We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behavior of a coupled cluster wavefunction representation, we propose new approaches based on an intuitive, well-defined condition for sampling weights and on sampling the expansion in cluster operators of different excitation levels. We term these modifications even and truncated selections, respectively. Utilising both approaches demonstrates dramatically improved calculation stability as well as reduced computational and memory costs. These modifications are particularly effective at higher truncation levels owing to the large number of terms within the cluster expansion that can be neglected, as demonstrated by the reduction of the number of terms to be sampled when truncating at triple excitations by 77% and hextuple excitations by 98%.

1.
T.
Helgaker
,
W.
Klopper
, and
D. P.
Tew
,
Mol. Phys.
106
,
2107
(
2008
).
2.
J.
Paldus
and
X.
Li
,
Adv. Chem. Phys.
110
,
1
(
1999
).
3.
T. D.
Crawford
and
H. F.
Schaefer
 III
,
Rev. Comput. Chem.
14
,
33
(
2000
).
4.
R. J.
Bartlett
and
M.
Musiał
,
Rev. Mod. Phys.
79
,
291
(
2007
).
6.
F.
Coester
and
H.
Kümmel
,
Nucl. Phys.
17
,
477
(
1960
).
7.
J.
Čížek
,
J. Chem. Phys.
45
,
4256
(
1966
).
8.
J.
Čížek
and
J.
Paldus
,
Int. J. Quantum Chem.
5
,
359
(
1971
).
9.
J.
Paldus
,
J.
Čížek
, and
I.
Shavitt
,
Phys. Rev. A
5
,
50
(
1972
).
10.
K.
Raghavachari
,
G. W.
Trucks
,
J. A.
Pople
, and
M.
Head-Gordon
,
Chem. Phys. Lett.
157
,
479
(
1989
).
11.
G. K.-L.
Chan
,
M.
Kállay
, and
J.
Gauss
,
J. Chem. Phys.
121
,
6110
(
2004
).
12.
M.
Schütz
and
H. J.
Werner
,
J. Chem. Phys.
114
,
661
(
2001
).
13.
M.
Schütz
,
Phys. Chem. Chem. Phys.
4
,
3941
(
2002
).
14.
M.
Schütz
and
F. R.
Manby
,
Phys. Chem. Chem. Phys.
5
,
3349
(
2003
).
15.
N.
Flocke
and
R. J.
Bartlett
,
J. Chem. Phys.
121
,
10935
(
2004
).
16.
J. E.
Subotnik
,
A.
Sodt
, and
M.
Head-Gordon
,
J. Chem. Phys.
125
,
074116
(
2006
).
17.
M.
Ziółkowski
,
B.
Jansík
,
T.
Kjærgaard
, and
P.
Jørgensen
,
J. Chem. Phys.
133
,
014107
(
2010
).
18.
C.
Riplinger
and
F.
Neese
,
J. Chem. Phys.
138
,
034106
(
2013
).
19.
C.
Riplinger
,
P.
Pinski
,
U.
Becker
,
E. F.
Valeev
, and
F.
Neese
,
J. Chem. Phys.
144
,
024109
(
2016
).
20.
T. F.
Hughes
,
N.
Flocke
, and
R. J.
Bartlett
,
J. Phys. Chem. A
112
,
5994
(
2008
).
21.
C.
Riplinger
,
B.
Sandhoefer
,
A.
Hansen
, and
F.
Neese
,
J. Chem. Phys.
139
,
134101
(
2013
).
22.
S.
Li
,
J.
Shen
,
W.
Li
, and
Y.
Jiang
,
J. Chem. Phys.
125
,
074109
(
2006
).
23.
W.
Li
,
P.
Piecuch
,
J. R.
Gour
, and
S.
Li
,
J. Chem. Phys.
131
,
114109
(
2009
).
24.
S.
Pal
,
M.
Rittby
,
R. J.
Bartlett
,
D.
Sinha
, and
D.
Mukherjee
,
Chem. Phys. Lett.
137
,
273
(
1987
).
25.
N.
Oliphant
and
L.
Adamowicz
,
J. Chem. Phys.
94
,
1229
(
1991
).
26.
P.
Piecuch
,
N.
