Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S2). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.
REFERENCES
1.
E.
Teller
, “The crossing of potential surfaces
,” J. Phys. Chem.
41
, 109
–116
(1937
).2.
D. R.
Yarkony
, “Diabolical conical intersections
,” Rev. Mod. Phys.
68
, 985
(1996
).3.
P.-F.
Loos
, A.
Scemama
, A.
Blondel
, Y.
Garniron
, M.
Caffarel
, and D.
Jacquemin
, “A mountaineering strategy to excited states: Highly accurate reference energies and benchmarks
,” J. Chem. Theory Comput.
14
, 4360
–4379
(2018
).4.
M.
Véril
, A.
Scemama
, M.
Caffarel
, F.
Lipparini
, M.
Boggio-Pasqua
, D.
Jacquemin
, and P.-F.
Loos
, “QUESTDB: A database of highly accurate excitation energies for the electronic structure community
,” WIREs Comput. Mol. Sci.
11
, e1517
(2021
).5.
J.
Liang
, X.
Feng
, D.
Hait
, and M.
Head-Gordon
, “Revisiting the performance of time-dependent density functional theory for electronic excitations: Assessment of 43 popular and recently developed functionals from rungs one to four
,” J. Chem. Theory Comput.
18
, 3460
–3473
(2022
).6.
B. F.
Curchod
and T. J.
Martínez
, “Ab initio nonadiabatic quantum molecular dynamics
,” Chem. Rev.
118
, 3305
–3336
(2018
).7.
R.
Crespo-Otero
and M.
Barbatti
, “Recent advances and perspectives on nonadiabatic mixed quantum–classical dynamics
,” Chem. Rev.
118
, 7026
–7068
(2018
).8.
H.
Timmers
, X.
Zhu
, Z.
Li
, Y.
Kobayashi
, M.
Sabbar
, M.
Hollstein
, M.
Reduzzi
, T. J.
Martínez
, D. M.
Neumark
, and S. R.
Leone
, “Disentangling conical intersection and coherent molecular dynamics in methyl bromide with attosecond transient absorption spectroscopy
,” Nat. Commun.
10
, 3133
(2019
).9.
T. J.
Wolf
, D. M.
Sanchez
, J.
Yang
, R.
Parrish
, J.
Nunes
, M.
Centurion
, R.
Coffee
, J.
Cryan
, M.
Gühr
, K.
Hegazy
et al, “The photochemical ring-opening of 1,3-cyclohexadiene imaged by ultrafast electron diffraction
,” Nat. Chem.
11
, 504
–509
(2019
).10.
J.
Yang
, X.
Zhu
, J. P.
F Nunes
, J. K.
Yu
, R. M.
Parrish
, T. J.
Wolf
, M.
Centurion
, M.
Gühr
, R.
Li
, Y.
Liu
et al, “Simultaneous observation of nuclear and electronic dynamics by ultrafast electron diffraction
,” Science
368
, 885
–889
(2020
).11.
K. S.
Zinchenko
, F.
Ardana-Lamas
, I.
Seidu
, S. P.
Neville
, J.
van der Veen
, V. U.
Lanfaloni
, M. S.
Schuurman
, and H. J.
Wörner
, “Sub-7-femtosecond conical-intersection dynamics probed at the carbon K-edge
,” Science
371
, 489
–494
(2021
).12.
E.
Ridente
, D.
Hait
, E. A.
Haugen
, A. D.
Ross
, D. M.
Neumark
, M.
Head-Gordon
, and S. R.
Leone
, “Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy
,” Science
380
, 713
–717
(2023
).13.
W. J.
Glover
, T.
Mori
, M. S.
Schuurman
, A. E.
Boguslavskiy
, O.
Schalk
, A.
Stolow
, and T. J.
Martínez
, “Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. II. Ab initio multiple spawning simulations
,” J. Chem. Phys.
148
, 164303
(2018
).14.
H.
Tao
, T. K.
Allison
, T. W.
Wright
, A. M.
Stooke
, C.
Khurmi
, J.
van Tilborg
, Y.
Liu
, R. W.
Falcone
, A.
Belkacem
, and T. J.
Martinez
, “Ultrafast internal conversion in ethylene. I. The excited state lifetime
,” J. Chem. Phys.
