A Molecular Dynamics Study of LiX and CsX - American Chemical

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Influence of a Counterion on the Ion Atmosphere of an Anion: A Molecular Dynamics Study of LiX and CsX (X = F−, Cl−, I−) in Methanol Parveen Kumar,† Anant D. Kulkarni,‡ and S. Yashonath*,†,§ †

Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India Centre for Computational Materials Science, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India § Center for Condensed Matter Theory, Indian Institute of Science, Bangalore 560012, India ‡

ABSTRACT: We report molecular dynamics (MD) simulations to explore the influence of a counterion on the structure and dynamics of cationic and anionic solvation shells for various ions in methanol at 298 K. We show that the variation in ionic size of either the cation or the anion in an ion pair influences the solvation structure of the other ion as well as the diffusivity in an electrolyte solution of methanol. The extent of ionic association between the cation and its counteranion of different ionic sizes has been investigated by analyzing the radial distribution functions (RDFs) and the orientation of methanol molecules in the first solvation shell (FSS) of ions. It is shown that the methanol in the FSS of the anion as well the cation exhibit quite different radial and orientational structures as compared to methanol which lie in the FSS of either the anion or the cation but not both. We find that the coordination number (CN) of F−, Cl−, and I− ions decreases with increasing size of the anion which is contrary to the trend reported for the anions in H2O. The mean residence time (MRT) of methanol molecules in the FSS of ions has been calculated using the stable states picture (SSP) approach. It is seen that the ion−counterion interaction has a considerable influence on the MRT of methanol molecules in the FSS of ions. We also discuss the stability order of the ion−counterion using the potentials of mean force (PMFs) for ion pairs with ions of different sizes. The PMF plots reveal that the Li+−F− pair (small−small) is highly stable and the Li+−I− pair is least stable (small−large) in electrolyte solutions.

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INTRODUCTION The solvation structure of ions and its dynamics in aqueous and nonaqueous solvents are of great interest due to their implications in various electrochemical, chemical, and biological processes.1−4 Although numerous experimental and theoretical studies have been reported on aqueous electrolyte solutions, the influence of specific ions on the solvation dynamics and its effect on the macroscopic properties remain poorly understood.3,5−11 For example, the most widely used classifications of ions as a structure maker or structure breaker are based on the experimental observations of the macroscopic properties like viscosity and entropy.12 Recently, on the basis of various experimental and simulation studies,3,10,13−15 the classification of the ions as a structure breaker/maker has been the subject of intense debate. In order to get the microscopic picture of solvation dynamics, it is important to understand the interplay between solvent−solvent, ion−solvent, and ion−ion interaction and its effect on various properties at the macroscopic level. An understanding of ion solvation and ionic association is crucial for obtaining the variation of conductivity with concentration, pressure, etc., in the relatively less explored nonaqueous electrolyte solutions. The formation of a contact ion pair (CIP)16 or ionic association reduces the conductivity of the individual ion in electrolyte solutions which in turn affects the © XXXX American Chemical Society

efficiency of the electrical energy storage (EES) devices like batteries, supercapacitors, etc. Among nonaqueous solvents, methanol is the simplest organic solvent which contains both hydrophobic and hydrophilic groups and also forms a strong intermolecular hydrogen bond. A variety of experimental techniques1,3,5,7,8 such as X-ray diffraction, neutron scattering, X-ray absorption spectroscopy, and infrared and Raman spectroscopy are available to understand the solvation structure of ions. Insight into the dynamics of solvent around the ions can be obtained from techniques such as femtosecond time-resolved infrared (fs-IR) vibrational spectroscopy, optical Kerr-effect spectroscopy, and dielectric relaxation (DR) spectroscopy. Computational techniques provide often complementary data and have proved to be an efficient tool to get insight about the solvation structure and its dynamics under diverse conditions of temperature, pressure, solvent, electrolyte concentrations, and so forth. The comparative analysis of the results from the Special Issue: Biman Bagchi Festschrift Received: January 16, 2015 Revised: April 12, 2015

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DOI: 10.1021/acs.jpcb.5b00481 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The cross terms of Lennard-Jones parameters (i.e., σij and ϵij) are calculated by using the Lorentz−Berthelot combination rule. All the interaction potential parameters are listed in Table 1.

experimental measurements and computer simulation can be helpful in understanding the processes at the microscopic level and its relation to the macroscopic properties like ionic conductivity, viscosity, entropy, etc.17 Both experimental and theoretical approaches have been used to explore the solvation structure of various monovalent ions such as17−31 Li+, Na+, K+, Rb+, Cs+, F−, Cl−, Br−, I−, and CH3O− and divalent ions32−43 such as Mg2+, Ca2+, Sr2+, Ni2+, and Zn2+ in methanol. Results from the experimental measurements mainly discuss the solvation structure of various ions in methanol and also the possibility of association between the ion and the counterion. Computer simulation studies have been employed to understand the solvation structure of the ion and the coordination number (CN) along with the dynamic properties like diffusivity and residence time calculation. Methods like X-ray and neutron diffraction can provide a precise microscopic picture of the solvation structure only at higher concentrations (greater than 1 M).42 Currently, a comprehensive picture at the microscopic level about the ion− ion, ion−solvent, and solvent−solvent interactions and its influence on the solvation dynamics for various ions in nonaqueous solvents like methanol is lacking. In this paper, we investigate the variation in interionic interaction with different combinations of ion−counterion and its impact on the structure of the solvation shell of ions and its dynamics, using a MD simulation study for alkali halides (i.e., LiX and CsX, where X = F−, Cl−, and I− ion) in methanol at 298 K. We have computed the radial distribution functions (RDFs), coordination number (CN), and orientation of the solvent molecules in the first solvation shell (FSS) of ions for the different ion pairs. We find that the strong interionic interaction leads to sharing of the solvation shell between the cation and its counteranion and also small anions like F− ion show an unusually high CN. We have also calculated the selfdiffusion coeffcient and velocity autocorrelation function (VACF) of ions along with the mean residence time (MRT) of methanol molecules in the FSS of ions. In the presence of weak interionic interaction, we found high diffusivity for ions and also less MRT of methanol molecules in the FSS of ions.

