A scheme for the calculation of molecular properties within the framework of unitary coupled-cluster (UCC) theory in both the electronic ground and excited states is presented. The scheme is based on an expectation-value ansatz, similar to the equation-of-motion coupled-cluster method or the intermediate state representation (ISR) approach of the algebraic–diagrammatic construction (ADC) scheme. Due to the UCC ansatz, the resulting equations cannot be given by closed-form expressions but need to be approximated. Explicit expressions for the expectation value of a general one-particle operator correct through second order in perturbation theory have been derived and coded for the electronic ground state as well as for excited states of predominant single-excitation character. The resulting equations are shown to be equivalent to those of the second-order ADC/ISR procedure. As first computational tests, the second-order UCC method (UCC2) and the one employing third-order amplitudes (also eigenvectors) together with the second-order density matrix, denoted as UCC3(2), are applied to the calculation of dipole moments for a series of small closed- and open-shell systems as well as 4-cyanoindole and 2,3-benzofuran and compared to full configuration interaction or experimental results. For the aromatic organic molecules, the UCC2 method is shown to be sufficient for the ground-state dipole moment, whereas the UCC3(2) scheme is superior for excited-state dipole moments.
REFERENCES
1.
R.
McWeeny
, Methods of Molecular Quantum Mechanics
, Theoretical Chemistry, 2nd ed. (Academic Press
, London
, 1992
).2.
Methods in Computational Molecular Physics
, edited by S.
Wilson
and G. H. F.
Diercksen
(Springer US
, Boston, MA
, 1992
).3.
F.
Neese
, Coord. Chem. Rev.
253
, 526
(2009
).4.
T.
Helgaker
, S.
Coriani
, P.
Jørgensen
, K.
Kristensen
, J.
Olsen
, and K.
Ruud
, Chem. Rev.
112
, 543
(2012
).5.
6.
R. P.
Feynman
, Phys. Rev.
56
, 340
(1939
).7.
G. W.
Trucks
, E. A.
Salter
, C.
Sosa
, and R. J.
Bartlett
, Chem. Phys. Lett.
147
, 359
(1988
).8.
M.
Hodecker
, D. R.
Rehn
, A.
Dreuw
, and S.
Höfener
, J. Chem. Phys.
150
, 164125
(2019
).9.
M.
Hodecker
, “Development and application of Hermitian methods for molecular properties and excited electronic states
,” Ph.D. thesis, Universität Heidelberg
, 2020
.10.
D. J.
Rowe
, Nucl. Phys.
80
, 209
(1966
).11.
A.
Heßelmann
and A.
Görling
, Mol. Phys.
109
, 2473
(2011
).12.
H.
Eshuis
, J. E.
Bates
, and F.
Furche
, Theor. Chem. Acc.
131
, 1084
(2012
).13.
E. S.
Nielsen
, P.
Jørgensen
, and J.
Oddershede
, J. Chem. Phys.
73
, 6238
(1980
).14.
J.
Oddershede
, Adv. Chem. Phys.
69
, 201
(1987
).15.
K. L.
Bak
, H.
Koch
, J.
Oddershede
, O.
Christiansen
, and S. P. A.
Sauer
, J. Chem. Phys.
112
, 4173
(2000
).16.
J.
Schirmer
, Phys. Rev. A
26
, 2395
(1982
).17.
A. B.
Trofimov
, G.
Stelter
, and J.
Schirmer
, J. Chem. Phys.
111
, 9982
(1999
).18.
A.
Dreuw
and M.
Wormit
, Wiley Interdiscip. Rev.: Comput. Mol. Sci.
5
, 82
(2015
).19.
J.
Schirmer
, Many-Body Methods for Atoms, Molecules and Clusters
(Springer International Publishing
, 2018
).20.
J.
Schirmer
, Phys. Rev. A
43
, 4647
(1991
).21.
J.
Schirmer
and A. B.
Trofimov
, J. Chem. Phys.
120
, 11449
(2004
).22.
R. J.
Bartlett
, Annu. Rev. Phys. Chem.
32
, 359
(1981
).23.
T. D.
Crawford
and H. F.
Schaefer
III, Rev. Comput. Chem.
14
, 33
(2000
).24.
R. J.
Bartlett
and M.
Musiał
, Rev. Mod. Phys.
