We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys.135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

1.
A. C.
Hurley
,
J.
Lennard-Jones
, and
J. A.
Pople
,
Proc. R. Soc. A
220
,
446
(
1953
).
2.
W.
Kutzelnigg
,
J. Chem. Phys.
40
,
3640
(
1964
).
3.
A. J.
Coleman
,
J. Math. Phys.
6
,
1425
(
1965
).
4.
W.
Kutzelnigg
,
Theoret. Chim. Acta
3
,
241
(
1965
).
5.
K. J.
Miller
and
R.
Klaus
,
J. Chem. Phys.
48
,
3444
(
1968
).
6.
J. V.
Ortiz
,
B.
Weiner
, and
Y.
Ohrn
,
Int. J. Quantum Chem.
S15
,
113
(
1981
).
7.
P. R.
Surján
,
Correlation and Localization
(
Springer
,
1999
), pp.
63
88
.
8.
P. R.
Surján
,
A.
Szabados
,
P.
Jeszenszki
, and
T.
Zoboki
,
J. Math. Chem.
50
,
534
(
2012
).
10.
R.
McWeeny
and
B. T.
Sutcliffe
,
Proc. R. Soc. A
273
,
103
(
1963
).
11.
R. J.
Bartlett
and
J. F.
Stanton
,
Rev. Comput. Chem.
5
,
65
(
1994
).
12.
R. J.
Bartlett
and
M.
Musiał
,
Rev. Mod. Phys.
79
,
291
(
2007
).
13.
K.
Boguslawski
,
P.
Tecmer
,
O.
Legeza
, and
M.
Reiher
,
J. Phys. Chem. Lett.
3
,
3129
(
2012
).
14.
P.
Cassam-Chenaï
,
J. Chem. Phys.
124
,
194109
(
2006
).
15.
P.
Cassam-Chenaï
and
G.
Granucci
,
Chem. Phys. Lett.
450
,
151
(
2007
).
16.
G. E.
Scuseria
and
T.
Tsuchimochi
,
J. Chem. Phys.
131
,
164119
(
2009
).
17.
G. E.
Scuseria
,
C. A.
Jiménez-Hoyos
,
T. M.
Henderson
,
K.
Samanta
, and
J. K.
Ellis
,
J. Chem. Phys.
135
,
124108
(
2011
).
18.
P. A.
Limacher
,
P. W.
Ayers
,
P. A.
Johnson
,
S.
De Baerdemacker
,
D.
Van Neck
, and
P.
Bultinck
,
J. Chem. Theory Comput.
9
,
1394
(
2013
).
19.
P. A.
Johnson
,
P. W.
Ayers
,
P. A.
Limacher
,
S.
De Baerdemacker
,
D.
Van Neck
, and
P.
Bultinck
,
Comput. Chem. Theory
1003
,
101
(
2013
).
20.
J. K.
Ellis
,
R. L.
Martin
, and
G. E.
Scuseria
,
J. Chem. Theory Comput.
9
,
2857
(
2013
).
21.
P.
Tecmer
,
K.
Boguslawski
,
P. A.
Limacher
,
P. A.
Johnson
,
M.
Chan
,
T.
Verstraelen
, and
P. W.
Ayers
, “
Assessing the accuracy of new geminal-based approaches
,”
J. Phys. Chem. A
(published online
2014
).
22.
T. M.
Henderson
,
J.
Dukelsky
,
G. E.
Scuseria
,
A.
Signoracci
, and
T.
Duguet
,
Phys. Rev. C
89
,
054305
(
2014
).
23.
T.
Stein
,
T. M.
Henderson
, and
G. E.
Scuseria
, “
Seniority zero pair coupled cluster doubles theory
,”
J. Chem. Phys.
140
,
214113
(
2014
).
24.
S.
Bratoz
and
P.
Durand
,
J. Chem. Phys.
43
,
2670
(
1965
).
25.
D. M.
Silver
,
J. Chem. Phys.
50
,
5108
(
1969
).
26.
D. M.
Silver
,
J. Chem. Phys.
52
,
299
(
1970
).