Table 1. Potential Parameters for Methanol−Methanol and Ion−Ion Interaction Employed in the Molecular Dynamics Simulation

i ,j,i≠j

ϵ (kJ/mol)

charge (q)

CH3OH

CH3 O H Li Cs F Cl I

3.861 3.083 0.000 1.5050 3.883 3.1170 4.4010 5.1670

0.7576 0.7309 0.000 0.6904 0.41843 0.75318 0.4184 0.41843

0.2970 −0.728 0.4310 +1 +1 −1 −1 −1

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RESULTS Structural Properties. We have obtained the optimized geometries of the ion−methanol complex and the lowest energy configuration. In order to see what the employed potential predicts, we computed the optimized geometry of the ion−methanol complex with the help of the intermolecular potential that has been used in the present study. We found that they agree well with the geometry from ab initio calculations within a 0.2 Å distance between the ion and the methanol molecule. The agreement is better between the cation and the methanol. On rotation of the methanol molecule away from that indicated by the optimized geometry obtained from ab initio, we found that the energy increases, suggesting that the orientations predicted by the intermolecular potential are exactly identical to the ab initio calculations. This suggests that the potential between the methanol and ions employed here is reasonable for the present study.

qiqj rij

σ (Å)

We have also carried out ab initio calculations on ion− methanol complexes employing Møller−Plesset second order perturbation theory (MP2) considering all electrons (MP2(full)) in conjugation with the aug-cc-pVTZ basis set for all of the systems. Gaussian 09 was used for geometry optimization as well as potential energy calculations with the option “scf=tight”.46 Simulation Details. Simulations were performed in the NVE ensemble using the DLPOLY program with the help of the velocity Verlet algorithm.47 The simulations were carried out on 16 ions surrounded by 848 methanol molecules in a cubic simulation box with a size of 38.810 748 Å. This corresponds to the experimental density of ρ = 0.7863 g cm−3 of methanol at 298 K. The ionic concentration of the solutions at which the simulations have been performed is 0.5 M. Periodic boundary conditions were applied in all three directions. Long-range forces were computed with the help of an Ewald sum.48 A time step of 1 fs was used which gave good conservation of energy. The system was equilibrated for 1 ns during which the velocities were scaled to the desired temperature followed by a 2.5 ns production run during which position coordinates and velocities of ions were stored at an interval of 50 fs. In the calculation of properties, the dipole vector for methanol has been taken to be the bisector of the HOC angle.

METHODS Intermolecular Potentials and Models. MD simulations have been carried out on LiX and CsX (where X = F, Cl, and I) in methanol. We have employed Haughney’s (H1) rigid threesite model for methanol.44 In this model, a united atom representation is used for the methyl group of methanol. Thus, methyl is represented by a single site. Two additional sites are used to represent oxygen and hydrogen of the OH group. All short-range interactions are modeled with the help of the Lennard-Jones potential. There is also a charge at these interaction sites

∑

atom/group

Li+ Cs+ F− Cl− I−

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⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij Φ(ri , rj) = 4ϵij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

solvent/ion

(1)

where ϵij is the well depth, σij is the diameter, and rij is the distance between atomic sites or ions. qi and qj are the charges at sites i and j, respectively. Interactions between the ion and methanol are also represented by a short-range Lennard-Jones and a long-range Coulombic term. Self-interaction parameters for ions have been taken from the work of Lee and Rasaiah.45 B

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oxygen RDFs for (a) LiX and (b) CsX, X = F−, Cl−, I−. It is seen that, for LiX solutions, the first peak in the F−−O RDF appears at ∼2.68 Å with a small shoulder at ∼3.23 Å. The position of the first peak shifts to a larger distance with increasing size of the anion, i.e., ∼3.28 and ∼3.68 Å for the Cl−−O and I−−O RDFs, respectively. This is in good agreement with the MD results of Impey et al.23 for the Cl−−O RDF where the first peak appears at 3.3 Å for LiCl in methanol. Experimental measurements report the first peak at 3.16 Å for the Cl−−O RDF and 3.37 Å for the I−−O RDF.30 The first minima in anion−oxygen RDFs appear at ∼3.8, ∼4.2, and ∼4.5 Å for the F−−O, Cl−−O, and I−−O RDFs, respectively. Also, the height of the first peak decreases with increasing size of the anions, i.e., g(rmax) is ∼7.8 for F−−O, ∼5.3 for Cl−− O, and ∼3.4 for I−−O RDFs. The decreasing height of the peak in anion−oxygen RDFs indicates the reduced affinity of the solvent molecules to the anion. This is expected due to the decrease in the charge density of the ion with increasing size of the anion. The plot of the running coordination number for the anion−oxygen RDFs is also shown in Figure 2a. The change in slope of n(r) near the minimum in the RDF after the FSS indicates clearly that a well-defined solvation shell exists. The CN which is the number of methanol molecules within the FSS shows a decrease with an increase in the size of the anion. In order to understand how the charge density of the cation influences the solvation shell of anions, we have calculated the anion−oxygen RDFs in the presence of a larger size cation, namely, Cs+ ion (see Figure 2b). Note that the positions of the first peak in anion−oxygen RDFs are 2.70 (F−−O), 3.30 (Cl−− O), and 3.70 (I−−O) which are essentially identical to the position of the first peak in the presence of Li+ ion. A welldefined first minimum appears at ∼3.4, ∼3.9, and ∼4.4 Å for the F−−O, Cl−−O, and I−−O RDFs, respectively. These are lower than the positions of the first minima (3.8, 4.2, and 4.5 Å, respectively) observed for the respective anion−oxygen RDFs in the presence of lithium ion. This decrease in the first minima of the anion−solvent RDF suggests stronger anion−methanol interaction with increasing size of the countercation (on going from Li+ to Cs+ ion). Thus, the presence of the lithium ion on the first solvation shell of the anion is to enlarge its diameter. This solvation shell of the anion shrinks in the presence of the other larger cations. We list the differences between the FSS of anions in the presence of lithium and cesium FSS in Table 2. Note also that the CN of anions is always higher in the presence of lithium counterion as compared to cesium

