
6
(
12
),
2326
2331
(
2015
).
73.
K.
Hansen
,
G.
Montavon
,
F.
Biegler
,
S.
Fazli
,
M.
Rupp
,
M.
Scheffler
,
O. A.
von Lilienfeld
,
A.
Tkatchenko
, and
K. R.
Muller
, “
Assessment and validation of machine learning methods for predicting molecular atomization energies
,”
J. Chem. Theory Comput.
9
(
8
),
3404
3419
(
2013
).
74.
C.
Qu
,
Q.
Yu
, and
J. M.
Bowman
, “
Permutationally invariant potential energy surfaces
,”
Annu. Rev. Phys. Chem.
69
,
151
175
(
2018
).
75.
J.
Li
,
R.
Stein
,
D. M.
Adrion
, and
S. A.
Lopez
, “
Machine-learning photodynamics simulations uncover the role of substituent effects on the photochemical formation of cubanes
,”
J. Am. Chem. Soc.
143
(
48
),
20166
20175
(
2021
).
76.
J.
Li
and
S. A.
Lopez
, “
Excited-state distortions promote the photochemical 4pi-electrocyclizations of fluorobenzenes via machine learning accelerated photodynamics simulations
,”
Chem. Eur. J.
28
,
e202200651
(
2022
).
77.
J.
Behler
, “
Atom-centered symmetry functions for constructing high-dimensional neural network potentials
,”
J. Chem. Phys.
134
(
7
),
074106
(
2011
).
78.
A. P.
Bartók
,
R.
Kondor
, and
G.
Csányi
, “
On representing chemical environments
,”
Phys. Rev. B: Condens. Matter
87
(
18
),
184115
(
2013
).
79.
A. S.
Christensen
,
L. A.
Bratholm
,
F. A.
Faber
, and
O.
Anatole von Lilienfeld
, “
FCHL revisited: Faster and more accurate quantum machine learning
,”
J. Chem. Phys.
152
(
4
),
044107
(
2020
).
80.
S. N.
Pozdnyakov
,
M. J.
Willatt
,
A. P.
Bartok
,
C.
Ortner
,
G.
Csanyi
, and
M.
Ceriotti
, “
Incompleteness of atomic structure representations
,”
Phys. Rev. Lett.
125
(
16
),
166001
(
2020
).
81.
J.
Gilmer
,
S. S.
Schoenholz
,
P. F.
Riley
,
O.
Vinyals
, and
G. E.
Dahl
, arXiv:1704.01212 (
2017
).
82.
K. T.
Schutt
,
H. E.
Sauceda
,
P. J.
Kindermans
,
A.
Tkatchenko
, and
K. R.
Muller
, “
SchNet—A deep learning architecture for molecules and materials
,”
J. Chem. Phys.
148
(
24
),
241722
(
2018
).
83.
N.
Lubbers
,
J. S.
Smith
, and
K.
Barros
, “
Hierarchical modeling of molecular energies using a deep neural network
,”
J. Chem. Phys.
148
(
24
),
241715
(
2018
).
84.
O. T.
Unke
,
S.
Chmiela
,
M.
Gastegger
,
K. T.
Schutt
,
H. E.
Sauceda
, and
K. R.
Muller
, “
SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects
,”
Nat. Commun.
12
(
1
),
7273
(
2021
).
85.
D.
Tang
,
L.
Jia
,
L.
Shen
, and
W. H.
Fang
, “
Fewest-switches surface hopping with long short-term memory networks
,”
J. Phys. Chem. Lett.
13
(
44
),
10377
10387
(
2022
).
86.
I.
Goodfellow
,
Y.
Bengio
, and
A.
Courville
,
Deep Learning
(
MIT Press
,
2016
).
87.
A. A.
Kananenka
,
C. Y.
Hsieh
,
J.
Cao
, and
E.
Geva
, “
Accurate long-time mixed quantum-classical Liouville dynamics via the transfer tensor method
,”
J. Phys. Chem. Lett.
7
(
23
),
4809
4814
(
2016
).
88.
K.
Lin
,
J.
Peng
,
F. L.
Gu
, and
Z.
Lan
, “
Simulation of open quantum dynamics with bootstrap-based long short-term memory recurrent neural network
,”
J. Phys. Chem. Lett.
12
(
41
),
10225
10234
(
2021
).
89.
K.
Lin
,
J.
Peng
,
C.
Xu
,
F. L.
Gu
, and
Z.
Lan
, “
Trajectory propagation of symmetrical quasi-classical dynamics with Meyer-Miller mapping Hamiltonian using machine learning
,”
J. Phys. Chem. Lett.
13
(
50
),
11678
11688
(
2022
).
90.
S.
Reiter
,
D.
Keefer
, and
R.
de Vivie-Riedle
, “
Exact quantum dynamics (wave packets) in reduced dimensionality
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
355
381
.
91.
F.
Agostini
and
E. K. U.
Gross
, “
Exact factorization of the electron–nuclear wave function: Theory and applications
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
531
562
.
92.
M.
Bonfanti
,
G. A.
Worth
, and
I.
