Solvation of calcium ion in methanol: Comparison of diffraction studies and molecular dynamics simulation

Chemical Physics 327 (2006) 415–426 www.elsevier.com/locate/chemphys

Solvation of calcium ion in methanol: Comparison of diffraction studies and molecular dynamics simulation Tu¨nde Megyes, Szabolcs Ba´lint, Imre Bako´ *, Tama´s Gro´sz, Tama´s Radnai, Ga´bor Pa´linka´s Institute of Structural Chemistry, Chemical Research Centre of the Hungarian Academy of Sciences, Pusztaszeri u´t 59-67, H-1025 Budapest, Hungary Received 22 March 2006; accepted 17 May 2006 Available online 22 May 2006

Abstract Molecular dynamics simulation and diffraction (X-ray and neutron) studies were compared on 1 and 2 M methanol solutions of calcium chloride with aiming at the determination of the solution structures. Beyond that, the capabilities of the methods to describe solution structure are discussed. It has been found that diffraction methods are performing very well in determination of Ca2+–O distances ˚ in average). Further on, by applying the X-ray diffraction method ion pairs could be observed easily for higher concentrated (2.39 A solution, but for neutron diffraction study, the most adequate isotope substitution method has to be chosen with care in order to be able to detect ion pairs in solution. The results of molecular dynamic simulation were found to be in general accordance with the experimental findings. The smaller discrepancies between simulation and experimental results are coming from small differences in the ion–methanol and ion–ion distances, and they may be due to both the potential model applied in the simulation and to the experimental uncertainties. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Calcium chloride; Methanol; Solution structure; Diffraction; Simulation

1. Introduction There is a great interest in calcium ion solvation because of its key role in several biological processes. Lots of experimental [1–13] and theoretical [14–29] reports are available about the hydration of calcium ion in water, but only a few solvation studies can be found in methanol and other alcohols [29–33]. The total solvation number of calcium chloride has been reported in methanol media [30], a Monte Carlo simulation was performed of calcium ion in several solvents including methanol [31], and dynamics of solvation [32,33] has also been studied. In our recent work [12] we have performed a detailed ab initio and X-ray diffraction study of calcium ion solvation in water and methanol solution, in wide range of concentration. We have applied the available most accurate ab initio methods and determined the binding energies

*

Corresponding author. Tel.: +36 1 4384141/586; fax: +36 1 3257554. E-mail address: [email protected] (I. Bako´).

0301-0104/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2006.05.014

of each solvent molecule added, one by one, to the 2þ CaðCH3 OHÞn solvates and concluded that when n is large enough, the binding energies change only slightly until they reach a value when they can already compete with hydrogen bonding energies between solvent molecules. This limit is reached at number n = 6. A series of water and methanol solutions of calcium ion have been studied by the X-ray diffraction method. It has been found that calcium solvation is sensitive to the sort of solvating molecule. The presence of methyl group in the molecule (compared to water) and the consequent break up of the extended hydrogen bonded structure in the bulk liquid led to the significant differences in solvation by smaller coordination number for methanol than water, and, in addition, the appearance of contact ion pairs beside the solvent separated ones at relatively high concentration. Beyond the determination of the solution structure the sensitivity of the experimental method has been also probed. We have found that the X-ray diffraction method is not sensitive enough, especially in low concentrated solutions, to decide the coordination number of calcium ion with high precision: in such a way, we face with an

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T. Megyes et al. / Chemical Physics 327 (2006) 415–426

unfortunate coincidence of the uncertainty of the method and the inherent uncertainty of solvation character of the ion in question. It is important to emphasize that while Xray diffraction method fails in precise determination of coordination number, the method is performing very well in determination of Ca2+–O distances: the obtained values ˚ for aqueous solutions and in case fell in range 2.43–2.46 A of methanol solutions they resulted in a slightly lower ˚ ) value, but well in the range of error limit. (2.39 A A special point of interest is the structure of solvates at high concentration range. Indeed, in methanol, when concentration of CaCl2 salts increases up to 2 mol dm3, the stoichiometry of the solutions will not allow for the formation of independent solvate shells neither for cations nor anions any more, and solvent separated and even contact ion pairs are expected to be formed in abundance in solution. There are a number of various possible structural forms displaying drastic changes both in the cationic solvates and in the bulk of the solution in comparison with the dilute solutions. Computer simulation studies can help us to resolve the microscopic structures as well. In present paper the first neutron diffraction experiments on calcium chloride methanol solutions by using H/D isotope substitution are reported. Molecular dynamics simulations for 1 and 2 M CaCl2 solution in methanol were also performed. The results of earlier X-ray diffraction and present neutron diffraction experiments are compared to molecular dynamics simulation studies.

˚ 1 of the ˚ 1 6 k 6 15.3 A responding to a range of 0.2 A scattering variable k = (4p/k) Æ sin H. Over 100,000 counts were collected at each of 150 discrete angles selected in ˚ 1 steps, in several repeated runs (10,000 counts Dk  0.1 A at each point). The measurement technique and data treatment were essentially the same as described previously [34]. The measured intensities were corrected for background, polarisation, absorption and Compton scattering [35]. The correction for Compton scattering is different from that for standard techniques, because of the location of the monochromator in the scattered beam. A semiempirical procedure has been followed in order to obtain the detailed shape of the Compton scattering curve. The Compton scattering correction is a low-frequency term in the reduced intensity function h(k). Its Fourier transform is therefore a peak at small distances in the radial distribution function. Re-inverting the radial distribution function we obtain the reduced intensity function h1(k). Setting zero the values up to the first important peak of the radial distribution function and re-inverting with cut-off at a fixed value we obtain the modified reduced intensity function h2(k). The difference between the two reduced intensity functions the correction curve with the effect of the high angle cut-off removed [36]. The Compton intensities needed for the corrections were calculated with analytical formulae [37,38]. The experimental structure function is defined as X hðkÞ ¼ IðkÞ  xa fa2 ðkÞMðkÞ ð1Þ a

2. Experimental and simulation details 2.1. X-ray scattering measurement and method of structural analysis The studied solutions were prepared from methanol of high purity (anhydrous, special grade, Merck), and from anhydrous CaCl2 (anhydrous, 99.99%, Aldrich). No further purification was performed. X-ray measurements were carried out on solutions of calcium chloride in methanol at two concentrations (Table 1). The X-ray scattering measurements have been performed at ambient temperature (24 ± 1 °C), with a H–H goniometer of symmetrical transmission geometry and by ˚ wavelength) with a using Mo Ka radiation (k = 0.7107 A graphite monochromator placed in the diffracted beam. The liquid sample holder had plane-parallel windows prepared from 6.3 lm thick mylar foils. The scattering angle range of measurement spanned over 1.28 6 2H 6 120° cor-

