Structural investigation of lithium iodide in liquid dimethyl sulfoxide: Comparison between experiment and computation

Chemical Physics 321 (2006) 100–110 www.elsevier.com/locate/chemphys

Structural investigation of lithium iodide in liquid dimethyl sulfoxide: Comparison between experiment and computation Tu¨nde Megyes a, Imre Bako´ a,*, Tama´s Radnai a, Tama´s Gro´sz a, Tama´s Kosztola´nyi a, Barbara Mroz b, Michael Probst b a

Institute of Structural Chemistry, Chemical Research Centre of the Hungarian Academy of Sciences, Pusztaszeri u´t 59-67, H-1025 Budapest II, Hungary b Institut fu¨r Ionenphysik, Universita¨t Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria Received 18 May 2005; accepted 9 August 2005 Available online 1 September 2005

Abstract We report a combined experimental (X-ray and neutron diffraction) and theoretical (ab initio calculations and molecular dynamics simulation) study of LiI in dimethyl sulfoxide (DMSO) solution. The total structure function computed from MD agrees well with those obtained from both X-ray and neutron diffraction experiments. Evidence was found for Li–I contact ion pair formation in solution. The overall coordination number of Li+ was found to be four, while the Li–DMSO coordination number is below four; the coordination sphere of the I
ion contains eight species (DMSO and lithium) in average and does not show any special geometrical arrangement. Ab initio calculations for clusters containing Li+ and up to six DMSO molecules have been performed with the B3LYP density functional and various basis sets. The calculations show an increase of the average ion–ligand distance from about ˚ when the number of DMSO molecules in the cluster increases from 1 to 4. The corresponding Li–DMSO interaction 1.71–1.96 A energy decreases accordingly; additional DMSO molecules are accommodated in the second shell, in agreement with the results from diffraction experiments and the simulation. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Solution; X-ray; Neutron diffraction; DFT; DMSO

1. Introduction The structure of solutions containing lithium ion has received unique attention in solution chemistry in recent years, due to its special features in forming solvate shells. Although it carries only one positive charge, its size, ˚ ), is very close characterized by its Pauling radius (0.6 A to that of a number of divalent metal ions such as Mg2+, Ni2+ and Fe2+. Therefore, despite of the similar ion–solvent first neighbour distances between Li cation and its nearest solvent molecules, the structure of the solvates is often rather different from the one in other solva*

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

0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.08.002

tion shells, as a consequence of the difference of the electrostatic interactions between the ion and its neighbours. Another factor that can influence the solvation shell structure is the higher mobility of lithium ion compared to cations of similar size. Further, lithium exhibits different tendencies towards the formation of ion pairs and complexes than transition metal ions. The most often used experimental methods for solution structure studies are X-ray and neutron diffraction. Unfortunately, in the case of lithium, both methods have serious drawbacks – the X-ray scattering power of lithium is too small to localize it easily and inelastic neutron scattering of lithium atoms so high that is causing problems when one intends to separate it from the elastic scattering, which includes the struc-

