Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water
Following a fairly comprehensive study on popular interaction potentials of water (Pusztai et al 2008, J. Chem. Phys., 129, 184103), here two more recent, polarizable potential sets, SWM4-DP (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245) and BK3 (Kiss et al. J. Chem. Phys., 2013, 138, 204507)...
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Інститут фізики конденсованих систем НАН України
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| Цитувати: | Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water / Z. Steinczinger, L. Pusztai // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43604:1-8. — Бібліогр.: 24 назв. — англ. |
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irk-123456789-1208552017-06-14T03:04:32Z Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water Steinczinger, Z. Pusztai, L. Following a fairly comprehensive study on popular interaction potentials of water (Pusztai et al 2008, J. Chem. Phys., 129, 184103), here two more recent, polarizable potential sets, SWM4-DP (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245) and BK3 (Kiss et al. J. Chem. Phys., 2013, 138, 204507) are compared to the TIP4P-2005 water potential (Abascal et al., J. Chem. Phys., 2005, 123, 234505) that had appeared the most favoravble previously. The basis of comparison was the compatibility with results of neutron and X-ray diffraction experiments on pure water, using the scheme applied by Pusztai et al. (2008). The scheme combines the experimental total scattering structure factors (TSSF) and partial radial distribution functions (PRDF) from molecular dynamics simulations in a single structural model. Goodness-of-fit values to the O-O, O-H and H-H simulated PRDF-s and to the experimental neutron and X-ray TSSF provided a measure that can characterize the level of consistency between interaction potentials and diffraction experiments. Among the sets of partial RDF-s investigated here, the ones corresponding to the SWM4-DP potential parameters have proven to be the most consistent with the particular diffraction results taken for the present study, by a hardly significant margin ahead of BK3. Perhaps more importantly, it is shown that the three sets of potential parameters produce nearly equivalent PRDF-s that may all be made consistent with diffraction data at a very high level. The largest differences can be detected in terms of the O-O partial radial distribution function. Слiдуючи досить повному вивченню популярних потенцiалiв взаємодiї для води (Pusztai et al., J. Chem. Phys., 2008, 129, 184103), у цiй роботi два бiльш сучасних потенцiали з врахуванням поляризованостi молекул типу SWM4-DP (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245) i BK3 (Kiss et al., J. Chem. Phys., 2013, 138, 204507) порiвняно з моделлю TIP4P-2005 (Abascal et al., J. Chem. Phys., 2005, 123, 234505), яка донедавна вважалася найуспiшнiшою. Основою для порiвняння є узгодження з результатами експериментiв по розсiянню нейтронiв та рентгенiвського випромiнювання для чистої води, використовуючи процедуру, розроблену Пустаї та iн. (2008). Ця процедера поєднує повнi структурнi фактори розсiяння i парцiальнi радiальнi функцiї розподiлу, що слiдують з молекулярної динамiки певної структурної моделi. Якiсть узгодження значень функцiй розподiлу O–O, O–H i H–H з моделювання пiсля їх перетворення до повних структурних факторiв i порiвняння з експериментальними факторами є мiрою для опису рiвня узгодження. Серед парцiальних функцiй розподiлу, дослiджених у цiй роботi, тi фактори, якi вiдповiдають моделi SWM4-DP виявилися найкращими, але лише незначно кращими вiд тих, що були отриманi з моделi BK3. Важливо вiдзначити, що усi три потенцiали дають майже еквiвалентнi радiальнi функцiї розподiлу, якi узгоджуються з експериментом, але невелика розбiжнiсть спостерiгається для функцiй розподiлу киснiв O–O. 2013 Article Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water / Z. Steinczinger, L. Pusztai // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43604:1-8. — Бібліогр.: 24 назв. — англ. 1607-324X PACS: 61.20.-p, 61.25.-f. 61.05.fm DOI:10.5488/CMP.16.43604 arXiv:1312.4557 http://dspace.nbuv.gov.ua/handle/123456789/120855 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Following a fairly comprehensive study on popular interaction potentials of water (Pusztai et al 2008, J. Chem. Phys., 129, 184103), here two more recent, polarizable potential sets, SWM4-DP (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245) and BK3 (Kiss et al. J. Chem. Phys., 2013, 138, 204507) are compared to the TIP4P-2005 water potential (Abascal et al., J. Chem. Phys., 2005, 123, 234505) that had appeared the most favoravble previously. The basis of comparison was the compatibility with results of neutron and X-ray diffraction experiments on pure water, using the scheme