27.
G.
Náray-Szabó
,
J. Chem. Phys.
58
,
1775
(
1973
).
28.
G.
Náray-Szabó
,
Int. J. Qunatum Chem.
9
,
9
(
1975
).
29.
P. R.
Surján
,
Phys. Rev. A
30
,
43
(
1984
).
30.
P. R.
Surján
,
Phys. Rev. A
32
,
748
(
1985
).
31.
P. R.
Surján
,
Int. J. Quantum Chem.
52
,
563
(
1994
).
32.
P. R.
Surján
,
Int. J. Quantum Chem.
55
,
109
(
1995
).
33.
E.
Rosta
and
P. R.
Surján
,
Int. J. Quantum Chem.
80
,
96
(
2000
).
34.
E.
Rosta
and
P. R.
Surján
,
J. Chem. Phys.
116
,
878
(
2002
).
35.
F.
Weinhold
and
E. B.
Wilson
,
J. Chem. Phys.
46
,
2752
(
1967
).
36.
J. M.
Parks
and
R. G.
Parr
,
J. Chem. Phys.
28
,
335
(
1958
).
37.
W. A.
Goddard
 III
and
A.
Amos
,
Chem. Phys. Lett.
13
,
30
(
1972
).
38.
W. A.
Goddard
 III
,
T. H.
Dunning
, Jr.
,
W. J.
Hunt
, and
P. J.
Hay
,
Acc. Chem. Res.
6
,
368
(
1973
).
39.
V. A.
Rassolov
,
J. Chem. Phys.
117
,
5978
(
2002
).
40.
K.
Boguslawski
,
P.
Tecmer
,
P. W.
Ayers
,
P.
Bultinck
,
S.
De Baerdemacker
, and
D.
Van Neck
,
Phys. Rev. B
89
,
201106
(R) (
2014
).
41.
T.
Helgaker
,
P.
Jørgensen
, and
J.
Olsen
,
Molecular Electronic-Structure Theory
(
Wiley
,
New York
,
2000
).
42.
G. E.
Scuseria
and
H. F.
Schaefer
 III
,
Chem. Phys. Lett.
142
,
354
(
1987
).
43.
A.
Köhn
and
J.
Olsen
,
J. Chem. Phys.
122
,
084116
(
2005
).
44.
U.
Bozkaya
,
J. M.
Turney
,
Y.
Yamaguchi
,
H. F.
Schaefer
, and
C. D.
Sherrill
,
J. Chem. Phys.
135
,
104103
(
2011
).
45.
P. A.
Limacher
,
T. D.
Kim
,
P. W.
Ayers
,
P. A.
Johnson
,
S.
De Baerdemacker
,
D.
Van Neck
, and
P.
Bultinck
,
Mol. Phys.
112
,
853
(
2014
).
46.
L.
Bytautas
,
T. M.
Henderson
,
C. A.
Jiménez-Hoyos
,
J. K.
Ellis
, and
G. E.
Scuseria
,
J. Chem. Phys.
135
,
044119
(
2011
).
47.
D. R.
Alcoba
,
A.
Torre
,
L.
Lain
,
G. E.
Massaccesi
, and
O. B.
Ona
,
J. Chem. Phys.
139
,
084103
(
2013
).
48.
K.
Giesbertz
,
Chem. Phys. Lett.
591
,
220
(
2014
).
49.
J.
Pian
and
C. S.
Sharma
,
J. Phys. A: Math. Gen.
14
,
1261
(
1981
).
50.
B.
Levy
and
G.
Berthier
,
Int. J. Quantum Chem.
2
,
307
(
1968
).
51.
R.
Lefebvre
and
M.
Moser
,
J. Chim. Phys.
53
,
393
(
1956
).
52.
U.
Kaldor
,
J. Chem. Phys.
48
,
835
(
1968
).
54.
F.
Grein
and
T. C.
Chang
,
Chem. Phys. Lett.
12
,
44
(
1971
).
55.
A.
Banerjee
and
F.
Grein
,
Int. J. Quantum Chem.
