The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting “universal” explicitly correlated approaches that fit into the FCIQMC framework: the [2]R12 method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mEh to 3-4 mEh. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.

1.
G. H.
Booth
,
A. J. W.
Thom
, and
A.
Alavi
,
J. Chem. Phys.
131
,
054106
(
2009
).
2.
G. H.
Booth
and
A.
Alavi
,
J. Chem. Phys.
132
,
174104
(
2010
).
3.
G. H.
Booth
,
D.
Cleland
,
A. J. W.
Thom
, and
A.
Alavi
,
J. Chem. Phys.
135
,
084104
(
2011
).
4.
R. E.
Thomas
,
C.
Overy
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Theor. Comput.
10
,
1915
(
2014
).
5.
C.
Daday
,
S.
Smart
,
G. H.
Booth
,
A.
Alavi
, and
C.
Filippi
,
J. Chem. Theor. Comput.
8
,
4441
(
2012
).
6.
D.
Cleland
,
G. H.
Booth
,
C.
Overy
, and
A.
Alavi
,
J. Chem. Theor. Comput.
8
,
4138
(
2012
).
7.
R. E.
Thomas
,
G. H.
Booth
, and
A.
Alavi
,
Phys. Rev. Lett.
114
,
033001
(
2015
).
8.
L. R.
Schwarz
,
G. H.
Booth
, and
A.
Alavi
,
Phys. Rev. B
91
,
045139
(
2015
).
9.
J. J.
Shepherd
,
G. H.
Booth
,
A.
Grüneis
, and
A.
Alavi
,
Phys. Rev. B
85
,
081103(R)
(
2012
).
10.
G. H.
Booth
,
A.
Gruneis
,
G.
Kresse
, and
A.
Alavi
,
Nature
493
,
365
(
2013
).
11.
D.
Cleland
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
132
,
041103
(
2010
).
12.
D. M.
Cleland
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
134
,
024112
(
2011
).
13.
F. R.
Petruzielo
,
A. A.
Holmes
,
H. J.
Changlani
,
M. P.
Nightingale
, and
C. J.
Umrigar
,
Phys. Rev. Lett.
109
,
230201
(
2012
).
14.
N. S.
Blunt
,
S. D.
Smart
,
J. A. F.
Kersten
,
J. S.
Spencer
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
142
,
184107
(
2015
).
15.
A.
Humeniuk
and
R.
Mitrić
,
J. Chem. Phys.
141
,
194104
(
2014
).
16.
N. S.
Blunt
,
A.
Alavi
, and
G. H.
Booth
,
Phys. Rev. Lett.
115
,
050603
(
2015
).
17.
G. H.
Booth
and
G.-L.
Chan
,
J. Chem. Phys.
137
,
191102
(
2012
).
18.
Y.
Ohtsuka
and
S.
Nagase
,
Theor. Chem. Acc.
130
,
501
(
2011
).
19.
S.
Ten-no
,
J. Chem. Phys.
138
,
164126
(
2013
).
20.
N.
Blunt
,
S. D.
Smart
,
G. H.
Booth
, and
A.
Alavi
,
J. Chem. Phys.
143
,
134117
(
2015
).
21.
N. S.
Blunt
,
T. W.
Rogers
,
J. S.
Spencer
, and
W. M. C.
Foulkes
,
Phys. Rev. B
89
,
245124
(
2014
).
22.
C.
Overy
,
G. H.
Booth
,
N. S.
Blunt
,
J. J.
Shepherd
,
D.
Cleland
, and
A.
Alavi
,
J. Chem. Phys.
141
,
244117
(
2014
).
23.
R. E.
Thomas
,
Q.
Sun
,
A.
Alavi
, and
G. H.
Booth
,
J. Chem. Theor. Comput.
11
,
5316
(
2015
).
24.
G. L.
Manni
,
S. D.
Smart
, and
A.
Alavi
,
J. Chem. Theor. Comput.
12
,
1245
(
2016
).
25.
26.
R. N.
Hill
,
J. Chem. Phys.
83
,
1173
(
1985
).
27.
W.
Kutzelnigg
and
J.
Morgan III
,
J. Chem. Phys.
96
,
4484
(
1992
).
28.
J. J.
Shepherd
,
A.
Grüneis
,
G. H.
Booth
,
G.
Kresse
, and
A.
Alavi
,
Phys. Rev. B
86
,
035111
(
2012
).
29.
30.
E. A.
Hylleraas
,
Z. Phys.
54
,
347
(
1929
).
31.
R.
T Pack
and
W. B.
Brown
,
J. Chem. Phys.
45
,
556
(
1966
).
32.
T.
Kato
,
Commun. Pure Appl. Math.
10
,
151
(
1957
).
33.
W.
Klopper
,
F. R.
Manby
,
S.
