A local approximation to the Schrödinger equation in a valence active space is suggested based on coupled cluster (CC) theory. Working in a pairing active space with one virtual orbital per occupied orbital, this perfect quadruples (PQ) model is defined such that electrons are strongly correlated up to “four-at-a-time” in up to two different (occupied-virtual) electron pairs. This is a truncation of the CC theory with up to quadruple substitutions (CCSDTQ) in the active space, such that the retained amplitudes in PQ are proportional to the fourth root of the number of CCSDTQ amplitudes. Despite the apparently drastic nature of the PQ truncation, in the cases examined this model is a very accurate approximation to complete active space self-consistent field. Examples include deformations of square , dissociation of two single bonds (water), a double bond (ethene), and a triple bond (nitrogen). The computational scaling of the model (fourth order with molecule size) is less than integral transformation, so relatively large systems can be addressed with improved accuracy relative to earlier methods such as perfect and imperfect pairing, which are truncations of CCSD in an active space.
Topics
Coupled-cluster singles, doubles, triples, and quadruples,
Coupled-cluster methods,
Complete-active space self-consistent field,
Correlation energy,
Dynamical correlation,
Electronic correlation,
Correlation-consistent basis sets,
Differential geometry,
Density matrix renormalization group,
Schrodinger equations
REFERENCES
1.
J. E.
Subotnik
, A.
Sodt
, and M.
Head-Gordon
, J. Chem. Phys.
125
, 074116
(2006
).2.
H. -J.
Werner
, F. R.
Manby
, and P. J.
Knowles
, J. Chem. Phys.
118
, 8149
(2003
).3.
T. D.
Crawford
and R. A.
King
, Chem. Phys. Lett.
366
, 611
(2002
).4.
C.
Hampel
and H. -J.
Werner
, J. Chem. Phys.
104
, 6286
(1996
).5.
R.
DiStasio
, Y.
Jung
, and M.
Head-Gordon
, J. Chem. Theory Comput.
1
, 862
(2005
).6.
M.
Schütz
, Phys. Chem. Chem. Phys.
4
, 3941
(2002
).7.
A. D.
Dutoi
and M.
Head-Gordon
, Chem. Phys. Lett.
422
, 230
(2006
).8.
B.
Roos
, Chem. Phys.
48
, 157
(1980
).9.
D.
Hegarty
and M. A.
Robb
, Mol. Phys.
38
, 1795
(1979
).10.
H.
Nakatsuji
, J. Chem. Phys.
113
, 2949
(2000
).11.
K.
Andersson
, P. A.
Malmqvist
, B. O.
Roos
, A. J.
Sadlej
, and K.
Wolinski
, J. Phys. Chem.
94
, 5483
(1990
).12.
X.
Li
and J.
Paldus
, J. Chem. Phys.
128
, 144119
(2008
).13.
X.
Li
and J.
Paldus
, J. Chem. Phys.
129
, 054104
(2008
).14.
J.
Paldus
, P.
Piecuch
, L.
Pylypow
, and B.
Jeziorski
, Phys. Rev. A
47
, 2738
(1993
).15.
U. S.
Mahapatra
, B.
Datta
, and D.
Mukherjee
, J. Chem. Phys.
110
, 6171
(1999
).16.
I.
Hubac
and S.
Wilson
, J. Phys. B
34
, 4259
(2001
).17.
P.
Piecuch
, N.
Oliphant
, and L.
Adamowicz
, J. Chem. Phys.
99
, 1875
(1993
).18.
P.
Piecuch
and L.
Adamowicz
, J. Chem. Phys.
100
, 5792
(1994
).19.
X.
Li
and J.
Paldus
, J. Chem. Phys.
129
, 174101
(2008
).20.
G.
Chan
and M.
Head-Gordon
, J. Chem. Phys.
116
, 4462
(2002
).21.
S. R.
White
, Phys. Rev. Lett.
69
, 2863
(1992
).22.
A. E.
DePrince
III, E.
Kamarchik
, and D. A.
Mazziotti
, J. Chem. Phys.
128
, 234103
(2008
).23.
J. H.
Sebold
and J. K.
Percus
, J. Chem. Phys.
104
, 6606
(1996
).24.
D. A.
Mazziotti
, J. Chem. Phys.
115
, 8305
(2001
).25.
F.
Faglioni
and W.
Goddard
, Int. J. Quantum Chem.
73
, 1
(1999
).26.
A. C.
Hurley
, J.
Lennard-Jones
, and J. A.
