With recent advances in electronic structure methods, first-principles calculations of electronic response properties, such as linear and nonlinear polarizabilities, have become possible for molecules with more than 100 atoms. Basis set incompleteness is typically the main source of error in such calculations since traditional diffuse augmented basis sets are too costly to use or suffer from near linear dependence. To address this problem, we construct the first comprehensive set of property-optimized augmented basis sets for elements H–Rn except lanthanides. The new basis sets build on the Karlsruhe segmented contracted basis sets of split-valence to quadruple-zeta valence quality and add a small number of moderately diffuse basis functions. The exponents are determined variationally by maximization of atomic Hartree–Fock polarizabilities using analytical derivative methods. The performance of the resulting basis sets is assessed using a set of 313 molecular static Hartree–Fock polarizabilities. The mean absolute basis set errors are 3.6%, 1.1%, and 0.3% for property-optimized basis sets of split-valence, triple-zeta, and quadruple-zeta valence quality, respectively. Density functional and second-order Møller–Plesset polarizabilities show similar basis set convergence. We demonstrate the efficiency of our basis sets by computing static polarizabilities of icosahedral fullerenes up to C720 using hybrid density functional theory.

1.
Computational Molecular Spectroscopy
, edited by
P. R.
Bunker
and
P.
Jensen
(
Wiley
,
Chichester
,
2000
).
2.
S.
Mukamel
,
Principles of Nonlinear Optical Spectroscopy
(
Oxford University Press
,
New York
,
1995
).
3.
F.
Neese
,
Coord. Chem. Rev.
253
,
526
(
2009
).
4.
Time-Dependent Density Functional Theory
,
Lecture Notes in Physics
Vol.
706
, edited by
M. A. L.
Marques
,
C. A.
Ullrich
,
F.
Nogueira
,
A.
Rubio
,
K.
Burke
, and
E. K. U.
Gross
(
Springer
,
Berlin
,
2006
).
5.
O.
Christiansen
,
P.
Jørgensen
, and
C.
Hättig
,
Int. J. Quantum Chem.
68
,
1
(
1998
).
6.
I.
Shavitt
and
R. J.
Bartlett
,
Many-Body Methods in Chemistry and Physics
(
Cambridge University Press
,
Cambridge
,
2009
).
7.
E. R.
Davidson
and
D.
Feller
,
Chem. Rev. (Washington, D.C.)
86
,
681
(
1986
).
8.
J. O.
Hirschfelder
,
W.
Byers Brown
, and
S. T.
Epstein
,
Adv. Quantum Chem.
1
,
255
(
1964
).
9.
J.
Chandrasekhar
,
J. G.
Andrade
, and
P.
von Ragué Schleyer
,
J. Am. Chem. Soc.
103
,
5609
(
1981
).
10.
T.
Clark
,
J.
Chandrasekhar
,
G. W.
Spitznagel
, and
P.
von Ragué Schleyer
,
J. Comput. Chem.
4
,
294
(
1983
).
11.
R. A.
Kendall
,
T. H.
Dunning
, Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
).
12.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
98
,
1358
(
1993
).
13.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
100
,
2975
(
1994
).
14.
F.
Jensen
,
J. Chem. Phys.
115
,
9113
(
2001
).
15.
F.
Jensen
,
J. Chem. Phys.
116
,
3502
(
2002
).
16.
F.
Jensen
,
J. Chem. Phys.
116
,
7372
(
2002
).
17.
F.
Jensen
,
J. Chem. Phys.
117
,
9234
(
2002
).
18.
P.
Manninen
and
J.
Vaara
,
J. Comput. Chem.
27
,
434
(
2006
).
19.
A. J.
Sadlej
,
Collect. Czech. Chem. Commun.
53
,
1995
(
1988
).
20.
A. J.
Sadlej
,
Theor. Chim. Acta
79
,
123
(
1991
).
21.
Z.
Benkova
,
A. J.
Sadlej
,
R. E.
Oakes
, and
S. E. J.
Bell
,
J. Comput. Chem.
26
,
145
(
2005
).
22.
Z.
Benkova
,
A. J.
Sadlej
,
R. E.
Oakes
, and
S. E. J.
Bell
,
Theor. Chem. Acc.
113
,
238
(
2005
).
23.
H. -J.
Werner
and
W.
Meyer
,
Mol. Phys.
31
,
855
(
1976
).
24.
E. A.
Hylleraas
,
Z. Phys.
65
,
209
(
1930
).
25.
D.
