Structure of liquid methylene chloride: Molecular dynamics simulation compared to diffraction experiments

Journal of Molecular Liquids 136 (2007) 257 – 266 www.elsevier.com/locate/molliq

Structure of liquid methylene chloride: Molecular dynamics simulation compared to diffraction experiments Szabolcs Bálint, Imre Bakó, Tamás Grósz, Tünde Megyes ⁎ Institute of Structural Chemistry, Chemical Research Center of the Hungarian Academy of Sciences, Pusztaszeri út 59-67, H-1025 Budapest, Hungary Available online 1 September 2007

Abstract Molecular dynamics simulation and diffraction (X-ray and neutron) studies are compared on methylene chloride with aiming at the determination of the liquid structure. Beyond that, the capabilities of the methods to describe liquid structure are discussed. For the studied liquid, the diffraction methods are performing very well in determination of intramolecular structure, but they do not give detailed structural information on the intermolecular structure. The good agreement between the diffraction experiments and the results of molecular dynamics simulations justify the use of simulations for the more detailed description of the liquid structure using partial radial distribution functions and orientational correlation functions. Liquid dichloromethane is described as a molecular liquid without strong intermolecular interactions like hydrogen bonding or halogen-halogen contacts, but with detectable orientational correlations resulting in antiparallel, tail-to-tail orientation of the first nearest neighbours, which is lost very quickly and slight preference of parallel head-to-tail and L-shaped orientation can be detected. On the other hand some orientational correlations between rather distant molecules can also be observed. © 2007 Elsevier B.V. All rights reserved. Keywords: Dichloromethane; Methylene chloride; X-ray diffraction; Neutron diffraction; Simulation; Liquid structure

1. Introduction Methylene chloride (dichloromethane), belongs to a group of low-permittivity, dipolar, aprotic solvents, which are ideal media for a variety of important chemical reactions. It is a widely used solvent in supramolecular [1] and polymer chemistry [2]. Methylene chloride is a particularly suitable organic diluent for liquid–liquid extraction by carriers such as crown ethers, since it can solubilize reasonable amounts of extractants and extracted species [3]. Further on, being a chlorinated hydrocarbon, it has also been widely used as solvent in processing of radioactive materials and contributes significantly to nuclear waste remediation problems [4]. Methylene chloride is a volatile organic compound, which pollutes the environment and adversely affects human health. The European Community has issued directives to restrict chlorinated compounds and currently investigating risks posed by chemicals including chlorohydrocarbons [5]. To obtain detailed understanding of the role of solvent in different chemical

⁎ Corresponding author. E-mail address: [email protected] (T. Megyes). 0167-7322/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2007.08.020

systems and environment, it is clearly essential to model the pure solvent and to study its structure. There exist various theoretical and experimental studies on the structure and properties of methylene chloride. Different spectroscopic methods (IR [6], Raman [7] and microwave [8,9] spectroscopic experiments, Rayleigh scattering [7a] and NMR relaxation [10]) were applied to study methylene chloride. Recently time resolved X-ray diffraction studies of liquid methylene chloride were conducted [11]. The parameters obtainable from spectroscopic experiments were compared to those calculated from molecular dynamics simulation. Liquid methylene chloride has been investigated by molecular dynamics simulation [12–14] using different potential models, molecular Ornstein–Zernike theory [15] and MonteCarlo simulation [16]. Methylene chloride was also studied by theoretical methods on liquid–liquid and liquid–vapor interfaces [17] and mixtures [18]. These studies were focused mainly on testing the developed model potentials and comparing their predictions with the experimentally accessible vibrational quantities and the overall dynamic [12a–14a,19] and thermodynamic [15a] behaviour of the liquid. However, the structural analysis did not go beyond the determination of the