Ten-No
, and
E. F.
Valeev
,
Int. Rev. Phys. Chem.
25
,
427
(
2006
).
34.
L.
Kong
,
F. A.
Bischoff
, and
E. F.
Valeev
,
Chem. Rev.
112
,
75
(
2012
).
35.
C.
Hättig
,
W.
Klopper
,
A.
Köhn
, and
D. P.
Tew
,
Chem. Rev.
112
,
4
(
2012
).
36.
W.
Kutzelnigg
,
Theor. Chim. Acta
68
,
445
(
1985
).
37.
V.
Termath
,
W.
Klopper
, and
W.
Kutzelnigg
,
J. Chem. Phys.
94
,
2002
(
1991
).
38.
W.
Kutzelnigg
and
W.
Klopper
,
J. Chem. Phys.
94
,
1985
(
1991
).
39.
J.
Noga
,
W.
Kutzelnigg
, and
W.
Klopper
,
Chem. Phys. Lett.
199
,
497
(
1992
).
40.
J.
Noga
and
W.
Kutzelnigg
,
J. Chem. Phys.
101
,
7738
(
1994
).
41.
W.
Klopper
and
C. C. M.
Samson
,
J. Chem. Phys.
116
,
6397
(
2002
).
42.
E. F.
Valeev
,
Chem. Phys. Lett.
395
,
190
(
2004
).
43.
A. J.
May
and
F. R.
Manby
,
J. Chem. Phys.
121
,
4479
(
2004
).
44.
F. R.
Manby
,
J. Chem. Phys.
119
,
4607
(
2003
).
45.
S.
Ten-no
,
J. Chem. Phys.
126
,
014108
(
2007
).
46.
S.
Ten-no
,
Chem. Phys. Lett.
330
,
169
(
2000
).
47.
S.
Ten-no
,
Chem. Phys. Lett.
330
,
175
(
2000
).
48.
49.
D. P.
Tew
and
W.
Klopper
,
J. Chem. Phys.
123
,
074101
(
2005
).
50.
A. J.
May
,
E.
Valeev
,
R.
Polly
, and
F. R.
Manby
,
Phys. Chem. Chem. Phys.
7
,
2710
(
2005
).
51.
S.
Ten-no
,
Chem. Phys. Lett.
447
,
175
(
2007
).
52.
R. J.
Gdanitz
,
Chem. Phys. Lett.
312
,
578
(
1999
).
53.
T.
Shiozaki
,
G.
Knizia
, and
H.-J.
Werner
,
J. Chem. Phys.
134
,
034113
(
2011
).
54.
T.
Shiozaki
and
H.-J.
Werner
,
J. Chem. Phys.
133
,
141103
(
2010
).
55.
M.
Torheyden
and
E. F.
Valeev
,
J. Chem. Phys.
131
,
171103
(
2009
).
56.
L.
Kong
and
E. F.
Valeev
,
J. Chem. Phys.
135
,
214105
(
2011
).
57.
T.
Yanai
and
T.
Shiozaki
,
J. Chem. Phys.
136
,
084107
(
2012
).
58.
T.
Yanai
and
G. K.-L.
Chan
,
J. Chem. Phys.
127
,
104107
(
2007
).
59.
G. H.
Booth
,
D.
Cleland
,
A.
Alavi
, and
D. P.
Tew
,
J. Chem. Phys.
137
,
164112
(
2012
).
60.
S.
Sharma
,
T.
Yanai
,
G. H.
Booth
,
C. J.
Umrigar
, and
G. K.-L.
Chan
,
J. Chem. Phys.
140
,
104112
(
2014
).
61.
J. A.
Pople
,
M.
Head-Gordon
,
D. J.
Fox
,
K.
Raghavachari
, and
L. A.
Curtiss
,
J. Chem. Phys.
90
,
5622
(
1989
).
62.
L. A.
Curtiss
,
C.
Jones
,
G. W.
Trucks
,
K.
Raghavachari
, and
J. A.
Pople
,
J. Chem. Phys.
93
,
2537
(
1990
).
63.
G. H.
Booth
,
S. D.
Smart
, and
A.
Alavi
,
Mol. Phys.
112
,
1855
(
2014
).
64.
L. B.
Roskop
,
L.
Kong
,
E. F.
Valeev
,
M. S.
Gordon
, and
T. L.
Windus
,
J. Chem. Theor. Comput.
10
,
90
(
2014
).
65.
W.
Kutzelnigg
and
D.
Mukherjee
,
J. Chem. Phys.
107
,
432
(
1997
).
66.
W.
Kutzelnigg
,
K. R.
Shamasundar
, and
D.
Mukherjee
,
Mol. Phys.
108
,
433
(
2010
).
67.
W.
Kutzelnigg
,
J. Chem. Phys.
125
,
171101
(
2006
).
