We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a active space and 268 atomic orbitals in the polyenes and a active space and 278 atomic orbitals in .
REFERENCES
1.
R.
Ahlrichs
, P.
Scharf
, and C.
Ehrhard
, J. Chem. Phys.
82
, 890
(1985
).2.
R. J.
Gdanitz
and R.
Ahlrichs
, Chem. Phys. Lett.
143
, 413
(1988
).3.
K.
Andersson
, P. -Å.
Malmqvist
, B. O.
Roos
, A. J.
Sadlej
, and K.
Wolinski
, J. Phys. Chem.
94
, 5483
(1990
).4.
K.
Hirao
, Chem. Phys. Lett.
190
, 374
(1992
).5.
S.
Grimme
and M.
Waletzke
, J. Chem. Phys.
111
, 5645
(1999
).6.
J.
Gräfenstein
and D.
Cremer
, Chem. Phys. Lett.
316
, 569
(2000
).7.
J.
Olsen
, B. O.
Roos
, P.
Jørgensen
, and H. J. A.
Jensen
, J. Chem. Phys.
89
, 2185
(1988
).8.
P. -Å.
Malmqvist
, A.
Rendell
, and B. O.
Roos
, J. Phys. Chem.
94
, 5477
(1990
).9.
F.
Faglioni
and W.
Goddard
, Int. J. Quantum Chem.
73
, 1
(1999
).10.
W. J.
Hunt
, P. J.
Hay
, and I. W. A.
Goddard
, J. Chem. Phys.
57
, 738
(1972
).11.
12.
T.
Van Voorhis
and M.
Head-Gordon
, J. Chem. Phys.
117
, 9190
(2002
).13.
V. A.
Rassolov
and F.
Xu
, J. Chem. Phys.
127
, 044104
(2007
).14.
J. A.
Parkhill
, K.
Lawler
, and M.
Head-Gordon
, J. Chem. Phys.
130
, 084101
(2009
).15.
P.
Piecuch
, N.
Oliphant
, and L.
Adamowicz
, J. Chem. Phys.
99
, 1875
(1993
).16.
P. D.
Fan
and S.
Hirata
, J. Chem. Phys.
124
, 104108
(2006
).17.
M.
Nakata
, H.
Nakatsuji
, M.
Ehara
, M.
Fukuda
, K.
Nakata
, and K.
Fujisawa
, J. Chem. Phys.
114
, 8282
(2001
).18.
D. A.
Mazziotti
, Phys. Rev. Lett.
93
, 213001
(2004
).19.
J.
Paldus
and X.
Li
, Adv. Chem. Phys.
110
, 1
(1999
).20.
S. R.
White
, Phys. Rev. Lett.
69
, 2863
(1992
).21.
S. R.
White
, Phys. Rev. B
48
, 10345
(1993
).22.
S. R.
White
and R. L.
Martin
, J. Chem. Phys.
110
, 4127
(1999
).23.
G. K.-L.
Chan
and M.
Head-Gordon
, J. Chem. Phys.
116
, 4462
(2002
).24.
G. K.-L.
Chan
and M.
Head-Gordon
, J. Chem. Phys.
118
, 8551
(2003
).25.
G. K.-L.
Chan
, J. Chem. Phys.
120
, 3172
(2004
).26.
G. K.-L.
Chan
, M.
Kállay
, and J.
Gauss
, J. Chem. Phys.
121
, 6110
(2004
).27.
G. K.-L.
Chan
and T.
Van Voorhis
, J. Chem. Phys.
122
, 204101
(2005
).28.
J.
Hachmann
, W.
Cardoen
, and G. K.-L.
Chan
, J. Chem. Phys.
125
, 144101
(2006
).29.
J.
Hachmann
, J. J.
Dorando
, M.
Avilés
, and G. K.-L.
Chan
, J. Chem. Phys.
127
, 134309
(2007
).30.
J. J.
Dorando
, J.
Hachmann
, and G. K.-L.
Chan
, J. Chem. Phys.
127
, 084109
(2007
).31.
D.
Ghosh
, J.
Hachmann
, T.
Yanai
, and G. K.-L.
Chan
, J. Chem. Phys.
128
, 144117
(2008
).32.