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partial correlation functions and the determination of several structure functions in order to be compared to the experimental results. Ab initio molecular orbital calculations were performed by Torii [16] and density functional calculation of methylene chloride clusters by Canepa [20]. Only one attempt has been made on the detailed structural study of liquid methylene chloride by Reverse Monte Carlo (RMC) simulation [21], using early X-ray and neutron diffraction data. Diffraction techniques serve, in principle, as direct method to determine the structure of the matter in condensed state. The crystalline structure of methylene chloride has been determined using single crystal X-ray diffraction [22]. Recently in situ high pressure single crystal X-ray study [23] of methylene chloride has been carried out focusing on the evaluation of crystal cohesion forces and behaviour of halogen contacts under compression. To the best of our knowledge, only one single X-ray diffraction study of liquid methylene chloride was conducted, by Orton et al. [24], but this experiment had been carried out in a limited k (0−10 Å− 1) range and the resulting structure function supposed to be rather inaccurate above 3 Å− 1. Jung et al. [25] performed neutron diffraction experiments on samples containing different isotopic mixtures. In the present study we performed X-ray experiments on methylene chloride, in combination with molecular dynamics simulation. In order to obtain a more reliable picture of the liquid in study, molecular dynamics simulation results are compared to our X-ray diffraction measurements and neutron diffraction performed by Jung et al. [25]. To learn more about the mutual orientation of methylene chloride molecules we have also performed an ab initio study of methylene chloride dimer on MP2 level. The paper is organized as follows: In the ‘methods’ section we describe the quantum chemical calculations, and the simulation details and after the X-ray measurements and data treatments. In ‘results and discussion’ we present the experimental and theoretical results and compare them before ‘conclusions’ summarizes the main results. 2. Computational details 2.1. Quantum chemical calculations All calculations were performed by using the Gaussian 03 program suite [26] at MP2 level of theory using the 6–311 + G⁎⁎ basis set. The behaviour of the calculated stationary points was characterized by their harmonic vibrational frequencies. The interaction energies for each minimum were corrected for basis set superposition error (BSSE) with the full counterpoise (CP) procedure, resulting in a more reliable estimate of the interaction energy [27]. The magnitude of the BSSE correction at the energy minimum configuration is about 50–60% of the total interaction energy at MP2 level of theory. In principle, since the BSSE causes the intermolecular interactions to be too attractive, the CP correction is expected to make the complexes less stable [28]. 2.2. Molecular dynamics simulation We have performed a classical MD simulation in the NVT ensemble. The simulation box contained 512 rigid methylene

Table 1 Interaction potential parameters for liquid methylene chloride σ (Å)

ɛ (kcal/mol)

qa

qb

qc

C H Cl

3.2 2.75 3.35

0.1013 0.0266 0.347

− 0.640 0.317 0.003

0.4474 − 0.0551 − 0.1686

− 0.109 0.098 0.002

a

Ref. [16]. Ref. [19]. Ref. [12].

b c

chloride molecules. Three set of intermolecular potentials were used, namely, Torii, model 2 [16], Rothschild [19] and Evans [12] as given in Table 1. The side length of the cube was 37.913 Å corresponding to the experimental density of 1.312 g cm− 3. During the 50,000 time steps of equilibration the Nosé– Hoover thermostat was used to control the temperature in the DLPOLY 2.15 software [29]. The simulations were performed for 200,000 time steps leading to the total time of 400 ps. 3. Experimental details X-ray diffraction measurement was carried out on liquid methylene chloride, anhydrous, special grade, produced by Aldrich. The physical properties of the methylene chloride were: density ρ = 1.31 g · cm− 3, linear X-ray absorption coefficient μ0 = 12.84 cm− 1, atomic number density ρ0 = 0.0464· 10− 24 cm− 3. The X-ray scattering measurements were performed at room temperature (24 ± 1 °C), with a Rigaku R-AXIS RAPID image plate diffractometer using MoKα radiation (λ = 0.7107 Å). Quartz capillaries (1.5 mm diameter, 0.01 mm wall thickness) were used as the liquid sample holder. The scattering angle range of measurement spannedover 4.80 ≤ 2Θ ≤ 138.88° corresponding to a range of 0.74 Å− 1 ≤ k ≤ 16.55 Å− 1 of the scattering variable k = (4π/λ) · sin(Θ). In order to expand the scattering range to lower angle values another set of measurements was performed at room temperature (24 ± 1 °C), with a Philips X'Pert goniometer in a vertical Bragg-Brentano geometry with a pyrographite monochromator in the scattered beam and proportional detector using MoKα radiation. In this case the scattering angle range of measurement spanned over 1.28 ≤ 2Θ ≤ 130.2° corresponding to a range of 0.2 Å − 1 ≤ k ≤ 16.06 Å− 1 of the scattering variable k = (4π/λ) · sinΘ. Background and absorption corrections were applied based on an algorithm reported by Paalman and Pings [30] for cylindrical sample holders. This algorithm assumes that significant coupling does not occur between the sample and cell [31], therefore the experimentally observed intensities are considered as linear combination of an independent component from the confined sample and a component from the sample cell. The correction procedure was applied using in house software written in a Fortran language. The polarization and Compton scattering corrections were applied using standard methods given in earlier works [32]. The experimental structure function is defined as: hð k Þ ¼ I ð k Þ 