10
,
123
(
1976
).
56.
T. D.
Crawford
and
J. F.
Stanton
,
J. Chem. Phys.
112
,
7873
(
2000
).
57.
S.
Wouters
,
W.
Poelmans
,
P. W.
Ayers
, and
D.
Van Neck
,
Comput. Phys. Commun.
185
,
1501
(
2014
).
58.
F. A.
Evangelista
,
J. Chem. Phys.
134
,
224102
(
2011
).
59.
K. A.
Peterson
,
J. Chem. Phys.
102
,
262
(
1995
).
60.
O.
Legeza
,
J.
Röder
, and
B. A.
Hess
,
Mol. Phys.
101
,
37
(
2009
).
61.
A. J. C.
Varandas
,
J. Chem. Phys.
131
,
124128
(
2009
).
62.
Horton 1.2.0, written by
T.
Verstraelen
,
S.
Vandenbrande
,
M.
Chan
,
F. H.
Zadeh
,
C.
Gonzalez
,
K.
Boguslawski
,
P.
Tecmer
,
P. A.
Limacher
, and
A.
Malek
,
2013
, see http://theochem.github.com/horton/.
63.
J. A.
Coxon
,
J. Mol. Spectrosc.
152
,
274
(
1992
).
64.
M.
Abramowitz
and
I. A.
Stegun
,
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
(
Dover
,
1970
).
65.
T. H.
Dunning
,
J. Chem. Phys.
90
,
1007
(
1989
).
67.
K.
Didier
,
B.
Elsethagen
,
L. G. T.
Sun
,
V.
Chase
,
J.
Li
, and
T. L.
Windus
,
J. Chem. Inf. Model.
47
,
1045
(
2007
).
68.
D. E.
Woon
and
T. H.
Dunning
,
J. Chem. Phys.
103
,
4572
(
1995
).
69.
W. J.
Hehre
,
R. F.
Stewart
, and
J. A.
Pople
,
J. Chem. Phys.
51
,
2657
(
1969
).
70.
J.
Hachmann
,
W.
Cardoen
, and
G. K.-L.
Chan
,
J. Chem. Phys.
125
,
144101
(
2006
).
71.
We should note that all calculations are performed in C1 symmetry (see computational details). Therefore, molecular orbitals cannot be labeled according to an irreducible representation of the molecular point group. The term “non-symmetry-broken” is used to emphasize that the optimized molecular orbitals are not symmetry-broken (e.g., localized, hybrid, etc.); this does not imply that the molecular orbitals transform as an irreducible representation of the molecular point group.
72.
M.
Mottet
,
P.
Tecmer
,
K.
Boguslawski
,
O.
Legeza
, and
M.
Reiher
,
Phys. Chem. Chem. Phys.
16
,
8872
(
2014
).
73.
A. D.
McLean
,
B. H.
Lengsfield
 III
,
J.
Pacansky
, and
Y.
Ellinger
,
J. Chem. Phys.
83
,
3567
(
1985
).
74.
Jmol, An Open-Source Java Viewer for Chemical Structures in 3D, see http://www.jmol.org/.
75.
T.
Tsuchimochi
and
G. E.
Scuseria
,
J. Chem. Phys.
131
,
121102
(
2009
).
76.
L.
Stella
,
C.
Attaccalite
,
S.
Sorella
, and
A.
Rubio
,
Phys. Rev. B
84
,
245117
(
2011
).
77.
N.
Lin
,
C. A.
Marianetti
,
A. J.
Millis
, and
D. R.
Reichman
,
Phys. Rev. Lett.
106
,
096402
(
2011
).
78.
M.
Kobayashi
,
A.
Szabados
,
H.
Nakai
, and
P. R.
Surján
,
J. Chem. Theory Comput.
6
,
2024
(
2010
).
79.
P.
Limacher
,
P.
Ayers
,
P.
Johnson
,
S.
De Baerdemacker
,
D.
Van Neck
, and
P.
Bultinck
,
Phys. Chem. Chem. Phys.
16
,
5061
(
2014
).
You do not currently have access to this content.