Rappoport
and
F.
Furche
,
J. Chem. Phys.
126
,
201104
(
2007
).
26.
F.
Weigend
and
R.
Ahlrichs
,
Phys. Chem. Chem. Phys.
7
,
3297
(
2005
).
27.
A.
Schäfer
,
H.
Horn
, and
R.
Ahlrichs
,
J. Chem. Phys.
97
,
2571
(
1992
).
28.
A.
Schäfer
,
C.
Huber
, and
R.
Ahlrichs
,
J. Chem. Phys.
100
,
5829
(
1994
).
29.
F.
Weigend
,
F.
Furche
, and
R.
Ahlrichs
,
J. Chem. Phys.
119
,
12753
(
2003
).
30.
K.
Faegri
, Jr.
and
J.
Almlöf
,
J. Comput. Chem.
7
,
396
(
1986
).
31.
F.
London
,
J. Phys. Radium
8
,
397
(
1937
).
32.
C. L.
Darling
and
H. B.
Schlegel
,
J. Phys. Chem.
98
,
5855
(
1994
).
33.
A. J.
Sadlej
,
Chem. Phys. Lett.
47
,
50
(
1977
).
34.
J. A.
Hudis
and
R.
Ditchfield
,
Chem. Phys. Lett.
77
,
202
(
1981
).
35.
T.
Helgaker
and
J.
Almlöf
,
J. Chem. Phys.
89
,
4889
(
1988
).
36.
F.
Furche
and
R.
Ahlrichs
,
J. Chem. Phys.
117
,
7433
(
2002
).
37.
F.
Furche
and
R.
Ahlrichs
,
J. Chem. Phys.
121
,
12772
(
2004
).
38.
R.
Ahlrichs
,
M.
Bär
,
M.
Häser
,
H.
Horn
, and
C.
Kölmel
,
Chem. Phys. Lett.
162
,
165
(
1989
).
39.
TURBOMOLE, version 6.2, see http://www.turbomole.com.
40.
J.
Stiehler
, and
J.
Hinze
,
J. Phys. B
28
,
4055
(
1995
).
41.
M.
Dolg
,
H.
Stoll
, and
H.
Preuss
,
J. Chem. Phys.
90
,
1730
(
1989
).
42.
D.
Andrae
,
U.
Häußermann
,
M.
Dolg
,
H.
Stoll
, and
H.
Preuß
,
Theor. Chim. Acta
77
,
123
(
1990
).
43.
A. J. H.
Wachters
,
J. Chem. Phys.
52
,
1033
(
1970
).
44.
See supplementary material at http://dx.doi.org/10.1063/1.3484283 for orbital occupations and HF energies of atoms and molecules in the test set, static isotropic HF, DFT, and MP2 polarizabilities of the test set, basis set definitions of augmented basis sets SVPD, TZVPD, TZVPPD, QZVPD, and QZVPPD.
45.
EMSL basis set exchange, see http://bse.pnl.gov.
46.
Compared to the test set of Weigend and Ahlrichs (Ref. 26), XeF2, XeF4, XeOF4, MnO3F, and HfF were removed. P4, At2, Bi4, PoO, PoO2, Cs2, and ZnO were added.
47.
D. J.
Thouless
,
The Quantum Mechanics of Many-Body Systems
, 2nd ed. (
Academic Press
,
New York
,
1972
).
48.
J.
Čížek
and
J.
Paldus
,
J. Chem. Phys.
47
,
3976
(
1967
).
49.
R.
Seeger
and
J. A.
Pople
,
J. Chem. Phys.
66
,
3045
(
1977
).
50.
M. G.
Papadopoulos
,
J.
Waite
, and
A. D.
Buckingham
,
J. Chem. Phys.
102
,
371
(
1995
).
51.
O.
Ventura
,
M.
Kieninger
, and
I.
Cernusak
,
J. Mol. Struct.
436–437
,
489
(
1997
).
52.
J. P.
Perdew
and
Y.
Wang
,
Phys. Rev. B
45
,
13244
(
1992
).
53.
A. D.
Becke
,
Phys. Rev. A
38
,
3098
(
1988
).
54.
J. P.
Perdew
,
Phys. Rev. B
33
,
8822
(
1986
).
55.
J. P.
Perdew
,
M.
Ernzerhof
, and
K.
Burke
,
J. Chem. Phys.
105
,
9982
(
1996
).
56.
E.
Baerends
,
D. E.
Ellis
, and
P.
Ros
,
Chem. Phys.
