In this work, we investigate how geometric changes influence the static dipole polarizability (α) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple-ζ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this ab initio surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order C6 dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H2O. Using first-order perturbation theory, we compute the zero-point vibrational correction to α at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic (αiso) and nearly 50% to the anisotropic (αaniso) polarizability values. In doing so, we find that αiso = 9.8307 bohr3, which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr3 provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

1.
K. D.
Bonin
and
V. V.
Kresin
,
Electric-Dipole Polarizabilities of Atoms, Molecules, and Clusters
(
World Scientific
,
Singapore
,
1997
).
2.
L.
Piela
,
Ideas of Quantum Chemistry
, 2nd ed. (
Elsevier
,
Amsterdam, Netherlands
,
2013
).
3.
A. J.
Stone
,
The Theory of Intermolecular Forces
, 2nd ed. (
Oxford University Press
,
Oxford, UK
,
2013
).
4.
T.
Helgaker
 et al.,
Chem. Rev.
112
,
543
(
2012
).
5.
E.
Harder
,
J. D.
Eaves
,
A.
Tokmakoff
, and
B. J.
Berne
,
Proc. Natl. Acad. Sci. U. S. A.
102
,
11611
(
2005
).
6.
S. Y.
Willow
,
X. C.
Zeng
,
S. S.
Xantheas
,
K. S.
Kim
, and
S.
Hirata
,
J. Phys. Chem. Lett.
7
,
680
(
2016
).
7.
V.
Babin
,
C.
Leforestier
, and
F.
Paesani
,
J. Chem. Theory Comput.
9
,
5395
(
2013
).
8.
J. F.
Ouyang
and
R. P. A.
Bettens
,
CHIMIA Int. J. Chem.
69
,
104
(
2015
).
9.
Y.
Mei
 et al.,
J. Phys. Chem. A
119
,
5865
(
2015
).
10.
H.
Jiang
,
O. A.
Moultos
,
I. G.
Economou
, and
A. Z.
Panagiotopoulos
,
J. Phys. Chem. B
120
,
12358
(
2016
).
11.
J. R.
Hammond
,
N.
Govind
,
K.
Kowalski
,
J.
Autschbach
, and
S. S.
Xantheas
,
J. Chem. Phys.
131
,
214103
(
2009
).
12.
M. A.
Spackman
,
J. Phys. Chem.
93
,
7594
(
1989
).
13.
P. E. S.
Wormer
and
H.
Hettema
,
J. Chem. Phys.
97
,
5592
(
1992
).
14.
C.
Voisin
,
A.
Cartier
, and
J. L.
Rivail
,
J. Phys. Chem.
96
,
7966
(
1992
).
15.
F.
Aiga
and
R.
Itoh
,
Chem. Phys. Lett.
251
,
372
(
1996
).
16.
J. M.
Luis
,
M.
Duran
, and
J. L.
Andrés
,
J. Chem. Phys.
107
,
1501
(
1997
).
17.
D.
Spelsberg
and
W.
Meyer
,
J. Chem. Phys.
108
,
1532
(
1998
).
18.
G.
Maroulis
,
Chem. Phys. Lett.
289
,
403
(
1998
).
19.
D. J.
Tozera
and
N. C.
Handy
,
J. Chem. Phys.
109
,
10180
(
1998
).
20.
A. J.
Cohen
and
Y.
Tantirungrotechai
,
Chem. Phys. Lett.
299
,
465
(
1999
).
21.
A. V.
Gubskaya
and
P. G.
Kusalik
,
Mol. Phys.
99
,
1107
(
2001
).
22.
M.
Torrent-Sucarrat
,
J. M.
Luis
, and
B.
Kirtman
,
J. Chem. Phys.
122
,
204108
(
2005
).
23.
R. J.
Wheatley
,
J. Comput. Chem.
29
,
445
(
2008
).
24.
D. M.
Elking
,
L.
Perera
,
R.
Duke
,
T.
Darden
, and
L. G.
Pedersen
,
J. Comput. Chem.
32
,
3283
(
2011
).
25.
A. J.
Thakkar
and
T.
Wu
,
J. Chem. Phys.
143
,
144302
(
2015
).
26.
A. S.
Sharipov
,
B. I.
Loukhovitski
, and
A. M.
Starik
,
J. Phys. B: At., Mol. Opt. Phys.
50
,
165101
(
2017
).
27.
Y.
Luo
 et al.,
J. Chem. Phys.
98
,
7159
(
1993
).
28.
K.
