Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree–Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.
REFERENCES
1.
H.
Flocard
, S. E.
Koonin
, and M. S.
Weiss
, “Three-dimensional time-dependent Hartree-Fock calculations: Application to 16O + 16O collisions
,” Phys. Rev. C
17
(5
), 1682
(1978
).2.
K.
Sekizawa
, “TDHF theory and its extensions for the multinucleon transfer reaction: A mini review
,” Front. Phys.
7
, 20
(2019
).3.
H.
Eshuis
, G. G.
Balint-Kurti
, and F. R.
Manby
, “Dynamics of molecules in strong oscillating electric fields using time-dependent Hartree–Fock theory
,” J. Chem. Phys.
128
(11
), 114113
(2008
).4.
C. M.
Isborn
and X.
Li
, “Singlet–triplet transitions in real-time time-dependent Hartree–Fock/density functional theory
,” J. Chem. Theory Comput.
5
(9
), 2415
(2009
).5.
U.
De Giovannini
, G.
Brunetto
, A.
Castro
, J.
Walkenhorst
, and A.
Rubio
, “Simulating pump–probe photoelectron and absorption spectroscopy on the attosecond timescale with time-dependent density functional theory
,” ChemPhysChem
14
(7
), 1363
(2013
).6.
M.
Wibowo
, T. J. P.
Irons
, and A. M.
Teale
, “Modeling ultrafast electron dynamics in strong magnetic fields using real-time time-dependent electronic structure methods
,” J. Chem. Theory Comput.
17
(4
), 2137
(2021
).7.
A.
Ghosal
and A. K.
Roy
, “A real-time TDDFT scheme for strong-field interaction in Cartesian coordinate grid
,” Chem. Phys. Lett.
796
, 139562
(2022
).8.
J.
Heslar
, D. A.
Telnov
, and S.-I.
Chu
, “Subcycle dynamics of high-harmonic generation in valence-shell and virtual states of Ar atoms: A self-interaction-free time-dependent density-functional-theory approach
,” Phys. Rev. A
91
(2
), 023420
(2015
).9.
E.
Coccia
and E.
Luppi
, “Time-dependent ab initio approaches for high-harmonic generation spectroscopy
,” J. Phys.: Condens. Matter
34
(7
), 073001
(2021
).10.
K.
Lopata
and N.
Govind
, “Modeling fast electron dynamics with real-time time-dependent density functional theory: Application to small molecules and chromophores
,” J. Chem. Theory Comput.
7
(5
), 1344
(2011
).11.
C.
Andrea Rozzi
, S.
Maria Falke
, N.
Spallanzani
, A.
Rubio
, E.
Molinari
, D.
Brida
, M.
Maiuri
, G.
Cerullo
, H.
Schramm
, J.
Christoffers
, and C.
Lienau
, “Quantum coherence controls the charge separation in a prototypical artificial light-harvesting system
,” Nat. Commun.
4
(1
), 1602
(2013
).12.
S. M.
Falke
, C. A.
Rozzi
, D.
Brida
, M.
Maiuri
, M.
Amato
, E.
Sommer
, A.
De Sio
, A.
Rubio
, G.
Cerullo
, E.
Molinari
, and C.
Lienau
, “Coherent ultrafast charge transfer in an organic photovoltaic blend
,” Science
344
(6187
), 1001
(2014
).13.
S. A.
Fischer
, C. J.
Cramer
, and N.
Govind
, “Excited state absorption from real-time time-dependent density functional theory
,” J. Chem. Theory Comput.
11
(9
), 4294
(2015
).14.
A.
Bruner
, S.
Hernandez
, F.
Mauger
, P. M.
Abanador
, D. J.
LaMaster
, M. B.
Gaarde
, K. J.
Schafer
, and K.
Lopata
, “Attosecond charge migration with TDDFT: Accurate dynamics from a well-defined initial state
,” J. Phys. Chem. Lett.
8
(17
), 3991
(2017
).15.
T.
Trepl
, I.
Schelter
, and S.
Kümmel
, “Analyzing excitation-energy transfer based on the time-dependent density functional theory in real time
,” J. Chem. Theory Comput.
18
(11
), 6577
(2022
).16.