applied by Pusztai et al. (2008). The scheme combines the experimental total scattering structure factors (TSSF) and partial radial distribution functions (PRDF) from molecular dynamics simulations in a single structural model. Goodness-of-fit values to the O-O, O-H and H-H simulated PRDF-s and to the experimental neutron and X-ray TSSF provided a measure that can characterize the level of consistency between interaction potentials and diffraction experiments. Among the sets of partial RDF-s investigated here, the ones corresponding to the SWM4-DP potential parameters have proven to be the most consistent with the particular diffraction results taken for the present study, by a hardly significant margin ahead of BK3. Perhaps more importantly, it is shown that the three sets of potential parameters produce nearly equivalent PRDF-s that may all be made consistent with diffraction data at a very high level. The largest differences can be detected in terms of the O-O partial radial distribution function. |
| format |
Article |
| author |
Steinczinger, Z. Pusztai, L. |
| spellingShingle |
Steinczinger, Z. Pusztai, L. Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water Condensed Matter Physics |
| author_facet |
Steinczinger, Z. Pusztai, L. |
| author_sort |
Steinczinger, Z. |
| title |
Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water |
| title_short |
Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water |
| title_full |
Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water |
| title_fullStr |
Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water |
| title_full_unstemmed |
Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water |
| title_sort |
comparison of the tip4p-2005, swm4-dp and bk3 interaction potentials of liquid water with respect to their consistency with neutron and x-ray diffraction data of pure water |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120855 |
| citation_txt |
Comparison of the TIP4P-2005, SWM4-DP and BK3 interaction potentials of liquid water with respect to their consistency with neutron and X-ray diffraction data of pure water / Z. Steinczinger, L. Pusztai // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43604:1-8. — Бібліогр.: 24 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT steinczingerz comparisonofthetip4p2005swm4dpandbk3interactionpotentialsofliquidwaterwithrespecttotheirconsistencywithneutronandxraydiffractiondataofpurewater AT pusztail comparisonofthetip4p2005swm4dpandbk3interactionpotentialsofliquidwaterwithrespecttotheirconsistencywithneutronandxraydiffractiondataofpurewater |
| first_indexed |
2025-07-08T18:44:17Z |
| last_indexed |
2025-07-08T18:44:17Z |
| _version_ |
1837105425996054528 |
| fulltext |
Condensed Matter Physics, 2013, Vol. 16, No 4, 43604: 1–8
DOI: 10.5488/CMP.16.43604
http://www.icmp.lviv.ua/journal
Comparison of the TIP4P-2005, SWM4-DP and BK3
interaction potentials of liquid water with respect to
their consistency with neutron and X-ray diffraction
data of pure water¤
Z. Steinczinger1, L. Pusztai2�
1 Budai Nagy Antal Secondary School, H–1121, Budapest, Anna utca 13–15, Hungary
2 Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of
Sciences, H–1525 Budapest, P.O. Box 49, Hungary
Received August 12, 2013, in final form September 2, 2013
Following a fairly comprehensive study on popular interaction potentials of water (Pusztai et al., J. Chem. Phys.,
2008, 129, 184103), here two more recent polarizable potential sets, SWM4-DP (Lamoureux et al., Chem. Phys.
Lett., 2006, 418, 245) and BK3 (Kiss et al., J. Chem. Phys., 2013, 138, 204507) are compared to the TIP4P-2005
water potential (Abascal et al., J. Chem. Phys., 2005, 123, 234505) that had previously appeared to be most favo-
ravble. The basis of comparison was the compatibility with the results of neutron and X-ray diffraction experi-
ments on pure water, using the scheme applied by Pusztai et al. (2008). The scheme combines the experimental
total scattering structure factors (TSSF) and partial radial distribution functions (PRDF) from molecular dynamics
simulations in a single structural model. Goodness-of-fit values to the O–O, O–H and H–H simulated PRDF-s and
to the experimental neutron and X-ray TSSF provided a measure that can characterize the level of consistency
between interaction potentials and diffraction experiments. Among the sets of partial RDF-s investigated here,
the ones corresponding to the SWM4-DP potential parameters have proven to be the most consistent with the
particular diffraction results taken for the present study, by a hardly significant margin ahead of BK3. Perhaps
more importantly, it is shown that the three sets of potential parameters produce nearly equivalent PRDF-s that
may all be made consistent with diffraction data at a very high level. The largest differences can be detected in
terms of the O–O partial radial distribution function.