134
, 244306
(2011
).15.
T.
Mori
, W. J.
Glover
, M. S.
Schuurman
, and T. J.
Martinez
, “Role of Rydberg states in the photochemical dynamics of ethylene
,” J. Phys. Chem. A
116
, 2808
–2818
(2012
).16.
T.
Kobayashi
, T.
Horio
, and T.
Suzuki
, “Ultrafast deactivation of the ππ*(V) state of ethylene studied using sub-20 fs time-resolved photoelectron imaging
,” J. Phys. Chem. A
119
, 9518
–9523
(2015
).17.
R.
Norrish
and C.
Bamford
, “Photodecomposition of aldehydes and ketones
,” Nature
138
, 1016
(1936
).18.
E. W.-G.
Diau
, C.
Kötting
, and A. H.
Zewail
, “Femtochemistry of norrish type-I reactions: II. The anomalous predissociation dynamics of cyclobutanone on the S1 surface
,” ChemPhysChem
2
, 294
–309
(2001
).19.
M.-H.
Kao
, R. K.
Venkatraman
, M. N.
Ashfold
, and A. J.
Orr-Ewing
, “Effects of ring-strain on the ultrafast photochemistry of cyclic ketones
,” Chem. Sci.
11
, 1991
–2000
(2020
).20.
S.-H.
Xia
, X.-Y.
Liu
, Q.
Fang
, and G.
Cui
, “Excited-state ring-opening mechanism of cyclic ketones: A MS-CASPT2//CASSCF study
,” J. Phys. Chem. A
119
, 3569
–3576
(2015
).21.
L.
Liu
and W.-H.
Fang
, “New insights into photodissociation dynamics of cyclobutanone from the aims dynamic simulation
,” J. Chem. Phys.
144
, 144317
(2016
).22.
M.
Centurion
, T. J.
Wolf
, and J.
Yang
, “Ultrafast imaging of molecules with electron diffraction
,” Annu. Rev. Phys. Chem.
73
, 21
–42
(2022
).23.
J.
Janos
and P.
Slavicek
, “What controls the quality of photodynamical simulations? Electronic structure versus nonadiabatic algorithm
,” J. Chem. Theory Comput.
19
, 8273
–8284
(2023
).24.
R. J.
Bartlett
and M.
Musiał
, “Coupled-cluster theory in quantum chemistry
,” Rev. Mod. Phys.
79
, 291
(2007
).25.
J. F.
Stanton
and R. J.
Bartlett
, “The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties
,” J. Chem. Phys.
98
, 7029
–7039
(1993
).26.
O.
Christiansen
, H.
Koch
, and P.
Jo/rgensen
, “Response functions in the CC3 iterative triple excitation model
,” J. Chem. Phys.
103
, 7429
–7441
(1995
).27.
H.
Koch
, O.
Christiansen
, P.
Jo/rgensen
, 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
).28.
M. E.
Casida
, “Time-dependent density functional response theory for molecules
,” in Recent Advances in Density Functional Methods: (Part I)
(World Scientific
, 1995
), pp. 155
–192
.29.
A.
Dreuw
and M.
Head-Gordon
, “Single-reference ab initio methods for the calculation of excited states of large molecules
,” Chem. Rev.
105
, 4009
–4037
(2005
).30.
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
, 1039
–1051
(2006
).31.
S.
Hirata
and M.
Head-Gordon
, “Time-dependent density functional theory within the Tamm–Dancoff approximation
,” Chem. Phys. Lett.
314
, 291
–299
(1999
).32.
D.
Hait
, A.
Rettig
, and M.
Head-Gordon
, “Beyond the Coulson–Fischer point: Characterizing single excitation CI and TDDFT for excited states in single bond dissociations
,” Phys. Chem. Chem. Phys.
21
, 21761
–21775
(2019
).33.
C.
Hättig
, “Structure optimizations for excited states with correlated second-order methods: CC2 and ADC(2)
,” Adv. Quantum Chem.
50
, 37
(2005
), part of Special Issue: Response Theory and Molecular Properties (A Tribute to Jan Linderberg and Poul Jørgensen) 34.
A.
Köhn
and A.