T. Megyes et al. / Chemical Physics 321 (2006) 100–110

tural information. These drawbacks lead, for example, to the fact that even the one of the simplest questions of structural solution chemistry, the coordination number of water molecules around lithium ions in solution, still awaits a definitive answer. The literature reports numbers between 4 and 6 and there is an ongoing discussion about its coordination geometry. The problem of the concentration dependence of the structure that follows from this ambiguity was exposed by Marcus [1] in his review paper. Nevertheless, X-ray and neutron diffraction methods proved to be useful in general and the main questions for the hydration of lithium ion and halide ions, as for example discussed in [2], can serve as a good basis for studies in non-aqueous solutions as well. Dimethyl sulfoxide (DMSO), (CH3)2SO is a remarkably versatile, theoretically interesting and technologically important compound with relevance in chemistry, biochemistry and environmental science. Besides applications in organic synthesis [3] it serves as an important solvent [4] because it is an aprotic but highly polar polyfunctional molecule with both a hydrophobic and a hydrophilic site. It is widely used as a solvent because it has the highest dipole moment (4.3 D [5]) and highest dielectric constant (48 at 20 °C) of any dipolar aprotic liquid. Moreover, it is the only pyramidal molecule among similar important organic compounds like dimethylformamide (HCON (CH3)2), acetonitrile (N„CCH3) and acetone (O@C (CH3)). A variety of theoretical and experimental studies on liquid DMSO [6–13], DMSO–electrolyte solutions [7,14–16] and solutions of biomolecules in DMSO [17,18] have been undertaken in recent years to study and understand the physical properties of DMSO solutions. Kruus and co-workers [19,20] performed the first calculations on the solvation of alkali halides in DMSO in 1975 with an electrostatic model potential. The solvation energies of a cluster of one ion with 4–6 solvent molecules and of ion pairs with 14 DMSO molecules were calculated. These energies as well as the solvent vaporization energies were in qualitative agreement with experimental data. The first real molecular dynamics simulation of ions in liquid DMSO was reported by Rao and Singh [7]. The main goal of their work was the determination of the differential free energy of solvation between two solutes in DMSO. Their studies showed that strong ion–dipole interactions lead to a well defined coordination sphere of five DMSO molecules around a Na+ ion. The Cl
ion was found to be surrounded by about seven DMSO molecules in a weakly defined coordination shell. Tembe and co-workers [14–16] used the method of constrained molecular dynamics for an investigation of the potential of mean force, the structure of the solvation shell around an Na+–Cl
ion pair and the dynamics

101

of the association of Na+–Cl
, Na+–Na+ and Cl
–Cl
pairs in DMSO. Adya and co-workers [21] report the results of simulations of liquid DMSO and of Na+/Cl
and Ca2+/Cl
ions dissolved in DMSO. Kalugin et al. [22] have done molecular dynamics simulation on different systems containing solvophilic and solvophobic ions in DMSO. They found for lithium ion a highly symmetric and well pronounced first solvation shell with fixed coordination number (6). Lithium halides have been less frequently studied in non-aqueous solutions than in aqueous ones. Solutions of LiI in methanol have been studied by neutron diffraction [23] and the same method was used to explore the solvation of LiBr in acetonitrile [24] and acetone [25]. Lithium halide solvation in methanol was also studied by X-ray diffraction [26]. Solutions of different transition metals in DMSO have also been the subject of experimental interest [27–32] but to our knowledge, rather few studies have focussed on alkali halides– DMSO systems. Bertagnolli and Schultz [33] studied a concentrated a KI–DMSO solution by X-ray and neutron diffraction and they have found evidence of solvent separated ion pairs in solution. They determined that the potassium ion is solvated by four and the iodide ion by six DMSO molecules. Kloss and Fawcett [34] performed ATR-FT-IR study on alkali metal nitrate– DMSO solutions. They found an apparent solvation number of lithium ion of four, lower than the one for the other alkali cations. A dielectric relaxation study was completed by Markarian and Stokhausen [35] on lithium salt solutions in DMSO. According to their findings the number of DMSO molecules per salt unit (z0) depends on the anion. They have obtained the following values for z0: 4.0 for LiCl, 5.4 for LiClO4, 4.7 for LiNO3. Wakabayashi et al. [36] carried out X-ray diffraction and Raman spectroscopic measurements to study the solvation of halide ions in DMSO. They have found that the number of solvating DMSO molecules increases with the ion radius from chloride to iodide; the chloride is solvated by six, the bromide by seven and the iodide by eight DMSO molecules. In this paper, we report the first comparison of experimental (X-ray and neutron diffraction) and computational (ab initio calculations and molecular dynamics simulation) studies on the LiI/DMSO system. This work is a continuation of studies involving DMSO and their solutions [13,37,38].