Burghardt
, “
Multi-configuration time-dependent Hartree methods: From quantum to semiclassical and quantum-classical
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
383
411
.
93.
B. F. E.
Curchod
, “
Full and ab initio multiple spawning
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
435
467
.
94.
R.
Kapral
, “
Quantum dynamics in open quantum-classical systems
,”
J. Phys.: Condens. Matter
27
(
7
),
073201
(
2015
).
95.
A.
Kirrander
and
M.
Vacher
, “
Ehrenfest methods for electron and nuclear dynamics
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
469
497
.
96.
S.
Mai
,
P.
Marquetand
, and
L.
González
, “
Surface hopping molecular dynamics
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
499
530
.
97.
G. W.
Richings
and
S.
Habershon
, “
Predicting molecular photochemistry using machine-learning-enhanced quantum dynamics simulations
,”
Acc. Chem. Res.
55
(
2
),
209
220
(
2022
).
98.
J. C.
Tully
and
R. K.
Preston
, “
Trajectory surface hopping approach to nonadiabatic molecular collisions: The reaction of H+ with D2
,”
J. Chem. Phys
55
(
2
),
562
572
(
1971
).
99.
J. C.
Tully
, “
Molecular dynamics with electronic transitions
,”
J. Chem. Phys.
93
(
2
),
1061
1071
(
1990
).
100.
S.
Hammes‐Schiffer
and
J. C.
Tully
, “
Proton transfer in solution: Molecular dynamics with quantum transitions
,”
J. Chem. Phys.
101
(
6
),
4657
4667
(
1994
).
101.
S.
Mai
,
P.
Marquetand
, and
L.
González
, “
A general method to describe intersystem crossing dynamics in trajectory surface hopping
,”
Int. J. Quantum Chem.
115
(
18
),
1215
1231
(
2015
).
102.
G.
Cui
and
W.
Thiel
, “
Generalized trajectory surface-hopping method for internal conversion and intersystem crossing
,”
J. Chem. Phys.
141
(
12
),
124101
(
2014
).
103.
W.
Park
,
J.
Shen
,
S.
Lee
,
P.
Piecuch
,
M.
Filatov
, and
C. H.
Choi
, “
Internal conversion between bright (1(1)Bu(+)) and dark (2(1)Ag(-)) states in s-trans-butadiene and s-trans-hexatriene
,”
J. Phys. Chem. Lett.
12
(
39
),
9720
9729
(
2021
).
104.
I.
Polyak
,
L.
Hutton
,
R.
Crespo-Otero
,
M.
Barbatti
, and
P. J.
Knowles
, “
Ultrafast photoinduced dynamics of 1,3-cyclohexadiene using XMS-CASPT2 surface hopping
,”
J. Chem. Theory Comput.
15
(
7
),
3929
3940
(
2019
).
105.
X.
Yang
,
M.
Manathunga
,
S.
Gozem
,
J.
Leonard
,
T.
Andruniow
, and
M.
Olivucci
, “
Quantum-classical simulations of rhodopsin reveal excited-state population splitting and its effects on quantum efficiency
,”
Nat. Chem.
14
(
4
),
441
449
(
2022
).
106.
M.
Ben-Nun
,
J.
Quenneville
, and
T. J.
Martínez
, “
Ab initio multiple spawning: Photochemistry from first principles quantum molecular dynamics
,”
J. Phys. Chem. A
104
(
22
),
5161
5175
(
2000
).
107.
M.
Ben-Nun
and
T. J.
Martínez
, “
Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem
,”
J. Chem. Phys.
108
(
17
),
7244
7257
(
1998
).
108.
J. K.
Yu
,
C.
Bannwarth
,
R.
Liang
,
E. G.
Hohenstein
, and
T. J.
Martinez
, “
Nonadiabatic dynamics simulation of the wavelength-dependent photochemistry of azobenzene excited to the npi* and pipi* excited states
,”
J. Am. Chem. Soc.
142
(
49
),
20680
20690
(
2020
).
109.
L.
Liu
,
W. H.
Fang
, and
T. J.
Martinez
, “
A nitrogen out-of-plane (NOOP) mechanism for imine-based light-driven molecular motors
,”
J. Am. Chem. Soc.
145
(
12
),
6888
6898
(
2023
).
110.
J.
Westermayr
,
M.
Gastegger
, and
P.
Marquetand
, “
Combining SchNet and SHARC: The SchNarc machine learning approach for excited-state dynamics
,”
J. Phys. Chem. Lett.
11
(
10
),
3828
3834
(
2020
).
111.
J.
Li
,
P.
Reiser
,
B. R.
Boswell
,
A.
Eberhard
,
N. Z.
Burns
,
P.
Friederich
, and
S. A.
Lopez
, “
Automatic discovery of photoisomerization mechanisms with nanosecond machine learning photodynamics simulations
,”
Chem. Sci.
12
(
14
),
5302
5314
(
2021
).
112.
D.
Hu
,
Y.
Xie
,
X.
Li
,
L.
Li
, and
Z.