2
,
41
(
1973
).
57.
B. I.
Dunlap
,
J. W. D.
Connolly
, and
J. R.
Sabin
,
J. Chem. Phys.
71
,
3396
(
1979
).
58.
K.
Eichkorn
,
O.
Treutler
,
H.
Öhm
,
M.
Häser
, and
R.
Ahlrichs
,
Chem. Phys. Lett.
242
,
652
(
1995
).
59.
F.
Weigend
,
Phys. Chem. Chem. Phys.
8
,
1057
(
2006
).
60.
F.
Weigend
,
M.
Kattannek
, and
R.
Ahlrichs
,
J. Chem. Phys.
130
,
164106
(
2009
).
61.
R.
Bauernschmitt
,
M.
Häser
,
O.
Treutler
, and
R.
Ahlrichs
,
Chem. Phys. Lett.
264
,
573
(
1997
).
62.
F.
Furche
and
D.
Rappoport
, in
Computational Photochemistry
, edited by
M.
Olivucci
(
Elsevier
,
Amsterdam
,
2005
), pp.
93
128
.
63.
F.
Pawłowski
,
P.
Jørgensen
,
J.
Olsen
,
F.
Hegelund
,
T.
Helgaker
,
J.
Gauss
,
K. L.
Bak
, and
J. F.
Stanton
,
J. Chem. Phys.
116
,
6482
(
2002
).
64.
G.
Graner
,
E.
Hirota
,
T.
Iijima
,
K.
Kuchitsu
,
D. A.
Ramsay
,
J.
Vogt
, and
N.
Vogt
, in
Springer Materials—The Landolt–Börnstein Database
, edited by
K.
Kuchitsu
(
Springer
,
Berlin
,
1998
), Vol.
25A
.
65.
A. L.
McClellan
,
Tables of Experimental Dipole Moments
(
Freeman
,
San Francisco
,
1963
).
66.
R.
Feng
,
G.
Cooper
,
G. R.
Burron
, and
C. E.
Brion
,
Chem. Phys.
240
,
371
(
1999
).
67.
M. A.
Spackman
,
J. Phys. Chem.
93
,
7594
(
1989
).
68.
C.
Van Caillie
and
R. D.
Amos
,
Chem. Phys. Lett.
291
,
71
(
1998
).
69.
O.
Christiansen
,
C.
Hättig
, and
J.
Gauss
,
J. Chem. Phys.
109
,
4745
(
1998
).
70.
S. J. A.
van Gisbergen
,
P. R. T.
Schipper
,
O. V.
Gritsenko
,
E. J.
Baerends
,
J. G.
Snijders
,
B.
Champagne
, and
B.
Kirtman
,
Phys. Rev. Lett.
83
,
694
(
1999
).
71.
C.
Van Caillie
and
R. D.
Amos
,
Chem. Phys. Lett.
328
,
446
(
2000
).
72.
C.
Adamo
,
M.
Cossi
,
G.
Scalmani
, and
V.
Barone
,
Chem. Phys. Lett.
307
,
265
(
1999
).
73.
K.
Ruud
,
D.
Jonsson
, and
P. R.
Taylor
,
J. Chem. Phys.
114
,
4331
(
2001
).
74.
T. B.
Pedersen
,
A. M. J.
Sánchez de Merás
, and
H.
Koch
,
J. Chem. Phys.
120
,
8887
(
2004
).
75.
K.
Kowalski
,
J.
Hammond
,
W.
de Jong
, and
A. J.
Sadlej
,
J. Chem. Phys.
129
,
226101
(
2008
).
76.
R.
Antoine
,
P.
Dugourd
,
D.
Rayane
,
E.
Benichou
, and
J.
Broyer
,
J. Chem. Phys.
110
,
9771
(
1999
).
77.
A.
Ballard
,
K.
Bonin
, and
J.
Louderback
,
J. Chem. Phys.
113
,
5732
(
2000
).
78.
A.
Ruiz
,
J.
Bretón
, and
J. M. G.
Llorente
,
J. Chem. Phys.
114
,
1272
(
2001
).
79.
R. R.
Zope
,
T.
Baruah
,
M. R.
Pederson
, and
B. I.
Dunlap
,
Phys. Rev. B
77
,
115452
(
2008
).
80.
R. C.
Haddon
,
G. E.
Scuseria
, and
R. E.
Smalley
,
Chem. Phys. Lett.
272
,
38
(
1997
).

Supplementary Material

You do not currently have access to this content.