2. Details of the experiments and calculations 2.1. X-ray scattering measurement and method of structural analysis An 1.337 M solution was prepared from DMSO of high purity (anhydrous, special grade, Aldrich) with a

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T. Megyes et al. / Chemical Physics 321 (2006) 100–110

mass density q = 1.193 g/cm3, a linear X-ray absorption coefficient l = 10.605 cm
1, and an atomic number density q0 = 0.0797 cm
24 and LiI (anhydrous, 99.99%, Aldrich) salt. The X-ray scattering measurement was performed at ambient temperature (24 ± 1 °C), with a H–H goniometer of symmetrical transmis˚ sion geometry using Mo Ka radiation (k = 0.7107 A wavelength) with 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 of the measurement spanned over the range 1.28 6 2H 6 120°, correspond˚
1 6 k 6 15.3 A ˚
1 of the scattering to a range of 0.2 A ing variable k = (4p/k) Æ sin(H). Over 100 000 counts were collected at each of 150 discrete angles selected ˚
1 in several repeated runs in steps of Dk  0.1 A (10 000 counts at each point). The measurement technique and the data treatment were essentially the same as described previously [39]. The measured intensities were corrected for background, polarization, absorption and Compton scattering [40]. The Compton contribution was evaluated by a semi-empirical method in order to account for the monochromator discrimination [41]. The Compton intensities needed for the corrections were calculated with analytical formulae [42,43]. The experimental structure function is defined as P IðkÞ
xa fa2 ðkÞ a hðkÞ ¼ ; ð1Þ MðkÞ

The observed structure functions kh(k) and pair correlation functions g(r) are shown in Fig. 1(a) and (b). As a first step, a visual evaluation and a preliminary semi-quantitative analysis of the curves were performed. Then the observed data were analysed by geometrical model constructions and by fitting the model structure functions to the corresponding experimental ones by a non-linear 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 from the following formulas:

where I(k) is the corrected coherent intensity of the scattered beam normalized to electron units [44]; fa(k) and xa are the scattering amplitude and mole fraction for a particle of type a, respectively; M(k) is P the modification function, M(k) = {[ xafa(k)]2}exp (
0.01k2). The coherent scattering amplitudes of the ions and the DMSO molecule were computed according to analytical formulae suggested by Hajdu [42] and Cromer and Waber [45]. The DMSO molecules were treated in an atomic representation. The necessary parameters were taken from the International Tables for X-ray Crystallography [46]. The experimental pair correlation function was computed from the structure function h(k) by Fourier transformation according to Z kmax 1 khðkÞ sinðkrÞ dk gðrÞ ¼ 1 þ 2 ; ð2Þ 2p rq0 kmin MðkÞ where r is the interatomic distance, kmin and kmax are the lower and upper limits of the experimental data, q0 is the bulk number density of the stoichiometric units. After repeated Fourier transformations when the non-physical peaks present in the g(r) at small r values were removed, the structure function was corrected for residual systematic errors according to [41].

Fig. 1. Structure function h(k) multiplied by k (a) and radial distribution functions (b) for 1.337 M LiI solution in DMSO. Circles (  ) show the intermolecular function which is the difference between the total structure function (radial distribution function) (——) and the intramolecular contribution from solvent molecules (– – –).

T. Megyes et al. / Chemical Physics 321 (2006) 100–110

hcalc ðkÞ ¼ hd ðkÞ
hc ðkÞ; ð2
dab Þxa xb fa fb ; cab ðkÞ ¼ MðkÞ ! X r2ab 2 nab sinðkrab Þ k ; hd ðkÞ ¼ cab ðkÞ exp
krab xb 2 ab X kRab cosðkRab Þ
sinðkRab Þ 4pq0 cab ðkÞ hc ðkÞ ¼ k3 ab ! C2ab 2 k ;  exp
2

ð4Þ ð5Þ ð6Þ

ð7Þ

where the cab are the 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 characterized 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. Consequently, one contribution for each type of interaction was involved in the hd(k) and hc(k) functions (Eqs. (6) and (7)), as shown in Table 1. A visual inspection of the total radial distribution function indicates that most pair distribution functions contribute to it over the whole range and not even its 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 predominant interactions, an extensive construction and fitting of structural models was necessary. Table 1 Structural parameters of the 1.337 M solution of LiI in dimethyl sulfoxide from the X-ray diffraction refinement with estimated errors in the last digits ˚ ˚ Pair r/A r/A n Li  O Li  S I  C I  S I  O Li  I S  S S  O S  C C  O

2.02(2) 3.01(1) 3.73(3) 4.39(3) 5.35(5) 2.79(1) 5.25(5) 4.62(5) 4.22(4) 3.02(1)

n is the coordination number.