X a

xa fa2 ðk ÞM ðk Þ

ð1Þ

S. Bálint et al. / Journal of Molecular Liquids 136 (2007) 257–266 Table 2 Geometrical parameters for methylene chloride molecule obtained with MP2 method compared to experimental data from literature

rC–H rC–Cl rCl⋯Cl ∠(HCH) ∠(ClCCl)

Present study

Gas a

Crystal b

1.0864 1.7673 2.948 110.98 113.02

1.068 1.7724 2.935 118.8 112.0

0.99 1.768 2.932 112 112

Atom–atom distances are given in Å. a Ref. [9]. b Ref. [22].

Z

kmax

khðk ÞsinðkrÞdk

analysis of the observed structure functions kh(k) and radial distribution 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 least-squares method. The fitting strategy was previously described in Refs. [32]. 4. Results and discussion 4.1. Quantum chemical calculations

where I(k) is the corrected coherent intensity of the scattered beam normalised to electron units [33]. fα(k) and xα are the scattering amplitude and mole fraction for a type of α particle, respectively; M(k) is the modification function, 1/[Σxα fα(k)]2. The coherent scattering amplitudes were calculated as previously described [32]. The methylene chloride molecules were treated in atomic representation, and the necessary parameters were taken from the International Tables for X-ray Crystallography [34]. The experimental radial distribution function was computed from the structure function h(k) by Fourier transformation according to Eq. (2) 1 g ðr Þ ¼ 1 þ 2 2p rq0

259

ð2Þ

kmin

where r is the interatomic distance, kmin and kmax are the lower and upper limits of the experimental data, ρ0 is the atomic number density. After repeated Fourier transformations the nonphysical peaks present in the g(r) at small r values were removed, and the structure function was corrected for residual systematic errors [35]. In order to characterise the structure of the liquid, as a first step, a visual evaluation and a preliminary semi-quantitative

The parameters obtained for the optimised structure of methylene chloride molecule with their experimental counterparts [9,22] are presented in Table 2. It can be observed that all geometrical parameters obtained are in good agreement with experimental results. As a result of geometry optimisation four structures have been obtained: A: dimer structure close to antidipole arrangement; B: L-shaped arrangement, conform to direction of dipoles, characteristic in the quadrupole–quadrupole interaction; C: antidipole arrangement; D: head-to-tail arrangement. The optimised geometry for the four dimers of methylene chloride molecules are shown in Fig. 1. Table 3 reports resulting parameter values for the all structures. Comparison between the geometries of the isolated monomer and the monomer geometry in the dimer shows no significant change. The C⋯C distances were found to vary between 3.74–4.23 Å, Cl⋯H distances 2.88– 3.15 Å and the shortest Cl⋯Cl distances between 3.81–4.25 Å. These parameters indicate on the one hand that in methylene chloride dimers no hydrogen-bond like interaction appears, and on the other hand Cl⋯Cl contacts do not play an accentuated role in the formation of the structure of the dimers as was supposed for the crystal [36]. The interaction energies are very small, with values between − 1.85 and − 1.08 kcal/mol, and are consistent with earlier calculation results [16,20]. The geometrical

Fig. 1. Ball and stick representation of methylene chloride dimers. a: structure close to antidipole arrangement; b: L-shaped arrangement; c: antidipole arrangement; d: head-to-tail arrangement.

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Table 3 Structural and energetic parameters for methylene chloride dimer obtained with MP2 method − ΔE(kcal/mol) − ΔEBSSE(kcal/mol) rC⋯C rCl⋯H rCl⋯Cl Dipole–dipole angle

A

B

C

D

4.26 1.27 3.74 2.88 4.01 153

4.71 1.85 3.92 2.98 3.93 109

4.1 1.31 3.88 2.91 3.86 180

3.44 1.08 4.23 3.15 4.25 0

The closest Cl⋯H and Cl⋯Cl distances are given. Atom–atom distances are given in Å, energies in kcal mol− 1.

optimization of the four dimers shown above, was performed also with B3LYP calculations, which do not describe properly the van der Waals interactions. From these calculations 30−70% smaller interaction energies have been obtained. This finding suggests that the structure determining forces, electrostatic (dipole–dipole and quadrupole–quadrupole) and van der Waals interactions, contribute in a similar magnitude. 4.2. MD Simulation results 4.2.1. Radial pair distribution functions (RDFs) The structure of liquid methylene chloride was analysed in terms of radial distribution functions (RDFs), denoted as gαβ(r), for the various atom-atom pairs. The corresponding running integration numbers nαβ(r) are defined by: Z nab ðrÞ ¼ 4pqb

r

gab ðrÞr2 dr

Fig. 2. Partial radial distribution functions obtained from three different molecular dynamics simulation.