79
, 291
(2007
).25.
I.
Shavitt
and R. J.
Bartlett
, Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory
(Cambridge University Press
, Cambridge
, 2009
).26.
J.
Geertsen
, M.
Rittby
, and R. J.
Bartlett
, Chem. Phys. Lett.
164
, 57
(1989
).27.
J. F.
Stanton
and R. J.
Bartlett
, J. Chem. Phys.
98
, 7029
(1993
).28.
A. I.
Krylov
, Annu. Rev. Phys. Chem.
59
, 433
(2008
).29.
R. J.
Bartlett
, Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 126
(2012
).30.
J.
Liu
, A.
Asthana
, L.
Cheng
, and D.
Mukherjee
, J. Chem. Phys.
148
, 244110
(2018
).31.
M.
Hodecker
, D. R.
Rehn
, and A.
Dreuw
, J. Chem. Phys.
152
, 094106
(2020
).32.
M.
Hodecker
, S. M.
Thielen
, J.
Liu
, D. R.
Rehn
, and A.
Dreuw
, J. Chem. Theory Comput.
16
, 3654
(2020
).33.
F.
Mertins
and J.
Schirmer
, Phys. Rev. A
53
, 2140
(1996
).34.
F.
Mertins
, J.
Schirmer
, and A.
Tarantelli
, Phys. Rev. A
53
, 2153
(1996
).35.
J.
Schirmer
and F.
Mertins
, Theor. Chem. Acc.
125
, 145
(2010
).36.
R. J.
Bartlett
, S. A.
Kucharski
, and J.
Noga
, Chem. Phys. Lett.
155
, 133
(1989
).37.
A. G.
Taube
and R. J.
Bartlett
, J. Chem. Phys.
130
, 144112
(2009
).38.
J. D.
Watts
, G. W.
Trucks
, and R. J.
Bartlett
, Chem. Phys. Lett.
164
, 502
(1989
).39.
J. D.
Watts
, G. W.
Trucks
, and R. J.
Bartlett
, Chem. Phys. Lett.
157
, 359
(1989
).40.
F. A.
Evangelista
, J. Chem. Phys.
134
, 224102
(2011
).41.
F.
Jensen
, Introduction to Computational Chemistry
, 2nd ed. (John Wiley & Sons
, USA
, 2006
).42.
G. W.
Trucks
, E. A.
Salter
, J.
Noga
, and R. J.
Bartlett
, Chem. Phys. Lett.
150
, 37
(1988
).43.
C. W.
Bauschlicher
and P. R.
Taylor
, Theor. Chim. Acta
71
, 263
(1987
).44.
C. W.
Bauschlicher
, S. R.
Langhoff
, and P. R.
Taylor
, Adv. Chem. Phys.
77
, 103
(1990
).45.
M.
Wormit
, D. R.
Rehn
, P. H. P.
Harbach
, J.
Wenzel
, C. M.
Krauter
, E.
Epifanovsky
, and A.
Dreuw
, Mol. Phys.
112
, 774
(2014
).46.
47.
48.
49.
A.
Szabo
and N. S.
Ostlund
, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory
(Dover
, Mineola, NY
, 1996
).50.
T.
Helgaker
, P.
Jørgensen
, and J.
Olsen
, Molecular Electronic-Structure Theory
(John Wiley & Sons, Ltd.
, 2000
).51.
M. D.
Prasad
, S.
Pal
, and D.
Mukherjee
, Phys. Rev. A
31
, 1287
(1985
).52.
D.
Mukherjee
and W.
Kutzelnigg
, in Many-Body Methods in Quantum Chemistry
, Lecture Notes in Chemistry, edited by U.
Kaldor
(Springer Berlin
, Heidelberg
, 1989
), Vol. 52, pp. 257
–274
.53.
W.
Kutzelnigg
, Theor. Chim. Acta
80
, 349
(1991
).54.
A. G.
Taube
and R. J.
Bartlett
, Int. J. Quantum Chem.
106
, 3393
(2006
).55.
W.
Kutzelnigg
and S.
Koch
, J. Chem. Phys.
79
, 4315
(1983
).56.
M. R.
Hoffmann
and J.
Simons
, J. Chem. Phys.
88
, 993
(1988
).57.
W.
Kutzelnigg
, J. Chem. Phys.
77
, 3081
(1982
).58.