Lan
, “
Inclusion of machine learning kernel ridge regression potential energy surfaces in on-the-fly nonadiabatic molecular dynamics simulation
,”
J. Phys. Chem. Lett.
9
(
11
),
2725
2732
(
2018
).
113.
W. K.
Chen
,
X. Y.
Liu
,
W. H.
Fang
,
P. O.
Dral
, and
G.
Cui
, “
Deep learning for nonadiabatic excited-state dynamics
,”
J. Phys. Chem. Lett.
9
(
23
),
6702
6708
(
2018
).
114.
M.
Ardiansyah
and
K. R.
Brorsen
, “
Mixed quantum-classical dynamics with machine learning-based potentials via Wigner sampling
,”
J. Phys. Chem. A
124
(
44
),
9326
9331
(
2020
).
115.
S.
Axelrod
,
E.
Shakhnovich
, and
R.
Gomez-Bombarelli
, “
Excited state non-adiabatic dynamics of large photoswitchable molecules using a chemically transferable machine learning potential
,”
Nat. Commun.
13
(
1
),
3440
(
2022
).
116.
T.
Ishida
,
S.
Nanbu
, and
H.
Nakamura
, “
Clarification of nonadiabatic chemical dynamics by the Zhu-Nakamura theory of nonadiabatic transition: From tri-atomic systems to reactions in solutions
,”
Int. Rev. Phys. Chem.
36
(
2
),
229
285
(
2017
).
117.
L.
Yu
,
C.
Xu
,
Y.
Lei
,
C.
Zhu
, and
Z.
Wen
, “
Trajectory-based nonadiabatic molecular dynamics without calculating nonadiabatic coupling in the avoided crossing case: Trans<–>cis photoisomerization in azobenzene
,”
Phys. Chem. Chem. Phys.
16
(
47
),
25883
25895
(
2014
).
118.
L.
Yue
,
L.
Yu
,
C.
Xu
,
C.
Zhu
, and
Y.
Liu
, “
Quantum yields of singlet and triplet chemiexcitation of dimethyl 1,2-dioxetane: Ab initio nonadiabatic molecular dynamic simulations
,”
Phys. Chem. Chem. Phys.
22
(
20
),
11440
11451
(
2020
).
119.
D.
Shchepanovska
,
R. J.
Shannon
,
B. F. E.
Curchod
, and
D. R.
Glowacki
, “
Nonadiabatic kinetics in the intermediate coupling regime: Comparing molecular dynamics to an energy-grained master equation
,”
J. Phys. Chem. A
125
(
16
),
3473
3488
(
2021
).
120.
L.
Yue
,
L.
Yu
,
C.
Xu
,
Y.
Lei
,
Y.
Liu
, and
C.
Zhu
, “
Benchmark performance of global switching versus local switching for trajectory surface hopping molecular dynamics simulation: Cis<–>trans azobenzene photoisomerization
,”
ChemPhysChem
18
(
10
),
1274
1287
(
2017
).
121.
M. T.
do Casal
,
J. M.
Toldo
,
M.
Pinheiro
, Jr.
, and
M.
Barbatti
, “
Fewest switches surface hopping with Baeck-An couplings
,”
Open Res. Europe
1
,
49
(
2022
).
122.
K. K.
Baeck
and
H.
An
, “
Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only
,”
J. Chem. Phys.
146
(
6
),
064107
(
2017
).
123.
Y.
Shu
,
L.
Zhang
,
X.
Chen
,
S.
Sun
,
Y.
Huang
, and
D. G.
Truhlar
, “
Nonadiabatic dynamics algorithms with only potential energies and gradients: Curvature-driven coherent switching with decay of mixing and curvature-driven trajectory surface hopping
,”
J. Chem. Theory Comput.
18
(
3
),
1320
1328
(
2022
).
124.
M.
Huix-Rotllant
,
N.
Ferré
, and
M.
Barbatti
, “
Time-dependent density functional theory
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
13
46
.
125.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
, “
The second-order approximate coupled cluster singles and doubles model CC2
,”
Chem. Phys. Lett.
243
(
5–6
),
409
418
(
1995
).
126.
M.
Wormit
,
D. R.
Rehn
,
P. H. P.
Harbach
,
J.
Wenzel
,
C. M.
Krauter
,
E.
Epifanovsky
, and
A.
Dreuw
, “
Investigating excited electronic states using the algebraic diagrammatic construction (ADC) approach of the polarisation propagator
,”
Mol. Phys.
112
(
5–6
),
774
784
(
2014
).
127.
A.
Dreuw
and
M.
Wormit
, “
The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
5
(
1
),
82
95
(
2015
).
128.
B. G.
Levine
,
C.
Ko
,
J.
Quenneville
, and
T. J.
MartÍnez
, “
Conical intersections and double excitations in time-dependent density functional theory
,”
Mol. Phys.
104
(
5–7
),
1039
1051
(
2007
).
129.
M.
Huix-Rotllant
,
A.
Nikiforov
,
W.
Thiel
, and
M.
Filatov
, “
Description of conical intersections with density functional methods
,”
Top. Curr. Chem.
368
,
445
476
(
2016
).