Key words: neutron diffraction, partial radial distribution functions, Reverse Monte Carlo modelling
PACS: 61.20.-p, 61.25.-f, 61.05.fm
1. Introduction
When assessing the results of computer simulations that use interaction potentials, comparison with
experimental data is essential. For the microscopic structure the proper quantity to compare with is the
total scattering structure factor (TSSF), F (Q), that is related to the partial radial distribution functions
(PRDF) via:
G(r )Æ
n
X
i , jÆ1
i
j
b
i
b
j
[g
i , j
(r )¡1℄, (1.1)
F (Q)Æ ½
0
1
Z
0
4¼r
2
G(r )[sin(Qr )/Q℄dr. (1.2)
¤Dedicated to Prof. Dr. Myroslav Holovko on the occasion of his 70th birthday
�pusztai.laszlo@wigner.mta.hu
© Z. Steinczinger, L. Pusztai, 2013 43604-1
http://dx.doi.org/10.5488/CMP.16.43604
http://www.icmp.lviv.ua/journal
Z. Steinczinger, L. Pusztai
In the above equations, c
i
and b
i
are the molar ratio and the neutron scattering length of species i, G(r)
is the total radial distribution function, ½
0
is the number density and Q is the scattering variable (propor-
tional to the scattering angle); indices i and j run through nuclear species. (For details of the formalism
used here, see reference [1]).
Pure liquid water is arguably the system that has been targeted by the greatest number of computer
simulation studies of all pure materials (see, e.g., works of Prof. Holovko on the subject [2, 3]), resulting
in an excessive number of interaction potential parameter sets. The importance of the issue is reflected
by the fact that new potential parameters have been introduced even in this very calendar year [4].
Reviews describing many of the available interaction potential models introduced for liquid water are,
for instance, references [5, 6]. Unfortunately, the overwhelming majority of computer simulation studies
show comparisons with the ‘experimental’ PRDF-s only [4, 7, 8], whose functions have been shown to
be only interpretations of the measured diffraction data [9–12]. The proper quantity to cross-check with
would be the direct experimental information, the total scattering structure factors. In order to simply
resolve this (mostly, technical) issue, a simple protocol was introduced some years ago [10], that was later
applied to the case of pure water [11]. The main finding of this latter investigation was, in short, that out
of the 8 water potential models considered therein, it was TIP4P-2005 [8] that proved to be consistent at
the highest level with a given neutron diffraction dataset [13] taken on pure liquid heavy water.
In this work, we wish to extend the investigation described in reference [11], by
(a) adding two recent polarizable water potential models, SWM4-DP [7] and BK3 [4]; the reasons for
picking exactly these two potential parameter sets was that, on the one hand, SWM4-DP could be
very successfully applied to structural studies of various concentrated aqueous electrolyte solutions
[14, 15], and, on the other hand, the very recent BK3 set is claimed to be capable of outperforming
most water potentials in a detailed comparison with a great number of properties [4];
(b) scrutinizing the compatibility not only with neutron-, but also with X-ray diffraction data.
Here, results for SWM4-DP and BK3will be compared to those obtained for TIP4P-2005; this is the way
we wish to find a direct link to our earlier study [11]. As experimental data, the same neutron diffraction
results as considered previously are taken from reference [13] on liquid heavy water together with one
of the most recent published sets of X-ray data of Fu et al. [16].
2. Reverse Monte Carlo modelling
The protocol mentioned above [10] is based on a now 25 year old technique of structural modelling,
the so-called Reverse Monte Carlo (RMC) method [17] and, therefore, a short description of the method
may be appropriate here.
