The advent of ever more powerful excited-state electronic structure methods has led to a tremendous increase in the predictive power of computation, but it has also rendered the analysis of these computations much more challenging and time-consuming. TheoDORE tackles this problem through providing tools for post-processing excited-state computations, which automate repetitive tasks and provide rigorous and reproducible descriptors. Interfaces are available for ten different quantum chemistry codes and a range of excited-state methods implemented therein. This article provides an overview of three popular functionalities within TheoDORE, a fragment-based analysis for assigning state character, the computation of exciton sizes for measuring charge transfer, and the natural transition orbitals used not only for visualization but also for quantifying multiconfigurational character. Using the examples of an organic push–pull chromophore and a transition metal complex, it is shown how these tools can be used for a rigorous and automated assignment of excited-state character. In the case of a conjugated polymer, we venture beyond the limits of the traditional molecular orbital picture to uncover spatial correlation effects using electron–hole correlation plots and conditional densities.
REFERENCES
1.
A. V.
Titov
, I. S.
Ufimtsev
, N.
Luehr
, and T. J.
Martinez
, “Generating efficient quantum chemistry codes for novel architectures
,” J. Chem. Theory Comput.
9
, 213
–221
(2013
).2.
A. I.
Krylov
and P. M.
Gill
, “Q-Chem: An engine for innovation
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
3
, 317
–326
(2013
).3.
M.
Vacher
, I. F.
Galván
, B.-W.
Ding
, S.
Schramm
, R.
Berraud-Pache
, P.
Naumov
, N.
Ferré
, Y.-J.
Liu
, I.
Navizet
, D.
Roca-Sanjuán
, W. J.
Baader
, and R.
Lindh
, “Chemi- and bioluminescence of cyclic peroxides
,” Chem. Rev.
118
, 6927
–6974
(2018
).4.
S.
Ghosh
, P.
Verma
, C. J.
Cramer
, L.
Gagliardi
, and D. G.
Truhlar
, “Combining wave function methods with density functional theory for excited states
,” Chem. Rev.
118
, 7249
–7292
(2018
).5.
H.
Lischka
, D.
Nachtigallová
, A. J. A.
Aquino
, P.
Szalay
, F.
Plasser
, F. B. C.
Machado
, and M.
Barbatti
, “Multireference approaches for excited states of molecules
,” Chem. Rev.
118
, 7293
–7361
(2018
).6.
M.
Head-Gordon
, A. M.
Grana
, D.
Maurice
, and C. A.
White
, “Analysis of electronic transitions as the difference of electron attachment and detachment densities
,” J. Chem. Phys.
99
, 14261
–14270
(1995
).7.
R. L.
Martin
, “Natural transition orbitals
,” J. Chem. Phys.
118
, 4775
–4777
(2003
).8.
F.
Plasser
, M.
Wormit
, and A.
Dreuw
, “New tools for the systematic analysis and visualization of electronic excitations. I. Formalism
,” J. Chem. Phys.
141
, 024106
(2014
).9.
M. J. G.
Peach
, P.
Benfield
, T.
Helgaker
, and D. J.
Tozer
, “Excitation energies in density functional theory: An evaluation and a diagnostic test
,” J. Chem. Phys.
128
, 044118
(2008
).10.
S. A.
Bäppler
, F.
Plasser
, M.
Wormit
, and A.
Dreuw
, “Exciton analysis of many-body wave functions: Bridging the gap between the quasiparticle and molecular orbital pictures
,” Phys. Rev. A
90
, 052521
(2014
).11.
E.
Ronca
, C.
Angeli
, L.
Belpassi
, F. D.
Angelis
, F.
Tarantelli
, and M.
Pastore
, “Density relaxation in time-dependent density functional theory: Combining relaxed density natural orbitals and multireference perturbation theories for an improved description of excited states
,” J. Chem. Theory Comput.
10
, 4014
–4024
(2014
).12.
T.
Etienne
, X.
Assfeld
, and A.