In order to see how well the present potential can reproduce the radial distribution function (RDF) between methanol and methanol in the liquid phase, we show the computed O−O methanol obtained from pure liquid methanol simulation at 300 K (see Figure 1). We also show the RDF obtained from DFT

Figure 1. Comparison of the O−O radial distribution function obtained from MD simulation and O−O RDFs from DFT calculations with different BLYP functionals,49 ab initio MD,50 and neutron diffraction experiments.51 Inset: Comparison of the O−O RDF of pure methanol and methanol in LiF solution.

calculations and ab initio simulations of Seiffert et al.49 as well as also the plots obtained from neutron measurements. It is evident that the RDF from the present calculation compares well with the experimental results and ab initio simulations and the DFT calculations predict a rather strongly structured liquid. We have also shown the RDF for LiF solution which exhibits little perturbation as compared to the pure methanol RDF. To investigate the solvation structure of the anions such as F−, Cl−, and I− in LiX and CsX, X = F−, Cl−, I− dissolved in methanol at 298 K, we have calculated the various radial distribution functions and also the running coordination number calculated using the following expression n(r ) = 4πρ

∫0

r

r′2 g (r′) dr′

(2)

where ρ is the number density, r′ is the separation between the two species, and g(r) is the RDF. Figure 2 shows the anion−

Figure 2. Radial distribution functions (RDFs) and running coordination numbers of F−, Cl−, and I− ion in the presence of (a) Li+ and (b) Cs+ ion as a countercation in methanol at 298 K. C

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The Journal of Physical Chemistry B Table 2. Comparison of the First Solvation Shell of the Anion X− (X = F−, Cl−, and I−) in Solvent Methanol in the Presence of Li+ and Cs+ Counterions Li+ rmax (Å) rmin (Å) CN height of FSS ρFSS (g·cm−3)

Cs+

F−

Cl−

I−

F−

Cl−

I−

2.68 (shld 3.23) 3.8 7.2 7.8 1.79

3.28

3.68

2.70

3.30

3.70

4.2 6.5 5.3 1.30

4.5 4.9 3.4 0.84

3.4 5.7 14.8 2.04

3.9 3.5 3.9 0.91

4.4 3.8 2.5 0.71

Figure 3. Plot showing how the strong interionic attraction leads to sharing of the solvation shell between the cation and anion. (a) F−−O RDF obtained from MD simulation (black solid line), F−−O RDF computed when the methanol is also present in the FSS of the Li+ ion (shared methanol, red dotted line), and F−−O RDF of methanol molecules not present in the FSS of the Li+ ion (unshared methanol, green dashed line). The MD includes both shared and unshared methanol giving rise to both the first peak and a shoulder. (b) Li+−F− RDF and Cs+−F− RDF in methanol at 298 K.

counterion. This arises from the fact that the lithium association with the anion brings with it additional methanol molecules. However, the rmin, the first minima of the FSS of anions in the presence of lithium, are also higher. Thus, does the presence of lithium lead to a higher density or lower density of the FSS of anions? To answer this question, we have computed the density of the FSS of various anions in the presence of both countercations. These are listed in Table 2. We see that the density of the FSS of fluoride ion is slightly lower in the presence of lithium as compared to when cesium is present as a countercation. However, in the case of the FSS of chloride as well as iodide, we see that the densities are higher in the presence of lithium as compared to when cesium is present. Let us now see how the densities of the FSS compare with those of the normal liquid density of methanol (ρm) at 298 K. Note that the density of the FSS of fluoride is about twice the normal liquid density, whereas the FSS of chloride has a density which is about 1.5 times higher than the ρm. However, the FSS of iodide has a density which is comparable to the normal liquid density of methanol at 298 K. The shoulder in the F−−O RDF disappears in the presence of Cs+ ion, and the peak height increases from 7.8 to 14.8 with increasing size of the cation. In contrast, the peak height decreases from 5.3 to 3.9 for the Cl−−O RDF and 3.4 to 2.5 for the I−−O RDF in the presence of Cs+ as compared to Li+ ion. This is because of the presence of the shoulder to the first peak in the case of LiF solution. The first coordination number for all three anions is lower in the presence of Cs+ ion as compared to LiX solutions. We attribute this to the strong ionic association between the Li+ ion and the anions studied here. Such a strong association leads to the presence of additional methanol around the anion. We have seen that only the F−−O RDF exhibits a shoulder to the first peak while all other RDFs exhibit a clearly defined single peak. In order to understand the origin of the shoulder, we have made the following analysis. We computed the anion− oxygen (of methanol) RDF for two distinct cases. First, the anion−oxygen RDF was computed by including only those methanol present in the FSS of the cation (Li+). This almost exclusively gives only the shoulder in the RDF. Another RDF was computed by including only those methanol not present in the FSS of the cation. This gives only the first peak in the RDF. The two additional RDFs are shown in Figure 3a along with the full MD computed RDF. These results show that the shoulder in the anion−oxygen RDF arises from methanol that also participates in the first solvation shell of Li+ ion. The first peak arises from almost exclusively those methanol which are not part of the FSS of Li+ ion. The MD includes both of these methanol molecules. The reason why the RDFs between the other anions and oxygen of methanol do not exhibit a shoulder

