The sources of error in electronic structure calculations arising from the truncation of the one-particle and n-particle expansions are examined with very large correlation consistent basis sets, in some cases up through valence 10ζ quality, and coupled cluster methods, up through connected quadruple excitations. A limited number of full configuration interaction corrections are also considered. For cases where full configuration interaction calculations were unavailable or prohibitively expensive, a continued fraction approximation was used. In addition, errors arising from core∕valence and relativistic corrections are also probed for a number of small chemical systems. The accuracies of several formulas for estimating total energies and atomization energies in the complete basis set limit are compared in light of the present large basis set findings. In agreement with previous work, the CCSD(T) method is found to provide results that are closer to the CCSDTQ and full configuration-interaction results than the less approximate CCSDT method.

1.
C. W.
Sherr
,
J. Chem. Phys.
23
,
569
(
1955
).
2.
A. C.
Hurley
,
Proc. Phys. Soc., London, Sect. A
69
,
767
(
1956
).
3.
E.
Thulstrup
and
A.
Andersen
,
J. Phys. B
8
,
965
(
1975
).
4.
K. P.
Huber
and
G.
Herzberg
,
Constants of Diatomic Molecules
,
Molecular Spectra and Molecular Structure
Vol.
IV
(
Van Nostrand Reinhold
, New York,
1979
).
5.
M. W.
Chase
, Jr.
,
J. Phys. Chem. Ref. Data Monogr.
9
,
1
(
1998
).
6.
L. A.
Curtiss
,
K.
Raghavachari
,
G. W.
Trucks
, and
J. A.
Pople
,
J. Chem. Phys.
94
,
7221
(
1991
).
7.
D.
Feller
and
K. A.
Peterson
,
J. Chem. Phys.
108
,
154
(
1998
).
8.
D.
Feller
and
K. A.
Peterson
,
J. Chem. Phys.
110
,
8384
(
1999
).
9.
D.
Feller
,
J. Comput. Chem.
17
,
1571
(
1996
).
10.
D.
Feller
,
D. A.
Dixon
, and
K. A.
Peterson
,
J. Phys. Chem.
102
,
7053
(
1998
);
D. A.
Dixon
and
D.
Feller
,
J. Phys. Chem. A
102
,
8209
(
1998
);
D. A.
Dixon
,
D.
Feller
, and
G.
Sandrone
,
J. Phys. Chem. A
103
,
4744
(
1999
);
D.
Feller
and
D. A.
Dixon
,
J. Phys. Chem. A
103
,
6413
(
1999
);
D.
Feller
and
D. A.
Dixon
,
J. Phys. Chem. A
104
,
3048
(
2000
);
D.
Feller
and
J. A.
Franz
,
J. Phys. Chem. A
104
,
9017
(
2000
);
B.
Ruscic
,
D.
Feller
,
D. A.
Dixon
,
K. A.
Peterson
,
L. B.
Harding
,
R. L.
Asher
, and
A. F.
Wagner
,
J. Phys. Chem. A
105
,
1
(
2001
);
D. A.
Dixon
,
W. A.
de Jong
,
K. A.
Peterson
, and
J. S.
Francisco
,
J. Phys. Chem. A
106
,
4725
(
2002
);
D.
Feller
,
D. A.
Dixon
, and
J. S.
Francisco
,
J. Phys. Chem. A
107
,
1604
(
2003
);
D.
Feller
and
D. A.
Dixon
,
J. Phys. Chem. A
107
,
10419
(
2003
);
N. B.
Balabanov
and
K. A.
Peterson
,
J. Phys. Chem. A
107
,
7465
(
2003
);
D. A.
Dixon
,
D.
Feller
,
K. O.
Christe
,
W. W.
Wilson
,
A.
Vij
,
V.
Vij
,
H. D. B.
Jenkins
,
R.
Olson
, and
M. S.
Gordon
,
J. Am. Chem. Soc.
126
,
834
(
2004
).
[PubMed]
11.
D.
Feller
and
D. A.
Dixon
,
J. Chem. Phys.
115
,
3484
(
2001
).
12.
B.
Ruscic
,
A. F.
Wagner
,
L. B.
Harding
 et al,
J. Phys. Chem. A
106
,
2727
(
2002
).
13.
D.
Feller
,
K. A.
Peterson
,
W. A.
de Jong
, and
D. A.
Dixon
,
J. Chem. Phys.
118
,
3510
(
2003
).
14.
D.
Feller
and
D. A.
Dixon
,
J. Phys. Chem. A
107
,
9641
(
2003
).
15.
L.