Monari
, “New insight into the topology of excited states through detachment/attachment density matrices-based centroids of charge
,” J. Chem. Theory Comput.
10
, 3906
–3914
(2014
).13.
C.
Adamo
, T.
Le Bahers
, M.
Savarese
, L.
Wilbraham
, G.
Garcia
, R.
Fukuda
, M.
Ehara
, N.
Rega
, and I.
Ciofini
, “Exploring excited states using time dependent density functional theory and density-based indexes
,” Coord. Chem. Rev.
304-305
, 166
–178
(2015
).14.
J.
Coe
and M.
Paterson
, “Characterising a configuration interaction excited state using natural transition geminals
,” Mol. Phys.
112
, 733
–739
(2014
).15.
S.
Matsika
, X.
Feng
, A. V.
Luzanov
, and A. I.
Krylov
, “What we can learn from the norms of one-particle density matrices, and what we can’t: Some results for interstate properties in model singlet fission systems
,” J. Phys. Chem. A
118
, 11943
–11955
(2014
).16.
G. M. J.
Barca
, A. T. B.
Gilbert
, and P. M. W.
Gill
, “Excitation number: Characterizing multiply excited states
,” J. Chem. Theory Comput.
14
, 9
–13
(2018
).17.
A. V.
Luzanov
and O. V.
Prezhdo
, “High-order entropy measures and spin-free quantum entanglement for molecular problems
,” Mol. Phys.
105
, 2879
–2891
(2007
).18.
K.
Boguslawski
, P.
Tecmer
, O.
Legeza
, and M.
Reiher
, “Entanglement measures for single- and multireference correlation effects
,” J. Phys. Chem. Lett.
3
, 3129
–3135
(2012
).19.
F.
Plasser
, “Entanglement entropy of electronic excitations
,” J. Chem. Phys.
144
, 194107
(2016
).20.
C. J.
Stein
and M.
Reiher
, “Measuring multi-configurational character by orbital entanglement
,” Mol. Phys.
115
, 2110
–2119
(2017
); arXiv:1609.02617.21.
E.
Zojer
, P.
Buchacher
, F.
Wudl
, J.
Cornil
, J. P.
Calbert
, J. L.
Brédas
, and G.
Leising
, “Excited state localization in organic molecules consisting of conjugated and nonconjugated segments
,” J. Chem. Phys.
113
, 10002
–10012
(2000
).22.
J.
Rissler
, H.
Bässler
, F.
Gebhard
, and P.
Schwerdtfeger
, “Excited states of ladder-type poly-p-phenylene oligomers
,” Phys. Rev. B
64
, 045122
(2001
).23.
S.
Tretiak
and S.
Mukamel
, “Density matrix analysis and simulation of electronic excitations in conjugated and aggregated molecules
,” Chem. Rev.
102
, 3171
–3212
(2002
).24.
J.
Cornil
, I.
Gueli
, A.
Dkhissi
, J. C.
Sancho-Garcia
, E.
Hennebicq
, J. P.
Calbert
, V.
Lemaur
, D.
Beljonne
, and J. L.
Brédas
, “Electronic and optical properties of polyfluorene and fluorene-based copolymers: A quantum-chemical characterization
,” J. Chem. Phys.
118
, 6615
–6623
(2003
).25.
F.
Plasser
and H.
Lischka
, “Analysis of excitonic and charge transfer interactions from quantum chemical calculations
,” J. Chem. Theory Comput.
8
, 2777
–2789
(2012
).26.
Y.
Li
and C. A.
Ullrich
, “The particle-hole map: A computational tool to visualize electronic excitations
,” J. Chem. Theory Comput.
11
, 5838
–5852
(2015
).27.
F.
Plasser
, “Visualisation of electronic excited-state correlation in real space
,” ChemPhotoChem
3
, 702
–706
(2019
).28.
F.
Plasser
, THEODORE: A package for theoretical density, orbital relaxation, and exciton analysis, 2019
, available at http://theodore-qc.sourceforge.net.29.
H.
Lischka
, R.
Shepard
, I.