Oliphant
, and
L.
Adamowicz
,
J. Chem. Phys.
99
,
1875
(
1993
).
27.
U. S.
Mahapatra
,
B.
Datta
, and
D.
Mukherjee
,
Mol. Phys.
94
,
157
(
1998
).
28.
U. S.
Mahapatra
,
B.
Datta
, and
D.
Mukherjee
,
J. Chem. Phys.
110
,
6171
(
1999
).
29.
D. I.
Lyakh
,
M.
Musiał
,
V. F.
Lotrich
, and
R. J.
Bartlett
,
Chem. Rev.
112
,
182
(
2012
).
30.
J.
Shen
and
P.
Piecuch
,
J. Chem. Theory Comput.
8
,
4968
(
2012
).
31.
N. P.
Bauman
,
J.
Shen
, and
P.
Piecuch
, “
Combining active-space coupled-cluster approaches with moment energy corrections via the CC(P;Q) methodology: connected quadruple excitations
,”
Mol. Phys.
(published online
2017
).
32.
W. M. C.
Foulkes
,
L.
Mitas
,
R. J.
Needs
, and
G.
Rajagopal
,
Rev. Mod. Phys.
73
,
33
(
2001
).
33.
L. K.
Wagner
,
M.
Bajdich
, and
L.
Mitas
,
J. Comput. Phys.
228
,
3390
(
2009
).
34.
R. J.
Needs
,
M. D.
Towler
,
N. D.
Drummond
, and
P.
López Ríos
,
J. Phys.: Condens. Matter
22
,
023201
(
2010
); e-print arXiv:1002.2127.
35.
J.
Kim
,
K. P.
Esler
,
J.
McMinis
,
M. A.
Morales
,
B. K.
Clark
,
L.
Shulenburger
, and
D. M.
Ceperley
,
J. Phys.: Conf. Ser.
402
,
012008
(
2012
).
36.
P. J.
Reynolds
,
D. M.
Ceperley
,
B. J.
Alder
, and
W. A.
Lester
,
J. Chem. Phys.
77
,
5593
(
1982
).
37.
C.
Filippi
and
C. J.
Umrigar
,
J. Chem. Phys.
105
,
213
(
1996
).
38.
M.
Bajdich
,
L.
Mitas
,
G.
Drobny
,
L. K.
Wagner
, and
K. E.
Schmidt
,
Phys. Rev. Lett.
96
,
130201
(
2006
); e-print arXiv:0512327 [cond-mat].
39.
M.
Bajdich
,
L.
Mitas
,
L. K.
Wagner
, and
K.
Schmidt
,
Phys. Rev. B
77
,
115112
(
2008
); e-print arXiv:0610850v2 [cond-mat].
40.
P.
López Ríos
,
A.
Ma
,
N. D.
Drummond
,
M. D.
Towler
, and
R. J.
Needs
,
Phys. Rev. E
74
,
066701
(
2006
); e-print arXiv:0801.0518.
41.
G. H.
Booth
,
A. J. W.
Thom
, and
A.
Alavi
,
J. Chem. Phys.
131
,
054106
(
2009
).
42.
D.
Cleland
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
132
,
041103
(
2010
).
43.
D. M.
Cleland
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
134
,
024112
(
2011
).
44.
G. H.
Booth
,
D.
Cleland
,
A. J. W.
Thom
, and
A.
Alavi
,
J. Chem. Phys.
135
,
084104
(
2011
).
45.
J. J.
Shepherd
,
G. H.
Booth
,
A.
Grüneis
, and
A.
Alavi
,
Phys. Rev. B
85
,
081103
(
2012
).
46.
G. H.
Booth
,
A.
Grüneis
,
G.
Kresse
, and
A.
Alavi
,
Nature
493
,
365
(
2013
).
47.
S.
Sharma
,
T.
Yanai
,
G. H.
Booth
,
C. J.
Umrigar
, and
G. K. L.
Chan
,
J. Chem. Phys.
140
,
104112
(
2014
); e-print arXiv:1408.5090v1.
48.
C.
Overy
,
G. H.
Booth
,
N. S.
Blunt
,
J. J.
Shepherd
,
D.
Cleland
, and
A.