Reverse Monte Carlo [17–21] is a simple tool for constructing large, three-dimensional structural mod-
els that are consistent with total scattering structure factors (within the estimated level of their errors)
obtained from diffraction experiments. Via random movements of particles, the difference between ex-
perimental and model total structure factors (calculated similarly to the Â2-statistics) is minimized. As a
result, by the end of the calculation, a particle configuration is available that is consistent with the ex-
perimental structure factor(s). If the structure is analyzed further, partial radial distribution functions,
as well as other structural characteristics (neighbor distributions, cosine distribution of bond angles) can
be calculated from the particle configurations.
A possible algorithm that can realize the above features may be outlined as follows [17]:
1. Start with an initial collection of particle coordinates in a cubic box; this may be a crystalline or a
random distribution of at least a few thousand of particles, or even the final particle distribution
from the previous simulation.
2. Calculate the partial radial distribution functions for the configuration. Compose total radial distri-
bution functions according to the experimental weighting factors. Use Fourier transformation for
calculating total scattering structure factors.
43604-2
Consistency of water potentials with diffraction data
3. Calculate differences between model and experimental functions as follows (shown here for one
single TSSF):
Â
2
[F (Q)℄Æ
X
i
£
F
C
(Q
i
)¡F
E
(Q
i
)
¤
2
±
¾
2
. (2.1)
The ‘C’ and ‘E’ superscripts refer to ‘calculated’ and ‘experimental’ functions, respectively; ¾ is a
control parameter that is related to the assumed level of experimental errors.
4. Move one particle at random.
5. Calculate PRDF-s, TRDF-s, TSSF-s and, from them, also the Â2, for the new position.
6. If the Â2 for the new position is smaller than it was for the old position (i.e., the difference between
simulated andmeasured TSSF-s has become smaller), then accept themove immediately. Otherwise
accept the move only with a probability that is proportional to exp(¡¢Â
2
); accepting ‘bad’ moves
with such small but finite probability will prevent calculations from sticking in local minima. If a
move is ‘accepted’ then the ‘new’ position becomes the ‘old’ one for the next attempted move.
7. Continue from step 4.
The most valuable feature of the RMC method concerning the present investigation is that it can
incorporate any piece of information that can be calculated directly from particle coordinates. Partial
radial distribution functions coming from computer simulations are obviously these types of data as well
as the measured total structure factors. If a consistency (i.e., agreement within errors) with all input data
is reached, then it may be stated that these input data are mutually consistent. On the other hand, if some
of the input data cannot be approached within their uncertainties, it means that a particular part of the
input data set is not consistent with the other pieces of input information. In our case, this would mean
that some of the input PRDF-s from MD simulations would not be consistent with the experimental input
total scattering structure factor(s).
In the RMC calculations that are the basis of the present work, one total scattering structure factor
from neutron diffraction [13], one TSSF from X-ray diffraction [16] and three partial radial distribution
functions (O–O, O–H and H–H) from references [4, 7, 8] are used as input data for each RMC calculation.
That is, in conjunction with each of the 3 potential parameter sets [4, 7, 8] RMC is performed with the re-
quirement that 5 input datasets (neutron TSSF, X-ray TSSF, and O–O, O–H andH–HPRDF-s frommolecular
dynamics simulations described in references [4, 7, 8]) should be approached within the errors simulta-
neously. The primary condition assumed that experimental data must be reproduced at the same level
as they are approached in the absence of PRDF-s from MD; this goal could be achieved by systematically
varying the ¾ control parameters (see above) for each individual dataset. On average, at least 5 inde-
pendent calculations were needed to find the proper balance between individual ¾ parameters; thus, the
total number of calculations reported in this study is over 40 (see table 1).