J. J.
Dorando
, J.
Hachmann
, and G. K.-L.
Chan
, J. Chem. Phys.
130
, 184111
(2009
).33.
G. K.-L.
Chan
, Phys. Chem. Chem. Phys.
10
, 3454
(2008
).34.
Y.
Kurashige
and T.
Yanai
, J. Chem. Phys.
130
, 234114
(2009
).35.
S.
Daul
, I.
Ciofini
, C.
Daul
, and S. R.
White
, Int. J. Quantum Chem.
79
, 331
(2000
).36.
A. O.
Mitrushenkov
, G.
Fano
, F.
Ortolani
, R.
Linguerri
, and P.
Palmieri
, J. Chem. Phys.
115
, 6815
(2001
).37.
A. O.
Mitrushenkov
, R.
Linguerri
, P.
Palmieri
, and G.
Fano
, J. Chem. Phys.
119
, 4148
(2003
).38.
Ö.
Legeza
, J.
Röder
, and B. A.
Hess
, Phys. Rev. B
67
, 125114
(2003
).39.
Ö.
Legeza
, J.
Röder
, and B. A.
Hess
, Mol. Phys.
101
, 2019
(2003
).40.
G.
Moritz
, B. A.
Hess
, and M.
Reiher
, J. Chem. Phys.
122
, 024107
(2005
).41.
G.
Moritz
, A.
Wolf
, and M.
Reiher
, J. Chem. Phys.
123
, 184105
(2005
).42.
K. H.
Marti
, I. M.
Ondík
, G.
Moritz
, and M.
Reiher
, J. Chem. Phys.
128
, 014104
(2008
).43.
D.
Zgid
and M.
Nooijen
, J. Chem. Phys.
128
, 014107
(2008
).44.
D.
Zgid
and M.
Nooijen
, J. Chem. Phys.
128
, 144116
(2008
).45.
D.
Zgid
and M.
Nooijen
, J. Chem. Phys.
128
, 144115
(2008
).46.
T.
Yanai
and G. K.-L.
Chan
, J. Chem. Phys.
124
, 194106
(2006
).47.
T.
Yanai
and G. K.-L.
Chan
, J. Chem. Phys.
127
, 104107
(2007
).48.
E.
Neuscamman
, T.
Yanai
, and G. K.-L.
Chan
, J. Chem. Phys.
130
, 124102
(2009
).49.
S. R.
White
, J. Chem. Phys.
117
, 7472
(2002
).50.
D.
Mukherjee
, in Recent Progress in Many-Body Theories
, edited by E.
Schachinger
(Plenum
, New York
, 1995
), Vol. 4
, p. 127
.51.
D.
Mukherjee
, Chem. Phys. Lett.
274
, 561
(1997
).52.
W.
Kutzelnigg
and D.
Mukherjee
, J. Chem. Phys.
107
, 432
(1997
).53.
F.
Colmenero
and C.
Valdemoro
, Phys. Rev. A
47
, 979
(1993
).54.
H.
Nakatsuji
and K.
Yasuda
, Phys. Rev. Lett.
76
, 1039
(1996
).55.
D. A.
Mazziotti
, Phys. Rev. A
57
, 4219
(1998
).56.
W.
Kutzelnigg
and D.
Mukherjee
, J. Chem. Phys.
110
, 2800
(1999
).57.
C.
Angeli
, R.
Cimiraglia
, S.
Evangelisti
, T.
Leininger
, and J. -P.
Malrieu
, J. Chem. Phys.
114
, 10252
(2001
).58.
E.
Neuscamman
, T.
Yanai
, and G. K.-L.
Chan
, J. Chem. Phys.
132
, 024106
(2010
).59.
E.
Neuscamman
, T.
Yanai
, and G. K.-L.
Chan
, “A Review of Canonical Transformation Theory
,” Int. Rev. Phys. Chem.
(submitted).60.
C.
Angeli
, M.
Pastore
, and R.
Cimiriglia
, Theor. Chem. Acc.
117
, 743
(2007
).61.
D.
Zgid
, D.
Ghosh
, E.
Neuscamman
, and G. K.-L.
Chan
, J. Chem. Phys.
130
, 194107
(2009
).62.
