An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for the COSCC approach are presented. Orbital-relaxation effects due to the electric-field perturbation are treated via the Z-vector technique. We present calculations of the dipole moments for a number of doublet radicals in their ground states using restricted open-shell Hartree-Fock (ROHF) and quasi-restricted HF (QRHF) orbitals in order to demonstrate the applicability of our analytic scheme for computing energy derivatives. We also report calculations of the chlorine electric-field gradients and nuclear quadrupole-coupling constants for the CCl, CH2Cl, ClO2, and SiCl radicals.
REFERENCES
1.
P.
Pulay
in Modern Electronic Structure Theory
, edited by D. R.
Yarkony
(World Scientific
, Singapore
, 1995
), Vol. 2
, p. 1191
.2.
J.
Gauss
in Modern Methods and Algorithms of Quantum Chemistry
, edited by J.
Grotendorst
(John von Neumann Institute for Computing
, Jülich, Germany
, 2000
), Vol. 3
, p. 541
.3.
J. F.
Stanton
, and J.
Gauss
, in Recent Advances in Computational Chemistry
, edited by R. J.
Bartlett
(World Scientific
, Singapore
, 1997
), Vol. 3
, p. 49
.4.
P.
Pulay
, WIREs Comput. Mol. Sci.
4
, 169
(2014
).5.
T.
Helgaker
, in The Encyclopedia of Computational Chemistry
, edited by P. V. R.
Schleyer
, N. L.
Allinger
, T.
Clark
, J.
Gasteiger
, P. A.
Kollman
, H. F.
Schaefer
III, and P. R.
Schreiner
(Wiley
, Chichester
, 1998
), Vol. 2
, p. 1157
.6.
P.
Pulay
, Mol. Phys.
17
, 197
(1969
).7.
J. A.
Pople
, R.
Krishnan
, H. B.
Schlegel
, and J. S.
Binkley
, Int. J. Quantum Chem.
16
, 225
(1979
).8.
G.
Fitzgerald
, R.
Harrison
, W. D.
Laidig
, and R. J.
Bartlett
, J. Chem. Phys.
82
, 4379
(1985
).9.
J.
Gauss
and D.
Cremer
, Chem. Phys. Lett.
138
, 131
(1987
).10.
J.
Gauss
and D.
Cremer
, Chem. Phys. Lett.
153
, 303
(1988
).11.
G. W.
Trucks
, J. D.
Watts
, E. A.
Salter
, and R. J.
Bartlett
, Chem. Phys. Lett.
153
, 490
(1988
).12.
B. R.
Brooks
, W. D.
Laidig
, P.
Saxe
, J. D.
Goddard
, Y.
Yamaguchi
, and H. F.
Schaefer
III, J. Chem. Phys.
72
, 4652
(1980
).13.
R.
Krishnan
, H. B.
Schlegel
, and J. A.
Pople
, J. Chem. Phys.
72
, 4654
(1980
).14.
R.
Shepard
, H.
Lischka
, P. G.
Szalay
, T.
Kovar
, and M.
Ernzerhof
, J. Chem. Phys.
96
, 2085
(1992
).15.
J.
Gauss
and D.
Cremer
, Chem. Phys. Lett.
150
, 280
(1988
).16.
J.
Gauss
and D.
Cremer
, Chem. Phys. Lett.
163
, 549
(1989
).17.
A. C.
Scheiner
, G. E.
Scuseria
, J. E.
Rice
, T. J.
Lee
, and H. F.
Schaefer
III, J. Chem. Phys.
87
, 5361
(1987
).18.
T. J.
Lee
and A. P.
Rendell
, J. Chem. Phys.
94
, 6229
(1991
).19.
J.
Gauss
, and J. F.
Stanton
, Phys. Chem. Chem. Phys.
2
, 2047
(2000
).20.
J.
Gauss
and J. F.
Stanton
, J. Chem. Phys.
116
, 1773
(2002
).21.
M.
Kállay
, J.
Gauss
, and P. G.
Szalay
, J. Chem. Phys.
119
, 2991
(2003
).22.
J.
Gauss
, J. F.
Stanton
, and R. J.
Bartlett
, J. Chem. Phys.
95
, 2623
(1991
).23.
J. D.
Watts
, J.
Gauss
, and R. J.
Bartlett
, Chem. Phys. Lett.
200
, 1
(1992
).24.
J.
Gauss
, W. J.
Lauderdale
, J. F.
Stanton
, J. D.
Watts
, and R. J.
Bartlett
, Chem. Phys. Lett.
182
, 207
(1991
).25.
J. D.
Watts
, J.
Gauss
, and R. J.
Bartlett
, J. Chem. Phys.
98
, 8718
(1993
).26.
J.
Gauss
, J. F.
Stanton
, and R. J.
Bartlett
, J. Chem. Phys.