0.15(1) 0.20(1) 0.18(1) 0.30(1) 0.32(1) 0.35(1) 0.40 0.30 0.30 0.21(1)

3.3(1) 3.3(1) 14.5(1) 7.2(1) 7.2(1) 0.8 11.5(3) 4.1(4) 2.4(4) 2.1(1)

103

At the beginning the ‘‘rough’’ structure of ionic shells was fixed by using the structural parameters obtained from the preliminary inspection of the radial distribution functions. In a second step the solvent–solvent and ion–ion intermolecular parameters were determined by a least square fitting method. There, the parameters of the discrete part of the structure as defined above were kept constant and those for continuum were adjusted. This refinement extended over a k range of ˚
1. In the next step the coordination 0.2 6 k 6 15.3 A numbers for intermolecular interactions were kept constant and distances and root mean square deviations were adjusted. Finally, most atom–atom coordination numbers for intermolecular interactions were allowed to vary. This process was repeated iteratively several times until a minimal value of the deviation Sres has been reached. Finally, an overall check was performed by allowing all parameters to vary over the entire range of k. 2.2. Neutron diffraction measurements A neutron diffraction experiment on an 1.3 M LiI/ (CD3)2SO solution was carried out on the hot-source diffractometer 7C2 of the Laboratoire Leo´n Brillouin ˚
1. The CEA-SACLAY in a range of 0.3 6 k 6 15.3 A solution was placed in a vanadium container of 6 and 0.1 mm wall thickness. The incident neutron wavelength ˚ . For standard corrections and normalization 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 normalized, by using scattering data on a vanadium sample. A more detailed description of the correction procedure can be found in [47–49]. The conversion of the observed total cross-section dr/dXe to an r-space representation was performed over the full k range with the help of MCGR (
Monte Carlo treatment of the experimental radial distribution function) method [50,51]. This method applies a 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 dr/dXt agrees with the experimentally measured dr/dXe within the limits of error. The agreement is shown in Fig. 2. 2.3. Ab initio calculations All calculations were performed by using the Gaussian 98 and Gaussian 03 program suites [52]. Most calculations used density functional theory and were performed with the three-parameter hybrid functional B3LYP [53] which is very suitable [54] for providing a

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T. Megyes et al. / Chemical Physics 321 (2006) 100–110

a

b

contained 393 dimethyl sulfoxide molecules, 32 Li+ cations and 32 I
anions corresponding to an 1.3 M LiI concentration, similar as in the measurements discussed ˚ correabove. The side length of the cube was 35.10 A sponding to the experimental density. Coulombic interactions were computed by using the Ewald summation technique. The dimethyl sulfoxide molecule was described by a rigid 10 site model. For the DMSO–DMSO, DMSO–Li+ and DMSO–I
interactions a recently developed pair potential function was employed which had been derived from quantum chemical calculations of the Li+/DMSO and I
/DMSO and DMSO/DMSO hypersurface [38]. The starting configuration was constructed from a pure DMSO system by replacing 64 molecules with the ions and a time step of 2 fs was selected. During an equilibration period of 25 000 time steps the Nose´–Hoover thermostat was used to control the temperature (310 K). Then the simulation was performed for 60 000 time steps leading to an elapsed time of 120 ps for the production run. The simulation was performed by using the DLPOLY 2.0 program [56].