A.
Sissay
, P.
Abanador
, F.
Mauger
, M.
Gaarde
, K. J.
Schafer
, and K.
Lopata
, “Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory
,” J. Chem. Phys.
145
(9
), 094105
(2016
).17.
T.
Akama
and H.
Nakai
, “Short-time Fourier transform analysis of real-time time-dependent Hartree–Fock and time-dependent density functional theory calculations with Gaussian basis functions
,” J. Chem. Phys.
132
(5
), 054104
(2010
).18.
A.
Bruner
, S. M.
Cavaletto
, N.
Govind
, and S.
Mukamel
, “Resonant X-ray sum-frequency-generation spectroscopy of K-edges in acetyl fluoride
,” J. Chem. Theory Comput.
15
(12
), 6832
(2019
).19.
M.
Chen
and K.
Lopata
, “First-principles simulations of X-ray transient absorption for probing attosecond electron dynamics
,” J. Chem. Theory Comput.
16
(7
), 4470
(2020
).20.
T. P.
Rossi
, M.
Kuisma
, M. J.
Puska
, R. M.
Nieminen
, and P.
Erhart
, “Kohn–Sham decomposition in real-time time-dependent density-functional theory: An efficient tool for analyzing plasmonic excitations
,” J. Chem. Theory Comput.
13
(10
), 4779
(2017
).21.
J.
Krumland
, A. M.
Valencia
, S.
Pittalis
, C. A.
Rozzi
, and C.
Cocchi
, “Understanding real-time time-dependent density-functional theory simulations of ultrafast laser-induced dynamics in organic molecules
,” J. Chem. Phys.
153
(5
), 054106
(2020
).22.
A.
Dreuw
, “Quantum chemical methods for the investigation of photoinitiated processes in biological systems: Theory and applications
,” ChemPhysChem
7
(11
), 2259
(2006
).23.
J.
Mattiat
and S.
Luber
, “Recent progress in the simulation of chiral systems with real time propagation methods
,” Helv. Chim. Acta
104
(12
), e2100154
(2021
).24.
J.
Mattiat
and S.
Luber
, “Comparison of length, velocity, and symmetric gauges for the calculation of absorption and electric circular dichroism spectra with real-time time-dependent density functional theory
,” J. Chem. Theory Comput.
18
(9
), 5513
(2022
).25.
E. W.
Draeger
, X.
Andrade
, J. A.
Gunnels
, A.
Bhatele
, A.
Schleife
, and A. A.
Correa
, “Massively parallel first-principles simulation of electron dynamics in materials
,” J. Parallel Distrib. Comput.
106
, 205
(2017
).26.
G. U.
Kuda-Singappulige
and C. M.
Aikens
, “Excited-state absorption in silver nanoclusters
,” J. Phys. Chem. C
125
(45
), 24996
(2021
).27.
L.
Bhan
, C.
Covington
, and K.
Varga
, “Signatures of atomic structure in subfemtosecond laser-driven electron dynamics in nanogaps
,” Phys. Rev. B
105
(8
), 085416
(2022
).28.
C.
Shepard
, R.
Zhou
, D. C.
Yost
, Y.
Yao
, and Y.
Kanai
, “Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation
,” J. Chem. Phys.
155
(10
), 100901
(2021
).29.
A.
Kononov
, C.-W.
Lee
, T. P.
dos Santos
, B.
Robinson
, Y.
Yao
, Y.
Yao
, X.
Andrade
, A. D.
Baczewski
, E.
Constantinescu
, A. A.
Correa
, Y.
Kanai
, N.
Modine
, and A.
Schleife
, “Electron dynamics in extended systems within real-time time-dependent density-functional theory
,” MRS Commun.
12
(6
), 1002
(2022
).30.
S.
Yamada
, M.
Noda
, K.
Nobusada
, and K.
Yabana
, “Time-dependent density functional theory for interaction of ultrashort light pulse with thin materials
,” Phys. Rev. B
98
(24
), 245147
(2018
).31.
T. S.
Haugland
, C.
Schäfer
, E.
Ronca
, A.
Rubio
, and H.
Koch
, “Intermolecular interactions in optical cavities: An ab initio QED study
,” J. Chem. Phys.