Pople
, Proc. R. Soc. London, Ser. A
220
, 446
(1953
).27.
W. J.
Hunt
, P. J.
Hay
, and W. A.
Goddard
, J. Chem. Phys.
57
, 738
(1972
).28.
J.
Cullen
, Chem. Phys.
202
, 217
(1996
).29.
J.
Cullen
, J. Comput. Chem.
20
, 999
(1999
).30.
V. A.
Rassolov
and F.
Xu
, J. Chem. Phys.
127
, 044104
(2007
).31.
K.
Kowalski
and P.
Piecuch
, J. Chem. Phys.
113
, 18
(2000
).32.
A. I.
Krylov
, Chem. Phys. Lett.
350
, 522
(2001
).33.
L. V.
Slipchenko
and A. I.
Krylov
, J. Chem. Phys.
117
, 4694
(2002
).34.
D.
Casanova
and M.
Head-Gordon
, J. Chem. Phys.
129
, 064104
(2008
).35.
P.
Pulay
and S.
Saebø
, Theor. Chim. Acta
69
, 357
(1986
).36.
S.
Saebo
and P.
Pulay
, Annu. Rev. Phys. Chem.
44
, 213
(1993
).37.
W.
Forner
, J.
Ladik
, P.
Otto
, and J.
Cizek
, Chem. Phys.
97
, 251
(1985
).38.
R. A.
Chiles
and C. E.
Dykstra
, J. Chem. Phys.
74
, 4544
(1981
).39.
J. E.
Subotnik
, A.
Sodt
, and M.
Head-Gordon
, J. Chem. Phys.
128
, 034103
(2008
).40.
H. -J.
Werner
, J. Chem. Phys.
129
, 101103
(2008
).41.
H.
Nakatsuji
, T.
Miyahara
, and R.
Fukuda
, J. Chem. Phys.
126
, 084104
(2007
).42.
A. I.
Krylov
, C. D.
Sherrill
, E. F. C.
Byrd
, and M.
Head-Gordon
, J. Chem. Phys.
109
, 10669
(1998
).43.
G. J. O.
Beran
and M.
Head-Gordon
, Mol. Phys.
104
, 1191
(2006
).44.
G.
Beran
, B.
Austin
, A.
Sodt
, and M.
Head-Gordon
, J. Phys. Chem. A
109
, 9183
(2005
).45.
W. A.
Goddard
and L. A.
Harding
, Annu. Rev. Phys. Chem.
29
, 363
(1978
).46.
T.
Van Voorhis
and M.
Head-Gordon
, J. Chem. Phys.
117
, 9190
(2002
).47.
T.
Van Voorhis
and M.
Head-Gordon
, Chem. Phys. Lett.
317
, 575
(2000
).48.
K. V.
Lawler
, G. J. O.
Beran
, and M.
Head-Gordon
, J. Chem. Phys.
128
, 024107
(2008
).49.
T.
Van Voorhis
and M.
Head-Gordon
, Chem. Phys. Lett.
330
, 585
(2000
).50.
E.
Byrd
, T.
Van Voorhis
, and M.
Head-Gordon
, J. Phys. Chem. B
106
, 8070
(2002
).51.
T.
Van Voorhis
and M.
Head-Gordon
, J. Chem. Phys.
117
, 9190
(2002
).52.
R. J.
Bartlett
and M.
Musial
, Rev. Mod. Phys.
79
, 291
(2007
).53.
D.
Crawford
and H. F.
Schaefer
III, Rev. Comput. Chem.
14
, 33
(2007
).54.
N.
Oliphant
and L.
Adamowicz
, J. Chem. Phys.
95
, 6645
(1991
).55.
S. A.
Kucharski
and R. J.
Bartlett
, J. Chem. Phys.
97
, 4282
(1992
).56.
A. D.
Bochevarov
and C. D.
Sherrill
, J. Chem. Phys.
121
, 3374
(2004
).57.
S.
Hirata
, P. -D.
Fan
, A. A.
Auer
, M.
Nooijen
, and P.
Piecuch
, J. Chem. Phys.
121
, 12197
(2004
).58.
M.
Kallay
and P. R.
Surjan
, J. Chem. Phys.
115
, 2945
(2001
).59.
A.
Kohn
and J.
Olsen
, J. Chem. Phys.
122
, 084116
(2005
).60.
T.
Van Voorhis
and M.
Head-Gordon
, J. Chem. Phys.
115
, 7814
(2001
).61.
K. V.
Lawler
, J. A.
Parkhill
, and M.
Head-Gordon
, Mol. Phys.