is also clear from the present analysis: it is because there are few methanol molecules which share the FSS of both the cation and the anion. This is a consequence of the fact that ionic association in all other solutions except LiF is relatively weak. The observed shoulder in the first peak of the F−−O RDF is due to the strong interionic attraction between Li+ and F− ion that results in the penetration of F− into the solvation shell of Li+ ion and vice versa. This is evident from the snapshots that are shown in Figure 10 of some of the ions as well as the RDF between the cation and the anion (see Figure 3b). We see that the LiF solution in methanol forms Bjerrum ion pairs. Ion association therefore alters not just the ionic conductivity but also the solvent structure of the anion. In the case of the Li+ and F− ions, it is seen that the ions form a contact-ion pair: there is no solvent between the two ions. The shared methanol molecules are therefore present such that the two ions and the methanol form a triangle, with methanol interacting favorably with both ions. Note that the oxygens of methanol interact favorably with the cations while the hydrogens interact favorably with the anions. In the presence of a larger cation, i.e., Cs+, the loss of a shoulder in the first peak of the F−−O RDF clearly indicates the domination of ion−solvent interaction over the interionic attraction, which is consistent with the increased height of the peak in the F−−O RDF in the presence of Cs+ as compared to Li+ ion. The peak height for the Cl−−O and I−−O RDFs, in contrast, decreases as compared to the corresponding RDFs in the presence of Li+ ion. This indicates a weak ion−solvent interaction for larger anions like Cl− and I− ion in the presence of Cs+ as the countercation. The running coordination number plot for anions in the presence of Cs+ ion shows a well-defined plateau region as compared to Li+ ion. Although the trend in the running coordination plots for anion−oxygen RDFs is similar, they appear at a low CN region in the presence of Cs+ as compared to the presence of Li+ ion. Solvation of the Cation: Influence of the Anion Radius. In Figure 4a, we have plotted the Li−−O RDFs in the presence of F−, Cl−, and I− ion as a counteranion. All three Li+−O RDFs exhibit a first peak at the same position, but the peak height increases with increasing size of the anions. This suggests better ordering of solvent molecules around Li+ ion in the presence of an anion with low charge density (i.e., I− ion) as compared to an anion with high charge density (i.e., F− ion). The first D

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the CN of anions also decreases from 5.7 for F− to 3.5 for Cl−, but I− ion shows a CN close to that of Cl− (i.e., 3.8). In contrast to this, in aqueous electrolyte solutions, the CN of monovalent anions in water increases with the increasing size of the ions, i.e., 6.6, 7.6, 7.7, and 7.9 for F−, Cl−, Br−, and I− ions, respectively.52,53 As we know, the dielectric strength of methanol (ϵ = 32.6)54 is lower than that of H2O (ϵ = 78.5).55 This results in weak shielding of ions in the solvation shell. This anomalous trend in the CN for the anions in methanol may be due to weak solvation of bigger anions as compared to smaller anions with high charge density. With increasing size of either the cation or anion in the ion pair, the strength of interionic interaction decreases, leading to a decrease in the probability of ionic association. The CN of Li+ ion in methanol increases from 2.7 to 4.4 with increasing size of the counteranions, i.e., F− to I− ion. The above observation that the CN of the anion decreases whereas that of the cation increases with increasing size of the anion suggests that the strength of interionic interaction may have some influence on the solvation structure of the cation as well as the anion. As expected, in the presence of Cl− as a counteranion, the CN of the cation increases with increasing size of the cation (i.e., 3.7 for Li+ and 4.9 for Cs+ ion). The CN of monovalent cations in water also increases with increasing size of the ion, i.e., 4.8, 6.2, 7.0, 7.2, and 7.9 for Li+, Na+, K+, Rb+, and Cs+, respectively.52,53,56−58 Our observations of the trend in the CN with increasing size of the ions are in agreement with the studies of the Chowdhuri and Chandra.19 They also observed a decrease in the CN with increasing size of the anion, i.e., 5.87, 5.38, 5.40, and 4.40 for F−, Cl−, Br−, and I−, respectively.19 Similarly, the CN of the cation increases with an increase in the size of the cation, i.e., 4.02, 5.66, 6.09, 6.24, and 6.82 for Li+, Na+, K+, Rb+, and Cs+, respectively. Although the trend is the same but the values of CN are different from the Chowdhuri and Chandra,19 this may be due to the presence of a different counterion for the cation or anion. The CN of methanol is ∼2.2 in lithium halide solutions; this is in agreement with the CN reported in the literature for methanol, i.e., 1.87−2.2.29,44,59,60 From the above analysis of the solvation structure, it is evident that the counterion exerts an important influence on the solvation structure of the ion. In the methanol, this influence appears to be significant. For example, in the presence of Li+ ion as a countercation, the CN of anions decreases with increasing size of the anions, i.e., 7.2, 6.5, and 4.9 for F−, Cl−, and I−, respectively. In the case of Cs+ ion, the CN of anions also decreases from 5.7 for F− to 3.5 for Cl−, but I− ion shows a CN close to that of Cl− (i.e., 3.8). Our observations of the trend in CN with increasing size of the ions are in agreement with the studies of the Chowdhuri and Chandra.19 They also observed a decrease in CN with increasing size of the anion, i.e., 5.87, 5.38, 5.40, and 4.40 for F−, Cl−, Br−, and I−, respectively.19 In contrast to this, in aqueous electrolyte solutions, the CN of monovalent anions in water increases with the increasing size of the ions, i.e., 6.6, 7.6, 7.7, and 7.9 for F−, Cl−, Br−, and I− ions, respectively.52,53 This might be due to the lower dielectric constant of methanol (ϵ = 32.6)54 which is lower than that of H2O (ϵ = 78.5).55 This might explain the opposing trends in the variation in CN with ionic radius of anions and cations in methanol as compared to water. Orientation of the Methanol Molecules in the FSS of Ions. Apart from the radial distribution functions, the solvation structure can also be characterized by the orientational

Figure 4. Radial distribution functions (RDFs) and running coordination numbers of (a) the Li+−O RDF in the presence of different counteranions and (b) the Li+−O and Cs+−O RDFs in the presence of Cl− ion as a counteranion.