3. Results and discussion 3.1. X-ray diffraction study of LiI in dimethyl sulfoxide

Fig. 2. (a) Total cross-section of the 1.3 M LiI solution in dimethyl sulfoxide (open circles: experimental values; solid line: theoretical values). Inset is the total structure function h(k). (b) Radial distribution functions g(r) obtained from the neutron diffraction experiment. See inset for the definition of the curves.

satisfactory description of ion–solvent systems. Additional calculations were performed with the MP2 method which is slower but shows a somewhat more uniform accuracy. Structures of Li+(DMSO)n, clusters with n = 1–4 were fully optimized at B3LYP/6-311+G** level of theory. The interaction energies at the optimized geometries were corrected for the basis set superposition error (BSSE) with the full counterpoise (CP) procedure, resulting in a more reliable estimate of the interaction energy [55]. The magnitude of the BSSE correction at the energy minimum configuration is about 2–3% of the total interaction energy at B3LYP level of theory. 2.4. Molecular dynamics simulations We performed classical molecular dynamics (MD) simulations in the NVT ensemble. The simulation box

A first semiquantitive analysis was done at the level of the radial distribution functions. For the first peak ˚ , intramolecular S@O, C–S and centered around 1.7 A C–H interactions are responsible. A small second peak ˚ . This peak can be observed in the range of 2.1–3.1 A can be assigned to the intramolecular C  C, C  O and S  H interactions arising from the atomic sites within the solvent molecule and to ion–solvent (Li  O, Li  S, Li  C) and ion–ion (Li  I) interactions. The intramolecular interactions arising from the solvent are shown in Fig. 1. The parameters to calculate the intramolecular contribution of DMSO molecule were taken from a previous study of pure liquid DMSO [13]. The subtraction of the intramolecular contributions of the solvent molecule from the total radial distribution function of the solution resulted in a radial distribution function that contains the different intermolecular interactions. On this difference radial distri˚ can be assigned to bution function, the peak at 2 A the Li  O distances and a shoulder can be observed ˚ which can be assigned to ion–solvent atom at 2.8 A pairs, namely Li  C, Li  I and also to C  O solvent–solvent intermolecular interaction in the solvent. ˚ . It is Another broad peak appears in the range 4–6 A difficult to resolve this peak which can mostly be attributed to various DMSO–DMSO intermolecular distances (I  C, I  O, I  S, S  C, S  O and S  S) and a model analysis can reveal the major contributions only tentatively.

T. Megyes et al. / Chemical Physics 321 (2006) 100–110

The structural parameters obtained from the leastsquares fit of the structure functions h(k) shown in Fig. 1(a) are given in Table 1. The fitting procedure resulted in 2.02 ± 0.02 and ˚ for Li  O and Li  S, respectively. 3.01 ± 0.01 A The Li  C distances could not be determined from this procedure because of two reasons: first, due to their low contribution to the structure function, second because they are in the same range as other more significant contributions like I  C, Li  S and Li  I. For anion–solvent interactions the following distances ˚ , I  S: have been obtained: I  C: 3.73 ± 0.03 A ˚ ˚ 4.39 ± 0.01 A and I  O: 5.35 ± 0.02 A. Evidence of ion pair formation in the solution was found at a Li  I distance of 2.79 ± 0.01 and a coordination number of 0.8. In accordance to earlier works lithium ion is solvated with four [38] and iodide ion with eight [36] DMSO molecules but due to the ion pair formation in the 1.337 M solution the number of coordinated solvent molecules was slightly less. The overall coordination number (the sum of Li–O and Li–I coordination numbers) for lithium is 4.1 and the one for iodide (the sum of I–C and Li–I coordination numbers) is 8, in agreement with earlier findings. Intermolecular interactions in the solvent were found ˚ (C  O), 4.22 A ˚ (S  C), 4.62 A ˚ (S  O) and at 3.02 A ˚ 5.25 A (S  S). Comparing the coordination numbers of these solvent–solvent intermolecular interactions in the solution with the pure solvent [13], a slight decrease can be observed, indicating that the structure of the solvent is modified in the solution. For example, the S  S coordination number in the pure solvent was 13.8 ± 0.3 [13] and in solution it was found to be 11.5 ± 0.3. The C  O coordination number decreases from 3 ± 0.1 [13] to 2.1 ± 0.1. This change in the bulk structure is reasonable, because most DMSO molecules are involved in the solvation of lithium and iodide ions. Due to their low contribution to the structure function, other intermolecular interactions, e.g., C  C and O  O, could not be determined. 3.2. Neutron diffraction study of LiI in dimethyl sulfoxide The total cross-section of the solution, the structure function h(k) and the total radial distribution function are presented in Fig. 2. The intramolecular distances were determined using a least squares fit procedure in which the contributions are represented by Gaussians. They have been found to be in agreement with the intramolecular distances from the neutron diffraction study of pure DMSO [13]. The intermolecular distances ob˚ , H  H 1.74 ± 0.05 A ˚ tained are: O  H 2.13 ± 0.01 A ˚ . The Li  O distance is and C  C 2.65 ± 0.02 A ˚ . In Fig. 5(b), we compare the neutron dif2.01 ± 0.02 A fraction results with the results from the molecular dynamics simulation.