Tajti
, “Can coupled-cluster theory treat conical intersections?
,” J. Chem. Phys.
127
, 044105
(2007
).35.
E. F.
Kjønstad
, R. H.
Myhre
, T. J.
Martínez
, and H.
Koch
, “Crossing conditions in coupled cluster theory
,” J. Chem. Phys.
147
, 164105
(2017
).36.
D. M.
Williams
, E. F.
Kjønstad
, and T. J.
Martinez
, “Geometric phase in coupled cluster theory
,” J. Chem. Phys.
158
, 214122
(2023
).37.
E. F.
Kjønstad
and H.
Koch
, “Resolving the notorious case of conical intersections for coupled cluster dynamics
,” J. Phys. Chem. Lett.
8
, 4801
–4807
(2017
).38.
E. F.
Kjønstad
and H.
Koch
, “An orbital invariant similarity constrained coupled cluster model
,” J. Chem. Theory Comput.
15
, 5386
–5397
(2019
).39.
H.
Keller-Rudek
, G. K.
Moortgat
, R.
Sander
, and R.
Sörensen
, “The MPI-Mainz UV/VIS spectral atlas of gaseous molecules of atmospheric interest
,” Earth Syst. Sci. Data
5
, 365
–373
(2013
).40.
A.
Udvarhazi
and M.
El-Sayed
, “Vacuum-ultraviolet spectra of cyclic ketones
,” J. Chem. Phys.
42
, 3335
–3336
(1965
).41.
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
, 5161
–5175
(2000
).42.
M.
Ben-Nun
and T. J.
Martínez
, “Ab initio quantum molecular dynamics
,” Adv. Chem. Phys.
121
, 439
–512
(2002
).43.
M. A.
Rohrdanz
and J. M.
Herbert
, “Simultaneous benchmarking of ground- and excited-state properties with long-range-corrected density functional theory
,” J. Chem. Phys.
129
(2008
).44.
T. H.
Dunning
, Jr., “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,” J. Chem. Phys.
90
, 1007
–1023
(1989
).45.
R. A.
Kendall
, T. H.
Dunning
, Jr., 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
).46.
S.
Seritan
, C.
Bannwarth
, B. S.
Fales
, E. G.
Hohenstein
, C. M.
Isborn
, S. I.
Kokkila-Schumacher
, X.
Li
, F.
Liu
, N.
Luehr
, J. W.
Snyder
, Jr. et al, “TeraChem: A graphical processing unit-accelerated electronic structure package for large-scale ab initio molecular dynamics
,” WIREs Comput. Mol. Sci.
11
, e1494
(2021
).47.
I. S.
Ufimtsev
and T. J.
Martinez
, “Quantum chemistry on graphical processing units. 1. Strategies for two-electron integral evaluation
,” J. Chem. Theory Comput.
4
, 222
–231
(2008
).48.
I. S.
Ufimtsev
and T. J.
Martinez
, “Quantum chemistry on graphical processing units. 2. Direct self-consistent-field implementation
,” J. Chem. Theory Comput.
5
, 1004
–1015
(2009
).49.
I. S.
Ufimtsev
and T. J.
Martinez
, “Quantum chemistry on graphical processing units. 3. Analytical energy gradients, geometry optimization, and first principles molecular dynamics
,” J. Chem. Theory Comput.
5
, 2619
–2628
(2009
).50.
D. J.
Tozer
and N. C.
Handy
, “Improving virtual Kohn–Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities
,” J. Chem. Phys.
109
, 10180
–10189
(1998
).51.
F.
Weigend
and R.
Ahlrichs
, “Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
,” Phys. Chem. Chem. Phys.
7
, 3297
–3305
(2005
).52.
D.
Rappoport
and F.
Furche
, “Property-optimized Gaussian basis sets for molecular response calculations
,” J. Chem. Phys.
133
, 134105
(2010
).53.
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
).54.
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
).55.
P. C.
Hariharan
and J. A.
Pople
, “The influence of polarization functions on molecular orbital hydrogenation energies
,” Theor. Chim. Acta
28
, 213
–222
(1973
).56.
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
).57.
S. D.
Folkestad
, E. F.
Kjønstad
, R. H.
Myhre
, J. H.