minimum in the Li−−O RDF appears at the same position, but the second peak shifts to a higher distance in the presence of Cl− and I− ion. The coordination number of lithium ion (defined as the number of methanol molecules within the FSS of lithium ion) increases with an increase in the anion radius: 2.7 (LiF−methanol), 3.7 (LiCl−methanol), and 4.4 (LiI− methanol). Smaller anions lead to a decrease in the CN of cations. This is in contrast to the finding earlier that smaller cations lead to an increase in the CN of anions. Thus, cations bring more solvent (methanol) molecules to the anion while smaller anions take away solvent molecules from the cations. This also explains why, for lithium fluoride solution, the CN around the cations (2.7) is lower than the CN around the anion (7.2). Thus, the fluoride provides a stronger attraction for the methanol as compared to lithium. Some changes are also seen in the second solvation shell (SSS). The RDF around lithium ion in the presence of fluoride anion exhibits a slightly larger SSS accommodating a greater number of methanol molecules as compared to solutions containing chloride and iodide anions. This is consistent with our finding that the smaller anions basically deplete the methanol molecules of the cation. The effect of increasing the size of the anion therefore leads to an increase in the CN of lithium ion. These findings obtained from MD simulations are consistent with the results from the diffraction30 and mass spectrometric31 experiments. These experimental measurements show that the number of methanol molecules increase around Li+ ion with increasing size of the anion (i.e., Cl−, Br−, and I−). Figure 4b shows the Li+−O and Cs+−O RDFs in the presence of Cl− as a counteranion along with the running coordination number. This figure provides the same information as Figure 2 but with cations replacing the anions and anions replacing the cations. The results are also similar: the peak height, rmax, rmin showing trends similar to that seen for anionic solvation shells. The coordination number, surprisingly, did not change when we went from lithium to cesium. We note that the present results for the lithium RDF are in good agreement with earlier reports. The position of the first peak in the Li+−O RDF falls in the range of the reported simulation results from Impey et al.23 (at 1.90 Å) and Paglia et al.26 (at 2.0 Å). The first peak is reported at 2.06 Å from experimental measurements.30 In the presence of Li+ ion as a countercation, the CN of anions decreases with increasing size of the anions, i.e., 7.2, 6.5, and 4.9 for F−, Cl−, and I−, respectively. In the case of Cs+ ion, E

DOI: 10.1021/acs.jpcb.5b00481 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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shown in Figure 6a, the peak at 56° (i.e., cos θ = 0.56) in the FSS of F− and at 53° (i.e., cos θ = 0.6) in the FSS of Cl− is due

structure of methanol in the FSS. Two angles θ and α suffice to specify the orientation of methanol with respect to the ion. The angle θ is defined as the angle between the ion−oxygen (of methanol) vector and dipole moment vector. The angle α is the angle between the ion−oxygen vector and the OH vector of methanol. Figure 5a shows the probability distribution of

Figure 6. Distribution of the angle θ for the methanol molecules in the FSS of anions F− and Cl− in the presence of Li+ ion. (a) Computed distribution for methanol exclusively in the FSS of anions and not in the FSS of cation (lithium ion) termed nonsharing methanol and (b) sharing methanol (those which lie in the FSS of the anion as well as the lithium countercation). All results at 298 K.

Figure 5. Distribution of the angle θ for methanol in the FSS of F−, Cl−, and I− anions in the presence of (a) Li+ and (b) Cs+ ions at 298 K.

to the nonshared methanol molecules. For the shared methanol molecules, a more pronounced peak appears at 150.5° (i.e., cos θ = −0.87) and 143.1° (i.e., cos θ = −0.8) for the F− and Cl− ions, respectively (see Figure 6b). Also, a small peak at 60° (i.e., cos θ = 0.5) for F− and at 58° (i.e., cos θ = 0.53) for Cl− ion arises due to the strong orientation of a few shared methanol molecules toward anion as compared to cation, but this contribution is significantly smaller. Thus, it can be seen that the presence of the lithium ion leads to considerable disruption in the solvation shell of the anions, especially when the anion is small like in F−. In Figure 7a, we have plotted the distribution of cos (θ) for methanol molecules in the FSS of Li+ ion in the presence of F−,

cos(θ) for the methanol molecules in the FSS of F−, Cl−, and I− ions but in the presence of Li+ as the countercation. For F− ion, the probability distribution of cos(θ) shows a pronounced peak at 0.56 (i.e., 56°) and another small peak at −0.87 (i.e., 150°), indicating the existence of two different types of orientation for methanol molecules in the FSS of ion. The distribution of cos(θ) for Cl− also exhibits two peaks, but the peak height at 0.59 (i.e., 54°) is higher in intensity while the peak at −0.8 (i.e., 143°) is lower in intensity as compared to F−. In the case of I−, a single peak appears at 0.61 (i.e., 52°) and this is more intense. The distribution near cos(θ) = 0.5 or around 55° can be rationalized: the OH vector points toward the anion, and the dipole vector essentially bisects the tetrahedral HÔ Me angle. Thus, the angle θ which is the angle between the OH vector and the dipole vector should be half of the tetrahedral angle. The increasing peak height for the range 0.56−0.61 (cos θ) and disappearance of the peak at ∼ −0.87 need to be understood as also the origin of the distribution close to ∼ −0.87 needs to be understood. We have also obtained the distribution of the angle cos(θ) for the anions in the presence of Cs+ as a countercation (see Figure 5b). We find a single peak for the probability distribution of cos(θ) for the F−, Cl−, and I− ions. A peak appears at 0.55 (i.e., 56.6°) for F− and Cl−, whereas for I− ion it appears at 0.59 (i.e., 53.8°). To confirm the origin of the peak at −0.87 in the distribution of cos θ for halide ions in the presence of Li+ as a countercation, we have calculated the angle (θ) for the methanol molecules within the first solvation shell of the cation as well as anion (i.e., shared methanol molecules) and also for methanol molecules present only in the FSS of anions (i.e., nonshared methanol molecules). The distribution of cos θ for halide ions for the shared methanol was computed by ensuring that these methanol molecules are within the first minimum of the cation−methanol and anion−methanol radial distribution functions (RDFs). For the nonshared methanol, we ensured that these methanol molecules were outside the first minimum of the cation−methanol RDF but were within the first minimum of the RDF of the anion−methanol RDF. The resulting distribution functions are shown in Figure 5. As

Figure 7. Distribution of the angle θ for the methanol molecules in the FSS of (a) Li+ and (b) Cs+ ions in the presence of counteranions F−, Cl−, and I−.