105

3.3. Simulation results The ion–solvent radial distribution functions (RDFs) between ion and the most important sites of the DMSO molecule are shown in Fig. 3(a) and (b) for Li+ and I
, respectively. We also evaluated the running coordination numbers, nxy(r), which are defined by Z r r2 gxy ðrÞ dr; ð8Þ nxy ðrÞ ¼ 4pq0 0

where q0 is the number density. The function n(r) gives the average number of molecules x within a sphere of radius r centred on species y. The characteristic values of the RDFs and the running coordination numbers are listed in Table 2. The Li+–O RDF shows a very sharp and well separated first peak. The solvation number for Li+ in this solution was found to be 3.19, which is different for the MD study of Kalugin et al. [22] in dilute solution where simple Lennard-Jones parameters were applied for describing the Li+–DMSO interaction. In our simulation the intermolecular potential was obtained from a multidimensional non-linear least squares procedure for the Li+–DMSO and I
–DMSO dimer interaction energy surface with a more flexible potential function. In our earlier simulation on one Li+ ion and one I
ion solvated in liquid DMSO, using the same potential function, the coordination number of Li+ ion was found to be 4 [38]. The preferred coordination of Li+ to DMSO molecule is via the oxygen site of the molecule. We have not found any indication of a second solvation shell around Li+. The first peak of the I–C radial distribution function ˚ ; it is not as well separated as in is centred about 3.92 A the case of the cation. The broad peak between 5.1 and ˚ indicates a coordination number between 10.6 and 5.4 A 11.6, corresponding to 6–7 DMSO molecules within the first shell of the anion. Ion–ion RDFs derived from the present simulation are shown in Fig. 3(a). The first sharp peak around ˚ in the Li–I RDF clearly indicates contact ion 2.75 A pair formation in the simulated solution. The integration of the first peak (nLi–I) yielded 0.8, indicating extended ion pair formation in solution. In the simulation, this explains the decrease of the coordination number from 4.0 to 3.2, compared to the
infinite dilute solution [38]. Fig. 3(c) shows some of the solvent–solvent RDFs. ˚ (C  O), 4.17 A ˚ The first maxima are at 3.05 A  ˚ ˚ ˚ (S  C), 4.24 A (S  O), 5.23 A (S S) and 2.02 A (O  H). These distances are the same as those found for pure DMSO [13]. Comparing the coordination numbers from this work with our 1.3 M solution, it can be seen that LiI leads to a decrease of the coordination numbers, indicating that the bulk structure in the solution changes slightly, compared to the pure solvent.

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T. Megyes et al. / Chemical Physics 321 (2006) 100–110

Fig. 3. Cation–solvent (a), anion–solvent (b) and solvent–solvent (c) radial distribution functions obtained from the simulation. In figure (a), the ion– ion Li–I radial distribution function is also shown.

