A revised water model intended for use in condensed phase simulations in the framework of the self consistent polarizable ion tight binding theory is constructed. The model is applied to water monomer, dimer, hexamers, ice, and liquid, where it demonstrates good agreement with theoretical results obtained by more accurate methods, such as DFT and CCSD(T), and with experiment. In particular, the temperature dependence of the self diffusion coefficient in liquid water predicted by the model, closely reproduces experimental curves in the temperature interval between 230 K and 350 K. In addition, and in contrast to standard DFT, the model properly orders the relative densities of liquid water and ice. A notable, but inevitable, shortcoming of the model is underestimation of the static dielectric constant by a factor of two. We demonstrate that the description of inter and intramolecular forces embodied in the tight binding approximation in quantum mechanics leads to a number of valuable insights which can be missing from ab initio quantum chemistry and classical force fields. These include a discussion of the origin of the enhanced molecular electric dipole moment in the condensed phases, and a detailed explanation for the increase of coordination number in liquid water as a function of temperature and compared with ice—leading to insights into the anomalous expansion on freezing. The theory holds out the prospect of an understanding of the currently unexplained density maximum of water near the freezing point.
REFERENCES
1.
T. J.
Sheppard
, A. Y.
Lozovoi
, D. L.
Pashov
, J. J.
Kohanoff
, and A. T.
Paxton
, J. Chem. Phys.
141
, 044503
(2014
).2.
M.
Del Ben
, M.
Schönherr
, J.
Hutter
, and J.
VandeVondele
, J. Phys. Chem. Lett.
4
, 3753
(2013
).3.
P. L.
Silvestrelli
and M.
Parrinello
, Phys. Rev. Lett.
82
, 3308
(1999
).4.
H. J. C.
Berendsen
, J. R.
Grigera
, and T. P.
Straatsma
, J. Phys. Chem.
91
, 6269
(1987
).5.
W. L.
Jorgensen
, J.
Chandrasekhar
, J. D.
Madura
, R. W.
Impey
, and M. L.
Klein
, J. Chem. Phys.
79
, 926
(1983
).6.
A. T.
Paxton
and J. J.
Kohanoff
, J. Chem. Phys.
134
, 044130
(2011
).7.
M. W.
Finnis
, A. T.
Paxton
, M.
Methfessel
, and M.
van Schilfgaarde
, Phys. Rev. Lett.
81
, 5149
(1998
).8.
A. T.
Paxton
, in Multiscale Simulation Methods in Molecular Sciences
, NIC Series
, Vol. 42
, edited by J.
Grotendorst
, N.
Attig
, S.
Blügel
, and D.
Marx
(Institute for Advanced Simulation
, Forschungszentrum Julich
, 2009
), pp. 145
–174
. Available on-line at http://webarchiv.fz-juelich.de/nic-series/volume42/volume42.html.9.
A. Y.
Lozovoi
, D. L.
Pashov
, T. J.
Sheppard
, J. J.
Kohanoff
, and A. T.
Paxton
, J. Chem. Phys.
141
, 044505
(2014
).10.
S.
Fabris
, A. T.
Paxton
, and M. W.
Finnis
, Phys. Rev. B
63
, 941011
(2001
).11.
M. W.
Finnis
, Interatomic Forces in Condensed Matter
(Oxford University Press
, Oxford, UK
, 2003
).12.
W.
Klopper
, J. G. C. M.
van Duijneveldt-van de Rijdt
, and F. B.
van Duijneveldt
, Phys. Chem. Chem. Phys.
2
, 2227
(2000
).13.
C. J.
Burnham
and S. S.
Xantheas
, J. Chem. Phys.
116
, 1479
(2002
).14.
L.
Goodwin
, A. J.
Skinner
, and D. G.
Pettifor
, Europhys. Lett.
9
, 701
(1989
).15.
D. J.
Chadi
, Phys. Rev. Lett.
41
, 1062
(1978
).16.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, J. Chem. Phys.
132
, 154104
(2010
).17.
W. A.
Harrison
, Electronic Structure and the Properties of Solids, the Physics of the Chemical Bond
(W. H. Freeman and Company
, San Francisco
, 1980
).18.