Shavitt
, R. M.
Pitzer
, M.
Dallos
, T.
Muller
, P. G.
Szalay
, F. B.
Brown
, R.
Ahlrichs
, H. J.
Boehm
, A.
Chang
, D. C.
Comeau
, R.
Gdanitz
, H.
Dachsel
, C.
Ehrhardt
, M.
Ernzerhof
, P.
Hoechtl
, S.
Irle
, G.
Kedziora
, T.
Kovar
, V.
Parasuk
, M. J. M.
Pepper
, P.
Scharf
, H.
Schiffer
, M.
Schindler
, M.
Schueler
, M.
Seth
, E. A.
Stahlberg
, J.-G.
Zhao
, S.
Yabushita
, Z.
Zhang
, M.
Barbatti
, S.
Matsika
, M.
Schuurmann
, D. R.
Yarkony
, S. R.
Brozell
, E. V.
Beck
, J.-P.
Blaudeau
, M.
Ruckenbauer
, B.
Sellner
, F.
Plasser
, R. F. K.
Szymczak
, J. J.
Spada
, and A.
Das
, Columbus: An ab initio electronic structure program, release 7.0, 2017
, www.univie.ac.at/columbus.30.
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
, L. F.
Chibotaru
, J.
Creutzberg
, N.
Dattani
, M. G.
Delcey
, S. S.
Dong
, A.
Dreuw
, L.
Freitag
, L. M.
Frutos
, L.
Gagliardi
, F.
Gendron
, A.
Giussani
, L.
González
, G.
Grell
, M.
Guo
, C. E.
Hoyer
, M.
Johansson
, S.
Keller
, S.
Knecht
, G.
Kovačević
, E.
Källman
, G.
Li Manni
, M.
Lundberg
, Y.
Ma
, S.
Mai
, J. P.
Malhado
, P. Å.
Malmqvist
, P.
Marquetand
, S. A.
Mewes
, J.
Norell
, M.
Olivucci
, M.
Oppel
, Q. M.
Phung
, K.
Pierloot
, F.
Plasser
, M.
Reiher
, A. M.
Sand
, I.
Schapiro
, P.
Sharma
, C. J.
Stein
, L. K.
Sørensen
, D. G.
Truhlar
, M.
Ugandi
, L.
Ungur
, A.
Valentini
, S.
Vancoillie
, V.
Veryazov
, O.
Weser
, T. A.
Wesołowski
, P.-O.
Widmark
, S.
Wouters
, A.
Zech
, J. P.
Zobel
, and R.
Lindh
, “OpenMolcas: From source code to insight
,” J. Chem. Theory Comput.
15
, 5925
–5964
(2019
).31.
Y.
Shao
, Z.
Gan
, E.
Epifanovsky
, A. T.
Gilbert
, M.
Wormit
, J.
Kussmann
, A. W.
Lange
, A.
Behn
, J.
Deng
, X.
Feng
, D.
Ghosh
, M.
Goldey
, P. R.
Horn
, L. D.
Jacobson
, I.
Kaliman
, R. Z.
Khaliullin
, T.
Kus
, A.
Landau
, J.
Liu
, E. I.
Proynov
, Y. M.
Rhee
, R. M.
Richard
, M. A.
Rohrdanz
, R. P.
Steele
, E. J.
Sundstrom
, H. L.
Woodcock
, P. M.
Zimmerman
, D.
Zuev
, B.
Albrecht
, E.
Alguire
, B.
Austin
, G. J.
Beran
, Y. A.
Bernard
, E.
Berquist
, K.
Brandhorst
, K. B.
Bravaya
, S. T.
Brown
, D.
Casanova
, C. M.
Chang
, Y.
Chen
, S. H.
Chien
, K. D.
Closser
, D. L.
Crittenden
, M.
Diedenhofen
, R. A.
Distasio
, H.
Do
, A. D.
Dutoi
, R. G.
Edgar
, S.
Fatehi
, L.
Fusti-Molnar
, A.
Ghysels
, A.