Cl−, and I− counteranions. The distribution function of the angle shows a peak at cos(θ) = −1 (i.e., θ = 180°), which suggests that the methanol molecule is oriented with oxygen pointing toward the lithium ion. That is, the dipole is pointing toward the lithium ion which has been often referred to as antidipole orientation. In the literature, the antidipole orientations of the methanol molecules are reported for the Na+ ion,61 Ca2+ ion,62 Zn2+ ion,36 and Sr2+ ion.35 Note that the height of the distribution increases with an increase in the anion radius. Thus, for larger anions, the methanol molecules around Li+ ion are more ordered with the dipole better aligned toward F

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Figure 8. Distribution of the angle α for methanol molecules in the FSS of the F−, Cl−, and I− in the presence of (a) Li+ and (b) Cs+ ions at 298 K. Schematic to show two different possibilites (c and d) of the angle α for methanol in the FSS of anions.

Figure 9a shows the probability distribution of cos(α) for Li+ ion in the presence of F−, Cl−, and I− as a counteranion. The

the line joining the lithium ion to the oxygen of methanol. The smaller anions such as fluoride have stronger association with lithium. This leads to a stronger influence of the anion on the solvation structure of lithium ion. In Figure 7b, we show the distribution for methanol in the FSS of cesium ion in the presence of different anions. The increasing peak height with increasing size of the anion suggests the strong antidipole orientation of methanol molecules in the FSS of Cs+ ion in the presence of a counteranion with low charge density (i.e., I− ion). The peak heights of the distribution functions in the presence of Cs+ ion are lower as compared to Li+ ion. This suggests a strong antidipole orientation of methanol molecules in the FSS of Li+ ion as compared to Cs+ ion. Also, the angle distribution for the Cs+ ion in the presence of F− ion exhibits a small shoulder at cos(θ) = ∼ −0.5 (i.e., ∼120°). This indicates that the dipole vector is tilted by about 60° with respect to the line joining the ion to the oxygen of methanol. Deviations from the antidipole orientation of 25° for Ca2+ and 16° for Zn2+ have been reported36,62 in the past. The larger charge density in the case of calcium and zinc might be responsible for their smaller angle as compared to 60° we obtain here. The probability distributions of cos(α) for methanol around the F−, Cl−, and I− in the presence of Li+ (see Figure 8a) and Cs+ (see Figure 8b) are shown. In both cases, the distribution of the angle α exhibits a sharp peak at cos(α) = 1 (i.e., 0°), which is the preferred orientation of the angle α. The second peak at cos(α) = −0.35 (i.e., 110.5°) is due to the methyl group of methanol molecules. It is possible for the methyl group to interact favorably with the anion, although this is a less preferred arrangement. These are evident from the distribution. The more preferred arrangement is the interaction of H of the OH group with the anion. For the anions with the lithium ion as the counterion, the intensity of the maximum near α = 0° is higher for iodide than for chloride which is higher than for fluoride. This is the reverse of what one normally expects. Thus, the probability of linear X···H−O (where X = F−, Cl−, and I−) H-bond formation decreases with increasing size of the anion in the presence of Cs+ counterion, while it increases with increasing size of the anion in the presence of Li+ counterion. This contrasting influence of the countercation on the strength of the anion−HOCH3 interaction arises from the fact that in the case of lithium ion the association between lithium and flouride is too strong which weakens the fluoride−methanol interaction. This is responsible for the less intense peak at α = 0°. In the case of cesium ion, the interaction between it and flouride (or other anions) is not strong enough and hence normal or expected behavior is restored: the solvation shells around smaller anions are better ordered and stronger.

Figure 9. Distribution of the angle α for the methanol molecules in the FSS of (a) Li+ and (b) Cs+ ions in the presence of F−, Cl−, and I− ions for ions in methanol at 298 K.

distribution exhibits a single peak at cos(α) = −0.58 (i.e., 125.5°), which is more pronounced in the presence of Cl− and I− ion. These show that the methanol molecules around the lithium ion are highly orientationally ordered in the FSS. The distribution is again most ordered for the Li+ FSS with iodide as the counterion and least ordered when fluoride is the counterion. For Cs+ ion, the distribution shows a broad single peak at cos(α) ∼ −0.52 (i.e., 121°) in the presence of I− counterion (see Figure 9b). The broad distribution suggests weak orientational ordering of the methanol molecules in the FSS of cesium ion. The distribution develops a shoulder around cos(α) = +0.5 in the presence of chloride and fluoride anions. This suggests a stronger influence of these anions on the solvation shell of cesium as compared to cesium itself. Note that the ionic association is not strong for cesium salts. Even then, the anions are exerting a strong influence on the solvation shell of cesium. The maximum near cos(α) = −0.5 corresponds to the orientation shown in Figure 9a. The additional shoulder at +0.5 or 60° corresponds to the methanol molecules which are in the neighborhood and attempt to reorient methanol so that the OH vector points toward the fluoride or chloride anion. Thus, in solutions of LiF, ionic association plays an important role in influencing the solvent molecules in the FSS of both anions and cations. However, this is not the only factor to influence the solvation shell of the ion; the smaller counterion often determines the orientation of the solvent molecules in the FSS as in the case of CsF. Fluoride exerts a strong influence on the FSS of cesium. Further, remember that the distribution of cos(θ) also showed a shoulder for methanol G

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Figure 10. Snapshots showing the solvation shell around (a) the Li+−F− ion pair, (b) the Cs+−F− ion pair, (c) the Li+−I− ion pair, and (d) the Cs+− I− ion pair. These were specifically selected from MD configurations to illustrate the influence of the counterion on the solvation shell of the ion. Note that the methanol molecules in the FSS of both of the ions, termed shared solvent molecules, are shown with oxygen in blue color; these are in the FSS of both ions. The methanol molecules with oxygen shown in red are those which belong to only the solvation shell of one of the two ions. Note that the orientations of the shared and nonshared methanol are quite different. In the case of CsF solution, the influence of fluoride dominates. In LiF, both exert a strong influence and strong ionic association plays an important role. For solutions in which both the cation and the anion are large like the Cs+−I− ion pair, there are no shared methanol molecules.