130.
S.
Lee
,
S.
Shostak
,
M.
Filatov
, and
C. H.
Choi
, “
Conical intersections in organic molecules: Benchmarking mixed-reference spin-flip time-dependent DFT (MRSF-TD-DFT) vs spin-flip TD-DFT
,”
J. Phys. Chem. A
123
(
30
),
6455
6462
(
2019
).
131.
D.
Casanova
and
A. I.
Krylov
, “
Spin-flip methods in quantum chemistry
,”
Phys. Chem. Chem. Phys.
22
(
8
),
4326
4342
(
2020
).
132.
Y.
Horbatenko
,
S.
Sadiq
,
S.
Lee
,
M.
Filatov
, and
C. H.
Choi
, “
Mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) as a simple yet accurate method for diradicals and diradicaloids
,”
J. Chem. Theory Comput.
17
(
2
),
848
859
(
2021
).
133.
I. S.
Lee
,
M.
Filatov
, and
S. K.
Min
, “
Formulation and implementation of the spin-restricted ensemble-referenced Kohn-Sham method in the context of the density functional tight binding approach
,”
J. Chem. Theory Comput.
15
(
5
),
3021
3032
(
2019
).
134.
Y.
Yang
,
L.
Shen
,
D.
Zhang
, and
W.
Yang
, “
Conical intersections from particle-particle random phase and Tamm-Dancoff approximations
,”
J. Phys. Chem. Lett.
7
(
13
),
2407
2411
(
2016
).
135.
Y.
Yang
,
D.
Peng
,
E. R.
Davidson
, and
W.
Yang
, “
Singlet-triplet energy gaps for diradicals from particle-particle random phase approximation
,”
J. Phys. Chem. A
119
(
20
),
4923
4932
(
2015
).
136.
H.
van Aggelen
,
Y.
Yang
, and
W.
Yang
, “
Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation
,”
Phys. Rev. A
88
(
3
),
030501
(
2013
).
137.
J. K.
Yu
,
C.
Bannwarth
,
E. G.
Hohenstein
, and
T. J.
Martinez
, “
Ab initio nonadiabatic molecular dynamics with hole-hole Tamm-Dancoff approximated density functional theory
,”
J. Chem. Theory Comput.
16
(
9
),
5499
5511
(
2020
).
138.
Q.
Yu
,
S.
Roy
, and
S.
Hammes-Schiffer
, “
Nonadiabatic dynamics of hydrogen tunneling with nuclear-electronic orbital multistate density functional theory
,”
J. Chem. Theory Comput.
18
(
12
),
7132
7141
(
2022
).
139.
Y.
Lu
and
J.
Gao
, “
Multistate density functional theory of excited states
,”
J. Phys. Chem. Lett.
13
(
33
),
7762
7769
(
2022
).
140.
J.
Gao
,
A.
Grofe
,
H.
Ren
, and
P.
Bao
, “
Beyond Kohn-Sham approximation: hybrid multistate wave function and density functional theory
,”
J. Phys. Chem. Lett.
7
(
24
),
5143
5149
(
2016
).
141.
K.
Andersson
,
P. A.
Malmqvist
,
B. O.
Roos
,
A. J.
Sadlej
, and
K.
Wolinski
, “
Second-order perturbation theory with a CASSCF reference function
,”
J. Phys. Chem.
94
(
14
),
5483
5488
(
2002
).
142.
K.
Andersson
,
P. Å.
Malmqvist
, and
B. O.
Roos
, “
Second‐order perturbation theory with a complete active space self‐consistent field reference function
,”
J. Chem. Phys.
96
(
2
),
1218
1226
(
1992
).
143.
P. G.
Szalay
,
T.
Muller
,
G.
Gidofalvi
,
H.
Lischka
, and
R.
Shepard
, “
Multiconfiguration self-consistent field and multireference configuration interaction methods and applications
,”
Chem. Rev.
112
(
1
),
108
181
(
2012
).
144.
D. C.
Sherrill
and
H. F.
Schaefer
, “
The configuration interaction method: Advances in highly correlated approaches
,” in
Advances in Quantum Chemistry
, edited by
J. R. S.
Per-Olov Löwdin
,
M. C.
Zerner
, and
E.
Brändas
(Academic,
1999
), pp.
143
269
.
145.
B. O.
Roos
,
R.
Lindh
,
P. Å.
Malmqvist
,
V.
Veryazov
, and
P.-O.
Widmark
,
Multiconfigurational Quantum Chemistry
(
Wiley
,
2016
).
146.
H.
Lischka
,
D.
Nachtigallova
,
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
(
15
),
7293
7361
(
2018
).
147.
T.
Shiozaki
,
W.
Gyorffy
,
P.
Celani
, and
H. J.
Werner
, “
Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients
,”
J. Chem. Phys.
135
(
8
),
081106
(
2011
).
148.
S.
Battaglia
and
R.
Lindh
, “
Extended dynamically weighted CASPT2: The best of two worlds
,”
J. Chem. Theory Comput.
16
(
3
),
1555
1567
(
2020
).
149.