154
(9
), 094113
(2021
).32.
C.-K.
Li
, J.-m.
Xue
, and F.-S.
Zhang
, “Channeling electronic stopping power of lithium ions in diamond: Contribution of projectile inner-shell electrons
,” Phys. Rev. A
106
(2
), 022807
(2022
).33.
E.
Runge
and E. K. U.
Gross
, “Density-functional theory for time-dependent systems
,” Phys. Rev. Lett.
52
(12
), 997
(1984
).34.
R.
van Leeuwen
, “Mapping from densities to potentials in time-dependent density-functional theory
,” Phys. Rev. Lett.
82
(19
), 3863
(1999
).35.
W.
Kohn
and L. J.
Sham
, “Self-consistent equations including exchange and correlation effects
,” Phys. Rev.
140
(4A
), A1133
(1965
).36.
N. T.
Maitra
, K.
Burke
, and C.
Woodward
, “Memory in time-dependent density functional theory
,” Phys. Rev. Lett.
89
(2
), 023002
(2002
).37.
L.
Mancini
, J. D.
Ramsden
, M. J. P.
Hodgson
, and R. W.
Godby
, “Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains
,” Phys. Rev. B
89
(19
), 195114
(2014
).38.
N. T.
Maitra
, “Perspective: Fundamental aspects of time-dependent density functional theory
,” J. Chem. Phys.
144
(22
), 220901
(2016
).39.
M. J. P.
Hodgson
and J.
Wetherell
, “Accurate real-time evolution of electron densities and ground-state properties from generalized Kohn-Sham theory
,” Phys. Rev. A
101
(3
), 032502
(2020
).40.
M. T.
Entwistle
and R. W.
Godby
, “Exact nonadiabatic part of the Kohn-Sham potential and its fluidic approximation
,” Phys. Rev. Mater.
4
(3
), 035002
(2020
).41.
D.
Dar
, L.
Lacombe
, and N. T.
Maitra
, “The exact exchange–correlation potential in time-dependent density functional theory: Choreographing electrons with steps and peaks
,” Chem. Phys. Rev.
3
(3
), 031307
(2022
).42.
N. T.
Maitra
, “Charge transfer in time-dependent density functisonal theory
,” J. Phys.: Condens. Matter
29
(42
), 423001
(2017
).43.
M. R.
Provorse
, B. F.
Habenicht
, and C. M.
Isborn
, “Peak-shifting in real-time time-dependent density functional theory
,” J. Chem. Theory Comput.
11
(10
), 4791
(2015
).44.
K.
Luo
, J. I.
Fuks
, and N. T.
Maitra
, “Studies of spuriously shifting resonances in time-dependent density functional theory
,” J. Chem. Phys.
145
(4
), 044101
(2016
).45.
J. I.
Fuks
, K.
Luo
, E. D.
Sandoval
, and N. T.
Maitra
, “Time-resolved spectroscopy in time-dependent density functional theory: An exact condition
,” Phys. Rev. Lett.
114
(18
), 183002
(2015
).46.
B. F.
Habenicht
, N. P.
Tani
, M. R.
Provorse
, and C. M.
Isborn
, “Two-electron Rabi oscillations in real-time time-dependent density-functional theory
,” J. Chem. Phys.
141
(18
), 184112
(2014
).47.
A.
Seidl
, A.
Görling
, P.
Vogl
, J. A.
Majewski
, and M.
Levy
, “Generalized Kohn-Sham schemes and the band-gap problem
,” Phys. Rev. B
53
(7
), 3764
(1996
).48.
C. M.
Isborn
and X.
Li
, “Modeling the doubly excited state with time-dependent Hartree–Fock and density functional theories
,” J. Chem. Phys.
129
(20
), 204107
(2008
).49.
M.
Ruggenthaler
and D.
Bauer
, “Rabi oscillations and few-level approximations in time-dependent density functional theory
,” Phys. Rev. Lett.
102
(23
), 233001
(2009
).50.
J. I.
Fuks
, P.
Elliott
, A.
Rubio
, and N. T.
Maitra
, “Dynamics of charge-transfer processes with time-dependent density functional theory
,” J. Phys. Chem. Lett.