106
, 2309
(2008
).62.
Y.
Shao
, L.
Fusti-Molnar
, Y.
Jung
, J.
Kussman
, C.
Ochsenfeld
, S. T.
Brown
, A. T. B.
Gilbert
, L. V.
Slipchenko
, S. V.
Levchenko
, D. P.
O'Neill
, R. A.
DiStasio
, Jr., R. C.
Lochan
, T.
Want
, G. J. O.
Beran
, N. A.
Besley
, J. M.
Herbert
, C. Y.
Lin
, T.
Van Voorhis
, S. H.
Chien
, A.
Sodt
, R. P.
Steele
, V. A.
Rasssolov
, P. E.
Maslen
, P. P.
Korambath
, R. D.
Adamson
, B.
Austin
, J.
Baker
, E. F. C.
Byrd
, H.
Dachsel
, R. J.
Doerksen
, A.
Dreuw
, B. D.
Dunietz
, A. D.
Dutoi
, T. R.
Furlani
, S. R.
Gwaltney
, A.
Heyden
, S.
Hirata
, C.-P.
Hsu
, G.
Kedziora
, R. Z.
Khalliulin
, P.
Klunzinger
, A. M.
Lee
, M. S.
Lee
, W.
Liang
, I.
Lotan
, N.
Nair
, B.
Peters
, E. I.
Proynov
, P. A.
Pieniazek
, Y. M.
Rhee
, J.
Ritchie
, E.
Rosta
, C. D.
Sherrill
, A. C.
Simmonett
, J. E.
Subotnik
, H. L.
Woodcock
III, W.
Zhang
, A. T.
Bell
, A. K.
Chakraborty
, D. M.
Chipman
, F. J.
Keil
, A.
Warshel
, W. J.
Hehre
, H. F.
Schaefer
III, J.
Kong
, A. I.
Krylov
, P. M.
Gill
, and M.
Head-Gordon
, Phys. Chem. Chem. Phys.
8
, 3172
(2006
).63.
P.
Pulay
, J. Comput. Chem.
3
, 556
(1982
).64.
F.
Aquilante
, T. B.
Pedersen
, R.
Lindh
, B. O.
Roos
, A.
Sanchez de Meras
, and H.
Koch
, J. Chem. Phys.
129
, 024113
(2008
).65.
M. W.
Schmidt
, K. K.
Baldridge
, J. A.
Boatz
, S. T.
Elbert
, M. S.
Gordon
, J. H.
Jensen
, S.
Koseki
, N.
Matsunaga
, K. A.
Nguyen
, S.
Su
, T. L.
Windus
, M.
Dupuis
, and J. A.
Montgomery
, J. Comput. Chem.
14
, 1347
(1993
).66.
A. J. W.
Thom
and M.
Head-Gordon
, Phys. Rev. Lett.
101
, 193001
(2008
).67.
K.
Jankowski
and J.
Paldus
, Int. J. Quantum Chem.
18
, 1243
(1980
).68.
M.
Schutz
and H. -J.
Werner
, Chem. Phys. Lett.
318
, 370
(2000
).69.
P. E.
Maslen
, M. S.
Lee
, and M.
Head-Gordon
, Chem. Phys. Lett.
319
, 205
(2000
).70.
G. K.-L.
Chan
, M.
Kallay
, and J.
Gauss
, J. Chem. Phys.
121
, 6110
(2004
).71.
X.
Li
and J.
Paldus
, Chem. Phys. Lett.
286
, 145
(1998
).72.
F. A.
Evangelista
, A. C.
Simmonett
, W. D.
Allen
, H. F.
Schaefer
III, and J.
Gauss
, J. Chem. Phys.
128
, 124104
(2008
).73.
G.
Gidofalvi
and D. A.
Mazziotti
, J. Chem. Phys.
129
, 134108
(2008
).74.
U.
Schollwock
, Rev. Mod. Phys.
77
, 259
(2005
).75.
T.
Yanai
and G. K.-L.
Chan
, J. Chem. Phys.
127
, 104107
(2007
).76.
D.
Small
and M.
Head-Gordon
, J. Chem. Phys.
(unpublished).77.
D.
Casanova
, L. V.
Slipchenko
, A. I.
Krylov
, and M.
Head-Gordon
, J. Chem. Phys.
130
, 044103
(2009
).78.
G. J. O.
Beran
, M.
Head-Gordon
, and S. R.
Gwaltney
, J. Chem. Phys.
124
, 114107
(2006
).© 2009 American Institute of Physics.
2009
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