Table 1 Physical properties of CaCl2 solutions studied: salt concentration c, mass density q, linear X-ray absorption coefficient l, and atomic number density q0 c (mol dm3)

q (g cm3)

l (cm1)

q0 (cm24)

1 2

0.89 1.98

2.07 3.49

0.0899 0.0895

where I(k) is the corrected coherent intensity of the scattered beam normalised to electron units [39]; fa(k) and xa are the scattering amplitude and mole fraction for a type a particle, respectively; M(k) is the modification function, P M(k) = 1/{[ xafa(k)]2}. The coherent scattering amplitudes of the ions and the methanol molecule were computed according to analytical formulae suggested by Hajdu [37] and Cromer and Weber [40]. The system studied (methanol and ions) were treated in atomic representation. The necessary parameters were taken from International Tables for X-ray Crystallography [41]. The experimental pair correlation function was computed from structure function h(k) by Fourier transformation according to Z kmax 1 gðrÞ ¼ 1 þ 2 khðkÞ sinðkrÞ dk ð2Þ 2p rq0 kmin where r is the interatomic distance, kmin and kmax are the lower and upper limits of the experimental data, q0 is the atomic number density of the stoichiometric units. In order to conclude the structures of solutions, as a first step, a visual evaluation and a preliminary semi-quantitative analysis of the observed structure functions kh(k) and pair correlation functions g(r) were performed. Further on, the observed data were analysed by geometrical model constructions and fitting the model structure functions to the corresponding experimental ones by the non-linear

T. Megyes et al. / Chemical Physics 327 (2006) 415–426

least-squares method (LSQ). The quality of fit was monitored through the Sres factor as defined by S res ¼

k max X

h i2 k 2 hðkÞexp  hðkÞcalc

ð3Þ

k min

The theoretical intensities h(k)calc were calculated by formulae hcalc ðkÞ ¼ hd ðkÞ þ hc ðkÞ ð2  dab Þxa xb fa fb MðkÞ ! X r2ab 2 nab sinðkrab Þ hd ðkÞ ¼ k cab ðkÞ exp  krab xb 2 ab

cab ðkÞ ¼

hc ðkÞ ¼

X

4pq0 cab ðkÞ

ab

 exp 

ð4Þ ð5Þ ð6Þ

kRab cosðkRab Þ  sinðkRab Þ k3 !

C2ab 2 k 2

ð7Þ

where cab means k-dependent weights of different scattering contributions; a, b refers to scattering centres of different chemical types; dab is the Kronecker delta function with values dab = 1 if a = b and dab = 0 if a 5 b. The first term hd(k) (‘‘discrete part’’) represents the short range interactions characterised by the interatomic distance rab, the root mean square deviation rab and the coordination number nab. The second term hc(k) (‘‘continuum part’’) accounts for the uniform distribution of b type particles around a types beyond a given distance; Rab and Cab define the related boundary of the uniform distribution of a, b type distances and their root mean square deviation, respectively. A visual inspection of the radial distribution functions indicated us that they are rather composite and no peaks, not even the main peak, can be uniquely assigned to certain kind of interactions. In order to give a quantitative description of the structure, i.e., to derive the structural parameters, the coordination numbers, mean interatomic distances and their root mean square deviations, at least for the contributions of the predominant interactions construction and fitting of extensive structural models was necessary. At the beginning the ‘‘rough’’ structure of ionic shells has been fixed by inserting the structural parameters obtained from the preliminary study of radial distribution functions. As a second step least-square fitting method was used to determine the solvent–solvent and ion–ion intermolecular parameters. The fitting strategy was the following. The parameters of the discrete structure were kept constant and those for continuum were adjusted. The ˚ 1. refinement extended over the k range 0.2 6 k 6 15.3 A In the next step the coordination numbers for intermolecular interactions were kept constant and distances and root mean square deviations have been adjusted. Next, most of the coordination numbers for intermolecular interactions were allowed to vary. This process was repeated alternately several times until the minimum Sres factor has been

417

reached. Finally an overall check was run, letting all parameters to vary, covering the entire k range. 2.2. Neutron diffraction measurements The use of hydrogen/deuterium isotopic substitution has become a routine method of studying hydrogen containing solutions, and is based on the fact that the coherent scattering amplitudes for hydrogen and deuterium are very much different; bH = 3.74 and bD = 6.67 fm. The H/D substitution on a single site of a molecule, HR where R is a radical or a group of atoms, means that measurements can be made on a range of isotopic mixtures [H/D]R. For substitution on a single site of a molecule represented as R [H/D] there are resulting in three partial correlation functions, RR, RH and HH, assuming that the H and D atoms occupy equivalent positions. It follows that three independent measurements of different isotopic composition will produce three total structure factor measurements, with different relative weights for the separate partial terms. The three individual partial functions can therefore be extracted from the data sets. This approach has been described in detail for the early work on methanol [42] and by now it has been extended to many other systems [43–46]. The same principles apply to the partial functions but the R term now includes the calcium chloride molecule and also the oxygen, carbon and hydrogen atoms bound to carbon atom in the methanol; these are the terms which are unaffected by the H/D substitution. The total cross-section for a single solution may be written in terms of the self and interference (distinct) terms such that dR i ðQÞ ¼ I Pl i ðQÞ þ I int ðQÞ dX

ð8Þ

where I iint ðQÞ ¼ c2R b2R H RR ðQÞ þ 2cR cH bR bH H RH ðQÞ þ c2H b2H H HH ðQÞ ð9Þ

The weighing factors are defined by X c j bj bR ¼ cR j6¼H

ð10Þ

and cR ¼

X

cj

ð11Þ

j6¼H

and cH = 1  cR is the combined atomic fraction of all distinct hydrogen sites on which substitutions are made and I Pl i ðQÞ is the scattering from individual atoms described by a polynomial equation of 6th order. In practice, the use of H/D substitution technique is complicated by the large incoherent scattering from hydrogen and the increased complexity of the inelasticity corrections arising from the analytic treatment of the crosssection measurements.