Ruud
,
P.-O.
Åstrand
, and
P. R.
Taylor
,
J. Chem. Phys.
112
,
2668
(
2000
).
29.
K.
Ruud
,
D.
Jonssona
, and
P. R.
Taylor
,
Phys. Chem. Chem. Phys.
2
,
2161
(
2000
).
30.
J.
Páleníková
,
M.
Kraus
,
P.
Neogrády
,
V.
Kellö
, and
M.
Urban
,
Mol. Phys.
106
,
2333
(
2008
).
31.
H.
Sekino
and
R. J.
Bartlett
,
J. Chem. Phys.
98
,
3022
(
1993
).
32.
T.
Pluta
,
J.
Noga
, and
R. J.
Bartlett
,
Int. J. Quantum Chem.
52
,
379
(
1994
).
33.
B.
Datta
,
P.
Sen
, and
D.
Mukherjee
,
J. Phys. Chem.
99
,
6441
(
1995
).
34.
A. G.
Ioannou
,
S. M.
Colwell
, and
R. D.
Amos
,
Chem. Phys. Lett.
278
,
278
(
1997
).
35.
E. K.
Dalskov
and
S. P. A.
Sauer
,
J. Phys. Chem. A
102
,
5269
(
1998
).
36.
O.
Christiansen
,
J.
Gauss
, and
J. F.
Stanton
,
Chem. Phys. Lett.
305
,
147
(
1999
).
37.
G.
Avila
,
J. Chem. Phys.
122
,
144310
(
2005
).
38.
P.
Sałek
 et al.,
Mol. Phys.
103
,
439
(
2005
).
39.
J.
Kongsted
and
O.
Christiansen
,
J. Chem. Phys.
125
,
124108
(
2006
).
40.
T.
Korona
,
Phys. Chem. Chem. Phys.
12
,
14977
(
2010
).
41.
R.
Monten
,
B.
Hajgató
, and
M. S.
Deleuze
,
Mol. Phys.
109
,
2317
(
2011
).
42.
43.
A. S.
Karne
 et al.,
Chem. Phys. Lett.
635
,
168
(
2015
).
44.
O.
Loboda
,
F.
Ingrosso
,
M. F.
Ruiz-López
,
H.
Reis
, and
C.
Millot
,
J. Comput. Chem.
37
,
2125
(
2016
).
45.
A.
Karton
and
J. M. L.
Martin
,
J. Chem. Phys.
133
,
144102
(
2010
).
46.
S. J. A.
van Gisbergen
 et al.,
J. Chem. Phys.
105
,
3142
(
1996
).
47.
D.
Porezag
and
M. R.
Pederson
,
Phys. Rev. B
54
,
7830
(
1996
).
48.
P.
Calaminici
,
K.
Jug
, and
A. M.
Köster
,
J. Chem. Phys.
109
,
7756
(
1998
).
49.
C.
Van Caillie
and
R. D.
Amos
,
Chem. Phys. Lett.
328
,
446
(
2000
).
50.
P. J.
Wilson
,
T. J.
Bradley
, and
D. J.
Tozer
,
J. Chem. Phys.
115
,
9233
(
2001
).
51.
M. R.
Pederson
,
T.
Baruah
,
P. B.
Allen
, and
C.
Schmidt
,
J. Chem. Theory Comput.
1
,
590
(
2005
).
52.
X.
Andrade
,
S.
Botti
,
M. A. L.
Marques
, and
A.
Rubio
,
J. Chem. Phys.
126
,
184106
(
2007
).
53.
D. M.
Bishop
and
L. M.
Cheung
,
J. Phys. Chem. Ref. Data
11
,
119
(
1982
).
54.
A. J.
Russell
and
M. A.
Spackman
,
Mol. Phys.
84
,
1239
(
1995
).
55.
D. M.
Bishop
,
Rev. Mod. Phys.
62
,
343
(
1990
).
56.
D. M.
Bishop
,
Adv. Chem. Phys.
104
,
1
(
1998
).
57.
H.-J.
Werner
and
W.
Meyer
,
Mol. Phys.
31
,
855
(
1976
).
58.
J. M.
Luis
,
M.
Duran
,
J. L.
Andrés
,
B.
Champagne
, and
B.
Kirtman
,
J. Chem. Phys.
111
,
875
(
1999
).
59.
O.
Quinet
,
B.
Champagne
, and
B.
Kirtman
,
J. Comput. Chem.
22
,
1920
(
2001
).
60.
H.
Reisa
,
S.