Table 2 Characteristic values for the radial distribution functions gab(r) ˚ ˚ Pair rmax/A g(rmax) rmin/A nab(rmin) Li  O Li  S Li  I I  C I  H I  S S  S S  O S  C C  O O  H

1.98 3.08 2.75 3.92 3.07 4.82 5.23 4.24 4.17 3.05 2.02

33.06 5.92 16.3 3.39 1.72 2.35 1.88 1.62 1.75 1.43 1.25

2.60 3.87 3.22 5.07 3.67 6.57 6.77 5.42 4.67 4.90 2.79

3.19 4.20 0.82 14.62 9.07 8.90 11.5 3.90 1.97 2.20 2.23

nab is the running integration number.

4. Ab initio calculations 4.1. Li+–dimethyl sulfoxide clusters Fig. 4(a) shows optimized geometries from calculations with the B3LYP density functional. The Li+ cation interacts with DMSO molecules always through the oxygen atom, the negative end of the DMSO molecular dipole. The Li+ ions were found to form stable solvate shells with up to 4 DMSO molecules. The DMSO mol-

ecules surround the central ion symmetrically to form so-called interior structures. As one would expect, the overall optimized geometry of the complex is linear for n = 2, it is trigonal for n = 3 and tetrahedral for n = 4. The characteristic geometrical parameters of the optimized clusters calculated by are given in Table 3. The cluster containing one DMSO molecule was also studied with MP2/6-311+G** method in order to investigate more extensively the effect of electron correlation on the results. These data are also shown in Table 3 and it can be seen that the total binding energy in Li+– DMSO from the B3LYP calculations is only about 2% smaller than the one obtained from the MP2 method (both energies include the correction for the basis set superposition error). Other authors found similar conclusions on different systems [57–60] and therefore only B3LYP was used for the larger systems since it requires far less computation time. Table 3 shows that the average Li–O distance increases from about 1.71 in Li+– ˚ in Li+(DMSO)4. The incremental DMSO to 1.96 A interaction energies decrease accordingly. Table 4 shows a comparison between the results of geometry optimizations of Li+(DMSO)4 and Li+(DMSO)6. The Li–O distances in the former complex are all around 1.96 (due to the unconstrained geometry optimization they are not exactly equal) while in the hexa-DMSO complex

T. Megyes et al. / Chemical Physics 321 (2006) 100–110

107

Fig. 4. Ball and stick representation of (a) the optimized Li+(DMSO)n, n = 1–4 clusters and (b) of the I
(DMSO) cluster.

Table 3 Calculated interaction energy (kJ/mol) for the investigated Li(DM SO)n clusters, together with the Li–O distance and the intramolecular ˚) S–O and S–C bond distances (A ˚ ˚ ˚ Method and n
DE rLi  O/A rS–O/A rC–S/A basis set B3LYP/ 6-311+G**

MP2/ 6-311+G**

Table 4 Li–DMSO interaction energies (kJ/mol) and optimized Li  O dis˚ ) in Li+(DMSO)4 and Li+(DMSO)6 calculated with three tances (A different methods and basis sets HF/6-31G(d,p)

B3LYP/6-31g(d,p)

B3LYP/CEP-31G

678.49 169.62

691.41 172.81

1.96 1.98 1.93 1.95

1.96 1.95 1.91 1.96

2.01 1.99 2.02 2.01

Li+(DMSO)6
DE 748.09
DE/n 124.68

762.72 127.11

785.08 130.83

1.95 1.98 2.00 2.00 3.41 4.05

2.01 2.01 2.04 2.04 3.81 4.11

+

1 2 3 4

247.67 421.72 533.03 599.33

1.706 1.765 1.869 1.961

1.554 (1.519) 1.542 1.538 1.536

1.816 (1.831) 1.818 1.819 1.820

1

224.75

1.725

1.548 (1.518)

1.791 (1.806)

The numbers in parenthesis give the respective distances of in pure DMSO liquid as obtained from previous X-ray diffraction study [13].

