Additional potential constraint in a reverse Monte

Physics Letters A 315 (2003) 463–466
Additional potential constraint in a reverse Monte Carlo (RMC)
Mohammed Kotbi a,∗ , Hong Xu b , Mohammed Habchi a , Zohra Dembahri c
a Department of Physical, LPM, A.B. Belkaid University, BP.119 Tlemcen, Algeria
b DPM, Bat 203, Université Claude Bernard Lyon 1, Bd 11 Nov. 1918, 69622 Villeurbanne, France
c Department of Chemistry, LPM, A.B. Belkaid University, BP.119 Tlemcen, Algeria
Received 17 February 2003; received in revised form 23 June 2003; accepted 25 June 2003
Communicated by V.M. Agranovich
A recent simulation method called reverse Monte Carlo (RMC) applicable without interaction potential is used to study the
aqueous electrolyte system LiCl–6H2 O. Artifacts are appeared in some pair distribution functions particularly a small pick
near the first coordination of gOO (r) and also near the gOCl (r) one. One try to remedy for that artifact with introducing a
specified potential for the oxygen atoms and a Coulomb potential for the rest of the atomic species. An improvement in the first
coordination of this function is noticed suggesting a useful test of an interaction potential model for classical methods as Monte
Carlo (MC) and molecular dynamic (MD).
 2003 Published by Elsevier B.V.
Keywords: Potential constraint; RMC simulation; LiCl–6H2 O
By a structural modelisation, the aqueous electrolyte of type LiCl–6H2O is studied. This system
presents the property of forming a glass in passing
via the metastable state supermelt when the temperature decreases. The method of simulation called reverse Monte Carlo or RMC [1] presents the interest
being applicable without specifying interactions (interatomic and/or intermolecular). It describes a tridimensional system on the atomic level based on the
available experimental data and some geometric criteria’s. Instead of introducing the interaction potential
* Corresponding author.
E-mail address: [email protected] (M. Kotbi).
0375-9601/$ – see front matter  2003 Published by Elsevier B.V.
as in the classical methods (MD, MC), one computes a
parameter χ 2 representing the difference between the
calculated structure function and that are of the experiment. The parameter χ 2 is expressed as:
χ2 =
ei2 /2σ 2 (ri ),
where ei is the difference between the structure
function calculated by RMC and the experimental
one at the distance ri and σ (ri ) is the standard
deviation supposed uniform via the distance variation.
Some experimental results obtained by the neutrons
scattering experiment and the technique of isotopic
substitution could be used [2,3]. In order to improve
M. Kotbi et al. / Physics Letters A 315 (2003) 463–466
Fig. 1. RMC with potential constraint and experimental: partial distribution functions Glm (r) of LiCl–6H2 O in the glassy state: correlation
functions are represented Hlm (r) = Glm (r) − 1 with the indices l, m are X (any of species different to hydrogen one), O, H, Cl, Li.
the results obtained in RMC [4], one could introduce
an additional constraint as a potential of interaction
with a weight parameter chosen in our case to be 0.5.
Then the parameter χ 2 is written as:
χ2 →
(ri ) − GRMC
(ri ) /2σ 2
+ w · U/kB T .
We studied the structure of LiCl–6H2 O using the RMC
with four functions taken from the experimental partial distribution functions. With some pair functions
directly calculated, one could determined characteristic parameters as coordination numbers, correlation
distances and compare the thermodynamic states of
the aqueous electrolyte liquid/glass/supermelt with respect to the pure water at the ambient temperature. Ar-
Fig. 2. RMC with and without potential constraint: pair distribution
function gOO (r) of LiCl–6H2 O in the glassy state and pure water at
room temperature.
M. Kotbi et al. / Physics Letters A 315 (2003) 463–466
Fig. 3. RMC with and without potential constraint: pair distribution function ion–oxygen gOCl (r), gOLi (r), ion–hydrogen gHCl (r), gHLi (r)
(a) and ion–ion gClLi (r), gClCl (r), gLiLi (r) (b) of LiCl–6H2 O in glassy state.
tifacts appeared in some curves representing the functions of radial distribution (FDR) gij (r) (i, j = O, H,
Li+ , Cl− ). To remedy for these artifacts, we intro-
duced for a first time, a Coulomb potential for all the
species atomic of the solution [5,6]. In another case, a
potential of Lenard–Jones added to Coulomb one was
M. Kotbi et al. / Physics Letters A 315 (2003) 463–466
used for the oxygen atomic and written as:
uOO = kαOO
e2 /rOO
+ 4εOO (σO /rOO )12 − (σO /rOO )6 ,
where αOO is the oxygen charge fraction, εOO /kB =
78.2 K and σO = 3.166 Å are the usual Lenard–Jones
potential parameters.
In the first case, the water molecule is represented
by some partial charge such as −0.8476 for the oxygen and +0.4238 electronic units for each hydrogen atoms [5,6]. The obtained results show a significant improvement of gOO (r), which shows an artificial peak, which was a distance 3.1 Å. This becomes
less deep but stays still visible. Another artifact at
2.3 Å was observed before introducing the constraint
to gClO (r) disappeared and the first minimum gLiO (r)
improved making the first coordination at 2.1 Å better marked. For the second model of interaction introduced, one also obtains that the calculated partial distribution functions curves and the experimental ones
are in good agreement at this time level of computation. One can observe (Fig. 1) the partial correlation functions (PCF) Hij (r) = Gkl (r) − 1 instead of
partial distribution functions Gkl (r) where k, l designate the atom X different to H , equal to O, Cl,
Li, respectively. Configurations compatible with these
data are generated as shown within the result. Then
the calculated partial functions and the experimental
ones show a net concordance and so there is no mismatch between RMC without or with potential constraint. So there is no conflict between the method
used in our study and the constraint of potential introduced. The peak accompanying the top of gOO (r)
has a tendency to disappear noting a slight shift to
larger distances r (Fig. 2). One can make the same
remark concerning the curve gOCl (r) RDF functions
(Fig. 3), no noticeable change with respect to the previous case was observed. One observes once again
the dependence of the lithium-hydrogen RDF with re-
spect to the ion chlorine one. The chlorine-hydrogen
curves show a well-marked first and second coordination at 2.5 and 3.8 Å, respectively. The curves correspondent to the ions seem to show a slight structure
at the first coordination level and dependent strongly
on their respective closest approach distances. In conclusion the RMC method allows exploring a certain
number of structural features of the system based on
experimental data limited to four partial distribution
functions (PDF). The results one obtains could include
some artifacts. To remedy for this, we could make a
propose choice of potential. One must take into account the mismatch between the interaction potential
between charges and the method of RMC simulation
based on experimental data. So following the atomic
or molecular species in presence, introducing a potential like additional constraint in the RMC simulation,
one could obtain some better results. Consequently, we
could suggest that the choice of the interaction model
as a function of atomic or molecular properties forming the system could bring a meaningful improvement
to the results. It suggests a useful test for a defined
interaction potential model used for conventional simulation methods as Monte Carlo (MC) and molecular
dynamic (MD).
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