Both experimental and simulation data were obtained at 298 K and 0.1 MPa (ambient conditions);
the molecular number density was 0.0334 molecules Å¡3 in each case. Molecular dynamics simulations
that resulted in the PRDF-s used in this work were performed in the canonical (NVT) ensemble [4, 7, 8]
at ambient conditions. Since the number of particles and the volume remain unchanged during a RMC
calculation, the NVT ensemble is a rather natural analogue for our Reverse Monte Carlo computations
as well (with the notion that temperature appears only implicitly, via the experimental number density
and diffraction data applied). In each Reverse Monte Carlo run, the simulation box contained 2000 water
molecules (6000 atoms). Typically, ‘equilibration’ (i.e., reaching the state where the fits to input data have
not improved further and started to fluctuate) last for a few million accepted moves. Shorter refinement
calculations (e.g., when small modifications of ¾ parameters for only one or two datasets were made)
were run for about 200000 accepted moves. Goodness-of-fit values, R
w
-s (which are sums of the squared
differences, see below), are reported in a normalised form, so that variations in terms of the number of
r and Q points considered would not affect the assessment; additionally, the applied r and Q ranges were
kept as uniform as possible.
43604-3
Z. Steinczinger, L. Pusztai
Definitions of the various R
w
-s used throughout this contribution are provided below (for PRDF-s,
only the example of the O–O g (r ) is shown):
R
w
2
[F (Q)℄Æ
X
i
£
F
C
(Q
i
)¡F
E
(Q
i
)
¤
2
±
X
i
F
E
(Q
i
)
2
, (2.2)
R
w
2
[gOO(r )℄Æ
X
j
£
g
C
OO
(r
j
)¡ g
E
OO
(r
j
)
¤
2
±
X
j
g
E
OO
(r
j
)
2
, (2.3)
where N
i
and N
j
are the numbers of Q and r points, respectively, for the experimental TSSF-s and ‘ex-
perimental’ (MD simulated) g (r )-s, respectively. Indices ‘C’ and ‘E’ refer to ‘RMC calculated’ and ‘experi-
mental’ quantities. In table 1 below, the square roots of the left hand side expressions are shown in the
units of ‘%’.
3. Results and discussion
Table 1 summarizes the main findings of the present work, namely the goodness-of-fit values for each
calculation reported here. It is instructive to look at figure 1 in parallel, so that the level of consistency
with experimental TSSF-s may be appreciated in terms of both numbers and ‘visual inspection’. It is clear
that each PRDF-containing RMC run produced a full agreement, within the estimated error levels and
without any visible sign of any disagreement, with both sets of diffraction data.
Figure 1. (Color online) RMC modelling partial radial distribution functions of liquid water from various
MD simulations [4, 7, 8], together with neutron diffraction TSSF of heavy water [13] (part a) and X-ray
diffraction TSSF of light water [16] (part b). Note that each curve runs together with the experimental
results, indicating the agreement without any visible deviations from experiment.
In table 1, the R
w
values for the reference RMC runs, containing either PRDF-s only or TSSF-s only, are
also quoted. Clearly, themodelling of TSSF-s and PRDF-s together causes the deterioration of the goodness-
of-fit; differences between R
w
-s obtained for ‘combined’ (TSSF+RSDF) and ‘PRDF-only’ calculations can
give an idea as to how far from the MD results the best match to the experimental TSSF-s lies. In this
sense, SWM4-DP PRDF-s seem to suffer the largest deviation from the end results of MD simulations [7],
whereas BK3 PRDF-s [4] should have changed the least.
The level of consistency between a given interatomic potential and the two sets of experimental TSSF-
s is measured by the overall R
w
values (‘R
w
sum’ in table 1) of the ‘combined’ Reverse Monte Carlo
calculations. According to this measure, it is the SWM4-DP potential [7] that comes out as the best (lowest
‘R
w
sum’), but only by a very small gap ahead of BK3 [4]. TIP4P-2005 [8] performs noticeably worse— but
still, the lag behind the two polarizable models is quite small. Considering that TIP4P-2005 was the clear
‘winner’ in the previous study (although using neutron diffraction data only) [11], the improvement of
43604-4
Consistency of water potentials with diffraction data
Table 1. Goodness-of-fit (R
w
) values for individual data sets [FN (Q), F X (Q) and the three partial g (r )-s]
for the three water potentials considered here. R
w
-s for calculations without experimental data are also
quoted, so that the influence of experimental datamay be assessed. (‘R
w
sum’ is the sum of the individual
R
w
values; ND: neutron diffraction; XRD: X-ray diffraction.)