S.
Battaglia
and
R.
Lindh
, “
On the role of symmetry in XDW-CASPT2
,”
J. Chem. Phys.
154
(
3
),
034102
(
2021
).
150.
C. J.
Stein
and
M.
Reiher
, “
Automated selection of active orbital spaces
,”
J. Chem. Theory Comput.
12
(
4
),
1760
1771
(
2016
).
151.
B. W.
Kaufold
,
N.
Chintala
,
P.
Pandeya
, and
S. S.
Dong
, “
Automated active space selection with dipole moments
,”
J. Chem. Theory Comput.
19
(
9
),
2469
2483
(
2023
).
152.
D. S.
Levine
,
D.
Hait
,
N. M.
Tubman
,
S.
Lehtola
,
K. B.
Whaley
, and
M.
Head-Gordon
, “
CASSCF with extremely large active spaces using the adaptive sampling configuration interaction method
,”
J. Chem. Theory Comput.
16
(
4
),
2340
2354
(
2020
).
153.
J. W.
Park
, “
Near-exact CASSCF-level geometry optimization with a large active space using adaptive sampling configuration interaction self-consistent field corrected with second-order perturbation theory (ASCI-SCF-PT2)
,”
J. Chem. Theory Comput.
17
(
7
),
4092
4104
(
2021
).
154.
L.
Freitag
and
M.
Reiher
, “
The density matrix renormalization group for strong correlation in ground and excited states
,” in
Quantum Chemistry and Dynamics of Excited States
(
Wiley
,
2020
), pp.
205
245
.
155.
L.
Freitag
,
Y.
Ma
,
A.
Baiardi
,
S.
Knecht
, and
M.
Reiher
, “
Approximate analytical gradients and nonadiabatic couplings for the state-average density matrix renormalization group self-consistent-field method
,”
J. Chem. Theory Comput.
15
(
12
),
6724
6737
(
2019
).
156.
S.
Mai
,
A. J.
Atkins
,
F.
Plasser
, and
L.
Gonzalez
, “
The influence of the electronic structure method on intersystem crossing dynamics. The case of thioformaldehyde
,”
J. Chem. Theory Comput.
15
(
6
),
3470
3480
(
2019
).
157.
S.
Gomez
,
L. M.
Ibele
, and
L.
Gonzalez
, “
The 3s Rydberg state as a doorway state in the ultrafast dynamics of 1,1-difluoroethylene
,”
Phys. Chem. Chem. Phys.
21
(
9
),
4871
4878
(
2019
).
158.
M. D. C.
Marin
,
D.
Agathangelou
,
Y.
Orozco-Gonzalez
,
A.
Valentini
,
Y.
Kato
,
R.
Abe-Yoshizumi
,
H.
Kandori
,
A.
Choi
,
K. H.
Jung
,
S.
Haacke
et al, “
Fluorescence enhancement of a microbial rhodopsin via electronic reprogramming
,”
J. Am. Chem. Soc.
141
(
1
),
262
271
(
2019
).
159.
B.
Helmich-Paris
, “
Benchmarks for electronically excited states with CASSCF methods
,”
J. Chem. Theory Comput.
15
(
7
),
4170
4179
(
2019
).
160.
G.
Li Manni
,
R. K.
Carlson
,
S.
Luo
,
D.
Ma
,
J.
Olsen
,
D. G.
Truhlar
, and
L.
Gagliardi
, “
Multiconfiguration pair-density functional theory
,”
J. Chem. Theory Comput.
10
(
9
),
3669
3680
(
2014
).
161.
A. O.
Lykhin
,
D. G.
Truhlar
, and
L.
Gagliardi
, “
Role of triplet states in the photodynamics of aniline
,”
J. Am. Chem. Soc.
143
(
15
),
5878
5889
(
2021
).
162.
L.
Gagliardi
,
D. G.
Truhlar
,
G.
Li Manni
,
R. K.
Carlson
,
C. E.
Hoyer
, and
J. L.
Bao
, “
Multiconfiguration pair-density functional theory: A new way to treat strongly correlated systems
,”
Acc. Chem. Res.
50
(
1
),
66
73
(
2017
).
163.
J.
Westermayr
,
M.
Gastegger
,
D.
Voros
,
L.
Panzenboeck
,
F.
Joerg
,
L.
Gonzalez
, and
P.
Marquetand
, “
Deep learning study of tyrosine reveals that roaming can lead to photodamage
,”
Nat. Chem.
14
(
8
),
914
919
(
2022
).
164.
N. M.
Kidwell
,
H.
Li
,
X.
Wang
,
J. M.
Bowman
, and
M. I.
Lester
, “
Unimolecular dissociation dynamics of vibrationally activated CH3CHOO Criegee intermediates to OH radical products
,”
Nat. Chem.
8
(
5
),
509
514
(
2016
).
165.
J. K.
Ha
,
K.
Kim
, and
S. K.
Min
, “
Machine learning-assisted excited state molecular dynamics with the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham approach
,”
J. Chem. Theory Comput.
17
(
2
),
694
702
(
2021
).
166.
G.