T. Megyes et al. / Chemical Physics 327 (2006) 415–426

2.3. Simulation details We performed classical MD simulations in the NVT ensemble. For the simulation of 1 M solution the simulation box contained 500 methanol molecules, 20 Ca2+ cations and 40 Cl anions. The side length of the cube was ˚ . A pure methanol simulation with suitably placed 32.18 A ions was used as a starting configuration. Molecular dynamics simulation for 1 M solution was reported in Ref. [52]. This simulation was revisited because in the potential function describing Ca2+–Cl interaction a misprint was found, which led to a relatively short Ca2+–Cl contact ion pair distance and simultaneously to the overestimation of ion pairing in 1 M solution. The following analytical function was used to fit the calculated Ca2+–methanol dimer potential energy surface to obtain a good pair potential that can be practically used in MD simulations. U¼

6 X 1 qi qCa2þ Ai Bi C i Di þ 12 þ 6 þ 4 þ 9 4pe ri ri ri ri ri 0 i¼1

ð12Þ

where i means the ith atomic site within a methanol molecule. Every atom was represented with one interaction site. The point charge of the ith sites qi was taken from the OPLS potential model and all of them were kept constant throughout the fit. The other parameters were obtained by using a multidimensional non-linear least-square procedure

Table 2 Parameters for the Ca2+–methanol potential according to Eq. (12) ˚ 12) Bi (kJ A ˚ 6) Ci (kJ A ˚ 4) Di (kJ A ˚ 9) qI (e) i Atom Ai (kJ A 1 2 3 4–6

C O H(-O) H(-C)

4.35 0.521 20340.70 8821.66

46281.12 23449.20 14157.06 16884.60

9930.32 3705.99 3817.91 4737.39

174372.6 9600.68 25622.26 20393.12

0.145 0.683 0.418 0.040

(Table 2). The Ca2+–Cl short range potential was described by a Lennard-Jones form with the following ˚ ). parameters (e = 0.2301 (kcal/mol) r = 3.4150 A 2+  40 Ca cations and 80 Cl anions were added to the last configuration of the pure methanol simulation with 500 methanol molecules for simulating the 2 M solution. ˚ . These The side length of the cube was changed to 32.73 A parameters corresponded to the 2 M concentration of CaCl2 solution. During the 20,000 time steps of equilibration the Nose´– Hoover thermostat was used to control the temperature. The simulations were performed for 60,000 time steps leading to the total time of 120 ps. The simulation was performed by using the DLPOLY 2.0 program [53]. 3. Results and discussion 3.1. X-ray diffraction study 1 and 2 M solutions of CaCl2 in methanol have been studied. The radial distribution functions, in D(r)  4pr2q0 representation, are shown in Fig. 1. The detailed analysis of the structure of solutions is given elsewhere [12]. In present paper we would wish to emphasize the main conclusions, which are necessary for the comparison of diffraction and simulation results. The contribution of intramolecular correlations in methanol molecules were calculated and subtracted from structure function of calcium chloride solutions. The radial distribution functions, in D(r)  4pr2q0 representation, are shown in Fig. 1. They witness about the trivial concentration dependence of magnitude of various contributions and of some structural changes as well. The

4

Cl-O Ca-Cl Ca-O

2

Ca-C Cl-C Ca-O-Cl II

2

Neutron diffraction experiment on 1 and 2 M solutions of CaCl2 in methanol was carried out on the 7C2 diffractometer of the Laboratoire Leo´n Brillouin CEA-SACLAY ˚ 1. Three sets of experiments in a range of 0.3 6 k 6 15.3 A were performed for both concentrations by using the following isotope substituted solvents: CD3OD (100%), CD3OH (100%), CD3OD/CD3OH (64%/36%). The solutions were kept in a vanadium container of 6 mm and 0.1-mm wall thickness. The incident neutron wavelength ˚ . For standard corrections and normalisation was 0.70 A procedures, additional runs (vanadium bar, cadmium bar, empty container and background) were also performed. The raw diffraction data were corrected for background, inelastic effects, container- and sample absorption, and multiple scattering, and then the intensities were normalised, by using scattering data on a vanadium sample. A more detailed description of the correction procedure can be found in Ref. [47–49]. The conversion of the observed total cross-section dr/ dXe function (over the full k range) to an r-space representation was performed with the MCGR [50,51] method (‘Monte Carlo treatment of the experimental radial distribution function’). This method applies an inverse procedure in which the radial distribution functions, either total or partial, are generated numerically and modified by a stepwise random Monte Carlo process until its inverse Fourier transform agrees with the experimentally measured one within the limits of error.

D(r)-4πr ρ0

418

Ca-O

0 -2 -4 0

2

4 r(Å)

6

8

Fig. 1. Radial distribution functions from X-ray diffraction in D(r)  4pr2q0 representation for 1 M (solid line) and 2 M (dashed line) calcium chloride solutions methanol. The expected main contributions to the pair interactions are indicated by legends.

T. Megyes et al. / Chemical Physics 327 (2006) 415–426

structural parameters obtained from the least-squares fit of the structure functions are given in Table 3. For the broad ˚ mostly Ca2+–O interaction is responsipeak around 2–3 A ble but, especially at higher concentration, it overlaps with ˚ ) and minor contributions from the O–O (around 2.8 A 2+  ˚ Ca –Cl (around 2.7 A) type interactions. On the radial distribution function for the 2 M solution the peak assigned to Ca2+–O interaction increases probably due to the common (technical) effect of increased weight of Ca2+–O type contributions and appearance of Ca2+–Cl contact ion pairs in higher concentrated solutions as well. The coordination number for the Ca2+ ion in 1 M solution resulted in six. From the Ca2+–O, OI–OI (interaction of oxygen atoms involved in the coordination shell) it can be concluded that the Ca2+–O solvation shell is octahedral. With increase in concentration the Ca2+–O coordination number slightly decreases and the change in OI–OI suggests that the octahedral coordination shell is destroyed. ˚ The O–O interaction can be observed around 2.85–2.9 A even at high concentrations, suggesting that the interaction among methanol molecules will not disappear completely. Taking into account the considerations above and the stoichiometry of the solutions this is only possible if contact and/or solvent separated ion pairs are formed and there remain hydrogen bonded methanol in the solution. In order to check whether solvent separated or contact ion pairs are present in solutions, we have tried to fit the structure function of the 1 and 2 M solutions with two different models, one including ion pairs and the other not. In 1 M solution the fit proved to be better when including solvent separated ion pairs in model. For 2 M solution the fit improved slightly by including the Ca2+–Cl solvent separated and contact ion pairs as well. The slight improvement of the fit by itself is not enough reason to decide whether ion pairs are present or not in solution. After the comparison of diffraction results to simulation ones, we think that the problem of ion pairing in calcium chloride methanol solution needs revising, in sense that the presence of both contact and solvent separated ion pairs has to be taken into Table 3 Structural parameters from the X-ray diffraction refinement with estimated errors in the last digits Bond type