Golubeva-Zadorozhnaya
, J.
Gomes
, M. W.
Hanson-Heine
, P. H.
Harbach
, A. W.
Hauser
, E. G.
Hohenstein
, Z. C.
Holden
, T. C.
Jagau
, H.
Ji
, B.
Kaduk
, K.
Khistyaev
, J.
Kim
, J.
Kim
, R. A.
King
, P.
Klunzinger
, D.
Kosenkov
, T.
Kowalczyk
, C. M.
Krauter
, K. U.
Lao
, A. D.
Laurent
, K. V.
Lawler
, S. V.
Levchenko
, C. Y.
Lin
, F.
Liu
, E.
Livshits
, R. C.
Lochan
, A.
Luenser
, P.
Manohar
, S. F.
Manzer
, S. P.
Mao
, N.
Mardirossian
, A. V.
Marenich
, S. A.
Maurer
, N. J.
Mayhall
, E.
Neuscamman
, C. M.
Oana
, R.
Olivares-Amaya
, D. P.
Oneill
, J. A.
Parkhill
, T. M.
Perrine
, R.
Peverati
, A.
Prociuk
, D. R.
Rehn
, E.
Rosta
, N. J.
Russ
, S. M.
Sharada
, S.
Sharma
, D. W.
Small
, A.
Sodt
, T.
Stein
, D.
Stück
, Y. C.
Su
, A. J.
Thom
, T.
Tsuchimochi
, V.
Vanovschi
, L.
Vogt
, O.
Vydrov
, T.
Wang
, M. A.
Watson
, J.
Wenzel
, A.
White
, C. F.
Williams
, J.
Yang
, S.
Yeganeh
, S. R.
Yost
, Z. Q.
You
, I. Y.
Zhang
, X.
Zhang
, Y.
Zhao
, B. R.
Brooks
, G. K.
Chan
, D. M.
Chipman
, C. J.
Cramer
, W. A.
Goddard
, M. S.
Gordon
, W. J.
Hehre
, A.
Klamt
, H. F.
Schaefer
, M. W.
Schmidt
, C. D.
Sherrill
, D. G.
Truhlar
, A.
Warshel
, X.
Xu
, A.
Aspuru-Guzik
, R.
Baer
, A. T.
Bell
, N. A.
Besley
, J. D.
Chai
, A.
Dreuw
, B. D.
Dunietz
, T. R.
Furlani
, S. R.
Gwaltney
, C. P.
Hsu
, Y.
Jung
, J.
Kong
, D. S.
Lambrecht
, W.
Liang
, C.
Ochsenfeld
, V. A.
Rassolov
, L. V.
Slipchenko
, J. E.
Subotnik
, T.
Van Voorhis
, J. M.
Herbert
, A. I.
Krylov
, P. M.
Gill
, and M.
Head-Gordon
, “Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
,” Mol. Phys.
113
, 184
–215
(2015
).32.
G.
te Velde
, F. M.
Bickelhaupt
, E. J.
Baerends
, C.
Fonseca Guerra
, S. J. A.
van Gisbergen
, J. G.
Snijders
, and T.
Ziegler
, “Chemistry with ADF
,” J. Comput. Chem.
22
, 931
–967
(2001
).33.
B.
Aradi
, B.
Hourahine
, and T.
Frauenheim
, “DFTB+, a sparse matrix-based implementation of the DFTB method
,” J. Phys. Chem. A
111
, 5678
–5684
(2007
).34.
A. A.
Granovsky
, Firefly version 8, 2017
.35.
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 16 Revision C.01, Gaussian, Inc.
, Wallingford, CT
, 2016
.36.
F.
Neese
, “Software update: The ORCA program system, version 4.0
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
, e1327
(2018
).37.
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
).38.
TURBOMOLE V7.2 2017, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007,
TURBOMOLE GmbH
, since 2007
, available at http://www.turbomole.com.39.
F.
Plasser
, A. J. A.
Aquino
, W. L.
Hase
, and H.