Montavon
,
M.
Rupp
,
V.
Gobre
,
A.
Vazquez-Mayagoitia
,
K.
Hansen
,
A.
Tkatchenko
,
K.-R.
Müller
, and
O.
Anatole von Lilienfeld
, “
Machine learning of molecular electronic properties in chemical compound space
,”
New J. Phys.
15
(
9
),
095003
(
2013
).
167.
R.
Ramakrishnan
,
M.
Hartmann
,
E.
Tapavicza
, and
O. A.
von Lilienfeld
, “
Electronic spectra from TDDFT and machine learning in chemical space
,”
J. Chem. Phys.
143
(
8
),
084111
(
2015
).
168.
R.
Ramakrishnan
,
P. O.
Dral
,
M.
Rupp
, and
O. A.
von Lilienfeld
, “
Quantum chemistry structures and properties of 134 kilo molecules
,”
Sci. Data
1
,
140022
(
2014
).
169.
S.
Chmiela
,
A.
Tkatchenko
,
H. E.
Sauceda
,
I.
Poltavsky
,
K. T.
Schutt
, and
K. R.
Muller
, “
Machine learning of accurate energy-conserving molecular force fields
,”
Sci. Adv.
3
(
5
),
e1603015
(
2017
).
170.
M.
Pinheiro
, Jr.
,
S.
Zhang
,
P. O.
Dral
, and
M.
Barbatti
, “
WS22 database, Wigner sampling and geometry interpolation for configurationally diverse molecular datasets
,”
Sci. Data
10
(
1
),
95
(
2023
).
171.
J.
Kästner
, “
Umbrella sampling
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
1
(
6
),
932
942
(
2011
).
172.
G.
Tao
, “
Trajectory-guided sampling for molecular dynamics simulation
,”
Theor. Chem. Acc.
138
(
3
),
34
(
2019
).
173.
Y. I.
Yang
,
Q.
Shao
,
J.
Zhang
,
L.
Yang
, and
Y. Q.
Gao
, “
Enhanced sampling in molecular dynamics
,”
J. Chem. Phys.
151
(
7
),
070902
(
2019
).
174.
J. E.
Herr
,
K.
Yao
,
R.
McIntyre
,
D. W.
Toth
, and
J.
Parkhill
, “
Metadynamics for training neural network model chemistries: A competitive assessment
,”
J. Chem. Phys.
148
(
24
),
241710
(
2018
).
175.
C.
Shang
and
Z. P.
Liu
, “
Stochastic surface walking method for structure prediction and pathway searching
,”
J. Chem. Theory Comput.
9
(
3
),
1838
1845
(
2013
).
176.
J. P.
Dahl
and
M.
Springborg
, “
The Morse oscillator in position space, momentum space, and phase space
,”
J. Chem. Phys.
88
(
7
),
4535
4547
(
1988
).
177.
N.
Artrith
and
J.
Behler
, “
High-dimensional neural network potentials for metal surfaces: A prototype study for copper
,”
Phys. Rev. B: Condens. Matter
85
(
4
),
045439
(
2012
).
178.
Q.
Cui
,
T.
Pal
, and
L.
Xie
, “
Biomolecular QM/MM simulations: What are some of the "burning issues
,”
J. Phys. Chem. B
125
(
3
),
689
702
(
2021
).
179.
K. S.
Csizi
and
M.
Reiher
, “
Universal QM/MM approaches for general nanoscale applications
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
13
(
4
),
e1656
(
2023
).
180.
H.
Lin
and
D. G.
Truhlar
, “
QM/MM: What have we learned, where are we, and where do we go from here?
,”
Theor. Chem. Acc.
117
(
2
),
185
199
(
2006
).
181.
H. M.
Senn
and
W.
Thiel
, “
QM/MM methods for biomolecular systems
,”
Angew. Chem. Int. Ed. Engl.
48
(
7
),
1198
1229
(
2009
).
182.
L. W.
Chung
,
W. M.
Sameera
,
R.
Ramozzi
,
A. J.
Page
,
M.
Hatanaka
,
G. P.
Petrova
,
T. V.
Harris
,
X.
Li
,
Z.
Ke
,
F.
Liu
et al, “
The ONIOM method and its applications
,”
Chem. Rev.
115
(
12
),
5678
5796
(
2015
).
183.
M.
Bondanza
,
M.
Nottoli
,
L.
Cupellini
,
F.
Lipparini
, and
B.
Mennucci
, “
Polarizable embedding QM/MM: The future gold standard for complex (bio)systems?
,”
Phys. Chem. Chem. Phys.
22
(
26
),
14433
14448
(
2020
).
184.
M.
Rivera
,
M.
Dommett
, and
R.
Crespo-Otero
, “
ONIOM(QM:QM') electrostatic embedding schemes for photochemistry in molecular crystals
,”
J. Chem. Theory Comput.
15
(
4
),
2504
2516
(
2019
).
185.
Y. J.
Zhang
,
A.
Khorshidi
,
G.