4
(5
), 735
(2013
).51.
S.
Raghunathan
and M.
Nest
, “The lack of resonance problem in coherent control with real-time time-dependent density functional theory
,” J. Chem. Theory Comput.
8
(3
), 806
(2012
).52.
D.
Dar
, L.
Lacombe
, J.
Feist
, and N. T.
Maitra
, “Exact time-dependent density-functional theory for nonperturbative dynamics of the helium atom
,” Phys. Rev. A
104
(3
), 032821
(2021
).53.
54.
D. A.
McQuarrie
and J. D.
Simon
, Physical Chemistry: A Molecular Approach
(University Science Books
, Sausalito, CA
, 1997
).55.
56.
R. J.
Bartlett
and M.
Musiał
, “Coupled-cluster theory in quantum chemistry
,” Rev. Mod. Phys.
79
(1
), 291
(2007
).57.
P.
Hoerner
, M. K.
Lee
, and H. B.
Schlegel
, “Angular dependence of strong field ionization of N2 by time-dependent configuration interaction using density functional theory and the Tamm-Dancoff approximation
,” J. Chem. Phys.
151
(5
), 054102
(2019
).58.
J. B.
Foresman
, M.
Head-Gordon
, J. A.
Pople
, and M. J.
Frisch
, “Toward a systematic molecular orbital theory for excited states
,” J. Phys. Chem.
96
(1
), 135
(1992
).59.
C.
David Sherrill
and H. F.
Schaefer
III, “The configuration interaction method: Advances in highly correlated approaches
,” Adv. Quantum Chem.
34
, 143
–269
(1999
).60.
T.
Klamroth
, “Laser-driven electron transfer through metal-insulator-metal contacts: Time-dependent configuration interaction singles calculations for a jellium model
,” Phys. Rev. B
68
(24
), 245421
(2003
).61.
F.
Casas
and A.
Iserles
, “Explicit Magnus expansions for nonlinear equations
,” J. Phys. A: Math. Gen.
39
(19
), 5445
(2006
).62.
S.
Blanes
, F.
Casas
, J. A.
Oteo
, and J.
Ros
, “The Magnus expansion and some of its applications
,” Phys. Rep.
470
(5–6
), 151
(2009
).63.
D.
Tannor
, Introduction to Quantum Mechanics
, 1st ed.
(University Science Books
, 2008
).64.
P.
Krause
, T.
Klamroth
, and P.
Saalfrank
, “Time-dependent configuration-interaction calculations of laser-pulse-driven many-electron dynamics: Controlled dipole switching in lithium cyanide
,” J. Chem. Phys.
123
(7
), 074105
(2005
).65.
P.
Krause
, T.
Klamroth
, and P.
Saalfrank
, “Molecular response properties from explicitly time-dependent configuration interaction methods
,” J. Chem. Phys.
127
(3
), 034107
(2007
).66.
H. B.
Schlegel
, S. M.
Smith
, and X.
Li
, “Electronic optical response of molecules in intense fields: Comparison of TD-HF, TD-CIS, and TD-CIS(D) approaches
,” J. Chem. Phys.
126
(24
), 244110
(2007
).67.
J. A.
Sonk
, M.
Caricato
, and H. B.
Schlegel
, “TD-CI simulation of the electronic optical response of molecules in intense fields: Comparison of RPA, CIS, CIS(D), and EOM-CCSD
,” J. Phys. Chem. A
115
(18
), 4678
(2011
).68.
W.-T.
Peng
, B. S.
Fales
, and B. G.
Levine
, “Simulating electron dynamics of complex molecules with time-dependent complete active space configuration interaction
,” J. Chem. Theory Comput.
14
(8
), 4129
(2018
).69.
R.
Ramakrishnan
, “Charge-transfer selectivity and quantum interference in real-time electron dynamics: Gaining insights from time-dependent configuration interaction simulations
,” J. Chem. Phys.
152
(19
), 194111
(2020
).70.
I. S.
Ulusoy
, Z.
Stewart
, and A. K.
Wilson
, “The role of the CI expansion length in time-dependent studies
,” J. Chem. Phys.