Andersen
, A.
Balbi
, S.
Coriani
, T.
Giovannini
, L.
Goletto
, T. S.
Haugland
, A.
Hutcheson
et al, “eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods
,” J. Chem. Phys.
152
, 184103
(2020
).58.
E. G.
Hohenstein
, R. M.
Parrish
, C. D.
Sherrill
, and T. J.
Martinez
, “Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions
,” J. Chem. Phys.
137
, 22101
(2012
).59.
E. G.
Hohenstein
, S. I. L.
Kokkila
, R. M.
Parrish
, and T. J.
Martinez
, “Tensor hypercontraction equation-of-motion second-order approximate coupled cluster: Electronic excitation energies in O(N4) time
,” J. Phys. Chem. B
117
, 12972
–12978
(2013
).60.
R. M.
Parrish
, Y.
Zhao
, E. G.
Hohenstein
, and T. J.
Martinez
, “Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions
,” J. Chem. Phys.
150
, 164118
(2019
).61.
E. G.
Hohenstein
, Y.
Zhao
, R. M.
Parrish
, and T. J.
Martinez
, “Rank reduced coupled cluster theory. II. Equation-of-motion coupled-cluster singles and doubles
,” J. Chem. Phys.
151
, 164121
(2019
).62.
E. G.
Hohenstein
, B. S.
Fales
, R. M.
Parrish
, and T. J.
Martinez
, “Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes
,” J. Chem. Phys.
156
, 054102
(2022
).63.
K. K.
Baeck
and T. J.
Martinez
, “Ab initio molecular dynamics with equation-of-motion coupled-cluster theory: Electronic absorption spectrum of ethylene
,” Chem. Phys. Lett.
375
, 299
–308
(2003
).64.
A. K.
Schnack-Petersen
, H.
Koch
, S.
Coriani
, and E. F.
Kjønstad
, “Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals
,” J. Chem. Phys.
156
, 244111
(2022
).65.
E. F.
Kjønstad
and H.
Koch
, “Communication: Non-adiabatic derivative coupling elements for the coupled cluster singles and doubles model
,” J. Chem. Phys.
158
, 161106
(2023
).66.
E. F.
Kjønstad
, O. J.
Fajen
, A. C.
Paul
, S.
Angelico
, D.
Mayer
, M.
Gühr
, T. J.
Wolf
, T. J.
Martínez
, and H.
Koch
, “Unexpected hydrogen dissociation in thymine: predictions from a novel coupled cluster theory
,” arXiv:2403.01045 (2024
).67.
A.
Tajti
and P. G.
Szalay
, “Analytic evaluation of the nonadiabatic coupling vector between excited states using equation-of-motion coupled-cluster theory
,” J. Chem. Phys.
131
, 124104
(2009
).68.
S.
Faraji
, S.
Matsika
, and A. I.
Krylov
, “Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods
,” J. Chem. Phys.
148
, 044103
(2018
).69.
B.
Efron
and R.
Tibshirani
, “Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy
,” Stat. Sci.
1
, 54
–75
(1986
).70.
E. F.
Kjønstad
, S.
Angelico
, and H.
Koch
, “Coupled cluster theory for nonadiabatic dynamics: nuclear gradients and nonadiabatic couplings in similarity constrained coupled cluster theory
,” arXiv:2403.01007 (2024
).71.
H.
Jónsson
, G.
Mills
, and K. W.
Jacobsen
, “Nudged elastic band method for finding minimum energy paths of transitions
,” in Classical and Quantum Dynamics in Condensed Phase Simulations
(World Scientific
, 1998
), pp. 385
–404
.72.
T. S.
Kuhlman
, W. J.
Glover
, T.
Mori
, K. B.
Møller
, and T. J.
Martínez
, “Between ethylene and polyenes - the non-adiabatic dynamics of cis-dienes
,” Faraday Discuss.
157
, 193
–212
(2012
).73.
J.
Baker
, “An algorithm for the location of transition states
,” J. Comput. Chem.
7
, 385
–395
(1986
).74.
J.
Kästner
, J. M.
Carr
, T. W.
Keal
, W.
Thiel
, A.
Wander
, and P.