95
, 2639
(1991
).27.
M.
Rittby
and R. J.
Bartlett
, J. Phys. Chem.
92
, 3033
(1988
).28.
H. B.
Schlegel
, J. Phys. Chem.
92
, 3075
(1988
).29.
G. D.
Purvis
, H.
Sekino
, and R. J.
Bartlett
, Collect. Czech. Chem. Commun.
53
, 2203
(1988
).30.
J. F.
Stanton
, J. Chem. Phys.
101
, 371
(1994
).31.
P. J.
Knowles
, C.
Hampel
, and H.-J.
Werner
, J. Chem. Phys.
99
, 5219
(1993
).32.
P.
Neogrády
, M.
Urban
, and I.
Hubač
, J. Chem. Phys.
100
, 3706
(1994
).33.
P. G.
Szalay
and J.
Gauss
, J. Chem. Phys.
107
, 9028
(1997
).34.
M.
Heckert
, O.
Heun
, J.
Gauss
, and P. G.
Szalay
, J. Chem. Phys.
124
, 124105
(2006
).35.
C. L.
Janssen
, and H. F.
Schaefer
III, Theor. Chim. Acta
79
, 1
(1991
).36.
X.
Li
and J.
Paldus
, J. Chem. Phys.
101
, 8812
(1994
).37.
X.
Li
, and J.
Paldus
, in Recent Advances in Computational Chemistry
, edited by R. J.
Bartlett
(World Scientific
, Singapore
, 1997
), Vol. 3
, p. 183
.38.
X.
Li
and J.
Paldus
, J. Chem. Phys.
102
, 8897
(1995
).39.
B.
Jeziorski
, J.
Paldus
, and P.
Jankowski
, Int. J. Quantum Chem.
56
, 129
(1995
).40.
P.
Jankowski
and B.
Jeziorski
, J. Chem. Phys.
111
, 1857
(1999
).41.
J.
Paldus
and X.
Li
, Can. J. Chem.
74
, 918
(1996
).42.
X.
Li
and J.
Paldus
, J. Chem. Phys.
104
, 9555
(1996
).43.
X.
Li
and J.
Paldus
, Mol. Phys.
94
, 41
(1998
).44.
M.
Urban
, P.
Neogrády
, and I.
Hubač
, in Recent Advances in Computational Chemistry
, edited by R. J.
Bartlett
(World Scientific
, Singapore
, 1997
), Vol. 3
, p. 275
.45.
M.
Medved
, M.
Urban
, V.
Kellö
, and G. H. F.
Diercksen
, J. Mol. Struct.: THEOCHEM
547
, 219
(2001
).46.
D.
Datta
and D.
Mukherjee
, Int. J. Quantum Chem.
108
, 2211
(2008
).47.
D.
Datta
and D.
Mukherjee
, J. Chem. Phys.
131
, 044124
(2009
).48.
D.
Datta
and D.
Mukherjee
, J. Chem. Phys.
134
, 054122
(2011
).49.
D.
Datta
and J.
Gauss
, J. Chem. Theor. Comput.
9
, 2639
(2013
).50.
H.
Koch
, H. J. Aa.
Jensen
, P.
Jørgensen
, T.
Helgaker
, G. E.
Scuseria
, and H. F.
Schaefer
III, J. Chem. Phys.
92
, 4924
(1990
).51.
H.
Koch
and P.
Jørgensen
, J. Chem. Phys.
93
, 3333
(1990
).52.
P. G.
Szalay
, Int. J. Quantum Chem.
55
, 151
(1995
).53.
J.
Arponen
, Ann. Phys. (N.Y.)
151
, 311
(1983
).54.
L.
Adamowicz
, W. D.
Laidig
, and R. J.
Bartlett
, Int. J. Quantum Chem.
26
, 245
(1984
).55.
E. A.
Salter
, G. W.
Trucks
, and R. J.
Bartlett
, J. Chem. Phys.
90
, 1752
(1989
).56.
J. E.
Rice
and R. D.
Amos
, Chem. Phys. Lett.
122
, 585
(1985
).57.
N. C.
Handy
and H. F.
Schaefer
III, J. Chem. Phys.
81
, 5031
(1984
).58.
CFOUR, Coupled-Cluster Techniques for Computational Chemistry, a quantum-chemical program package by
J. F.
Stanton
, J.
Gauss
, M. E.
Harding
, P. G.
Szalay
with contributions from A. A.
Auer
, R. J.
Bartlett
, U.
Benedikt
, C.
Berger
, D. E.
Bernholdt
, Y. J.
Bomble
, L.
Cheng
, O.
Christiansen
, M.
Heckert
, O.
Heun
, C.
Huber
, T.-C.
Jagau
, D.
Jonsson
, J.
Jusélius
, K.
Klein
, W. J.