Lischka
, “UV absorption spectrum of alternating DNA duplexes. Analysis of excitonic and charge transfer interactions
,” J. Phys. Chem. A
116
, 11151
–11160
(2012
).40.
J. J.
Nogueira
, F.
Plasser
, and L.
González
, “Electronic delocalization, charge transfer and hypochromism in the UV absorption spectrum of polyadenine unravelled by multiscale computations and quantitative wavefunction analysis
,” Chem. Sci.
8
, 5682
–5691
(2017
).41.
F.
Glöcklhofer
, A.
Rosspeintner
, P.
Pasitsuparoad
, S.
Eder
, J.
Fröhlich
, G.
Angulo
, E.
Vauthey
, and F.
Plasser
, “Effect of symmetric and asymmetric substitution on the optoelectronic properties of 9,10-dicyanoanthracene
,” Mol. Syst. Des. Eng.
4
, 951
–961
(2019
).42.
F.
Plasser
and A.
Dreuw
, “High-level ab initio computations of the absorption spectra of organic iridium complexes
,” J. Phys. Chem. A
119
, 1023
–1026
(2015
).43.
S.
Mai
, F.
Plasser
, J.
Dorn
, M.
Fumanal
, C.
Daniel
, and L.
González
, “Quantitative wave function analysis for excited states of transition metal complexes
,” Coord. Chem. Rev.
361
, 74
–97
(2018
).44.
S. A.
Mewes
, J.-M.
Mewes
, F.
Plasser
, and A.
Dreuw
, “Excitons in poly(para phenylene vinylene): A quantum-chemical perspective based on high-level ab initio calculations
,” Phys. Chem. Chem. Phys.
18
, 2548
–2563
(2016
).45.
F.
Plasser
, B.
Thomitzni
, S. A.
Bäppler
, J.
Wenzel
, D. R.
Rehn
, M.
Wormit
, and A.
Dreuw
, “Statistical analysis of electronic excitation processes: Spatial location, compactness, charge transfer, and electron-hole correlation
,” J. Comput. Chem.
36
, 1609
–1620
(2015
).46.
A. V.
Luzanov
and O. A.
Zhikol
, “Electron invariants and excited state structural analysis for electronic transitions within CIS, RPA, and TDDFT models
,” Int. J. Quantum Chem.
110
, 902
–924
(2010
).47.
I.
Mayer
, “Bond order and valence: Relations to Mulliken’s population analysis
,” Int. J. Quantum Chem.
26
, 151
–154
(1984
).48.
A. A.
Voityuk
, “Fragment transition density method to calculate electronic coupling for excitation energy transfer
,” J. Chem. Phys.
140
, 244117
(2014
).49.
F.
Plasser
, G.
Granucci
, J.
Pittner
, M.
Barbatti
, M.
Persico
, and H.
Lischka
, “Surface hopping dynamics using a locally diabatic formalism: Charge transfer in the ethylene dimer cation and excited state dynamics in the 2-pyridone dimer
,” J. Chem. Phys.
137
, 22A514
(2012
).50.
S.
Mai
and L.
González
, “Unconventional two-step spin relaxation dynamics of [Re(CO)3 (im)(phen)]+ in aqueous solution
,” Chem. Sci.
10
, 10405
–10411
(2019
).51.
K.
Hummer
and C.
Ambrosch-Draxl
, “Oligoacene exciton binding energies: Their dependence on molecular size
,” Phys. Rev. B
71
, 081202
(2005
).52.
W.
Aggoune
, C.
Cocchi
, D.
Nabok
, K.
Rezouali
, M. A.
Belkhir
, and C.
Draxl
, “Dimensionality of excitons in stacked van der Waals materials: The example of hexagonal boron nitride
,” Phys. Rev. B
97
, 241114
(2018
).53.
P.
Bultinck
, D. L.
Cooper
, and R.
Ponec
, “Influence of atoms-in-molecules methods on shared-electron distribution indices and domain-averaged fermi holes
,” J. Phys. Chem. A
114
, 8754
–8763
(2010
).54.