ð3Þ

0

The value of this integral up to the first minimum (rm1) in g(r) is the number of coordinating atoms of type β around atoms of type α at a distance r and ρβ is the number density of the atoms of type β. The molecular dynamics simulation produces individual pair distribution functions for each of the interactions and these can be analysed to get an insight into the arrangement of the molecules in the liquid. The RDFs of the liquid methylene chloride obtained from three simulations are presented in Fig. 2. The essential features of the RDFs in the three types of simulations agree with each other showing that the RDFs are rather insensitive on the charge distribution of methylene chloride molecule. Further on we will discuss the RDFs obtained with Torii's model 2 potential. The characteristic values of RDFs obtained are given in Table 4. The number of neighbours belonging to the first coordination shell can only be determined with high inaccuracy from these RDFs due to the fact that the corresponding minima cannot be localized accurately. This means that the first coordination shell is not very well defined in this liquid. The first peak of gC⋯C(r) is located at 4.63 Å and integrating up to 7.03 Å a coordination number of 13 was obtained. In the case of gC⋯H(r) there is a peak at 5.33 Å and a shoulder around 4.0 Å, the gH⋯H(r) has similar shape with a shoulder about 3 Å and the maximum at 5.13 Å. From RMC simulation results [21] it has been found that supposedly molecules in close H-H con-

tacts may be present in liquid methylene chloride. The origin of the shoulder on C⋯H, H⋯H RDFs could be from the first two neighbour molecules. It can be seen that C⋯Cl, H⋯Cl and Cl⋯Cl RDFs have two peaks. This feature do not refers too any special structural characteristic, but is a simple consequence of the fact that molecular pair contributes with more than one distance values to these functions. The first maximum of gCl⋯Cl(r) and gH⋯Cl(r) was found to be at 3.63 and 3.13 Å, respectively. The Cl⋯Cl and H⋯Cl coordination numbers are 5.91 and 3.68. These parameters indicate that in liquid methylene chloride no hydrogen-bond like interaction appears. 4.2.2. Orientation of the methylene chloride molecules The spatial distribution of the nearest neighbours around a central methylene chloride molecule was investigated. The Table 4 Characteristic values for the radial distribution functions gαβ (r) Bond type

rmax

gαβ (rmax)

rmin

Nαβ (rmin)

C⋯C C⋯Cl C⋯H Cl⋯Cl Cl⋯H H⋯H

4.63 3.93 5.33 3.63 3.13 5.13

1.52 1.48 1.2 1.36 1.13 1.23

7.03 4.73 7.63 4.63 4.13 7.63

13.0 6.87 29.8 5.91 3.68 33.5

nαβ is the running integration number. Atom–atom distances are given in Å.

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Fig. 4. Distance dependent angular distribution function. Θ: angle between the dipole moment vector of centre and neighbouring molecules. Fig. 3. The spatial distribution of the nearest neighbours around a central methylene chloride molecule. a) C⋯C b 4.63 Å; b) C⋯C b 5 Å; c) C⋯C b 7.03 Å.