Pollack
,
T. L.
Windus
,
W. A.
de Jong
, and
D. A.
Dixon
,
J. Phys. Chem. A
109
,
6934
(
2005
).
16.
N. B.
Balabanov
and
K. A.
Peterson
,
J. Chem. Phys.
123
,
064107
(
2005
).
17.
R. S.
Grev
,
C. L.
Janssen
, and
H. F.
Schaefer
 III
,
J. Chem. Phys.
95
,
5128
(
1991
).
18.
E. R.
Davidson
and
D.
Feller
,
Chem. Rev. (Washington, D.C.)
86
,
681
(
1986
);
D.
Feller
and
E. R.
Davidson
,
Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions
(
VCH
, New York,
1990
).
19.
J.
Almlöf
and
P. R.
Taylor
,
J. Chem. Phys.
86
,
4070
(
1987
).
20.
K.
Jankowski
,
R.
Becherer
,
P.
Scharf
,
H.
Schiffer
, and
R.
Alhrichs
,
J. Chem. Phys.
82
,
1413
(
1985
).
21.
R. C.
Raffenetti
,
J. Chem. Phys.
58
,
4452
(
1973
).
22.
W. J.
Hehre
,
R.
Ditchfield
, and
J. A.
Pople
,
J. Chem. Phys.
56
,
2257
(
1972
);
P. C.
Hariharan
and
J. A.
Pople
,
Theor. Chim. Acta
28
,
213
(
1973
).
23.
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
90
,
1007
(
1989
).
24.
R. A.
Kendall
,
T. H.
Dunning
,Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
);
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
100
,
2975
(
1994
).
25.
D. E.
Woon
and
T. H.
Dunning
,Jr.
,
J. Chem. Phys.
103
,
4572
(
1995
);
K. A.
Peterson
and
T. H.
Dunning
,Jr.
,
J. Chem. Phys.
117
,
10548
(
2002
);
J.
Koput
and
K. A.
Peterson
,
J. Phys. Chem. A
106
,
9595
(
2002
).
26.
W. A.
de Jong
,
R. J.
Harrison
, and
D. A.
Dixon
,
J. Chem. Phys.
114
,
48
(
2001
).
27.
D.
Woon
and
T. H.
Dunning
,Jr.
,
J. Chem. Phys.
98
,
1358
(
1993
);
A. K.
Wilson
,
D. E.
Woon
,
K. A.
Peterson
, and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
110
,
7667
(
1999
).
28.
K. A.
Peterson
,
J. Chem. Phys.
119
,
11099
(
2003
);
K. A.
Peterson
,
D.
Figgen
,
E.
Goll
,
H.
Stoll
, and
M.
Dolg
,
J. Chem. Phys.
119
,
11113
(
2003
);
K. A.
Peterson
and
C.
Puzzarini
,
Theor. Chem. Acc.
114
,
283
(
2005
).
29.
A. K.
Wilson
,
T.
van Mourik
, and
T. H.
Dunning
,Jr.
,
J. Mol. Struct.: THEOCHEM
388
,
339
(
1996
);
T.
van Mourik
and
T. H.
Dunning
, Jr.
,
Int. J. Quantum Chem.
76
,
205
(
1999
).
30.
D.
Feller
,
J. Chem. Phys.
96
,
6104
(
1992
);
S. S.
Xantheas
and
T. H.
Dunning
,Jr.
,
J. Phys. Chem.
97
,
18
(
1993
);
D.
Feller
,
J. Chem. Phys.
98
,
7059
(
1993
).
31.
C.
Moller
and
M. S.
Plesset
,
Phys. Rev.
46
,
618
(
1934
).
32.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
99
,
1914
(
1993
).
33.
D. G.
Truhlar
,
Chem. Phys. Lett.
294
,
45
(
1998
);
P. L.
Fast
,
M. L.
Sánchez
, and
D. G.
Truhlar
,
J. Chem. Phys.
111
,
2921
(
1999
).
34.
G. A.
Petersson
,
A.
Bennett
,
T. G.
Tensfeldt
,
M. A.
Al-Laham
,
W. A.
Shirley
, and
J.
Mantzaris
,
J. Chem. Phys.
89
,
2193
(
1988
);
G. A.
Petersson
and
M. A.
Al-Laham
,
J. Chem. Phys.
94
,
6081
(
1989
);
G. A.
Petersson
, in
Computational Thermochemistry: Predictions and Estimation of Molecular Thermodynamics
,
ACS Symposium Series
Vol.
667
edited by
K. K.
Irikura
and
D. J.
Frurip
(
ACS
, Washington, DC,
1998
).