148
(1
), 014107
(2018
).71.
V.
Kochetov
and S. I.
Bokarev
, “RhoDyn: A ρ-TD-RASCI framework to study ultrafast electron dynamics in molecules
,” J. Chem. Theory Comput.
18
(1
), 46
(2022
).72.
C. A.
Ullrich
, Time-Dependent Density-Functional Theory
(Oxford University Press
, 2011
).73.
Fundamentals of Time-Dependent Density Functional Theory
, edited by M. A. L.
Marques
, N. T.
Maitra
, F.
Nogueira
, E. K. U.
Gross
, and A.
Rubio
(Springer
, 2012
).74.
R.
Baer
, “Prevalence of the adiabatic exchange-correlation potential approximation in time-dependent density functional theory
,” J. Mol. Struct.: THEOCHEM
914
(1–3
), 19
(2009
).75.
I. S.
Wahyutama
, D. D.
Jayasinghe
, F.
Mauger
, K.
Lopata
, M. B.
Gaarde
, and K. J.
Schafer
, “All-electron, density-functional-based method for angle-resolved tunneling ionization in the adiabatic regime
,” Phys. Rev. A
106
(5
), 052211
(2022
).76.
C. A.
Ullrich
and K.
Burke
, “Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation
,” J. Chem. Phys.
121
(1
), 28
(2004
).77.
H. O.
Wijewardane
and C. A.
Ullrich
, “Time-dependent Kohn-Sham theory with memory
,” Phys. Rev. Lett.
95
(8
), 086401
(2005
).78.
H. O.
Wijewardane
and C. A.
Ullrich
, “Real-time electron dynamics with exact-exchange time-dependent density-functional theory
,” Phys. Rev. Lett.
100
(5
), 056404
(2008
).79.
J. I.
Fuks
, L.
Lacombe
, S. E. B.
Nielsen
, and N. T.
Maitra
, “Exploring non-adiabatic approximations to the exchange-correlation functional of TDDFT
,” Phys. Chem. Chem. Phys.
20
(41
), 26145
(2018
).80.
A. D.
McLachlan
and M. A.
Ball
, “Time-dependent Hartree–Fock theory for molecules
,” Rev. Mod. Phys.
36
(3
), 844
(1964
).81.
R.
Baer
and L.
Kronik
, “Time-dependent generalized Kohn–Sham theory
,” Eur. Phys. J. B
91
(7
), 170
(2018
).82.
X.
Li
, S. M.
Smith
, A. N.
Markevitch
, D. A.
Romanov
, R. J.
Levis
, and H. B.
Schlegel
, “A time-dependent Hartree–Fock approach for studying the electronic optical response of molecules in intense fields
,” Phys. Chem. Chem. Phys.
7
(2
), 233
(2005
).83.
W.
Liang
, C. T.
Chapman
, and X.
Li
, “Efficient first-principles electronic dynamics
,” J. Chem. Phys.
134
(18
), 184102
(2011
).84.
A.
Gómez Pueyo
, M. A. L.
Marques
, A.
Rubio
, and A.
Castro
, “Propagators for the time-dependent Kohn–Sham equations: Multistep, Runge–Kutta, exponential Runge–Kutta, and commutator free Magnus methods
,” J. Chem. Theory Comput.
14
(6
), 3040
(2018
).85.
Y.
Zhu
and J. M.
Herbert
, “Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation
,” J. Chem. Phys.
148
(4
), 044117
(2018
).86.
D. B.
Williams-Young
, A.
Petrone
, S.
Sun
, T. F.
Stetina
, P.
Lestrange
, C. E.
Hoyer
, D. R.
Nascimento
, L.
Koulias
, A.
Wildman
, J.
Kasper
, J. J.
Goings
, F.
Ding
, A.
Eugene DePrince
, E. F.
Valeev
, and X.
Li
, “The Chronus Quantum software package
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci. Sci.
10
(2
), e1436
(2019
).87.
S.
Hirata
and M.
Head-Gordon
, “Time-dependent density functional theory within the Tamm–Dancoff approximation
,” Chem. Phys. Lett.
314
(3–4
), 291
(1999
).88.
F.
Cordova
, L. J.