Kastlunger
, and
A. A.
Peterson
, “
The potential for machine learning in hybrid QM/MM calculations
,”
J. Chem. Phys.
148
(
24
),
241740
(
2018
).
186.
W. K.
Chen
,
W. H.
Fang
, and
G.
Cui
, “
Integrating machine learning with the multilayer energy-based fragment method for excited states of large systems
,”
J. Phys. Chem. Lett.
10
(
24
),
7836
7841
(
2019
).
187.
J.
Wu
,
L.
Shen
, and
W.
Yang
, “
Internal force corrections with machine learning for quantum mechanics/molecular mechanics simulations
,”
J. Chem. Phys.
147
(
16
),
161732
(
2017
).
188.
L.
Shen
,
J.
Wu
, and
W.
Yang
, “
Multiscale quantum mechanics/molecular mechanics simulations with neural networks
,”
J. Chem. Theory Comput.
12
(
10
),
4934
4946
(
2016
).
189.
L.
Boselt
,
M.
Thurlemann
, and
S.
Riniker
, “
Machine learning in QM/MM molecular dynamics simulations of condensed-phase systems
,”
J. Chem. Theory Comput.
17
(
5
),
2641
2658
(
2021
).
190.
X.
Pan
,
J.
Yang
,
R.
Van
,
E.
Epifanovsky
,
J.
Ho
,
J.
Huang
,
J.
Pu
,
Y.
Mei
,
K.
Nam
, and
Y.
Shao
, “
Machine-learning-assisted free energy simulation of solution-phase and enzyme reactions
,”
J. Chem. Theory Comput.
17
(
9
),
5745
5758
(
2021
).
191.
L.
Shen
and
W.
Yang
, “
Molecular dynamics simulations with quantum mechanics/molecular mechanics and adaptive neural networks
,”
J. Chem. Theory Comput.
14
(
3
),
1442
1455
(
2018
).
192.
M.
Gastegger
,
K. T.
Schutt
, and
K. R.
Muller
, “
Machine learning of solvent effects on molecular spectra and reactions
,”
Chem. Sci.
12
(
34
),
11473
11483
(
2021
).
193.
J.
Zeng
,
T. J.
Giese
,
S.
Ekesan
, and
D. M.
York
, “
Development of range-corrected deep learning potentials for fast, accurate quantum mechanical/molecular mechanical simulations of chemical reactions in solution
,”
J. Chem. Theory Comput.
17
(
11
),
6993
7009
(
2021
).
194.
K.
Zinovjev
, “
Electrostatic embedding of machine learning potentials
,”
J. Chem. Theory Comput.
19
(
6
),
1888
1897
(
2023
).
195.
Y.
Zhang
,
C.
Hu
, and
B.
Jiang
, “
Embedded atom neural network potentials: Efficient and accurate machine learning with a physically inspired representation
,”
J. Phys. Chem. Lett.
10
(
17
),
4962
4967
(
2019
).
196.
Y.
Zhang
,
J.
Xia
, and
B.
Jiang
, “
Physically motivated recursively embedded atom neural networks: Incorporating local completeness and nonlocality
,”
Phys. Rev. Lett.
127
(
15
),
156002
(
2021
).
197.
B.
Lier
,
P.
Poliak
,
P.
Marquetand
,
J.
Westermayr
, and
C.
Oostenbrink
, “
BuRNN: Buffer region neural network approach for polarizable-embedding neural network/molecular mechanics simulations
,”
J. Phys. Chem. Lett.
13
(
17
),
3812
3818
(
2022
).
198.
P. O.
Dral
,
M.
Barbatti
, and
W.
Thiel
, “
Nonadiabatic excited-state dynamics with machine learning
,”
J. Phys. Chem. Lett.
9
(
19
),
5660
5663
(
2018
).
199.
G. W.
Richings
and
S.
Habershon
, “
Direct quantum dynamics using grid-based wave function propagation and machine-learned potential energy surfaces
,”
J. Chem. Theory Comput.
13
(
9
),
4012
4024
(
2017
).
200.
A.
Ullah
and
P. O.
Dral
, “
Speeding up quantum dissipative dynamics of open systems with kernel methods
,”
New J. Phys.
23
(
11
),
113019
(
2021
).
201.
A.
Ullah
and
P. O.
Dral
, “
One-shot trajectory learning of open quantum systems dynamics
,”
J. Phys. Chem. Lett.
13
(
26
),
6037
6041
(
2022
).
202.
S.
Han
,
A. G. S.
de Oliveira-Filho
,
Y.
Shu
,
D. G.
Truhlar
, and
H.
Guo
, “
Semiclassical trajectory studies of reactive and nonreactive scattering of OH(A (2) Sigma(+)) by H(2) based on an improved full-dimensional ab initio diabatic potential energy matrix
,”
ChemPhysChem
23
(
8
),
e202200039
(
2022
).
203.
B.
Zhao
,
S.
Han
,
C. L.
Malbon
,
U.
Manthe
,
D. R.
Yarkony
, and
H.
Guo
, “
Full-dimensional quantum stereodynamics of the non-adiabatic quenching of OH(A(2)Sigma(+)) by H(2)
,”
Nat. Chem.