The cutoff functions used in the present study are fifth order polynomials P5(x) that produce a smooth step between 1 and 0 with continuous second derivatives: Any function f (r) can be smoothly cut to zero between cutoff radii
\begin{eqnarray*}P_5(0) &=& 1, \qquad P_5^\prime (0) = P_5^{\prime \prime }(0) = 0,\\[3pt]P_5(1) &=& 0, \qquad P_5^\prime (1) = P_5^{\prime \prime }(1) = 0.\end{eqnarray*}
$r_{\rm cut}^{(1)}$
and $r_{\rm cut}^{(2)}$
as $\tilde{f}(r) = f(r) \, P_5[(r-{r_{\rm cut}^{(1)}})/({r_{\rm cut}^{(2)}}-{r_{\rm cut}^{(1)}})].$
It is straightforward to demonstrate that function $\tilde{f}(r)$
and its first two derivatives coincide with those of f (r) at $r < {r_{\rm cut}^{(1)}}$
, are equal to 0 at $r > {r_{\rm cut}^{(2)}}$
, and are continuously differentiable up to the second order in the whole interval where f″(r) exists and is continuous.19.
A. J.
Skinner
and D. G.
Pettifor
, J. Phys.: Condens. Matter
3
, 2029
(1991
).20.
CRC Handbook of Chemistry and Physics
, 83rd ed., edited by D. R.
Lide
(CRC Press
, Boca Raton, FL
, 2002
).21.
G.
Herzberg
, Molecular Spectra and Molecular Structure II: Infrared and Raman Spectra of Polyatomic Molecules
(Krieger Publishing
, Malabar, FL
, 1991
).22.
P.
Cabral do Couto
, S. G.
Estcio
, and B. J.
Costa Cabral
, J. Chem. Phys.
123
, 054510
(2005
).23.
Empirical Tight Binding computer program (TBE) is a part of the LM electronic structure package (http://www.lmsuite.org/).
24.
A. T.
Paxton
and M. W.
Finnis
, Phys. Rev. B
77
, 024428
(2008
).25.
A. T.
Paxton
and C.
Elsässer
, Phys. Rev. B
87
, 224110
(2013
).26.
G. J.
Martyna
, M. E.
Tuckerman
, D. J.
Tobias
, and M. L.
Klein
, Mol. Phys.
87
, 1117
(1996
).27.
P.
Piecuch
, S. A.
Kucharski
, K.
Kowalski
, and M.
Musial
, Comput. Phys. Commun.
149
, 71
(2002
).28.
S. S.
Xantheas
, C. J.
Burnham
, and R. J.
Harrison
, J. Chem. Phys.
116
, 1493
(2002
).29.
See http://cccbdb.nist.gov for the experimental atomization energy of water monomer.
30.
R. M.
Olson
, J. L.
Bentz
, R. A.
Kendall
, M. W.
Schmidt
, and M. S.
Gordon
, J. Chem. Theory Comput.
3
, 1312
(2007
).31.
B.
Santra
, A.
Michaelides
, M.
Fuchs
, A.
Tkatchenko
, C.
Filippi
, and M.
Scheffler
, J. Chem. Phys.
129
, 194111
(2008
).32.
A. K.
Soper
, Chem. Phys.
258
, 121
(2000
).33.
See www.isis.stfc.ac.uk/groups/disordered-materials/database/ for ISIS disordered materials database.
34.
T. K.
Hirsch
and L.
Ojamäe
, J. Phys. Chem. B
108
, 15856
(2004
).35.
Z.
Ma
, Y.
Zhang
, and M. E.
Tuckerman
, J. Chem. Phys.
137
, 044506
(2012
).36.
F.
Labat
, C.
Pouchan
, C.
Adamo
, and G. E.
Scuseria
, J. Comput. Chem.
32
, 2177
(2011
).37.
Z.
Raza
, D.
Alfè
, C. G.
Salzmann
, J.
Klimeš
, A.
Michaelides
, and B.
Slater
, Phys. Chem. Chem. Phys.
13
, 19788
(2011
).38.
C. M. B.
Line
and R. W.
Whitworth
, J. Chem. Phys.
104
, 10008
(1996
).39.
P. J.
Feibelman
, Science
295
, 99
(2002
).40.
S. M.
Jackson
, V. M.
Nield
, R. W.
Whitworth
, M.
Oguro
, and C. C.
Wilson
, J. Phys. Chem. B
101
, 6142
(1997
).41.