TIP4P-2005 TIP4P-2005 SWM4-DP SWM4-DP BK3 BK3 Exp
Exp+MD MD Exp+MD MD Exp+MD MD
R
w
[ND F (Q)] 2.0% – 2.2% – 2.6% – 1.2%
R
w
[XRD F (Q)] 5.2% – 4.1% – 4.9% – 4.1%
R
w
[gOO(r )] 10.0% 4.5% 11.5% 0.1% 8.4% 6.6% –
R
w
[gOH(r )] 8.0% 4.0% 6.3% 2.0% 7.7% 4.3% –
R
w
[gHH(r )] 4.5% 1.8% 4.0% 1.0% 4.7% 2.6% –
R
w
sum 29.7% (11.3%) 28.1% ( 3.1%) 28.3% ( 13.5%) –
water potentials in terms of the structure is remarkable (even though only ambient pure water has been
investigated here).
Figure 2 displays comparisons of MD [4, 7, 8] and RMC calculated O–O, O–H and H–H PRDF-s in groups
of ‘worst’ and ‘best’ fits. Clearly, the O–O PRDF-s seem to be the hardest to be made consistent with exper-
imental data (see also table 1). This is very different from the findings reported in reference [11], where
the O–H partial appeared to be the most problematic. In this respect, the fact that in reference [11] only
one experimental neutron TSSF was used makes a huge difference: the relevant contribution (‘weight-
ing factor’) of the O–O PRDF to the neutron-weighted TSSF of pure heavy water is somewhat less than
10 %. That is, the neutron data considered [13] are rather insensitive to the variations of the O–O PRDF.
The appearance of X-ray diffraction data makes a huge difference: such data for water are sometimes
evaluated so that purely the O–O contribution (in the form of a ‘center-of-mass TSSF’ [16, 23]) is quoted
as final results. That is, the TSSF from X-ray diffraction experiments poses a very strong constraint (and
consequently, leaves very little freedom) for the O–O partial. Since there is still a controversy about the
most appropriate way of measuring and correcting X-ray diffraction data on water (see, e.g., reference
Figure 2. (Color online) RMC modelling MD simulated O–O (upper panels), O–H (mid panels) and H–H
(bottom panels) partial radial distribution functions of liquid water, together with the neutron diffraction
TSSF of heavy water[13] and X-ray diffraction TSSF of light water[16]. Left hand panels: worst cases; right
hand panels: best cases. Note that differences between ‘worst’ and ‘best’ are hardly visible.
43604-5
Z. Steinczinger, L. Pusztai
[24]), the issue should be investigated further in more detail, involving old [23] and new [24] results alike.
Figure 3 compares PRDF-s resulting fromMD simulations of the three water potentials [4, 7, 8] consid-
ered in this work. From a distance (even from a short one), the corresponding partials look remarkably
similar to each other, much more so than reported by figure 3 of reference [11]. Therefore, it is quite in
order to diagnose that over the past few years, the two-particle level structure of ambient liquid water
brought about by variousmodern interatomic potential parameter sets seems to be converging. However,
it is still worthwhile emphasizing some of the clear (although small) differences that may help develop
the potentials even further on. The most successful O–O PRDF (see table 1), from BK3, appears to be more
structured than its SWM4-DP equivalent but has a clearly weaker first maximum than that from TIP4P-
2005. Also note that, unlike for the other two partials, there is no dispute about the position of the main
peak here. As concerns the O–H PRDF, SWM4-DP turns out to bemost appropriate: this potential produces
the longest H-bonding distance (which is the first intermolecular O. . .H distance). This is consistent with
the findings of references [9, 11]. Also, SWM4-DP causes the most definite oscillations at higher r values.
Finally, for the H–H PRDF SWM4-DP, that seems to be somewhat better than the other two potentials,
brings about the longest first intermolecular H. . .H distance, again, with a little better defined ordering
at larger distances. In summary, it seems surprising that for all the three PRDF-s, the potential that pro-
duced the strongest long range ordering (by however small a margin) always turned out to be the best
performer.
Figure 3. (Color online) Partial radial distribution functions of MD simulated liquid water. Upper panel:
gOO(r ); mid panel: gOH(r ); bottom panel: gHH(r ). Note that differences between corresponding partials
are much smaller than reported in reference [11].