analysis was performed in a coordinate system fixed to the central molecule. The origin of the coordinate system is defined by the position of the carbon atom. The x axis coincides with the main symmetry axis of the molecule being the x coordinates of the chloride atoms positive and that of hydrogen atoms negative. The Cl–C–Cl plane defines the xy and H–C–H plane defines the xz plane of the coordinate system. Fig. 3 shows the spatial distributions in the following three cases: a) when C⋯C distances are shorter than the first maximum on gC⋯C(r), 4.63 Å; b) when C⋯C distances are shorter than 5 Å; c) when C···C distances are shorter than the first minimum on gC⋯C(r), 7.03 Å. The coordination number up to the first maximum on gC⋯C(r) is 2. Fig. 3a shows that only a very narrow distribution appears around hydrogen atoms consequently the molecules closer than 4.63 Å to the central molecule are preferentially located around the chloride atoms. As the C⋯C distance is growing, at 5 Å coordination number is 4, more molecules appear around hydrogen atoms but at 5 Å the distribution is still narrow (Fig. 3b). In the minimum (Fig. 3c) the spatial distribution is spherical, meaning that the distribution of molecules around central molecule is uniform. The orientations of the neighbouring molecules can be characterised by the angle dependent radial distribution function. Specifically, we have calculated the angle distribution of the angle Θ, defined between the dipole moment vector of centre and neighbouring molecules as a function of C···C distance shown in Fig. 4. The distribution of cos(Θ) of neighbours closer than 4 Å shows a clear broad peak at − 1 corresponding to the antiparallel alignment of the molecules, but this preference decreases rapidly and vanishes within the first coordination shell. Another peak appears at − 0.14 corresponding to the L-shape arrangement (type B in Fig. 1). The distribution of neighbours between 4−6 Å shows slight preference to parallel alignment, and those above 6 Å have again very slight preference to antiparallel alignment.

The Φ angle distribution, angle between the dipole moment of central molecule and the centre-centre vector, as a function of C···C distance is shown in Fig. 5. Below 4 Å the peak at − 0.8 corresponds to angle about 143° is probably given by neighbours below and above the central molecule showing tail-to-tail arrangement. The next peak appears at 0.3; this peak can appear due to molecules in L-shape arrangement. A preference of molecules between 4.5–5.5 Å can be observed in head-to-tail (type D in Fig. 1) arrangement, but this preference vanishes and above 6 Å a slight preference to tail-to-tail arrangement occurs again, corresponding to a uniform distribution of the molecules (P(cos(Φ)) = 0.01). The correlation of the relative orientation of the molecules in the liquid state can be characterised by the coefficients of a spherical harmonic expansion of the orientational radial distribution function. The details of the spherical harmonics expansion as well as the orientational correlations function's calculation using this expansion are given elsewhere [37]. Here

Fig. 5. Distance dependent angular distribution function. Φ: angle between the dipole moment of central molecule and the centre–centre vector.

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S. Bálint et al. / Journal of Molecular Liquids 136 (2007) 257–266 Table 5 Structural parameters from the X-ray diffraction refinement with estimated errors in the last digits. Bond type

ra

σa

na

rb

rc

C–Cl Cl–Cl C⋯Cl Cl⋯Cl

1.75(1) 2.95(1) 4.05(5) 3.80(5)

0.10(1) 0.20(2) 0.30(3) 0.35(2)

2 1 6.0(5) 5.2(5)

1.76 2.95 – –

1.773 2.938 – –

n is the coordination number. Intramolecular distances are compared to the earlier studies. Distances (r) and their mean-square deviations (σ) are given in Å. a Present X-ray diffraction study. b Ref. [25]. c Ref. [8].

with the first minimum at 7 Å it contains 12.8 Å molecules 110 coefficient is proportional to b− cos(Θ)N, in average. The g00 where Θ is the angle between the dipolar axes of the two molecules. This function shows a maximum around 3.75 Å, which is a sign of the preference of the molecular dipoles in an antiparallel alignment. The other term, which is connected to the 220 101 202 angle of the dipole vectors, is the g00 . The g00 and g00 terms 2 are proportional with the bcos(Φ)N and bcos (Φ)N terms, respectively, where Φ is the angle between the dipole vector of a central molecule and the vector connecting the two molecules. 101 g00 has a minimum at 4 Å and turns to positive values above

Fig. 6. Spherical harmonic coefficients of liquid methylene chloride as determined from molecular dynamics simulation.

we summarize the technique, following the notation used by Grey and Gubbins [38]. According to this formalism the total correlation function g(r, ω1, ω2) can be expanded by the following equation: XX gðl1 l2 l : n1 n2 : rÞUl1 l2 l;n1 n2 ðx1 ; x2 Þ gðr; x1 ; x2 Þ ¼ l1 ;l2 ;l n1 ;n2

ð4Þ where Ul1 l2 l;n1 n2 ðx1 x2 Þ are the generalized spherical harmonics functions, g(l1l2l:n1n2:r) functions are the r dependent expansion coefficients, which can be written into the following form: gðl1 l2 l : n1 n2 : rÞ ¼ 4p