35.
K.
Raghavachari
,
G. W.
Trucks
,
J. A.
Pople
, and
M.
Head-Gordon
,
Chem. Phys. Lett.
157
,
479
(
1989
).
36.
R. D.
Amos
,
A.
Bernhardsson
,
A.
Berning
 et al, MOLPRO2002.6, a package of ab initio programs (
Universität Stüttgart
, Stüttgart, Germany∕University of Birmingham, Birmingham, United Kingdom,
2002
).
37.
T. D.
Crawford
,
C. D.
Sherrill
,
E. F.
Valeev
 et al, PSI, version 3.2 (
2005
).
38.
C.
Angeli
,
K. L.
Bak
,
V.
Bakken
 et al, DALTON2.0 (
2005
).
39.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
 et al, GAUSSIAN 03, revision C.02, Gaussian, Inc., Wallingford, CT,
2004
.
40.
E.
Aprà
,
T. L.
Windus
,
T. P.
Straatsma
 et al, NWCHEM4.7, a computational chemistry package for parallel computers (
Pacific Northwest National Laboratory
, Richland, Washington,
2005
).
41.
in
Methods in Computational Physics
, edited by
B. J.
Alder
,
S.
Fernbach
, and
M.
Rotenberg
(
Academic
, New York,
1963
), Vol.
2
, p.
262
.
42.
W.
Kutzelnigg
and
J. D.
Morgan
,
J. Chem. Phys.
96
,
4484
(
1992
).
43.
J. M. L.
Martin
,
Chem. Phys. Lett.
259
,
669
(
1996
);
T.
Helgaker
,
W.
Klopper
,
H.
Koch
, and
J.
Nago
,
J. Chem. Phys.
106
,
9639
(
1997
).
44.
J. M. L.
Martin
and
T. J.
Lee
,
Chem. Phys. Lett.
258
,
136
(
1996
).
45.
A.
Halkier
,
T.
Helgaker
,
P.
Jorgensen
,
W.
Klopper
,
H.
Koch
,
J.
Olsen
, and
A. K.
Wilson
,
Chem. Phys. Lett.
286
,
243
(
1998
).
46.
K. A.
Peterson
,
D. E.
Woon
, and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
100
,
7410
(
1994
).
47.
A. K.
Wilson
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
106
,
8718
(
1997
).
49.
E. F.
Valeev
,
W. D.
Allen
,
R.
Hernandez
,
C. D.
Scherrill
, and
H. F.
Schaefer
 III
,
J. Chem. Phys.
118
,
8594
(
2003
).
50.
W.
Kutzelnigg
,
Theor. Chim. Acta
68
,
445
(
1985
);
W.
Klopper
and
W.
Kutzelnigg
,
Chem. Phys. Lett.
134
,
17
(
1987
);
W.
Klopper
and
W.
Kutzelnigg
,
J. Phys. Chem.
94
,
5625
(
1990
);
W.
Kutzelnigg
and
W.
Klopper
,
J. Chem. Phys.
94
,
1985
(
1991
).
51.
W.
Klopper
and
J.
Gauss
(private communication).
52.
D.
Feller
and
J. A.
Sordo
,
J. Chem. Phys.
113
,
485
(
2000
).
53.
T.
Kato
,
Pure Appl. Math.
10
,
151
(
1957
).
54.
55.
K. A.
Peterson
,
A. K.
Wilson
,
D. E.
Woon
, and
T. H.
Dunning
, Jr.
,
Theor. Chem. Acc.
97
,
251
(
1997
).
56.
W.
Klopper
and
T.
Helgaker
(private communication).
57.
T. H.
Dunning
, Jr.
,
K. A.
Peterson
, and
A. K.
Wilson
,
J. Chem. Phys.
114
,
9244
(
2001
).
58.
C.
Hampel
,
K. A.
Peterson
, and
H. J.
Werner
,
Chem. Phys. Lett.
190
,
1
(
1990
);
M. J. O.
Deegan
and
P. J.
Knowles
,
Chem. Phys. Lett.
227
,
321
(
1994
);
P. J.
Knowles
,
C.
Hampel
, and
H. J.
Werner
,
J. Chem. Phys.
99
,
5219
(
1993
).
59.
T. A.
Ruden
,
T.
Helgaker
,
P.
Jørgensen
, and
J.
Olsen
,
Chem. Phys. Lett.
371
,
62
(
2003
).
60.
K. A.
Peterson
and
T. H.
Dunning
, Jr.
,
J. Phys. Chem. A
101
,
6280
(
1997
).