68.
The FCIQMC code can be obtained from https://github.com/ghb24/NECI_STABLE.git.
69.
C. L.
Janssen
,
I. B.
Nielsen
,
M. L.
Leininger
,
E. F.
Valeev
,
J. P.
Kenny
, and
E. T.
Seidl
, The massively parallel quantum chemistry program (MPQC), version 2.4.0, 2006.
70.
C.
Janssen
,
E.
Seidl
, and
M.
Colvin
, in
ACS Symposium Series, Parallel Computing in Computational Chemistry
(
American Chemical Society
,
1995
), Vol.
592
.
71.
J. O.
Hirschfelder
,
J. Chem. Phys.
39
,
3145
(
1963
).
72.
S. F.
Boys
and
N. C.
Handy
,
Proc. R. Soc. London, Ser. A
309
,
209
(
1969
).
73.
S. F.
Boys
and
N. C.
Handy
,
Proc. R. Soc. London, Ser. A
310
,
43
(
1969
).
74.
S. F.
Boys
and
N. C.
Handy
,
Proc. R. Soc. London, Ser. A
310
,
63
(
1969
).
75.
N.
Umezawa
and
S.
Tsuneyuki
,
J. Chem. Phys.
119
,
10015
(
2003
).
76.
N.
Umezawa
and
S.
Tsuneyuki
,
Phys. Rev. B
69
(
2004
).
77.
H.
Luo
,
J. Chem. Phys.
133
,
154109
(
2010
).
78.
H.
Luo
,
J. Chem. Phys.
135
,
024109
(
2011
).
79.
H.
Luo
,
J. Chem. Phys.
136
,
224111
(
2012
).
80.
S. R.
White
,
J. Chem. Phys.
117
,
7472
(
2002
).
81.
E.
Neuscamman
,
T.
Yanai
, and
G.-L.
Chan
,
Int. Rev. Phys. Chem.
29
,
231
(
2010
).
82.
T.
Yanai
and
G.-L.
Chan
,
J. Chem. Phys.
124
,
194106
(
2006
).
83.
G.-L.
Chan
and
T.
Yanai
,
Adv. Chem. Phys.
134
,
343
(
2007
).
84.
E.
Neuscamman
,
T.
Yanai
, and
G.-L.
Chan
,
J. Chem. Phys.
130
,
124102
(
2009
).
85.
E.
Neuscamman
,
T.
Yanai
, and
G.-L.
Chan
,
J. Chem. Phys.
132
,
024106
(
2010
).
86.
T.
Yanai
,
Y.
Kurashige
,
E.
Neuscamman
, and
G.-L.
Chan
,
J. Chem. Phys.
132
,
024105
(
2010
).
87.
T.
Yanai
,
Y.
Kurashige
,
E.
Neuscamman
, and
G.-L.
Chan
,
Phys. Chem. Chem. Phys.
14
,
7809
(
2012
).
88.
T.
Watson
and
G.-L.
Chan
,
J. Chem. Theor. Comput.
12
,
512
(
2016
).
89.
S.
Kedžuch
,
M.
Milko
, and
J.
Noga
,
Int. J. Quantum Chem.
105
,
929
(
2005
).
90.
T.
Shiozaki
,
Chem. Phys. Lett.
479
,
160
(
2009
).
91.
T.
Shiozaki
,
J. Unsolved Quest.
1
,
1
(
2011
), http://junq.info/?p=348; accessed on 30 December 2011.
92.
T.
Shiozaki
, PolyR12, the program for explicitly correlated electron-correlation calculations of molecules and solids, can be obtained from https://github.com/nubakery/libslater, 2014.
93.
D.
Feller
,
K. A.
Peterson
, and
D. A.
Dixon
,
J. Chem. Phys.
129
,
204105
(
2008
).
94.
J. C.
Grossman
,
J. Chem. Phys.
117
,
1434
(
2002
).
95.
A. D.
Becke
,
J. Chem. Phys.
96
,
2155
(
1992
).
96.
M.
Ernzerhof
and
G. E.
Scuseria
,
J. Chem. Phys.
110
,
5029
(
1999
).
97.
N.
Nemec
,
M. D.
Towler
, and
R. J.
Needs
,
J. Chem. Phys.
132
,
034111
(
2010
).
98.
M. A.
Morales
,
J.
McMinis
,
B. K.
Clark
,
J.
Kim
, and
G. E.
Scuseria
,
J. Chem. Theor. Comput.
8
,
2181
(
2012
).
99.
H.
Flyvbjerg
and
H. G.
Petersen
,
J. Chem. Phys.
91
,
461
(
1989
).
100.
T. B.
Adler
,
G.
Knizia
, and
H.-J.
Werner
,
J. Chem. Phys.
127
,
221106
(
2007
).
101.
A.