˚ in averfour Li–O distances are slightly longer (1.98 A age) than in Li+(DMSO)4 and two DMSO molecules ˚ clearly belong to the with Li–O distances around 4 A second solvation shell. From the corresponding interaction energies it can also be seen that these two DMSO

Li (DMSO)4
DE 677.32
DE/n 169.33 ˚ rLi–O/A

˚ rLi–O/A

1.95 1.99 2.00 2.00 3.67 4.36

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T. Megyes et al. / Chemical Physics 321 (2006) 100–110

molecules are much weaker (about 42 kJ/mol each) bound. 4.2. I
–DMSO cluster The effect of anion on the geometry of the DMSO molecules has already been presented elsewhere [37,61]. In the present study, we have found, in good agreement with previous studies, that the I
ion binds close to the carbon atom of the methyl group of the DMSO molecule. The interaction energy is about 58.5 kJ/mol at the MP2/aug-cc-pVTZ level of theory for the 1:1 complex. The optimized geometry of this complex is shown in Fig. 4(b).

5. Comparison of experiments and simulation The radial distribution functions obtained from the X-ray and neutron diffraction experiments are compared with those obtained from simulation in Fig. 5(a) and (b), respectively. The total structure factor relevant to the solution structure (not including the intramolecular contribu-

tion) has been calculated from the partial radial distribution functions according to the following equation: X X ð2
dab Þxa xb fa fb hab ðkÞ H ðkÞ ¼ ; ð9Þ MðkÞ aPb 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. ð10Þ hab ðkÞ ¼ 4pq r2 ðgab ðrÞ
1Þ kr 0 The total distinct radial distribution function is defined as the Fourier transform of the structure function. The agreement between the experimental X-ray diffraction and the theoretical radial distribution functions shown is quite good. All the intermolecular distances and coordination numbers for lithium and iodide, resulting from X-ray diffraction agree with those obtained from the MD simulation within the estimated experimental errors. Concerning the comparison of radial distribution functions resulted from neutron diffraction experiment and simulation it can be observed that there appears a ˚ on both curves. Examination of the rapeak around 2 A dial distribution function from neutron diffraction yields an O  H coordination number of 2.2. This is in agreement with the O  H coordination number determined from simulation (2.23). Taking into account the O  H, C  O and S  C coordination numbers and distances from X-ray and neutron diffraction and from the MD simulation, the structure analysis of DMSO solution leads to the conclusion that the closest neighbours of one O of a DMSO molecule are two hydrogen atoms belonging to two other DMSO molecules. This is also in agreement with the MD simulation results.

6. Summary

Fig. 5. Comparison between g(r) from experiment and simulation. Solid line: simulation, circles: experiment.

Experimental (X-ray and neutron diffraction) and theoretical (ab initio calculation and molecular dynamics simulation) studies on LiI solution in DMSO were carried out. The interaction of the Li+ cation with DMSO molecules has been studied by using various high level ab initio methods like B3LYP and MP2 with the 6-311+G** basis set. The two computational methods gave similar results in the case of Li(DMSO)1 cluster. The average ion–ligand distance increases with increasing number of DMSO molecules in the cluster. Evidence of Li–I contact ion pair formation in the solution has been found. The average coordination number for the lithium ion is four and that for the iodide ion

T. Megyes et al. / Chemical Physics 321 (2006) 100–110

is eight. These results are in agreement with previous findings. The structure of the solvent is slightly modified compared to the pure liquid. Based on the O  H, C  O and S  C coordination numbers from X-ray, neutron diffraction and simulation, present structure analysis of DMSO solution leads to the conclusion that the closest neighbours of one O atom of a DMSO molecule are two hydrogen atoms belonging to two other DMSO molecules. The total structure functions from MD simulation and diffraction experiments agree very well, lending credibility to the details of the simulation and the measurements.

Acknowledgements Support from the Hungarian/Austrian WTZ collaboration project A15/2002 is gratefully acknowledged. I.B. thanks for supporting this work with a Bolyai stipend (Hungarian Academy of Science). Support from the EU project HPRN-CT-2000-19 is gratefully acknowledged. The authors want to 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.

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