Alavi
,
J. Chem. Phys.
141
,
244117
(
2014
).
49.
R. E.
Thomas
,
D.
Opalka
,
C.
Overy
,
P. J.
Knowles
,
A.
Alavi
, and
G. H.
Booth
,
J. Chem. Phys.
143
,
054108
(
2015
).
50.
N. S.
Blunt
,
S. D.
Smart
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
143
,
134117
(
2015
); e-print arXiv:1508.04680v2.
51.
N. S.
Blunt
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
146
,
244105
(
2017
).
52.
G. L.
Manni
,
S. D.
Smart
, and
A.
Alavi
,
J. Chem. Theory Comput.
12
,
1245
(
2016
).
53.
R. E.
Thomas
,
Q.
Sun
,
A.
Alavi
, and
G. H.
Booth
,
J. Chem. Theory Comput.
11
,
5316
(
2015
).
54.
J. A. F.
Kersten
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
145
,
054117
(
2016
); e-print arXiv:1605.07065.
55.
G. H.
Booth
,
S. D.
Smart
, and
A.
Alavi
,
Mol. Phys.
112
,
1855
(
2014
); e-print arXiv:1305.6981.
56.
L. R.
Schwarz
,
A.
Alavi
, and
G. H.
Booth
,
Phys. Rev. Lett.
118
,
176403
(
2017
); e-print arXiv:1610.09326.
57.
A. J. W.
Thom
,
Phys. Rev. Lett.
105
,
263004
(
2010
).
58.
J. S.
Spencer
and
A. J. W.
Thom
,
J. Chem. Phys.
144
,
084108
(
2016
); e-print arXiv:1511.05752.
59.

Following previous work,60 to ensure convergence when S does not average to the coupled cluster energy these dynamics are modified to include the projected energy explicitly, though this does not affect the sampling of ΨCC.

60.
R. S. T.
Franklin
,
J. S.
Spencer
,
A.
Zoccante
, and
A. J. W.
Thom
,
J. Chem. Phys.
144
,
044111
(
2016
); e-print arXiv:1511.08129.
61.
G. H.
Booth
and
A.
Alavi
,
J. Chem. Phys.
132
,
174104
(
2010
).
62.
C. J.
Umrigar
,
M. P.
Nightingale
, and
K. J.
Runge
,
J. Chem. Phys.
99
,
2865
(
1993
).
63.
H.
Flyvbjerg
and
H. G.
Petersen
,
J. Chem. Phys.
91
,
461
(
1989
).
64.
A. A.
Holmes
,
H. J.
Changlani
, and
C. J.
Umrigar
,
J. Chem. Theory Comput.
12
,
1561
(
2016
); e-print arXiv:1512.03757.
65.
J. R.
Trail
,
Phys. Rev. E
77
,
016703
(
2008
).
66.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
); e-print arXiv:1011.1669v3.
67.
W. A.
Vigor
, “
Investigating quantum Monte Carlo methods in Slater determinant bases
,” Ph.D. thesis,
Imperial College London
,
2015
.
68.
W. A.
Vigor
,
J. S.
Spencer
,
M. J.
Bearpark
, and
A. J. W.
Thom
,
J. Chem. Phys.
144
,
094110
(
2016
); e-print arXiv:1601.00865.
69.
S. F.
Boys
,
Rev. Mod. Phys.
32
,
296
(
1960
).
70.
J. S.
Spencer
,
N. S.
Blunt
,
W. A.
Vigor
,
F. D.
Malone
,
W. M. C.
Foulkes
,
J. J.
Shepherd
, and
A. J. W.
Thom
,
J. Open Res. Software
3
,
1
(
2015
).
71.
Q.
Sun
,
T. C.
Berkelbach
,
N. S.
Blunt
,
G. H.
Booth
,
S.
Guo
,
Z.
Li
,
J.
Liu
,
J.
McClain
,
E. R.
Sayfutyarova
,
S.
Sharma
,
S.
Wouters
, and
G. K.-L.
Chan
, e-print arXiv:1701.08223 (
2017
).
72.
J. D.
Hunter
,
Comput. Sci. Eng.
9
,
90
(
2007
).
You do not currently have access to this content.