ð2l1 þ 1Þð2l2 þ 1Þ ⁎ gcc ðrÞUl1 l2 l;n1 n2 ðx1 x2 Þ ð2l þ 1Þ

ð5Þ where gcc(r) is the centre-centre (in our case the C⋯C) radial ⁎ distribution function and Ul1 l2 l;n1 n2 ðx1 x2 Þare the complex conjugate of the generalized spherical harmonics functions. The spherical harmonic coefficients for the total correlation function were determined in liquid methylene chloride from the present molecular dynamics simulation. Some of these coefficients are summarized in Fig. 6. 000 g00 is proportional to the centre-centre pair correlation function. Defining the boundary of the first coordination shell

Fig. 7. a) Structure functions h(k) multiplied by k for liquid methylene chloride obtained by X-ray diffraction. Circles: experimental values, solid line: calculated from molecular dynamics simulation; b) radial distribution functions for liquid methylene chloride obtained from X-ray diffraction. Circles: experimental values; dashed line: intramolecular contribution; open circles: intermolecular contribution; solid line: intermolecular contribution obtained from molecular dynamics simulation.

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263

contained in angle-averaged RDFs is rather limited, consequently for better understanding of the liquid structure by using computer simulations, it is necessary to analyse the obtained configurations as detailed as possible. 4.3. Structural results from X-ray diffraction

Fig. 8. Contribution of different interactions to the total radial distribution function measured by X-ray diffraction as determined from molecular dynamics simulation.

4.5 Å, which is a sign of the preference of tail-to-tail orientation below 4 Å and head-to-tail orientation above this distance value. On the basis of simulation study it can be concluded that, in liquid methylene chloride only the first nearest neighbours tend to be oriented in an antiparallel, tail-to-tail form. For C⋯C distances longer than 4.0 Å, the antiparallel tail-to-tail orientation is lost very quickly and slight preference of parallel headto-tail and L-shaped orientation can be detected. On the other hand some orientational correlations between rather distant molecules can also be observed. It should be mentioned, that we have obtained this structural information based on the detailed analysis of the molecular dynamics simulations. The previous MD studies did not provide any comprehensive structural information, for they were focused mainly on testing the newly developed model potentials and comparing their predictions with the experimentally accessible vibrational quantities and the overall thermodynamic behaviour of the liquid. The information

At first a semi-quantitative analysis was done at the level of the radial distribution functions; as a second step a least square fitting method was used to determine the intra- and intermolecular structural parameters. The average scattering weighting factors of the different partial distribution functions were: C⋯C: 0.02, C⋯Cl: 0.23, Cl⋯Cl: 0.65. After examination of the weights of the contributions to the structure function one contribution for each type of interatomic distance listed in Table 5 was involved in the fitting procedure. The X-ray structure functions, derived from experiment are shown in Fig. 7a, and the radial distribution functions are shown in Fig. 7b. For the first peak centred around 1.75 Å, intramolecular C– Cl interactions are responsible. A small second peak can be observed at 2.95 Å. This peak can be assigned to Cl⋯Cl distances. Another broad peak appears in the range 3.25–4.50 Å. For this peak mainly intermolecular C⋯C, C⋯Cl and Cl⋯Cl is responsible and it is difficult to resolve because of its complexity. The structural parameters obtained from the least-squares fit of the structure functions kh(k) shown in Fig. 7a are given in Table 5. The fitting procedure resulted in 1.75 ± 0.01 Å and 2.95 ± 0.01 Å for the intramolecular C–Cl and the Cl⋯Cl distances, respectively. Once the intramolecular structure was found, various models were tested to determine the intermolecular structure of the liquid. Trial models containing methylene

Fig. 9. Contribution of different interactions to the total radial distribution function measured by neutron diffraction as determined from molecular dynamics simulation.