J. B.
Schriber
, K. P.
Hannon
, C.
Li
, and F. A.
Evangelista
, “A combined selected configuration interaction and many-body treatment of static and dynamical correlation in oligoacenes
,” J. Chem. Theory Comput.
14
, 6295
–6305
(2018
).55.
S. A.
Mewes
, F.
Plasser
, and A.
Dreuw
, “Communication: Exciton analysis in time-dependent density functional theory: How functionals shape excited-state characters
,” J. Chem. Phys.
143
, 171101
(2015
).56.
F.
Plasser
, M.
Wormit
, S. A.
Mewes
, B.
Thomitzni
, and A.
Dreuw
, LIBWFA: Wave-function analysis tool library for quantum chemical applications, 2019
, available at https://github.com/libwfa/libwfa.57.
P.
Kautny
, F.
Glöcklhofer
, T.
Kader
, J.-M.
Mewes
, B.
Stöger
, J.
Fröhlich
, D.
Lumpi
, and F.
Plasser
, “Charge-transfer states in triazole linked donor–acceptor materials: Strong effects of chemical modification and solvation
,” Phys. Chem. Chem. Phys.
19
, 18055
–18067
(2017
).58.
S. I.
Bokarev
, O. S.
Bokareva
, and O.
Kühn
, “Electronic excitation spectrum of the photosensitizer [Ir(ppy)2(bpy)]+
,” J. Chem. Phys.
136
, 214305
(2012
).59.
B. J.
Powell
, “Theories of phosphorescence in organo-transition metal complexes—From relativistic effects to simple models and design principles for organic light-emitting diodes
,” Coord. Chem. Rev.
295
, 46
–79
(2015
).60.
B.
Beyer
, C.
Ulbricht
, D.
Escudero
, C.
Friebe
, A.
Winter
, L.
González
, and U. S.
Schubert
, “Phenyl-1H-[1,2,3]triazoles as new cyclometalating ligands for iridium(III) complexes
,” Organometallics
28
, 5478
–5488
(2009
).61.
P. A.
Scattergood
and P. I.
Elliott
, “An unexpected journey from highly tunable phosphorescence to novel photochemistry of 1,2,3-triazole-based complexes
,” Dalton Trans.
46
, 16343
–16356
(2017
).62.
S. A.
Mewes
, F.
Plasser
, and A.
Dreuw
, “Universal exciton size in organic polymers is determined by non-local orbital exchange in TDDFT
,” J. Phys. Chem. Lett.
8
, 1205
–1210
(2017
).63.
W.
Barford
, “Excitons in conjugated polymers: A tale of two particles
,” J. Phys. Chem. A
117
, 2665
–2671
(2013
).64.
T.
Rosenau
, A.
Potthast
, N. S.
Zwirchmayr
, H.
Hettegger
, F.
Plasser
, T.
Hosoya
, M.
Bacher
, K.
Krainz
, and T.
Dietz
, “Chromophores from hexeneuronic acids: Identification of HexA-derived chromophores
,” Cellulose
24
, 3671
–3687
(2017
).65.
N. S.
Zwirchmayr
, T.
Hosoya
, H.
Hettegger
, M.
Bacher
, K.
Krainz
, T.
Dietz
, U.
Henniges
, A.
Potthast
, and T.
Rosenau
, “Chromophores from hexeneuronic acids: Chemical behavior under peroxide bleaching conditions
,” Cellulose
24
, 3689
–3702
(2017
).66.
A.
Kumar
, G.
Cappellini
, and F.
Delogu
, “Electronic and optical properties of chromophores from hexeneuronic acids
,” Cellulose
26
, 1489
–1501
(2019
).67.
A. N.
Panda
, F.
Plasser
, A. J. A.
Aquino
, I.
Burghardt
, and H.
Lischka
, “Electronically excited states in poly(p-phenylenevinylene): Vertical excitations and torsional potentials from high-level ab initio calculations
,” J. Phys. Chem. A
117
, 2181
–2189
(2013
).68.
S.
van der Walt
, S. C.