Raptis
, and
M.
Papadopoulos
,
Chem. Phys.
263
,
301
(
2001
).
61.
Y.
Wang
,
X.
Huang
,
B. C.
Shepler
,
B. J.
Braams
, and
J. M.
Bowman
,
J. Chem. Phys.
134
,
094509
(
2011
).
62.
V.
Babin
,
G. R.
Medders
, and
F.
Paesani
,
J. Chem. Theory Comput.
10
,
1599
(
2014
).
63.
G. R.
Medders
,
V.
Babin
, and
F.
Paesani
,
J. Chem. Theory Comput.
10
,
2906
(
2014
).
64.
P.
Jankowski
 et al.,
J. Phys. Chem. A
119
,
2940
(
2015
).
65.
D. M.
Bishop
and
L. M.
Cheung
,
Chem. Phys. Lett.
66
,
467
(
1979
).
66.
C. E.
Dykstra
,
J. Chem. Educ.
65
,
198
(
1988
).
67.
M.
Kállay
and
J.
Gauss
,
J. Mol. Struct.: THEOCHEM
768
,
71
(
2006
).
68.
K. D.
Nanda
and
A. I.
Krylov
,
J. Chem. Phys.
145
,
204116
(
2016
).
69.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
100
,
2975
(
1994
).
70.
G. R.
Medders
,
A. W.
Götz
,
M. A.
Morales
,
P.
Bajaj
, and
F.
Paesani
,
J. Chem. Phys.
143
,
104102
(
2015
).
71.
A.
Grisafi
,
D. M.
Wilkins
,
G.
Csányi
, and
M.
Ceriotti
,
Phys. Rev. Lett.
120
,
036002
(
2018
).
72.
T.
Bereau
,
R. A.
DiStasio
, Jr.
,
A.
Tkatchenko
, and
O. A.
von Lilienfeld
,
J. Chem. Phys.
148
,
241706
(
2018
).
73.
H.
Partridge
and
D. W.
Schwenke
,
J. Chem. Phys.
106
,
4618
(
1997
).
74.
O. L.
Polyansky
 et al.,
Science
299
,
539
(
2003
).
75.
A. G.
Császár
 et al.,
J. Chem. Phys.
122
,
214305
(
2005
).
76.
G. S.
Fanourgakis
and
S. S.
Xantheas
,
J. Phys. Chem. A
110
,
4100
(
2006
).
77.
C. J.
Burnham
and
S. S.
Xantheas
,
J. Chem. Phys.
116
,
5115
(
2002
).
78.
G. S.
Fanourgakis
and
S. S.
Xantheas
,
J. Chem. Phys.
128
,
074506
(
2008
).
79.
C. J.
Burnham
,
D. J.
Anick
,
P. K.
Mankoo
, and
G. F.
Reiter
,
J. Chem. Phys.
128
,
154519
(
2008
).
80.
R.
Bukowski
,
K.
Szalewicz
,
G. C.
Groenenboom
, and
A.
van der Avoird
,
Science
315
,
1249
(
2007
).
81.
Y.
Wang
and
J. M.
Bowman
,
J. Chem. Phys.
134
,
154510
(
2011
).
82.
C.
Cuthbertson
and
M.
Cuthbertson
,
Philos. Trans. R. Soc. A
213
,
1
(
1914
).
83.
R.
Bukowski
,
K.
Szalewicz
,
G. C.
Groenenboom
, and
A.
van der Avoird
,
J. Chem. Phys.
128
,
094313
(
2008
).
84.
K. B.
Newbound
,
J. Opt. Soc. Am.
39
,
835
(
1949
).
85.
H.
Barrell
and
J. E.
Sears
,
Philos. Trans. R. Soc. A
238
,
1
(
1939
).
86.
G. D.
Zeiss
and
W. J.
Meath
,
Mol. Phys.
30
,
161
(
1975
).
87.
U.
Hohm
,
J. Mol. Struct.
1054-1055
,
282
(
2013
).
88.
A. R.
Hoy
and
P. R.
Bunker
,
J. Mol. Spectrosc.
74
,
1
(
1979
).
89.
T.
Hasegawa
and
Y.
Tanimura
,
J. Phys. Chem. B
115
,
5545
(
2011
).
90.
O.
Loboda
,
F.
Ingrosso
,
M. F.
Ruiz-López
,
K.
Szalewicz
, and
C.
Millot
,
J. Chem. Phys.
144
,
034304
(
2016
).
91.
O.
Loboda
and
C.