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have been determined. The Cl⋯Cl and C⋯Cl coordination numbers could have been determined with large uncertainty. A comparison of the intermolecular radial distribution functions obtained by X-ray diffraction and molecular dynamics simulation could help to make suggestions on the structure of liquid methylene chloride. (see Section 5.) 5. Comparison of experiments and simulations The total structure function relevant to the liquid structure (not including the intramolecular contribution) has been calculated from the partial radial distribution functions according to the equation   X X 2  dab xa xb fa fb hab ðk Þ ð6Þ H ðk Þ ¼ M ðk Þ azb where fα is the scattering length or scattering factor of the αtype atom (which depend on k in the case of X-ray diffraction), and xα is the mole fraction of the α atom. hαβ (k) is defined according to the following equation: Z

rmax

hab ðk Þ ¼ 4pq 0

Fig. 10. a) Structure functions and b) radial distribution functions, obtained from the neutron diffraction compared to molecular dynamics simulation results. Circles: experimental values; solid line: intermolecular contribution obtained from molecular dynamics simulation.

chloride dimers in parallel and/or anti-parallel orientations failed completely. Then a decision has been made not to assume any initial intermolecular geometrical picture for the structure at the beginning of the fitting procedure. Cl⋯Cl and C⋯Cl intermolecular interactions were found to be 3.80 ± 0.05 Å and 4.05 ± 0.05 Å respectively. Due to the low contribution to the total scattering picture, intermolecular interactions C⋯C could not

  sinðkrÞ dr r2 gab ðrÞ  1 kr

ð7Þ

The total radial distribution function is defined as the Fourier transform of the structure function. Fig. 8 shows the contributions of each interaction to the total intermolecular radial distribution function, obtained from molecular dynamics simulation. It can be observed that the two interactions, C···C and H⋯Cl contribute in nearly the same, very low ratio to the total intermolecular radial distribution function. The contribution of C⋯Cl is higher, and that of Cl⋯Cl is the highest. That's the reason why only these last two distances could have been determined and for the noteworthy uncertainty of the X-ray diffraction method in determination of intermolecular structure of liquid methylene chloride. The only suggestion could be the comparison between the X-ray diffraction and the theoretical radial distribution functions. Jung et al. [25] measured liquid methylene chloride with different isotopic mixtures by neutron diffraction. The samples are referred as CH2Cl2 (containing 100% light hydrogen), CZ2Cl2 (containing 64% light hydrogen and 36% deuterium, resulting in a zero average coherent scattering length of the hydrogen atoms), CM2Cl2 (containing 50% light hydrogen and 50% deuterium), CD2Cl2 (containing fully deuterated methylene chloride). Fig. 9 shows the contributions of each interaction to the total intermolecular radial distribution function, obtained from molecular dynamics simulation, for the case of neutron data. It can be observed that the situation is even worse than in the case of X-ray diffraction. In the case of deuterated sample all the interactions considered, except H⋯Cl (30%) and C⋯C (2%), contribute with 10-20% to the total intermolecular radial distribution function and there is not a real chance to resolve them. For sample CZ2Cl2 the distribution of scattering weight is similar to that of X-ray diffraction. When the content of hydrogen is growing, the

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scattering weight of Cl⋯Cl and C⋯Cl interactions is higher, but here appears the negative scattering weight of the hydrogen containing interactions, which is difficult to handle. The radial distribution functions obtained from present X-ray diffraction and neutron experiments performed by Jung et al. [25] are compared with those obtained from simulation in Figs. 7 and 10, respectively. The agreement between the radial distribution function obtained by X-ray diffraction and the theoretical radial distribution function is very good, meaning that the average picture of the structure liquid methylene chloride obtained by molecular dynamics simulation is confirmed by X-ray diffraction. We could perform the comparison of the total radial distribution functions resulted from neutron diffraction experiment for CD2Cl2 and CM2Cl2 isotopic mixtures and the simulation. After scanning and checking the experimental data for CH2Cl2 and CZ2Cl2 we have found a significant error in the structure function, which possibly originates from the inadequate correction of incoherent scattering of hydrogenated liquids. We could not remove this large error consequently we were not able to do the comparison of structure functions of these systems. The neutron diffraction measurements of Jung et al. [25] were already compared to molecular dynamics simulation results by Kneller et al. [14]. One can find significant difference between original data published by Jung et al. [25] and those presented by Kneller et al. [14]. A new set of neutron diffraction measurement could help to resolve this contradiction. Concerning the comparison of neutron diffraction experiments for CD2Cl2 and CM2Cl2 isotopic mixtures and our simulation results a slight shift between them can be observed, but the overall agreement is satisfactory. 6. Conclusions A combined theoretical and experimental study of liquid methylene chloride was carried out. The results of molecular dynamics simulations and diffraction experiments were compared in order to obtain a more reliable picture of the structure of the liquid. Besides the limitations of the applied methods are discussed. The diffraction methods are known for the solution chemists as “direct methods for structural determination”. This would mean that the parameters obtainable from radial distributions are characteristic of local structures in the liquid directly and no further speculation is needed for extracting them from the experimental data. However, the methylene chloride is a very good example when one can see that the local structure of the liquid cannot be determined completely only on the basis of the diffraction data. Four optimised geometries for the dimers of methylene chloride were obtained, in various arrangements. On the basis of quantum chemical calculations it can be seen that the structure determining forces, electrostatic (dipole-dipole and quadrupole–quadrupole) and van der Waals interactions, play similar role in formation of the dimer structure. The essential features of the RDFs in three different molecular dynamics simulations agree with each other meaning that the RDFs are rather insensitive on the charge distribution of