1M

2M

r

r

n

r

r

n

Ca–O Ca–OII Ca–Cl Ca–ClII Ca–C Cl–O Cl–C OI–OI O–O C–O C–C

2.39 (1) 4.44 (5)

0.19 0.22

6.0 11.2 (9)

4.90 3.52 3.19 4.14 3.40 2.85 3.61 4.90

0.4 0.20 0.20 0.22 0.20 0.20 0.20 0.23

0.3 6.0 6.0 6.0 4.0 1.7 (4) 2.7 (1) 5.5

2.39 4.37 2.70 4.60 3.67 3.22 4.04 3.12 2.90 3.64 4.84

0.19 0.25 0.18 0.4 0.20 0.20 0.23 0.20 0.20 0.20 0.25

5.1 9.2 1.1 0.5 5.5 6.0 6.0 2.5 1.5 2.5 5.0

(1) (1) (5) (2) (5) (1) (3)

(5) (3) (1) (5) (2) (2) (2) (5)

(9) (1)

(1) (5)

n is the coordination number. Distances (r) and their mean-square devi˚. ations (r) are given in A

419

account in 2 M solution. For this reason the parameters resulted from the fit of the model including ion pairs are shown in Table 3. In 1 M solution the solvent separated ˚ and the ion pair distance was found to be around 4.9 A coordination number is 0.3. In 2 M solution solvent sepa˚ and their coordinarated ion pairs can be detected at 4.6 A tion number slightly grows to 0.5. Ca2+–Cl contact ion ˚ , with coordination pairs can be detected around 2.75 A number 1.1 only in the higher concentrated solution. The Cl ion is solvated by six methanol molecules as it can be revealed from Cl–O and Cl–C parameters. 3.2. Neutron diffraction study With the substitution on the hydrogen atom bound to the oxygen in methanol three partial pair correlation functions may be evaluated as described in Section 2.2. The three data sets may be used systematically to determine the RR and RH partial functions by using the MCGR routine for each solution. The HH partial function could not be determined due to the low weight of the hydrogen– hydrogen (bound to the oxygen atom) contribution to the total scattering picture. In Section 3.4 the effect of the low weight of different contributions to the total radial distribution function will be discussed. The separation of the radial distribution functions for 2 M solution is shown in Fig. 2b. Table 4 contains the structural parameters obtained for both solutions. In ˚ corresponds to the intraRH RDF the first peak at 0.94 A molecular O–H bond in the methanol. The second peak is a very broad peak with two shoulders. Lots of interactions give contributions to this peak, e.g. C–H, Cl–H, H–HC (HC – hydrogen bound to carbon atom) and the intermo˚ , H– lecular O–H. The C–H was found to be around 1.9 A ˚ . The Cl–H interaction appears usually HC around 2.31 A ˚ [55] but it has the lowest contribution to around 2.29 A the total radial distribution function among all interac˚ ) consequently it could not tions in this region (1.5–3 A be determined. The intermolecular O–H resulted to be ˚ for 1 and 2 M solutions, respectively. 1.90 and 1.87 A Due to the low contribution to the total scattering picture of the Ca2+–Ca2+, Ca2+–O, Ca2+–Cl, Cl–O, Cl–Cl, O–O interactions, the RR radial distribution function is very difficult to resolve. The Ca2+–O distance was found ˚ for 1 and 2 M solutions to be around 2.45 and 2.43 A respectively, the coordination number slightly decreases ˚ in from 6.1 to 5.5. The O–O distance resulted in 2.81 A ˚ in 2 M solution. With increase in concen1 M and 2.85 A tration the O–H and O–O coordination numbers slightly decrease, representing that hydrogen bonding is reduced in small amount with increase in concentration. This finding is in agreement with the X-ray diffraction result, namely that by addition of calcium chloride salt to pure methanol only a part of methanol molecules form the solvation shell of different ions and hydrogen bonded methanol is present in the solution. Unfortunately due to the low contribution of different ion pairs to the total radial

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T. Megyes et al. / Chemical Physics 327 (2006) 415–426 16

(a)

14

(b)

RR RH

O-H

8

C-O,C-H

10

g(r)

dσ/dω

12

CD3OH

8

CD3OD/H

3 2

HC-HC,HC-O C-H,H---O,H-HC,Cl-H

6

CD3OD

4

1

2

Ca-O

0

2

4

6

8

10

12

0

14

1

O-O

2

-1

3

4

5

r (Å)

Q(Å ) 3

(c)

2 CD3OD

1 1

4

2

3

4

5

3 2

CD3OD/H

1 1

4

2

3

4

2

5 CD3OH

0 -2

1

2

3

4

5

r(Å)

Fig. 2. (a) Total cross-section of 1 and 2 M CaCl2 solution in methanol (solid circles: experimental values for 1 M solution; open circles: experimental values for 2 M solution; solid line: theoretical values). (b) Radial distribution functions g(r) obtained from the neutron diffraction experiment for 2 M solution (RR-solid line, RH-dashed line, where R = Ca, Cl, C, O, HC. The expected main contributions are indicated by legends. (c) Radial distribution functions g(r) obtained from the neutron diffraction experiment for 2 M solution (solid circles: intramolecular interaction; open circles: intermolecular interaction; solid line: total radial distribution function.) The solvents used are written in the figure. Table 4 Structural parameters from neutron diffraction with estimated errors in the last digits Bond type

1M

2M

r H–HC1 H–HC HC–HC C–HC C–H O–HC O–H C–O O–HHB O–O Ca–O

2.80 2.31 1.79 1.07 1.91 2.06 0.94 1.45 1.90 2.81 2.45

r (4) (5) (6) (2) (2) (7) (3) (7) (3) (3) (5)

0.23 0.20 0.14 0.11 0.14 0.18 0.10 0.12 0.13 0.16 0.13

(3) (5) (2) (2) (4) (5) (3) (3) (6) (5) (4)

n

r

1 2 2 3 1 3 1 1 0.91 (1) 1.82 (2) 6.10 (2)

2.81 2.32 1.80 1.08 1.89 2.07 0.95 1.46 1.87 2.85 2.43

n

r (6) (7) (2) (3) (4) (5) (5) (7) (3) (3) (4)

0.23 0.21 0.14 0.12 0.15 0.21 0.10 0.12 0.15 0.15 0.13

(3) (2) (2) (3) (2) (2) (2) (2) (5) (3) (3)

1 2 2 3 1 3 1 1 0.87 (7) 1.65 (6) 5.50 (1)

n is the coordination number. Distances (r) and their mean-square devi˚. ations (r) are given in A

distribution function it is not possible to give any details about ion pairing from neutron diffraction experiment. Fig. 2c shows the separation of total radial distribution function to intra- and intermolecular part for 2 M solution. The intermolecular radial distribution functions are to be compared to those obtained from simulation in Section 3.4.