A. K.
Soper
and C. J.
Benmore
, Phys. Rev. Lett.
101
, 065502
(2008
).42.
A. V.
Gubskaya
and P. G.
Kusalik
, J. Chem. Phys.
117
, 5290
(2002
).43.
D. P.
Fernández
, Y.
Mulev
, A. R. H.
Goodwin
, and J. M. H.
Levelt Sengers
, J. Phys. Chem. Ref. Data
24
, 33
(1995
).44.
K. T.
Gillen
, D. C.
Douglass
, and M. J. R.
Hoch
, J. Chem. Phys.
57
, 5117
(1972
).45.
R.
Mills
, J. Phys. Chem.
77
, 685
(1973
).46.
M.
Sharma
, R.
Resta
, and R.
Car
, Phys. Rev. Lett.
98
, 247401
(2007
).47.
H.-S.
Lee
and M. E.
Tuckerman
, J. Chem. Phys.
126
, 164501
(2007
).48.
M.-V.
Fernández-Serra
and E.
Artacho
, J. Chem. Phys.
121
, 11136
(2004
).49.
R.
Jonchiere
, A. P.
Seitsonen
, G.
Ferlat
, A. M.
Saitta
, and R.
Vuilleumier
, J. Chem. Phys.
135
, 154503
(2011
).50.
J.
Wang
, G.
Román-Pérez
, J. M.
Soler
, E.
Artacho
, and M.-V.
Fernández-Serra
, J. Chem. Phys.
134
, 024516
(2011
).51.
I.-C.
Lin
, A. P.
Seitsonen
, M. D.
Coutinho-Neto
, I.
Tavernelli
, and U.
Rothlisberger
, J. Phys. Chem. B
113
, 1127
(2009
).52.
M.
Ji
, K.
Umemoto
, C.-Z.
Wang
, K.-M.
Ho
, and R. M.
Wentzcovitch
, Phys. Rev. B
84
, 220105
(2011
).53.
A.
Bernas
, C.
Ferradini
, and J.-P.
Jay-Gerin
, Chem. Phys.
222
, 151
(1997
).54.
C.
Pinilla
, A. H.
Irani
, N.
Seriani
, and S.
Scandolo
, J. Chem. Phys.
136
, 114511
(2012
).55.
G.
Lever
, D. J.
Cole
, N. D. M.
Hine
, P. D.
Haynes
, and M. C.
Payne
, J. Phys.: Conden. Matter
25
, 152101
(2013
).56.
W.
Wagner
and A.
Pruß
, J. Phys. Chem. Ref. Data
31
, 387
(2002
).57.
C. M.
Maupin
, B.
Aradi
, and G. A.
Voth
, J. Phys. Chem. B
114
, 6922
(2010
).58.
G.
Monard
, M. I.
Bernal-Uruchurtu
, A.
van der Vaart
, K. M.
Merz
Jr., and M. F.
Ruiz-López
, J. Phys. Chem. A
109
, 3425
(2005
).59.
Y.
Wu
, H. L.
Tepper
, and G. A.
Voth
, J. Chem. Phys.
124
, 024503
(2006
).60.
A.
Glättli
, X.
Daura
, and W. F.
van Gunsteren
, J. Chem. Phys.
116
, 9811
(2002
).61.
C. A.
Coulson
and D.
Eisenberg
, Proc. R. Soc. London, Ser. A
291
, 445
(1965
).62.
M.
Uematsu
and E. U.
Frank
, J. Phys. Chem. Ref. Data
9
, 1291
(1980
).63.
64.
65.
K. R.
Harris
and L. A.
Woolf
, J. Chem. Soc., Faraday Trans. 1
76
, 377
(1980
).66.
M.
Holz
, S. R.
Heil
, and A.
Sacco
, Phys. Chem. Chem. Phys.
2
, 4740
(2000
).67.
M. E.
Tuckerman
, Statistical Mechanics: Theory and Molecular Simulation
(Oxford University Press
, New York, USA
, 2010
).68.
R. J.
Speedy
and C. A.
Angell
, J. Chem. Phys.
65
, 851
(1976
).69.
S.
Grimme
, WIREs Comput. Mol. Sci.
1
, 211
(2011
).© 2014 AIP Publishing LLC.
2014
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