R. J.
Buenker
and S. D.
Peyerimhoff
, Theor. Chim. Acta
35
, 33
(1974
).63.
P. E. M.
Siegbahn
, J. Chem. Phys.
72
, 1647
(1980
).64.
H. -J.
Werner
and P. J.
Knowles
, J. Chem. Phys.
89
, 5803
(1988
).65.
P.
Celani
and H.
Werner
, J. Chem. Phys.
112
, 5546
(2000
).66.
A.
Banerjee
and J.
Simons
, Int. J. Quantum Chem.
19
, 207
(1981
).67.
A.
Banerjee
and J.
Simons
, J. Chem. Phys.
76
, 4548
(1982
).68.
M. R.
Hoffmann
and J.
Simons
, J. Chem. Phys.
88
, 993
(1988
).69.
L. G.
Kong
, K. R.
Shamasundar
, O.
Demel
, and M.
Nooijen
, J. Chem. Phys.
130
, 114101
(2009
).70.
D.
Mukherjee
and W.
Kutzelnigg
, J. Chem. Phys.
114
, 2047
(2001
).71.
D. A.
Mazziotti
, Phys. Rev. Lett.
97
, 143002
(2006
).72.
A. E.
DePrince
III and D. A.
Mazziotti
, J. Chem. Phys.
127
, 104104
(2007
).73.
C. J.
Cramer
, M.
Włoch
, P.
Piecuch
, C.
Puzzarini
, and L.
Gagliardi
, J. Phys. Chem. A
110
, 1991
(2006
).74.
P. -Å.
Malmqvist
, K.
Pierloot
, A. R. M.
Shahi
, C. J.
Cramer
, and L.
Gagliardi
, J. Chem. Phys.
128
, 204109
(2008
).75.
G. K.-L.
Chan
, J. J.
Dorando
, D.
Ghosh
, J.
Hachmann
, E.
Neuscamman
, H.
Wang
, and T.
Yanai
, Prog. Theor. Chem. Phys.
18
, 49
(2008
);G. K.-L.
Chan
, J. J.
Dorando
, D.
Ghosh
, J.
Hachmann
, E.
Neuscamman
, H.
Wang
, and T.
Yanai
, e-print arXiv:0711.1398.76.
U.
Schollwöck
, Rev. Mod. Phys.
77
, 259
(2005
).77.
K.
Ruedenberg
, M. W.
Schmidt
, M. M.
Gilbert
, and S. T.
Elbert
, Chem. Phys.
71
, 41
(1982
).78.
B. O.
Roos
, Adv. Chem. Phys.
69
, 399
(1987
).79.
T.
Yanai
, Y.
Kurashige
, D.
Ghosh
, and G. K.-L.
Chan
, Int. J. Quantum Chem.
109
, 2178
(2009
).80.
W. J.
Hehre
, R.
Ditchfield
, and J.
Pople
, J. Chem. Phys.
56
, 2257
(1972
).81.
MOLPRO, a package of ab initio programs designed by
H. -J.
Werner
and P. J.
Knowles
, version 2006
, R. D.
Amos
, A.
Bernhardsson
, A.
Berning
et al.82.
E. I.
Solomon
, U. M.
Sundaram
, and T. E.
Machonkin
, Chem. Rev. (Washington, D.C.)
96
, 2563
(1996
).83.
B. F.
Gherman
and C. J.
Cramer
, Coord. Chem. Rev.
253
, 723
(2009
).84.
M.
Flock
and K.
Pierloot
, J. Phys. Chem. A
103
, 95
(1999
).85.
M. F.
Rode
and H. -J.
Werner
, Theor. Chem. Acc.
114
, 309
(2005
).86.
M.
Dolg
, U.
Wedig
, H.
Stoll
, and H.
Preuss
, J. Chem. Phys.
86
, 866
(1987
).87.
P. O.
Widmark
, P. -Å.
Malmqvist
, and B. O.
Roos
, Theor. Chim. Acta
77
, 291
(1990
).88.
R.
Pou-Amérigo
, M.
Merchan
, I.
Nebot-Gil
, P. O.
Widmark
, and B. O.
Roos
, Theor. Chim. Acta
92
, 149
(1995
).© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.