Millot
,
J. Chem. Phys.
147
,
161718
(
2017
).
92.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
103
,
4572
(
1995
).
93.
P. A. M.
Dirac
,
Math. Proc. Cambridge Philos. Soc.
26
,
376
(
1930
).
94.
S. H.
Vosko
,
L.
Wilk
, and
M.
Nusair
,
Can. J. Phys.
58
,
1200
(
1980
).
95.
A. D.
Becke
,
Phys. Rev. A
38
,
3098
(
1988
).
96.
C.
Lee
,
W.
Yang
, and
R. G.
Parr
,
Phys. Rev. B
37
,
785
(
1988
).
97.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
98.
A. D.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
).
99.
P. J.
Stephens
,
F. J.
Devlin
,
C. F.
Chabalowski
, and
M. J.
Frisch
,
J. Phys. Chem.
98
,
11623
(
1994
).
100.
C.
Adamo
and
V.
Barone
,
J. Chem. Phys.
110
,
6158
(
1999
).
101.
R.
Peverati
and
D. G.
Truhlar
,
J. Phys. Chem. Lett.
2
,
2810
(
2011
).
102.
J.-D.
Chai
and
M.
Head-Gordon
,
Phys. Chem. Chem. Phys.
10
,
6615
(
2008
).
103.
H. S.
Yu
,
X.
He
,
S. L.
Li
, and
D. G.
Truhlar
,
Chem. Sci.
7
,
5032
(
2016
).
104.
N.
Mardirossian
and
M.
Head-Gordon
,
J. Chem. Phys.
142
,
074111
(
2015
).
105.
N.
Mardirossian
and
M.
Head-Gordon
,
Phys. Chem. Chem. Phys.
16
,
9904
(
2014
).
106.
N.
Mardirossian
and
M.
Head-Gordon
,
J. Chem. Phys.
144
,
214110
(
2016
).
107.
J.
Sun
 et al.,
J. Chem. Phys.
138
,
044113
(
2013
).
108.
J.
Sun
,
J. P.
Perdew
, and
A.
Ruzsinszky
,
Proc. Natl. Acad. Sci. U. S. A.
112
,
685
(
2015
).
109.
J.
Sun
,
A.
Ruzsinszky
, and
J.
Perdew
,
Phys. Rev. Lett.
115
,
036402
(
2015
).
110.
K.
Hui
and
J.-D.
Chai
,
J. Chem. Phys.
144
,
044114
(
2016
).
111.
J.
Wellendorff
,
K. T.
Lundgaard
,
K. W.
Jacobsen
, and
T.
Bligaard
,
J. Chem. Phys.
140
,
144107
(
2014
).
112.
H. B. G.
Casimir
and
B.
Polder
,
Phys. Rev.
73
,
360
(
1948
).
113.
C.
Hättig
,
O.
Christiansen
, and
P.
Jørgensen
,
J. Chem. Phys.
107
,
10592
(
1997
).
114.
O.
Christiansen
,
A.
Halkier
,
H.
Koch
, and
P.
Jørgensen
,
J. Chem. Phys.
108
,
2801
(
1998
).
115.
P. W.
Langhoff
and
M.
Karplus
,
J. Chem. Phys.
53
,
233
(
1970
).
116.
O.
Christiansen
,
H.
Koch
, and
P.
Jørgensen
,
Chem. Phys. Lett.
243
,
409
(
1995
).
117.
G.
Chałasiński
and
M. M.
Szczȩśniak
,
Mol. Phys.
63
,
205
(
1988
).
118.
S. M.
Cybulski
,
G.
Chałasiński
, and
R.
Moszyński
,
J. Chem. Phys.
92
,
4357
(
1990
).
119.
S. M.
Cybulski
and
M. L.
Lytle
,
J. Chem. Phys.
127
,
141102
(
2007
).
120.
A.
Tkatchenko
,
R. A.
DiStasio
, Jr.
,
M.
Head-Gordon
, and
M.
Scheffler
,
J. Chem. Phys.
131
,
094106
(
2009
).
121.
W.
Rijks
and
P. E. S.
Wormer
,
J. Chem. Phys.
88
,
5704
(
1988
).
122.
A.
Osted
,
J.
Kongsted
,
K. V.
Mikkelsen
, and
O.
Christiansen
,
J. Phys. Chem. A
108
,
8646
(
2004
).
123.
J.
Marti
and
D. M.
Bishop
,
J. Chem. Phys.
99
,
3860
(
1993
).
124.