Lauderdale
, D. A.
Matthews
, T.
Metzroth
, L. A.
Mück
, D. P.
O’Neill
, D. R.
Price
, E.
Prochnow
, C.
Puzzarini
, K.
Ruud
, F.
Schiffmann
, W.
Schwalbach
, S.
Stopkowicz
, A.
Tajti
, J.
Vázquez
, F.
Wang
, J. D.
Watts
and the integral packages MOLECULE (J.
Almlöf
and P. R.
Taylor
), PROPS (P. R.
Taylor
), ABACUS (T.
Helgaker
, H. J. Aa.
Jensen
, P.
Jørgensen
, and J.
Olsen
), and ECP routines by A. V.
Mitin
and C.
van Wüllen
. For the current version, see http://www.cfour.de.59.
M.
Nooijen
and R. J.
Bartlett
, J. Chem. Phys.
104
, 2652
(1996
).60.
The terms involving more than one t(1) amplitudes, where there are no t(1) − t(1) contractions and each t(1) amplitude is contracted only to the Hamiltonian, are also strongly connected. Since each t(1) amplitude has an uncontracted active index u, the total number of uncontracted active indices in these terms exceeds one. As a result, these terms excite more than one electrons to the active orbital u, which is already singly occupied in the reference function |Φu⟩. Therefore, these terms annihilate the reference function |Φu⟩, and thus do not contribute to the amplitude equations.
61.
G. C.
Wick
, Phys. Rev.
80
, 268
(1950
).62.
W.
Kutzelnigg
, J. Chem. Phys.
77
, 3081
(1982
);W.
Kutzelnigg
, J. Chem. Phys.
80
, 822
(1984
);W.
Kutzelnigg
, J. Chem. Phys.
82
, 4166
(1985
).63.
M.
Nooijen
, J. Chem. Phys.
104
, 2638
(1996
).64.
65.
R. M.
Stevens
, R. M.
Pitzer
, and W. N.
Lipscomb
, J. Chem. Phys.
38
, 550
(1963
).66.
J.
Gerratt
and I. M.
Mills
, J. Chem. Phys.
49
, 1719
(1968
).67.
N. C.
Handy
, J. A.
Pople
, M.
Head-Gordon
, K.
Raghavachari
, and G. W.
Trucks
, Chem. Phys. Lett.
164
, 185
(1989
).68.
R. A.
Kendall
, T. H.
Dunning
Jr. , and R. J.
Harrison
, J. Chem. Phys.
96
, 6796
(1992
);D. E.
Woon
and T. H.
Dunning
Jr. , J. Chem. Phys.
98
, 1358
(1993
);D. E.
Woon
and T. H.
Dunning
Jr., J. Chem. Phys.
103
, 4572
(1995
).69.
K. A.
Peterson
and T. H.
Dunning
Jr., J. Chem. Phys.
117
, 10548
(2002
).70.
M.
Urban
, P.
Neogrády
, J.
Raab
, and G. H. F.
Diercksen
, Collect. Czech. Chem. Commun.
63
, 1409
(1998
).71.
P. G.
Szalay
, J.
Gauss
, and J. F.
Stanton
, Theor. Chem. Acc.
100
, 5
(1998
).72.
J. F.
Stanton
and J.
Gauss
, J. Chem. Phys.
101
, 8938
(1994
).73.
S.
Saito
and T.
Amano
, J. Mol. Spectrosc.
34
, 383
(1970
).74.
P.
Schwerdtfeger
, M.
Pernpointner
, and J. K.
Laerdahl
, J. Chem. Phys.
111
, 3357
(1999
).75.
L.
Cheng
, S.
Stopkowicz
, J. F.
Stanton
, and J.
Gauss
, J. Chem. Phys.
137
, 224302
(2012
).76.
P.
Pyykkö
, Mol. Phys.
106
, 1965
(2008
).77.
Y.
Endo
, S.
Saito
, and E.
Hirota
, J. Mol. Spectrosc.
94
, 199
(1982
).78.
From the data reported by
W. C.
Bailey
, see http://nqcc.wcbailey.net.79.
K.
Miyazaki
, M.
Tanoura
, K.
Tanaka
, and T.
Tanaka
, J. Mol. Spectrosc.
116
, 435
(1986
).80.
M.
Tanimoto
, S.
Saito
, Y.
Endo
, and E.
Hirota
, J. Mol. Spectrosc.
103
, 330
(1984
).81.
S.
Bailleux
, P.
Dréan
, Z.
Zelinger
, and M.
Godon
, J. Mol. Spectrosc.
229
, 140
(2005
).82.
M.
Tanoura
, K.
Chiba
, K.
Tanaka
, and T.
Tanaka
, J .Mol. Spectrosc.
95
, 157
(1982
).© 2014 AIP Publishing LLC.
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