Doriol
, A.
Ipatov
, M. E.
Casida
, C.
Filippi
, and A.
Vela
, “Troubleshooting time-dependent density-functional theory for photochemical applications: Oxirane
,” J. Chem. Phys.
127
(16
), 164111
(2007
).89.
C. M.
Isborn
, N.
Luehr
, I. S.
Ufimtsev
, and T. J.
Martínez
, “Excited-state electronic structure with configuration interaction singles and Tamm–Dancoff time-dependent density functional theory on graphical processing units
,” J. Chem. Theory Comput.
7
(6
), 1814
(2011
).90.
J. E.
Subotnik
, “Communication: Configuration interaction singles has a large systematic bias against charge-transfer states
,” J. Chem. Phys.
135
(7
), 071104
(2011
).91.
S.
Grimme
, “A simplified Tamm-Dancoff density functional approach for the electronic excitation spectra of very large molecules
,” J. Chem. Phys.
138
(24
), 244104
(2013
).92.
A. D.
Becke
, “Density-functional thermochemistry. III. The role of exact exchange
,” J. Chem. Phys.
98
(7
), 5648
(1993
).93.
P. J.
Stephens
, F. J.
Devlin
, C. F.
Chabalowski
, and M. J.
Frisch
, “Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields
,” J. Phys. Chem.
98
(45
), 11623
(1994
).94.
B. P.
Pritchard
, D.
Altarawy
, B.
Didier
, T. D.
Gibson
, and T. L.
Windus
, “New basis set exchange: An open, up-to-date resource for the molecular sciences community
,” J. Chem. Inf. Model.
59
(11
), 4814
(2019
).95.
M. J.
Frisch
, G. W.
Trucks
, H. B.
Schlegel
, G. E.
Scuseria
, M. A.
Robb
, J. R.
Cheeseman
, G.
Scalmani
, V.
Barone
, G. A.
Petersson
, H.
Nakatsuji
, X.
Li
, M.
Caricato
, A. V.
Marenich
, J.
Bloino
, B. G.
Janesko
, R.
Gomperts
, B.
Mennucci
, H. P.
Hratchian
, J. V.
Ortiz
, A. F.
Izmaylov
, J. L.
Sonnenberg
,D.
Williams-Young
, F.
Ding
, F.
Lipparini
, F.
Egidi
, J.
Goings
, B.
Peng
, A.
Petrone
, T.
Henderson
, D.
Ranasinghe
, V. G.
Zakrzewski
, J.
Gao
, N.
Rega
, G.
Zheng
, W.
Liang
, M.
Hada
, M.
Ehara
, K.
Toyota
, R.
Fukuda
, J.
Hasegawa
, M.
Ishida
, T.
Nakajima
, Y.
Honda
, O.
Kitao
, H.
Nakai
, T.
Vreven
, K.
Throssell
, J. A.
Montgomery
, Jr., J. E.
Peralta
, F.
Ogliaro
, M. J.
Bearpark
, J. J.
Heyd
, E. N.
Brothers
, K. N.
Kudin
, V. N.
Staroverov
, T. A.
Keith
, R.
Kobayashi
, J.
Normand
, K.
Raghavachari
, A. P.
Rendell
, J. C.
Burant
, S. S.
Iyengar
, J.
Tomasi
, M.
Cossi
, J. M.
Millam
, M.
Klene
, C.
Adamo
, R.
Cammi
, J. W.
Ochterski
, R. L.
Martin
, K.
Morokuma
, O.
Farkas
, J. B.
Foresman
, and D. J.
Fox
, Gaussian Development Version Revision I.14+, Gaussian, Inc.
, Wallingford, CT
, 2018
.96.
M. W.
Schmidt
and M. S.
Gordon
, “The construction and interpretation of MCSCF wavefunctions
,” Annu. Rev. Phys. Chem.
49
(1
), 233
(1998
).97.
98.
J. I.
Fuks
, N.
Helbig
, I. V.
Tokatly
, and A.
Rubio
, “Nonlinear phenomena in time-dependent density-functional theory: What Rabi oscillations can teach us
,” Phys. Rev. B
84
(7
), 075107
(2011
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
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