in the FSS of cesium with fluoride responsible for the additional shoulder. Thus, it appears that the smaller of the two ions plays a more predominant role in the FSS of not only that ion but also for the FSS of the counterion. Analysis of the RDFs and the angle of orientation of methanol molecules in the FSS of ions suggests that the interionic interaction of ion pairs plays an important role in the solvation structure of ions. When the ionic association is weak, the smaller ion exerts a greater influence on the solvation shell of the ions. To view how the strength of interionic interaction of ions influences the structure of the solvation shell of ions, we have taken MD configurations when the two ions are within the first minimum of the cation−anion RDF. Along with the ions, we also include the methanol molecules which are within the FSS of both ions. In Figure 10a and b, the solvation shells of F− ion in the presence of Li+ (i.e., ion with high charge density) and Cs+ (i.e., ion with low charge density) are shown. Due to the high charge density of Li+ ion, the interionic attraction dominates. The associated ions determine the structure of the solvation shell. The orientation of the methanol molecules in the FSS of Li+ ion provides direct insight into the discussion provided earlier with regard to the solvation structure in the solution of LiF (see Figure 10a). Figure 10c and d shows the solvation shell of I− in the presence of Li+ and Cs+ ion as a countercation. In the case of Li+ ion, the solvation shell of Li+ ion is more structured as compared to that of I− ion. However, in the presence of Cs+ ion, the solvation shell of the cation as well as the anion is less structured. On the basis of the above

observations, we can conclude that the ions with high charge density will exhibit strong domination of interionic attraction over the ion−solvent attraction that results in ion association. However, decreasing charge density of either the cation or the anion will decrease the influence of interionic interaction on the solvation structure of ions. Dynamical Properties. Diffusivity of Ions in Methanol. We now report properties relating to the dynamics of the ions in methanolic electrolyte solutions. A few sample mean squared displacements (MSDs) are shown in Figure 11. In Figure 11a, we show the plot of mean square displacement (MSD) for F−, Cl−, and I− in the presence of Li+ as a countercation. As shown in the figure, the slope for the halide ions increases with

Figure 11. (a) Mean square displacement (MSD) of (a) F−, Cl−, and I− ions in the presence of Li+ as a countercation in methanol at 298 K. (b) MSD of Li+ and Cs+ ions in methanolic solution in the presence of F− as a counteranion. H

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The Journal of Physical Chemistry B Table 3. Self-Diffusion Coefficient (D) and Limiting Ion Conductivity (λ°)63 Ions in Methanol at 298 K ion (counterion) −

+

F (Li ) Cl− (Li+) I− (Li+) Li+ (F−) Li+ (Cl−) Li+ (I−)

109 D (m2 s−1) 0.54 0.82 1.29 0.55 0.65 0.71

109 D (m2 s−1)

ion (counterion) −

+

F (Cs ) Cl− (Cs+) I− (Cs+) Cs+ (F−) Cs+ (Cl−) Cs+ (I−)

0.65 0.70 0.98 0.71 0.65 0.83

ion −

F Cl− I− Li+ Cs+

λ° (S cm2 mol−1) 41.99 52.36 62.74 39.74 60.58

Figure 12. Comparison of the velocity auto correlation function (VACF) plot of (a) Li+ ion in the presence of F−, Cl−, and I− as a counteranion in methanol. VACF plot for (b) F−, (c) Cl−, and (d) I− in the presence of Li+ and Cs+ ion as a countercation.

due to strong association between lithium and fluoride ions which retards both of the ions. This is also responsible for very similar diffusivities of both lithium and fluoride ions in methanol. In lithium salts, the diffusivity of Li+ ion increases with increasing size of the anions presumably due to a decrease in ion association between the ion and counterion. In Figure 12a, we show the velocity autocorrelation function (VACF) plot of Li+ ion in the presence of F−, Cl−, and I− ion as counteranions. It is interesting to note the large amplitude oscillations in the VACF plot of Li+ ion in the presence of I− as a counteranion than F− or Cl− ion. This suggests that the stability of the Li+ ion solvation shell increases with increasing size of the counteranions. Despite an increase in the caging effect, the diffusivity of Li+ ion increases with increasing size of the counteranions. Figure 12b−d shows VACF plots for F−, Cl−, and I− in the presence of Li+ and Cs+ as countercations. It shows slightly larger amplitude oscillations in VACF for anions in the presence of Cs+ as a countercation rather than Li+ as a counterion. Recently, we have shown that the variation in limiting ion conductivity or diffusivity with ionic radius is determined by the void distribution present within the liquid, whereas the viscosity influences the magnitude of the ionic conductivity.17

increasing size of the anions. Figure 11b shows the MSD plot for Li+ and Cs+ ion in the presence of F− as a counteranion. The slope for the Cs+ ion is higher as compared to that for the Li+ ion. Diffusivities have been calculated from the slope of the MSD using Einstein’s equation48 D=

⟨u 2(t )⟩ 2dt

(3)

where ⟨u (t)⟩ is the average mean squared displacement over time t and d is the dimensionality taken to be 3. In Table 3, we have listed the self-diffusion coefficient (D) of F−, Cl−, and I− along with the Li+ and Cs+ in methanol from MD simulation. The limiting ion conductivities λ° of Li+, Cs+, and halide ions in Table 3 are taken from the literature.63 The self-diffusion coefficient (D) of halide ions (i.e., F−, Cl−, and I−) increases with increasing size of the anion. Experimental measurements of λ° as a function of ionic radii for halide ions shows a similar trend as observed here. The reason for such an increase has been widely discussed, and different theories have been proposed.64 We have recently proposed a novel underlying reason for the increase in the diffusivity with ionic radius.65,66 Also, the diffusivity of F− ion is higher in the presence of Cs+ as a countercation as compared to Li+ ion. As we have seen, this is 2

I

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The Journal of Physical Chemistry B We have also computed the velocity autocorrelation function and the power spectra of pure methanol and salt solutions of methanol. In Figure 13, we show the power spectra. For pure