Halkier
,
T.
Helgaker
,
P.
Jørgensen
,
W.
Klopper
, and
J.
Olsen
,
Chem. Phys. Lett.
302
,
437
(
1999
).
102.
L.
Kong
and
E. F.
Valeev
,
J. Chem. Phys.
133
,
174126
(
2010
).
103.
H.
Werner
,
P.
Knowles
,
G.
Knizia
,
F.
Manby
,
M.
Schütz
 et al, molpro, version 2012.1, a package ofab initio programs, 2012, see http://www.molpro.net.
104.
G.
Knizia
,
T. B.
Adler
, and
H.-J.
Werner
,
J. Chem. Phys.
130
,
054104
(
2009
).
105.
M.
Chase
, Jr.
and
N.-J. T.
Tables
,
J. Phys. Chem. Ref. Data
1
(
1998
).
106.
K.
Huber
and
G.
Herzberg
,
Constants of Diatomic Molecules
,
Molecular Spectra and Molecular Structure
Vol.
4
(
Van Nostrand Reinhold, New York
,
1979
).
107.
K. R.
Way
and
W. C.
Stwalley
,
J. Chem. Phys.
59
,
5298
(
1973
).
108.
Y.
Huang
,
S. A.
Barts
, and
J. B.
Halpern
,
J. Phys. Chem.
96
,
425
(
1992
).
109.
R.
Lengel
and
R.
Zare
,
J. Am. Chem. Soc.
100
,
7495
(
1978
).
110.
A.
McKellar
,
P.
Bunker
,
T. J.
Sears
,
K.
Evenson
,
R. J.
Saykally
, and
S.
Langhoff
,
J. Chem. Phys.
79
,
5251
(
1983
).
111.
D.
Baulch
,
R.
Cox
,
P.
Crutzen
,
R.
Hampson
, Jr.
,
J.
Kerr
,
J.
Troe
,
R.
Watson
 et al,
J. Phys. Chem. Ref. Data
11
,
327
(
1982
).
112.
S.
Gibson
,
J.
Greene
, and
J.
Berkowitz
,
J. Chem. Phys.
83
,
4319
(
1985
).
113.
D. D.
Wagman
,
W. H.
Evans
,
V. B.
Parker
,
R. H.
Schumm
,
I.
Halow
,
S. M.
Bailey
,
K. L.
Churney
, and
R. L.
Nuttall
,
J. Phys. Chem. Ref. Data, Suppl.
2
,
11
(
1982
).
114.
S.
Lias
,
J.
Bartmess
,
J.
Liebman
,
J.
Holmes
,
R.
Levin
, and
W. G.
Mallard
, Ion Energetics Data, NIST Chemistry Web-Book, NIST Standard Reference Database Number 69, edited by P. J. Linstrom and W. G. Mallard, National Institute of Standards and Technology, Gaithersburg MD 20899, 1988.
115.
V. P.
Glushko
,
L. V.
Gurvich
,
G. A.
Bergman
,
I. V.
Veitz
,
V. A.
Medvedev
,
G. A.
Khachkuruzov
, and
V. S.
Jungman
,
Thermodynamic Properties of Pure Substances
(
Nauka, Moscow, USSR
,
1978
).
116.
J.
Berkowitz
,
J. P.
Greene
,
H.
Cho
, and
B.
Rui
,
J. Chem. Phys.
86
,
1235
(
1987
).
117.
J. E.
Butler
,
K.
Kawaguchi
, and
E.
Hirota
,
J. Mol. Spectrosc.
101
,
161
(
1983
).
118.
J.
Berkowitz
,
L.
Curtiss
,
S.
Gibson
,
J.
Greene
,
G.
Hillhouse
, and
J.
Pople
,
J. Chem. Phys.
84
,
375
(
1986
).
119.
N. S.
Dattani
,
J. Mol. Spectrosc.
311
,
76
(
2015
).
120.
R. J.
Le Roy
,
N. S.
Dattani
,
J. A.
Coxon
,
A. J.
Ross
,
P.
Crozet
, and
C.
Linton
,
J. Chem. Phys.
131
,
204309
(
2009
).
121.
D.
Feller
and
K. A.
Peterson
,
J. Chem. Phys.
110
,
8384
(
1999
).
122.
M.
Fréchet
,
Annales de la Societe Polonaise de Mathematique
6
,
93
(
1927
).
123.
W.
Weibull
,
ASME J. Appl. Mech.
18
,
293
(
1951
).
124.
A.
Gruneis
,
J. J.
Shepherd
,
A.
Alavi
,
P. T.
Tew
, and
G. H.
Booth
,
J. Chem. Phys.
139
,
084112
(
2013
).
125.
126.
D.
Usvyat
,
J. Chem. Phys.
139
,
194101
(
2013
).
You do not currently have access to this content.