Previous neutron diffraction studies on methanol resulted in a wide range of distances for each intramolecu˚ , C–O 1.42–1.56 A ˚ , C–H lar interaction: O–H 0.94–1.03 A ˚ , [54]. Comparing these findings to our results 1.06–1.09 A it can be observed that the intramolecular methanol structure is not influenced to any observable extent by addition of calcium chloride salt to pure methanol. O–HHB intermolecular coordination number was found to be 0.91 and 0.87 for 1 and 2 M solutions, respectively. These numbers are in accordance with previous findings for number of hydrogen bonds in pure methanol, which is in range 0.5–0.92 [54], meaning again that bulk methanol remains in solution. As it was found in the X-ray diffraction study, bulk methanol can remain in solution only if ion pairing occurs in solution, especially in higher concentrated one. Unfortunately ion pairing cannot be studied by the H/D isotope substitution method. It should also be remarked that the determination of hydrogen bond number is uncertain because intermolecular interactions, C–H, H–H, HC–HC give also contributions to the total scattering picture in this range. The Ca2+–O distance and coordination number is in agreement, within the limits of error, with previous results obtained for calcium–water systems from neutron diffraction experiments in water [6,10,55].

T. Megyes et al. / Chemical Physics 327 (2006) 415–426

421

3.3. Simulation results

Table 5 Characteristic values for the radial distribution functions gab(r)

The Ca2+–O, Ca2+–H, Cl–O, Cl–H, O–O and O–H partial radial distribution functions (RDF) are shown in Fig. 3 both for the 1 M (solid line) and 2 M (dashed line) solutions. The running coordination numbers nxy(r) are defined by Z r r2 gxy ðrÞ dr ð13Þ nxy ðrÞ ¼ 4pq0

Bond type

rmax 1M

2M

1M

2M

1M

2M

1M

2M

Ca–O Ca–C Cl–O Cl–C Cl–H Ca–Cl O–O O–H Ca–OII Ca–ClII

2.42 3.70 3.32 3.92 2.37 2.87 2.82 1.77 4.37 4.87

2.42 3.70 3.32 3.92 2.27 2.87 2.77 1.77 4.27 4.50

19.2 5.20 3.51 3.92 5.65 12.5 3.15 2.30 1.55 0.25

13.20 3.42 3.70 3.31 4.81 26.30 3.16 2.61 1.47 0.50

3.4 4.5 4.37 5.5 3.87 3.77 2.95 2.40 5.22 5.8

3.4 4.5 4.27 5.5 3.87 3.77 3.9 2.50 4.83 5.8

6.40 6.80 5.10 5.45 2.30 0.26 3.30 0.74 11.5 0.23

5.10 6.00 5.90 5.95 1.20 1.20 2.68 0.70 9.60 0.51

0

where q0 is the atomic number density of the y atom. The characteristic values of these RDFs, as peak positions, peak heights, and coordination numbers obtained by integration of the peaks up to the next first minima, are listed in Table 5. The first solvation shell of the cations is very well defined and separated from the second one. The Ca2+–O nearest neighbour distances are very similar. The effect of the increased concentration results apparently only in lowering of the first peaks and slightly less pronounced second neighbour distributions, in all RDFs. The average number of methanol molecules in the first solvation shell of the cations resulted in 6.4 for 1 M solution and in 5.1 for 2 M solution. 20 1M 2M

8

15

6 10 4

2

2 0

Ca-H

4

Ca-O

2

4

2

6

4

6

8

6

g(r)

4 4 Cl-O

2

Cl-H 1

4

6

2

4

6

8

6

8

3 2 2

O-H

O-O 1

1

2

4

6 r(Å)

8

2

4 r(Å)

Fig. 3. Cation–solvent, anion–solvent and solvent–solvent radial distribution functions obtained from simulation.

g(rmax)

rmin

nab(rmin)

nab is the running integration number. Atom–atom distances are given in ˚. A

˚ up to about 4.5 A ˚ in Ca2+– The region from about 3.5 A O RDF shows the second solvation shell with its maximum ˚ for the 1 and 2 M value at a distance of 4.37 and 4.27 A solutions, respectively. The number of methanol molecules belonging to the second shell decreases from 11.5 to 9.60 with increase of the concentration. The first peak position of the gCIO(r) is centred at ˚ . The coordination number of the chloride ion can 3.32 A be evaluated as 5.10 and 5.90 from nCIO(r) running coordination numbers at the position of the first minimum for 1 and 2 M solutions, respectively. The Cl–O coordination number increases, with increase in concentration. This apparently contradicting effect can be explained by simultaneous examination of the Cl–H and Cl–O RDFs together. On Cl–H RDF new peaks appear on the RDF of 2 M solution, meaning that more Cl–H distances are in 2 M than in 1 M solution. The chloride ions are solvated not only by the hydrogen atoms bound to the oxygen but by those bound to the carbon atom. As the concentration increases the ion species are forced to share more and more solvent molecules, and consequently the number of mixed, contact and solvent separated ion pairs, increases. For this reason various Cl–H distances can appear. If a chloride ion is solvated by methanol molecules via the methyl group ˚ depending on the Cl–O distances can be around 3.5–4.2 A the orientation of the methanol molecule. Consequently the Cl–O coordination number grows because these distances appear under the first peak of Cl–O RDF together with ˚ ) when the methanol molthe other Cl–O distance (3.32 A ecule solvates the chloride ion via the hydroxide group. Ca2+–Cl RDFs derived from the present simulation are shown in Fig. 4 and their characteristic values are given ˚ in RDF in Table 5. The first sharp peak at about 2.87 A clearly indicates contact ion pair formation in both simulated solutions of CaCl2. The integration of the first peak (nCa–Cl) resulted in 0.26 and 1.20 for 1 and 2 M solutions, respectively. The solvation shells of the calcium and chloride ions share methanol molecules when they form contact ion pairs. A direct analysis of the simulated configurations ˚ distance criteria, showed that 23% of based on rCa–Cl < 3 A cations are engaged in contact ion pair formation. In 2 M