J.
Schirmer
and F.
Mertins
, Int. J. Quantum Chem.
58
, 329
(1996
).59.
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.
Kús
, 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
III, P. M.
Zimmerman
, D.
Zuev
, B.
Albrecht
, E.
Alguire
, B.
Austin
, G. J. O.
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
, Jr., 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.
O’Neill
, 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
III, M. S.
Gordon
, W. J.
Hehre
, A.
Klamt
, H. F.
Schaefer
III, 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. V.
Voorhis
, J. M.
Herbert
, A. I.
Krylov
, P. M.
Gill
, and M.
Head-Gordon
, Mol. Phys.
113
, 184
(2015
).60.
J. S.
Binkley
, J. A.
Pople
, and W. J.
Hehre
, J. Am. Chem. Soc.
102
, 939
(1980
).61.
C. W.
Bauschlicher
and P. R.
Taylor
, J. Chem. Phys.
85
, 6510
(1986
).62.
C. W.
Bauschlicher
and P. R.
Taylor
, J. Chem. Phys.
86
, 1420
(1987
).63.
A. L.
Dempwolff
, A. C.
Paul
, A. M.
Belogolova
, A. B.
Trofimov
, and A.
Dreuw
, J. Chem. Phys.
152
, 024113
(2020
).64.
T. H.
Dunning
, J. Chem. Phys.
90
, 1007
(1989
).65.
R. A.
Kendall
, T. H.
Dunning
, Jr., and R. J.
Harrison
, J. Chem. Phys.
96
, 6796
(1992
).66.
M.-L.
Hebestreit
, M.
Schneider
, H.
Lartian
, V.
Betz
, M.
Heinrich
, M.
Lindic
, M. Y.
Choi
, and M.
Schmitt
, Phys. Chem. Chem. Phys.
21
, 14766
(2019
).67.
R. G.
Parr
and W.
Yang
, Density-Functional Theory of Atoms and Molecules
(Oxford University Press
, USA
, 1994
).68.
A. D.
Becke
, J. Chem. Phys.
98
, 5648
(1993
).69.
F.
Weigend
and R.
Ahlrichs
, Phys. Chem. Chem. Phys.
7
, 3297
(2005
).70.
C. A.
Burrus
, J. Chem. Phys.
28
, 427
(1958
).71.
L.
Wharton
, L. P.
Gold
, and W.
Klemperer
, J. Chem. Phys.
33
, 1255
(1960
).72.
D. K.
Coles
, W. E.
Good
, J. K.
Bragg
, and A. H.
Sharbaugh
, Phys. Rev.
82
, 877
(1951
).73.
K. P.
Huber
and G.
Herzberg
, Molecular Spectra and Molecular Structure. IV: Constants of Diatomic Molecules
(Springer US
, Boston, MA
, 1979
).74.
R.
Weiss
, Phys. Rev.
131
, 659
(1963
).75.
B. N.
Bhattacharya
and W.
Gordy
, Phys. Rev.
119
, 144
(1960
).76.
J. M.
Brown
, S. W.
Chalkley
, and F. D.
Wayne
, Mol. Phys.
38
, 1521
(1979
).77.
F. X.
Powell
and D. R.
Lide
, J. Chem. Phys.
42
, 4201
(1965
).78.
R.
Thomson
and F. W.
Dalby
, Can. J. Phys.
46
, 2815
(1968
).79.
J. A.
Hodgeson
, E. E.
Sibert
, and R. F.
Curl
, J. Phys. Chem.
67
, 2833
(1963
).80.
P. H. P.
Harbach
, M.
Wormit
, and A.
Dreuw
, J. Chem. Phys.
141
, 064113
(2014
).81.
M.-L.
Hebestreit
, H.
Lartian
, M.
Schneider
, R.
Kühnemuth
, A. Y.
Torres-Boy
, S.
Romero-Servin
, J. A.
Ruiz-Santoyo
, L.
Alvarez-Valtierra
, W. L.
Meerts
, and M.
Schmitt
, J. Mol. Struct.
1210
, 127992
(2020
).82.
M.
Schmitt
and L.
Meerts
, in Frontiers and Advances in Molecular Spectroscopy
, edited by J.
Laane
(Elsevier
, 2018
), Chap. 5, pp. 143
–193
.© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