Colbert
, and G.
Varoquaux
, “The NumPy array: A structure for efficient numerical computation
,” Comput. Sci. Eng.
13
, 22
–30
(2011
).69.
J. D.
Hunter
, “Matplotlib: A 2D graphics environment
,” Comput. Sci. Eng.
9
, 90
–95
(2007
).70.
N. M.
O’Boyle
, M.
Banck
, C. A.
James
, C.
Morley
, T.
Vandermeersch
, and G. R.
Hutchison
, “Open Babel: An open chemical toolbox
,” J. Cheminf.
3
, 33
(2011
).71.
N. M.
O’Boyle
, A. L.
Tenderholt
, and K. M.
Langner
, “cclib: A library for package-independent computational chemistry algorithms
,” J. Comput. Chem.
29
, 839
–845
(2008
).72.
G.
Hermann
, V.
Pohl
, J. C.
Tremblay
, B.
Paulus
, H. C.
Hege
, and A.
Schild
, “ORBKIT: A modular python toolbox for cross-platform postprocessing of quantum chemical wavefunction data
,” J. Comput. Chem.
37
, 1511
–1520
(2016
); arXiv:1601.03069.73.
M. D.
Hanwell
, D. E.
Curtis
, D. C.
Lonie
, T.
Vandermeersch
, E.
Zurek
, and G. R.
Hutchison
, “Avogadro: An advanced semantic chemical editor, visualization, and analysis platform
,” J. Cheminf.
4
, 17
(2012
).74.
JMOL: An open-source Java viewer for chemical structures in 3D, available at http://www.jmol.org/.
75.
W.
Humphrey
, A.
Dalke
, and K.
Schulten
, “VMD: Visual molecular dynamics
,” J. Mol. Graphics
14
, 33
–38
(1996
).76.
Schrödinger, LLC
, The PyMOL molecular graphics system, version 1.8, 2015
.77.
F.
Plasser
, qc_pymol: Scripts for using pymol together with quantum chemistry programs, 2019
, available at https://github.com/felixplasser/qc_pymol.78.
C.
Hattig
, “Structure optimizations for excited states with correlated second-order methods: CC2 and ADC(2)
,” Adv. Quantum Chem.
50
, 37
–60
(2005
).79.
A.
Schafer
, H.
Horn
, and R.
Ahlrichs
, “Fully optimized contracted Gaussian-basis sets for atoms Li to Kr
,” J. Chem. Phys.
97
, 2571
–2577
(1992
).80.
S.
Hirata
and M.
Head-Gordon
, “Time-dependent density functional theory within the Tamm–Dancoff approximation
,” Chem. Phys. Lett.
314
, 291
–299
(1999
).81.
C.
Adamo
and V.
Barone
, “Toward reliable density functional methods without adjustable parameters: The PBE0 model
,” J. Chem. Phys.
110
, 6158
–6170
(1999
).82.
A. D.
Becke
, “Density-functional thermochemistry. III. The role of exact exchange
,” J. Chem. Phys.
98
, 5648
–5652
(1993
).83.
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
).84.
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
).85.
F.
Neese
, F.
Wennmohs
, A.
Hansen
, and U.
Becker
, “Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange
,” Chem. Phys.
356
, 98
–109
(2009
).86.
Supporting research data available: Molecular geometries, input/output files of the employed quantum chemistry programs and TheoDORE; data and LaTeX/TikZ source files underlying the figures, .
87.
S. A.
Mewes
, F.
Plasser
, A.
Krylov
, and A.
Dreuw
, “Benchmarking excited-state calculations using exciton properties
,” J. Chem. Theory Comput.
14
, 710
–725
(2018
).88.
M.
Hoffmann
, S. A.
Mewes
, S.
Wieland
, C.
Popp
, and A.
Dreuw
, “Electron–hole correlation as unambiguous and universal classification for the nature of low-lying ππ* states of nitrogen heterocycles
,” J. Phys. Chem. Lett.
10
, 6112
–6117
(2019
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.