Sherwood
, “DL-FIND: An open-source geometry optimizer for atomistic simulations
,” J. Phys. Chem. A
113
, 11856
–11865
(2009
).75.
S.
Metz
, J.
Kästner
, A. A.
Sokol
, T. W.
Keal
, and P.
Sherwood
, “ChemShell—A modular software package for QM/MM simulations
,” WIREs Comput. Mol. Sci.
4
, 101
–110
(2014
).76.
P.
Sherwood
, A. H.
de Vries
, M. F.
Guest
, G.
Schreckenbach
, C. A.
Catlow
, S. A.
French
, A. A.
Sokol
, S. T.
Bromley
, W.
Thiel
, A. J.
Turner
et al, “QUASI: A general purpose implementation of the QM/MM approach and its application to problems in catalysis
,” J. Mol. Struct.: THEOCHEM
632
, 1
–28
(2003
).77.
F.
Salvat
, A.
Jablonski
, and C. J.
Powell
, “ELSEPA—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules
,” Comput. Phys. Commun.
165
, 157
–190
(2005
).78.
T. S.
Kuhlman
, T. I.
Sølling
, and K. B.
Møller
, “Coherent motion reveals non-ergodic nature of internal conversion between excited states
,” ChemPhysChem
13
, 820
–827
(2012
).79.
A.
Stolow
, A. E.
Bragg
, and D. M.
Neumark
, “Femtosecond time-resolved photoelectron spectroscopy
,” Chem. Rev.
104
, 1719
–1758
(2004
).80.
H. R.
Hudock
, B. G.
Levine
, A. L.
Thompson
, H.
Satzger
, D.
Townsend
, N.
Gador
, S.
Ullrich
, A.
Stolow
, and T. J.
Martínez
, “Ab initio molecular dynamics and time-resolved photoelectron spectroscopy of electronically excited uracil and thymine
,” J. Phys. Chem. A
111
, 8500
–8508
(2007
).81.
C.
Melania Oana
and A. I.
Krylov
, “Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: Theory, implementation, and examples
,” J. Chem. Phys.
127
, 234106
(2007
).82.
R. M.
Parrish
and T. J.
Martinez
, “Ab initio computation of rotationally-averaged pump-probe X-ray and electron diffraction signals
,” J. Chem. Theory Comput.
15
, 1523
–1537
(2019
).83.
H.
Yong
, N.
Zotev
, J. M.
Ruddock
, B.
Stankus
, M.
Simmermacher
, A. M.
Carrascosa
, W.
Du
, N.
Goff
, Y.
Chang
, D.
Bellshaw
, M.
Liang
, S.
Carbajo
, J. E.
Koglin
, J. S.
Robinson
, S.
Boutet
, M. P.
Minitti
, A.
Kirrander
, and P. M.
Weber
, “Observation of the molecular response to light upon photoexcitation
,” Nat. Commun.
11
, 2157
(2020
).84.
E. G.
Champenois
, N. H.
List
, M.
Ware
, M.
Britton
, P. H.
Bucksbaum
, X.
Cheng
, M.
Centurion
, J. P.
Cryan
, R.
Forbes
, I.
Gabalski
, K.
Hegazy
, M. C.
Hoffmann
, A. J.
Howard
, F.
Ji
, M.-F.
Lin
, J. P. F.
Nunes
, X.
Shen
, J.
Yang
, X.
Wang
, T. J.
Martinez
, and T. J. A.
Wolf
, “Femtosecond electronic and hydrogen structural dynamics in ammonia imaged with ultrafast electron diffraction
,” Phys. Rev. Lett.
131
, 143001
(2023
).85.
K.
Tamagawa
and R.
Hilderbrandt
, “Molecular structure of cyclobutanone as determined by combined analysis of electron diffraction and spectroscopic data
,” J. Phys. Chem.
87
, 5508
–5516
(1983
).86.
D.
Hait
, D.
Lahana
, O. J.
Fajen
, A. S. P.
Paz
, P. A.
Unzueta
, B.
Rana
, L.
Lu
, Y.
Wang
, E. F.
Kjønstad
, H.
Koch
, and T. J.
Martinez
(2024
). “Raw data for prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning
,” 10.5281/zenodo.11159627.© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