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methylene chloride molecule. Analysing the RDFs it can be observed that the number of neighbours belonging to the first coordination shell can only be determined with high inaccuracy meaning that the first coordination shell is not very well defined in this liquid. The RDFs parameters indicate that in liquid methylene chloride no hydrogen-bond like interaction appears. Neighbouring molecules slightly prefer an antiparallel, tailto-tail orientation over a parallel one. For C⋯C distances longer than 4.0 Å, the antiparallel tail-to-tail orientation is lost very quickly and slight preference of parallel head-to-tail and Lshaped orientation can be detected. On the other hand some orientational correlations between rather distant molecules can also be observed. The total radial distribution functions of MD simulation and X-ray diffraction agree very well. The small discrepancy between the radial distribution function obtained by simulation and neutron diffraction results may be due to both the potential model applied in the simulation and to the experimental uncertainties but the theoretical and experimental findings are in general accordance. It should be emphasized, that we have obtained structural information of liquid methylene chloride only by a combination of diffraction and simulation techniques the eludicidation of the liquid structure, therefore for deeper understanding of the liquid structure it is advisable to apply simultaneous theoretical and experimental methods. Acknowledgement The research was supported by projects NAP VENEUS05 OMFB-00650/2005, the Hungarian Scientific Research Funds (OTKA), project number K 68498 and the Hungarian/Austrian WTZ collaboration project A12/2006. A diffractometer purchase grant from the National Office for Research and Technology (MU-00338/2003) is gratefully acknowledged. References [1] a) J.M. Lehn, Supramolecular Chemistry: Concepts and Perspectives, VCH, New York, 1995; b) S.R. Seidel, P.J. Stang, Acc. Chem. Res. 35 (2002) 972. [2] M.J. Purdue, J.M.D. MacElroy, D.F. O'Shea, M.O. Okuom, F.D. Blum, J. Chem. Phys. 125 (2006) 114902. [3] A. Zouhri, M. Burgard, D. Lakkis, Hydrometallurgy 38 (1995) 299. [4] W.R. Haag, C.C.D. Yao, Environ. Sci. Technol. 26 (1992) 1005. [5] P. Stringer, P. Johnston, Chlorine and the Environment: An Overview of the Chlorine Industry, Kluwer, Dordrecht, 2001 chap. 14. [6] W.G. Rothschild, J. Chem. Phys. 53 (1970) 990. [7] a) P. van Konynenburg, W.A. Steele, J. Chem. Phys. 56 (1972) 4776; b) H. Shimizu, Chem. Phys. Lett. 105 (1984) 268; c) K. Fukushi, T. Fukuda, M. Kimura, J. Raman Spectrosc. 18 (1987) 47. [8] M.D. Harmony, S.N. Mathur, S.J. Merdian, J. Mol. Spect. 75 (1979) 144. [9] R.J. Meyers, W.D. Gwinn, J. Chem. Phys. 20 (1952) 1420. [10] P.N. Brier, A. Perry, Advan, Mol. Rel. Int. Proc. 13 (1978) 1. [11] P. Georgiou, J. Vincent, M. Andersson, A.B. Wöhri, P. Gourdon, J. Poulsen, J. Davidsson, R. Neutze, J. Chem. Phys. 124 (2006) 234507. [12] a) M. Ferrario, M.W. Evans, Chem. Phys. 72 (1982) 141; b) M. Ferrario, M.W. Evans, Chem. Phys. 72 (1982) 147. [13] a) H.J. Böhm, R. Aldrichs, Mol. Phys. 54 (1985) 1261; b) H.J. Böhm, R. Aldrichs, P. Scharf, H. Schiffer, J. Chem. Phys. 81 (1984) 1389.

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