D. M.
Bishop
and
S. P. A.
Sauer
,
J. Chem. Phys.
107
,
8502
(
1997
).
125.
A. R.
Hoy
,
I. M.
Mills
, and
G.
Strey
,
Mol. Phys.
24
,
1265
(
1972
).
126.
H. H.
Nielsen
,
Rev. Mod. Phys.
23
,
90
(
1951
).
127.
128.
129.
W.
Schneider
and
W.
Thiel
,
Chem. Phys. Lett.
157
,
367
(
1989
).
130.
J. R.
Hammond
,
K.
Kowalski
, and
W. A.
deJong
,
J. Chem. Phys.
127
,
144105
(
2007
).
131.
J. R.
Hammond
,
M.
Valiev
,
W. A.
deJong
, and
K.
Kowalski
,
J. Phys. Chem. A
111
,
5492
(
2007
).
132.
J. R.
Hammond
,
W. A.
deJong
, and
K.
Kowalski
,
J. Chem. Phys.
128
,
224102
(
2008
).
133.
M.
Valiev
 et al.,
Comput. Phys. Comm.
181
,
1477
(
2010
).
134.
K.
Aidas
 et al.,
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
4
,
269
(
2014
).
135.
DALTON, a molecular electronic structure program, Release Dalton2016.0,
2015
, see http://daltonprogram.org.
136.
Y.
Shao
 et al.,
Mol. Phys.
113
,
184
(
2015
).
137.
P. M. W.
Gill
,
B. G.
Johnson
, and
J. A.
Pople
,
Chem. Phys. Lett.
209
,
506
(
1993
).
138.
O. A.
Vydrov
and
T.
Van Voorhis
,
J. Chem. Phys.
133
,
244103
(
2010
).
139.

The range of αxz ≈ 0–4 bohr3 applies to water molecules with r1r2 (for water molecules with r1 > r2, there will be a sign change in this component).

140.
T.
Brinck
,
J. S.
Murray
, and
P.
Politzer
,
J. Chem. Phys.
98
,
4305
(
1993
).
141.
M.
Thomas
,
M.
Brehm
,
R.
Fligg
,
P.
Vöhringer
, and
B.
Kirchner
,
Phys. Chem. Chem. Phys.
15
,
6608
(
2013
).
142.
143.
T.
Janowski
and
P.
Pulay
,
Chem. Phys. Lett.
447
,
27
(
2007
).
144.
S. K.
Min
 et al.,
J. Comput. Chem.
29
,
1208
(
2008
).
145.
C. D.
Sherrill
,
T.
Takatani
, and
E. G.
Hohenstein
,
J. Phys. Chem. A
113
,
010146
(
2009
).
146.
M. S.
Marshall
,
L. A.
Burns
, and
C. D.
Sherrill
,
J. Chem. Phys.
135
,
194102
(
2011
).
147.
G. D.
Zeiss
and
W. J.
Meath
,
Mol. Phys.
33
,
1155
(
1977
).
148.
K. U.
Lao
and
J. M.
Herbert
,
J. Phys. Chem. A
119
,
235
(
2015
).
149.
K. U.
Lao
,
R.
Schäffer
,
G.
Jansen
, and
J. M.
Herbert
,
J. Chem. Theory Comput.
11
,
2473
(
2015
).
150.
K. U.
Lao
,
K.-Y.
Liu
,
R. M.
Richard
, and
J. M.
Herbert
,
J. Chem. Phys.
144
,
164105
(
2016
).
151.
D.
Hait
and
M.
Head-Gordon
,
Phys. Chem. Chem. Phys.
20
,
19800
(
2018
).
152.
T.
Korona
,
M.
Przybytek
, and
B.
Jeziorski
,
Mol. Phys.
104
,
2303
(
2006
).
153.
R. D.
Amos
,
Adv. Chem. Phys.
67
,
99
(
1987
).
154.
O.
Christiansen
,
C.
Hättig
, and
J.
Gauss
,
J. Chem. Phys.
109
,
4745
(
1998
).
155.
F.
Egidi
 et al.,
J. Chem. Theory Comput.
10
,
2456
(
2014
).
156.
E.
Bichoutskaia
,
M. P.
Hodges
, and
R. J.
Wheatley
,
J. Comput. Methods Sci. Eng.
2
,
391
(
2002
).
157.
A. S.
Tulegenov
,
R. J.
Wheatley
,
M. P.
Hodges
, and
A. H.
Harvey
,
J. Chem. Phys.
126
,
094305
(
2007
).

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