13
(
9
),
909
915
(
2021
).
204.
Z.
Yin
,
Y.
Guan
,
B.
Fu
, and
D. H.
Zhang
, “
Two-state diabatic potential energy surfaces of ClH(2) based on nonadiabatic couplings with neural networks
,”
Phys. Chem. Chem. Phys.
21
(
36
),
20372
20383
(
2019
).
205.
Y.
Guan
,
C.
Xie
,
D. R.
Yarkony
, and
H.
Guo
, “
High-fidelity first principles nonadiabaticity: Diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics
,”
Phys. Chem. Chem. Phys.
23
(
44
),
24962
24983
(
2021
).
206.
Y.
Guan
,
D. H.
Zhang
,
H.
Guo
, and
D. R.
Yarkony
, “
Representation of coupled adiabatic potential energy surfaces using neural network based quasi-diabatic Hamiltonians: 1,2 (2)A' states of LiFH
,”
Phys. Chem. Chem. Phys.
21
(
26
),
14205
14213
(
2019
).
207.
K. T.
Schütt
,
O. T.
Unke
, and
M.
Gastegger
, “
Equivariant message passing for the prediction of tensorial properties and molecular spectra
,” arXiv:2102.03150 (
2021
).
208.
M.
Inamori
,
T.
Yoshikawa
,
Y.
Ikabata
,
Y.
Nishimura
, and
H.
Nakai
, “
Spin-flip approach within time-dependent density functional tight-binding method: Theory and applications
,”
J. Comput. Chem.
41
(
16
),
1538
1548
(
2020
).
209.
O. P.
Vieuxmaire
,
Z.
Lan
,
A. L.
Sobolewski
, and
W.
Domcke
, “
Ab initio characterization of the conical intersections involved in the photochemistry of phenol
,”
J. Chem. Phys.
129
(
22
),
224307
(
2008
).
210.
A. L.
Sobolewski
,
W.
Domcke
,
C.
Dedonder-Lardeux
, and
C.
Jouvet
, “
Excited-state hydrogen detachment and hydrogen transfer driven by repulsive 1πσ* states: A new paradigm for nonradiative decay in aromatic biomolecules
,”
Phys. Chem. Chem. Phys.
4
(
7
),
1093
1100
(
2002
).
211.
A. L.
Sobolewski
and
W.
Domcke
, “
Photoinduced electron and proton transfer in phenol and its clusters with water and ammonia
,”
J. Phys. Chem. A
105
(
40
),
9275
9283
(
2001
).
212.
X.
Xu
,
J.
Zheng
,
K. R.
Yang
, and
D. G.
Truhlar
, “
Photodissociation dynamics of phenol: Multistate trajectory simulations including tunneling
,”
J. Am. Chem. Soc.
136
(
46
),
16378
16386
(
2014
).
213.
K. R.
Yang
,
X.
Xu
,
J.
Zheng
, and
D. G.
Truhlar
, “
Full-dimensional potentials and state couplings and multidimensional tunneling calculations for the photodissociation of phenol
,”
Chem. Sci.
5
(
12
),
4661
4680
(
2014
).
214.
C.
Xie
,
B.
Zhao
,
C. L.
Malbon
,
D. R.
Yarkony
,
D.
Xie
, and
H.
Guo
, “
Insights into the mechanism of nonadiabatic photodissociation from product vibrational distributions. The remarkable case of phenol
,”
J. Phys. Chem. Lett.
11
(
1
),
191
198
(
2020
).
215.
G.
Tomasello
,
M.
Wohlgemuth
,
J.
Petersen
, and
R.
Mitric
, “
Photodynamics of free and solvated tyrosine
,”
J. Phys. Chem. B
116
(
30
),
8762
8770
(
2012
).
216.
A. L.
Sobolewski
,
D.
Shemesh
, and
W.
Domcke
, “
Computational studies of the photophysics of neutral and zwitterionic amino acids in an aqueous environment: Tyrosine-(H(2)O)(2) and tryptophan-(H(2)O)(2) clusters
,”
J. Phys. Chem. A
113
(
3
),
542
550
(
2009
).
217.
A.
Iqbal
and
V. G.
Stavros
, “
Active participation of 1πσ* states in the photodissociation of tyrosine and its subunits
,”
J. Phys. Chem. Lett.
1
(
15
),
2274
2278
(
2010
).
218.
S.
Mai
,
P.
Marquetand
, and
L.
Gonzalez
, “
Nonadiabatic dynamics: The SHARC approach
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
8
(
6
),
e1370
(
2018
).
219.
D.
Tuna
,
D.
Lefrancois
,
L.
Wolanski
,
S.
Gozem
,
I.
Schapiro
,
T.
Andruniow
,
A.
Dreuw
, and
M.
Olivucci
, “
Assessment of approximate coupled-cluster and algebraic-diagrammatic-construction methods for ground- and excited-state reaction paths and the conical-intersection seam of a retinal-chromophore model
,”
J. Chem. Theory Comput.
11
(
12
),
5758
5781
(
2015
).
You do not currently have access to this content.