61.
62.
M.
Douglas
and
N. M.
Kroll
,
Ann. Phys.
82
,
89
(
1974
);
G.
Jansen
and
B. A.
Hess
,
Phys. Rev. A
39
,
6016
(
1989
).
63.
C. E.
Moore
,
Atomic Energy Levels
,
Natl. Bur. Stand. (U.S.) Circ. No. 37
(
U.S. GPO
, Washington, D.C.,
1971
).
64.
A. G.
Maki
and
R. L.
Sams
,
J. Mol. Spectrosc.
52
,
233
(
1974
).
65.
T.
Shimanouchi
,
Tables of Molecular Vibrational Frequencies Consolidated
(
National Bureau of Standards
, Washington, D.C.,
1972
).
66.
J.
Senekowitsch
, Ph.D. thesis,
Universität Frankfurt
,
1988
.
67.
A. D.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
);
C.
Lee
,
W.
Yang
, and
R. G.
Parr
,
Phys. Rev. B
37
,
785
(
1988
).
68.
C. W.
Bauschlicher
, Jr.
and
H.
Partridge
,
Chem. Phys. Lett.
240
,
533
(
1995
).
A. D.
Boese
and
J. M. L.
Martin
,
J. Chem. Phys.
119
,
3005
(
2003
);
N. X.
Wang
and
A. K.
Wilson
,
J. Chem. Phys.
121
,
7632
(
2004
);
[PubMed]
N. X.
Wang
and
A. K.
Wilson
,
Mol. Phys.
103
,
345
(
2005
).
70.
R. J.
Bartlett
and
J. F.
Stanton
,
Reviews in Computational Chemistry
(
VCH
, New York,
1994
), Vol.
5
.
71.
D.
Feller
,
J. Chem. Phys.
111
,
4373
(
1999
).
72.
D.
Feller
and
J. A.
Sordo
,
J. Chem. Phys.
112
,
5604
(
2000
).
73.
P. A.
Denis
,
Chem. Phys. Lett.
382
,
65
(
2003
).
74.
T.
Helgaker
,
W.
Klopper
,
A.
Halkier
,
K. L.
Bak
,
P.
Jørgensen
, and
J.
Olsen
(
Kluwer
, Dordrecht,
2001
), Vol.
22
, p.
1
.
75.
A. D.
Boese
,
M.
Oren
,
O.
Atasoylu
,
J. M. L.
Martin
,
M.
Kallay
, and
J.
Gauss
,
J. Chem. Phys.
120
,
4129
(
2004
).
76.
A.
Tajti
,
P. G.
Szalay
,
A. G.
Császár
,
M.
Kallay
,
J.
Gauss
,
E. F.
Valeev
,
B. A.
Flowers
,
J.
Vázquez
, and
J. F.
Stanton
,
J. Chem. Phys.
121
,
11599
(
2004
).
77.
K.
Raghavachari
,
J. A.
Pople
,
E. S.
Replogle
, and
M.
Head-Gordon
,
J. Phys. Chem.
94
,
5579
(
1990
).
78.
R. J.
Bartlett
,
J. D.
Watts
,
S. A.
Kucharski
, and
J.
Noga
,
Chem. Phys. Lett.
165
,
513
(
1990
).
79.
T. A.
Ruden
,
T.
Helgaker
,
P.
Jørgensen
, and
J.
Olsen
,
J. Chem. Phys.
121
,
5874
(
2004
).
80.
D. Z.
Goodson
,
J. Chem. Phys.
116
,
6948
(
2002
).
81.
D.
Cremer
and
Z.
He
,
J. Phys. Chem.
100
,
6173
(
1996
).
82.
T.
Yanai
,
M.
Kamiya
,
Y.
Kawashima
 et al,
UTCHEM
2004 B (
2004
).
83.
S. L.
Mielke
,
D. W.
Schwenke
, and
K. A.
Peterson
,
J. Chem. Phys.
122
,
224313
(
2005
).
84.
N. C.
Handy
,
Y.
Yamaguchi
, and
H. F.
Schaefer
 III
,
J. Chem. Phys.
84
,
4481
(
1986
).
85.
E. F.
Valeev
and
C. D.
Scherrill
,
J. Chem. Phys.
118
,
3921
(
2003
).
86.
D. W.
Schwenke
,
J. Chem. Phys.
122
,
014107
(
2005
).
87.
M. L.
Leininger
,
W. D.
Allen
,
H. F.
Schaefer
 III
, and
C. D.
Sherrill
,
J. Chem. Phys.
112
,
9213
(
2000
).
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