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with formation of Ca2+–Cl contact ion pairs in solution as it can be observed on Fig. 6. An optional geometrical configuration of the atoms around calcium ion is an octahedral one consequently the calcium ion is six coordinated but with five oxygen and one chloride atom. The distribution of anion solvation numbers in Fig. 5b has one peak only at both concentrations. The increase in concentration is reflected only by shift of the peak position towards lower value and by broadening of the distribution. The Ca–O radial distribution function in Fig. 3 was calculated for the cations, regardless whether they belong to the class of contact ion pair forming ones or are far from anions. The calculation of average coordination number for cations, with solvation shell free from anions (76%), resulted in 6.95 for 1 M solution. For 2 M solution the average coordination number for cations, with solvation shell free from anions (50%) is 6.63. In the light of the above results one can conclude that when extended ion pair formation appears in solutions, besides the coordination number of individual ions, the solvation shell of contact ion pairs has also to be studied. It is easy to provide in a MD simulation, contrary to the analysis of diffraction data. We selected the solvation shell molecules of contact ion pairs in the simulated configurations by setting a distance criterium by choosing the positions ˚ or rCl–O < 3.5 A ˚ in radial of the first minima rCa–O < 3.30 A

30 1M 2M

20

g(r)

10 4 2 2

4

6

8

10

12

r(Å) Fig. 4. Ca2+–Cl radial distribution function obtained from simulation.

solution this ratio grows to 47% (Fig. 6). Two additional broad peaks appear on the Ca2+–Cl RDF. The first one can be attributed to solvent separated ion pairs, when the cation and anion share the methanol molecules via their ˚ can be hydroxide group. The second one, around 8 A attributed to solvent separated ion pairs via the methyl group of the methanol molecules. The distribution of cation solvation numbers, including cations whose solvation shell is free from anions, has a maximum at 7.2 for 1 M solution. For 2 M solution the distribution of methanol molecules has two maxima: one at 4.9 and the second one at 7. This shift can be explained

40

(a)

1M 2M

40

(b)

1M 2M 30

rel. %

rel. %

30

20

20

10

10

0

0

2

4

6

8

10

2

4

n

6

8

10

n 50

(c)

1M 2M

40

rel. %

30

20

10

0 4

6

8

10

12

14

16

18

n

Fig. 5. Fraction of cations (a) and anions (b) with n methanol molecules in their solvation shells. (c) Distribution of methanol molecules around Ca2+–Cl contact ion pairs.

T. Megyes et al. / Chemical Physics 327 (2006) 415–426 Ca-O

1M 2M

rel. %

75

Ca-Cl-Cl Ca-O-O Ca-nO-Cl

50 Ca-Cl-nO

25 Ca-mCl-nO

0

Fig. 6. Fraction of cations with no anions in the first solvation shell (Ca– O), with one anion in the first solvation shell (Ca–Cl–nO), with m anions in the first solvation shell (Ca–mCl–nO), with no anions neither in first nor in second solvation shell (Ca–O–O), with no anions in the first solvation shell and one anion in the second solvation shell (Ca–nO–Cl) and with one anion in both the first and second solvation shells (Ca–Cl–Cl).

distribution functions for limiting distances. The resulted distributions of the numbers of methanol molecules in the solvation shell of contact ion pairs for both solutions

423

are shown in Fig. 5c. The calculation of mean coordination number of contact ion pairs led to 11.1 and 10.0 for the 1 and 2 M solutions, respectively. The distribution of the number of solvation shell molecules for both sets of species has one peak only. Fig. 6 shows the distribution of different species, fully and partially solvated ions, in studied solutions. There are 76% fully solvated calcium ions in 1 M solution and 24% form contact ion pairs with one chloride ion. 29% of calcium ions form solvent separated ion pairs, this fraction grows to 47% in 2 M solution. Cations forming contact ion pairs with more than one chloride ions appear only in the higher concentrated solution (10%). Fully solvated calcium ions, with first and second shells free from anions, are 47% for 1 M solution and this fraction decreases drastically to 4% in 2 M solution. As an example for demonstration, a contact ion pair solvated by ten methanol molecules is depicted in Fig. 7a. In the configuration selected on the above distance criterium both ions have six nearest neighbour methanol molecules and the ions are sharing three sol-

Fig. 7. Ball and stick representation of contact ion pairs: (a) solvent separated ion pair and (b) 1, contact ion pair; 2, solvent separated ion pair via hydroxide group; 3, solvent separated ion pair via methyl group. Snapshots were obtained from simulation.

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T. Megyes et al. / Chemical Physics 327 (2006) 415–426

vent molecules from the ten solvation shell molecules. Fig. 7b shows another calcium ion involved in both, contact and solvent separated ion pair formation. Interesting is that there are two types of solvent separated ion pairs presented in figure, one formed via hydroxide group and another one through the methyl group of the methanol molecule.

where fa is the scattering length or scattering factor of the a-type particle (which depend on k in the case of X-ray diffraction), and xa is the mole fraction of the a particle. hab(k) is defined according to the following equation: Z rmax sinðkrÞ dr ð15Þ hab ðkÞ ¼ 4pq r2 ðgab ðrÞ  1Þ kr 0

3.4. Comparison of experiments and simulation

The total distinct radial distribution function is defined as the Fourier transform of the structure function. The agreement between the experimental X-ray and neutron diffraction and the theoretical radial distribution functions shown is quite good. The intermolecular distances and coordination numbers for calcium and chloride, resulting from diffraction agree with those obtained from the MD simulation within the estimated experimental errors. The comparison shows that the simulation leads to a fair enough description of the structure of the solutions. The discrepancies between the simulation and the experimental results from small differences in the ion–methanol and ion– ion distances, which, in turn, may be due to the potential

The radial distribution functions obtained from the X-ray and neutron diffraction experiments are compared with those obtained from simulation in Figs. 8 and 9, respectively. The total structure factor relevant to the solution structure (not including the intramolecular contribution) has been calculated from the partial radial distribution functions according to the equation XX H ðkÞ ¼ ð2  dab Þxa xb fa fb hab ðkÞMðkÞ ð14Þ aPb

1.5

1.5

(a)

1.0

(b)

g(r)

g(r)

1.0

0.5

0.5

0

2

4

6

8

0

10

2

4

r(Å)

6

8

10

r(Å)

Fig. 8. Comparison of the calculated g(r) from X-ray diffraction experiment and simulation. Solid line: simulation, circles: experiment, (a) 1 M and (b) 2 M solutions.