4. Conclusions and outlook
It has been shown that threemodern interaction potential parameter sets for liquid water, TIP4P-2005
[8], SWM4-DP [7] and BK3 [4], are nearly equally consistent with themeasured neutron [13] and X-ray [16]
diffraction data of liquid water at ambient conditions (see figure 2). Meticulous comparison (see table 1)
reveals that a distinction may be made between the 2 polarizable potentials (SWM4-DP and BK3) and the
non-polarizable one (TIP4P-2005): in terms of the structure, these up-to-date polarizable models perform
somewhat better than the ‘champion’ of the previous, analogous investigation [11].
The findings of the current contribution call for amore comprehensive study of interatomic potentials
of water, involving a larger number of potential parameter sets and, most importantly, further recent X-
ray diffraction data sets. This latter issue seems to have become outstanding recently: the latest large
scale comparison between the available X-ray diffraction results [24] shows that even during the past 5
years, the measured X-ray weighted TSSF of pure liquid water keeps changing. On the other hand, the
neutron weighted TSSF of pure heavy water has not been altered over at least the recent 15 years: this
43604-6
Consistency of water potentials with diffraction data
fact suggests that a detailed investigation concerning the consistency between the measured neutron-
and X-ray diffraction data would seem desirable, with the neutron data acting as the cornerstone TSSF.
Acknowledgements
This work has been supported by the Hungarian Basic Research Fund (OTKA), Grant No. K083529.
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http://dx.doi.org/10.1063/1.3273874
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Z. Steinczinger, L. Pusztai
Порiвняння потенцiалiв взаємодiї TIP4P-2005, SWM4-DP i BK3
для рiдкої фази води з точки зору їх узгодження з даними
по розсiянню нейтронiв i рентгенiвського випромiнювання
для чистої води
Ж. Штеiнцiнгер1, Л. Пустаї2
1 Школа другого ступеня Будаi Надь Антал, H–1121, Будапешт, Угорщина
2 Iнститут фiзики i оптики твердого тiла, Вiгнерiвський дослiдний центр фiзики, Угорська академiя наук,
H–1525 Будапешт, Угорщина
Слiдуючи досить повному вивченню популярних потенцiалiв взаємодiї для води (Pusztai et al., J. Chem.
Phys., 2008, 129, 184103), у цiй роботi два бiльш сучасних потенцiали з врахуванням поляризованостi мо-
лекул типу SWM4-DP (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245) i BK3 (Kiss et al., J. Chem. Phys., 2013,
138, 204507) порiвняно з моделлю TIP4P-2005 (Abascal et al., J. Chem. Phys., 2005, 123, 234505), яка донедав-
на вважалася найуспiшнiшою. Основою для порiвняння є узгодження з результатами експериментiв по
розсiянню нейтронiв та рентгенiвського випромiнювання для чистої води, використовуючи процедуру,
розроблену Пустаї та iн. (2008). Ця процедера поєднує повнi структурнi фактори розсiяння i парцiаль-
нi радiальнi функцiї розподiлу, що слiдують з молекулярної динамiки певної структурної моделi. Якiсть
узгодження значень функцiй розподiлу O–O, O–H i H–H з моделювання пiсля їх перетворення до повних
структурних факторiв i порiвняння з експериментальними факторами є мiрою для опису рiвня узгодже-
ння. Серед парцiальних функцiй розподiлу, дослiджених у цiй роботi, тi фактори, якi вiдповiдають моделi
SWM4-DP виявилися найкращими, але лише незначно кращими вiд тих, що були отриманi з моделi BK3.
Важливо вiдзначити, що усi три потенцiали дають майже еквiвалентнi радiальнi функцiї розподiлу, якi
узгоджуються з експериментом, але невелика розбiжнiсть спостерiгається для функцiй розподiлу киснiв
O–O.
Ключовi слова: нейтронна дифракцiя, парцiальнi радiальнi функцiї розподiлу, метод реверсного Монте
Карло
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Introduction
Reverse Monte Carlo modelling
Results and discussion
Conclusions and outlook
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