1M solution

(a)

2M solution

(b)

1.0

1.0 CD3OD

CD3OD

0.5

0.5

2

4

6

2

8

4

6

8

1.0

1.0

CD3OD/H

CD3OD/H

0.5

0.5

2

4

6

2

8

1.0 CD3OH

4

6

8

1.0 CD3OH

0.5 0.5

0.0 2

4

6

r(Å)

8

2

4

6

8

r(Å)

Fig. 9. Comparison of the calculated g(r) from neutron diffraction experiment and simulation. Solid line: simulation, open circles: experiment, (a) 1 M and (b) 2 M solutions.

T. Megyes et al. / Chemical Physics 327 (2006) 415–426

1.0

0.5

(b)

Total CH3OH-CH3OH Ca-CH3OH Cl-CH3OH Ca-Cl

1.5

g(r)

g(r)

(a)

Total CH3OH-CH3OH Ca-CH3OH Cl-CH3OH Ca-Cl

1.5

425

1.0

0.5

0

2

4 r(Å)

6

8

0

2

4 r(Å)

6

8

Fig. 10. Contribution of different interactions to the total radial distribution function measured by X-ray diffraction for (a) 1 M and (b) 2 M solutions.

1.5 (a)

1.5 (b) 0.1

Total RR RH HH MeOH-MeOH Ca-MeOH Cl-MeOH Ca-Cl

0.0

1.0

4

r(Å) 2

g(r)

g(r)

1.0

0.1

Ca-Cl g(r)

Total RR RH HH MeOH-MeOH Ca-MeOH Cl-MeOH Ca-Cl

Ca-Cl 0.0 2

4

0.5

0.5

0

2

4

6

0

2

r(Å)

4 r(Å)

6

Fig. 11. Contribution of different interactions to the total radial distribution function measured by neutron diffraction for (a) 1 M and (b) 2 M solutions.

model applied in the simulation and also to the experimental uncertainties. Fig. 10 shows the contribution of each interaction to the total radial distribution function. It can be observed that the main contribution to the total radial distribution function has the methanol–methanol interaction, the next one is the calcium–methanol and the third one the chloride–methanol interaction. The calcium–chloride ion pair’s contribution to the total radial distribution function, and obviously to the total scattering picture of the solution, is the lowest. That’s the reason for the noteworthy uncertainty of the X-ray diffraction method in determination of ion pairs in calcium chloride solutions. It reveals that with increase in concentration the contribution of the calcium chloride ion pairs to the total radial distribution function increases. Consequently in higher concentrated solutions it is easier to decide for or against the presence of ion pairs than in low concentrated solution. This is one possible explanation of the diffuse picture of the structure of low concentrated calcium-chloride solutions. Fig. 11 shows the contributions of individual interactions to the total radial distribution function. It is easy to observe that the lowest contribution to the total scattering picture have the Ca2+–Cl ion pair and the hydrogen– hydrogen interaction, even in the case of 2 M solution. These contributions are so low that it can be stated that it is impossible to determine from a simple neutron diffraction experiment. Isotope substitution method applied

either on calcium or on chloride, might give us detailed information on ion pairing in calcium chloride methanol solution. With increasing concentration the solvation sphere of the ions in solution might become incomplete, thus contact- and solvent separated ion pairs are formed in solution. The formation of ion pairs was confirmed by simulation and X-ray diffraction; for further verification, use of neutron diffraction for structure determination of aqueous solutions has to be done carefully and the most adequate isotope substitution method has to be applied. 4. Conclusions We have investigated 1 and 2 M methanol solutions of calcium chloride by the X-ray diffraction method. It has ˚ been found that the calcium–oxygen distance is 2.43 A and coordination number is around six. A concentration effect has been found: with increasing concentration the coordination number of calcium slightly decreased. The decrease in coordination number due to the lack of solvent molecules at high concentration supports the idea that calcium ion is ready to loose its solvating molecules and thus rearranging the solvation structure; the chloride ion again keeps being six coordinated even when the concentration is high enough. In the case of 1 M solution, it is not possible to decide by using only X-ray diffraction method whether there are ion pairs present in solution. We have revised our previous results [12] concerning this system

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on the basis of molecular dynamics simulation results, namely both, contact and solvent separated ion pairs were included in the model structure of 2 M solution. First neutron diffraction measurement was performed on calcium chloride methanol solution. Analysing the contribution of each interaction to the total scattering picture it can be concluded, that the contribution of ion pairs to the total scattering picture is extremely low. Consequently to obtain a real picture of the solution the most adequate neutron diffraction sample composition has to be chosen. The results obtained by MD simulation in this work are in general accordance with the above experimental findings. The conventional models used for the interpretation of diffraction data include contributions to the structure functions from ion-solvation shells, from solvent–solvent and ion–ion interactions. The detailed analysis of the configurations of the present MD simulation proved the necessity to introduce contribution of solvation shell molecules of contact ion pairs into the models in order to detect the presence of ion pairs. Acknowledgements The research was supported by projects NAP VENEUS05 OMFB-00650/2005 and the Hungarian Scientific Research Funds (OTKA), project number T 043676. The authors thank to Marie-Claire Bellisent-Funel for the opportunity to effectuate the neutron diffraction measurements on the diffractometer 7C2 of the Laboratoire Leo´n Brillouin CEA-SACLAY. References [1] T. Radnai, H. Ohtaki, Chem. Rev. 93 (1993) 1157. [2] G. Licheri, G. Piccaluga, G. Pinna, J. Chem. Phys. 64 (1976) 2437. [3] M.M. Probst, T. Radnai, K. Heinzinger, P. Bopp, B.M. Rode, J. Phys. Chem. 89 (1985) 753. [4] P. Smirnov, M. Yamagami, H. Wakita, T. Yamaguchi, J. Mol. Liq. 73–74 (1997) 305. [5] S. Cummings, J.E. Enderby, R.A. Howe, J. Phys. C 13 (1980) 1. [6] N.A. Hewish, G.W. Neilson, J.E. Enderby, Nature 297 (1982) 138. [7] D. Spangberg, K. Hermansson, P. Lindqvist-Reis, F. Jalilehvand, M. Sandstro¨m, I. Persson, J. Phys. Chem. B 104 (2000) 10467. [8] F. Jalilehvand, D. Spangberg, P. Lindqvist-Reis, K. Hermansson, I. Persson, M. Sandstro¨m, J. Am. Chem. Soc. 123 (2001) 431. [9] L. Fulton, M.S. Heald, Y.S. Badyal, J.M. Simonson, J. Phys. Chem. A 107 (2003) 4688. [10] Y.S. Badyal, A.C. Barnes, G.J. Cuello, J.M. Simonson, J. Phys. Chem. A 108 (2004) 11819. [11] M. Gaspar, M. Alves Marques, M.I. Cabaco, M.I. Barros Marques, T. Buslaps, V. Honkimaki, J. Mol. Liq. 110 (2004) 15. [12] T. Megyes, T. Gro´sz, T. Radnai, I. Bako´, G. Pa´linka´s, J. Phys. Chem. A 108 (2004) 7261. [13] R. Li, Z. Jiang, S. Shi, H. Yang, J. Mol. Struct. 645 (2003) 69. [14] G. Pa´linka´s, K. Heinzinger, Chem. Phys. Lett. 126 (1986) 251.

[15] F.M. Floris, M. Persico, A. Tani, J. Thomasi, Chem. Phys. Lett. 227 (1994) 126. [16] M.I. Bernal-Uruchurtu, I. Ortega-Blake, J. Chem. Phys. 103 (1995) 1588. [17] S.G. Kalko, G. Sese´, J.A. Padro, J. Chem. Phys. 104 (1996) 9578. [18] S. Obst, H. Bradaczek, J. Phys. Chem. 100 (1996) 15677. [19] A. Tongraar, K.R. Liedl, B.M. Rode, J. Phys. Chem. A 101 (1997) 6299. [20] M. Pavlov, E.M. Siegbahn, M. Sandstro¨m, J. Phys. Chem. A 102 (1998) 219. [21] C.F. Schwenk, H.H. Loeffler, B.M. Rode, J. Chem. Phys. 115 (2001) 10808. [22] A. Katz Kaufmann, J.P. Glusker, S.A. Beebe, C.W. Bock, J. Am. Chem. Soc. 118 (1996) 5752. [23] I. Bako´, J. Hutter, G. Pa´linka´s, J. Chem. Phys. 117 (2002) 9838. [24] M.M. Naor, V.K. Nostrand, C. Dellago, Chem. Phys. Lett. 369 (2003) 159. [25] F.C. Lightstone, E. Scwegler, M. Allesch, F. Gygi, G. Galli, Phys. Chem. Phys. 6 (2005) 1745. [26] A. Chialvo, J.M. Simonson, J. Chem. Phys. 119 (2003) 8052. [27] A. Chialvo, J.M. Simonson, J. Mol. Liq. 112 (2004) 99. [28] F.E. Sowrey, L.J. Skipper, D.M. Pickup, K.O. Drake, Z. Lin, M.E. Smith, R.J. Newport, Phys. Chem. Chem. Phys. 6 (2004) 188. [29] K. Bujnicka, E. Hawlicka, J. Mol. Liq. 125 (2006) 151. [30] A. Wahab, S. Mahiuddin, J. Chem. Eng. Data 46 (2001) 1457. [31] H.S. Kim, J. Mol. Struct.: Theochem. 541 (2001) 59. [32] M.A. Kahlow, W. Jarzeba, T.J. Kang, P.F. Barbara, J. Chem. Phys. 90 (1989) 151. [33] S. Roy, B. Bagchi, J. Chem. Phys. 101 (1994) 4150. [34] T. Radnai, H. Ohtaki, Mol. Phys. 87 (1996) 103. [35] F. Hajdu, G. Pa´linka´s, J. Appl. Crystallogr. 5 (1972) 395. [36] H.A. Levy, M.D. Danford, A.H. Narten, Oak Ridge National Laboratory Rep., No. 3960, 1966. [37] F. Hajdu, Acta Crystallogr. A28 (1972) 250. [38] G. Pa´linka´s, T. Radnai, Acta Crystallogr. A32 (1976) 666. [39] K. Krogh-Moe, J. Acta Crystallogr. 2 (1956) 951. [40] D.T. Cromer, J.T. Waber, Acta Crystallogr. A32 (1965) 104. [41] International Tables for X-ray Crystallography, vol. 4, The Kynoch Press, 1974. [42] D.G. Montague, J.C. Dore, Mol. Phys. 57 (1986) 1035. [43] J.Z. Turner, A.K. Soper, J. Chem. Phys. 101 (1994) 6116. [44] J.Z. Turner, A.K. Soper, J.L. Finney, J. Chem. Phys. 102 (1995) 5438. [45] A.K. Soper, A. Luzar, J. Chem. Phys. 97 (1992) 1320. [46] I. Bako´, G. Pa´linka´s, J.C. Dore, H. Fisher, Chem. Phys. Lett. 303 (1999) 315. [47] A.K. Soper, P.A. Egelstaff, Mol. Phys. 42 (1981) 399. [48] J.Z. Turner, A.K. Soper, J.L. Finney, Mol. Phys. 70 (1990) 679. [49] (a) I.P. Gibson, J.C. Dore, Mol. Phys. 37 (1979) 1281; (b) H. Bertagnolli, P. Chieux, M.D. Zeidler, Mol. Phys. 32 (1976) 759. [50] R.L. McGreevy, L. Pusztai, Physica B 357 (1997) 234. [51] The MCGR programme and its description can be found at . [52] T. Kosztola´nyi, I. Bako´, G. Pa´linka´s, J. Mol. Liq. 126 (2006) 1. [53] DL_POLY is a package of molecular simulation routines written by W. Smith and T. Forester, CCLRC, Daresbury Laboratory, Daresbury, Nr. Warrington, 1996. [54] (a) T. Weitkamp, J. Neuefeind, H.E. Fischer, M.D. Zeidler, Mol. Phys. 98 (2000) 125; (b) T. Yamaguchi, K. Hidaka, A. Soper, Mol. Phys. 96 (1999) 1159; (c) A.K. Adya, L. Bianchi, C.J. Wormald, J. Chem. Phys. 112 (2000) 4231; (d) B. Tomberli, P.A. Egelstaff, C.J. Benmore, J. Neuefeind, J. Phys. Cond. Matt. 13 (2001) 11405. [55] T. Megyes, I. Bako´, S. Ba´lint, T. Gro´sz, T. Radnai, J. Mol. Liq., accepted for publication.