The MRT has been calculated using the expression suggested by Laage and Hynes.67,68 res

1 − ⟨PR (0)PP(t )⟩ = e−t / τSSP

(4)

where PR is the probability of stable reactant at time 0, PP is the probability of stable product at time t, and τres SSP is the MRT. In order to obtain the stable reactant and product configurations, we have also calculated the potential of mean force (PMF) G(r)

G(r ) = −kBT ln g (r )

(5)

where kB is the Boltzmann constant, T is the temperature, and g(r) is the pair distribution function of the required pair (i.e., ion−solvent or solvent−solvent). We have chosen the same criteria as discussed by Laage and Hynes68 for the position of the reactant and product separatix. The reactant product separatrix are positioned at exactly half the height of the potential well. Figure 14a shows the schematic representation of the reactant and product separatix, and the values obtained for all g(r) are given in Table 4. Figure 13. Comparison of power spectra of the oxygen VACF of pure methanol and methanol in LiX solution, where X = F−, Cl−, and I−.

Table 4. Residence Time of Methanol in the FSS of Anions and Cations at 298 K, Calculated Using the Stable State Picture (SSP) Approach68

methanol, there is a maximum around 50 cm−1 suggesting low frequency motion of methanol in the liquid phase. In the salt solutions of methanol, there is a distinct shoulder around 250 cm−1. This shoulder exists for all the lithium containing salt solutions of methanol irrespective of the anion. This suggests that the shoulder at 250 cm−1 appears to be related to the cation. We believe that this shoulder is due to the methanol in the first solvation shell of lithium ion. These methanol molecules are essentially performing somewhat higher frequency oscillations. This is consistent with the results of Tamura et al.37 who found that methanol in the first solvation shell of Mg2+ exhibits a maximum in the power spectra between 200 and 250 cm−1 (see Figure 19 of Tamura et al.37). Residence Time of Methanol in the FSS and beyond the FSS. To get insight into the effect of interionic interactions on the dynamics of the solvent molecules in the vicinity of ions, we have calculated the mean residence time (MRT) of methanol molecules in the FSS of the anion, cation, and other methanol molecules using the stable states picture (SSP) approach.67,68

g(r)/solvent

reactant separatix (Å)

product separatix (Å)

τssp (ps)

Li −O (LiF) Li+−O (LiCl) Li+−O (LiI) F−−O (LiF) F−−O (CsF) O−O (LiF) O−O (LiCl) O−O (LiI)

2.26 2.22 2.22 3.50 3.00 3.07 3.10 3.10

2.95 3.35 3.39 4.39 4.03 4.05 4.06 4.10

19.41 21.63 22.54 18.38 19.87 10.16 10.55 10.37

+

Figure 14b shows the PMF plot for the F−, Cl−, and I− ions with oxygen of the methanol molecules in the presence of Li+ as a countercation. It is clear from the figure that the stability of the contact between anion and methanol molecules decreases with increasing size of the anions. In the presence of Li+ as a countercation, the MRT of methanol molecules in the FSS of anions are 18.38, 13.92, and 11.07 ps for F−, Cl−, and I−, respectively. On the other hand, the PMF plot of Li+−O shows

Figure 14. (a) Plot showing the position of the reactant separatix and product separatix used in the SSP method for the calculation of the residence time of solvent in the vicinity of ions or other solvent molecules. (b) PMF plot for F−, Cl−, and I− in the presence of Li+ ion. (c) PMF plot for Li+ ion in the presence of F−, Cl−, and I− ion as a counteranion. J

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and F− ions results in the ionic association, and the probability of ionic association decreases with increasing size of the counteranion. Also, the MRT of methanol molecules in the FSS of Li+ ion increases with increasing size of the counteranions, suggesting weak Li+−methanol interaction in the presence of a bigger counteranion.

that the stability of methanol in the FSS of Li+ ion increases with increasing size of the counteranions (see Figure 14c). As given in Table 4, the MRT of methanol molecules in the FSS Li+ ion increases with increasing size of the counteranion, suggesting a stable solvation structure for Li+ ion in the presence of a bigger counteranion (i.e., I− ion). Also, the MRT of methanol molecules in the FSS of F− ion is higher in the presence of Cs+ as a countercation than Li+ ion. The MRT of methanol molecules in the FSS of methanol is ∼10.5 ps in all LiX solutions. In order to understand the effect of ionic size or charge density of ions on the interionic separation and stability of the ion pair, we have also calculated the PMFs of lithium halides (LiX). As shown in Figure 15a, the interionic separation

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CONCLUSIONS Lithium fluoride in methanol shows that ions are strongly associated. This leads to properties for this solution which are quite different from the solutions of other salts. It is seen that the radial distribution function, CN, density of methanol in FSS, and orientation of methanol in the FSS all indicate the influence of the counterion on the solvation of the ion. In the RDF, the shoulder at a larger distance is seen to be associated with shared solvent molecules. The counterion influences the solvation structure of the ion in two ways. First, ionic association leads to influence of the counterion on the solvation structure due to proximity of the counterion to the solvation shell of the ion. When strong ionic association is absent, it is seen that the smaller of the two ions generally exerts an influence on the solvation shell of the larger ion. More specifically, we see that the CN of the anions decreases with an increase in the radius of the anion. This is opposite to the trend seen in water, where the CN increases with an increase in the radius of the anion. Both the radial distribution as well as the angular distributions of the methanol in the FSS of the ion are seen to be strongly influenced by the counterion.

Figure 15. PMF plot for (a) LiF, LiCl, and LiI and (b) LiF, CsF, CsI, and LiI in methanol at 298 K.

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between lithium ion and its counteranion increases and also its stability decreases with increasing size of the anion. Collins and co-workers4,69,70 as well as others71,72 have reported that the stability of the ion pair in aqueous electrolyte solutions follows the “law of matching water affinities”. This suggests that the ion pair involving small−small or large−large ions shows stronger associative behavior as compared to those with dissimilar ionic sizes. The ion pair with dissimilar ionic sizes dissociates readily in water due to the domination of ion−water affinity over ion− ion affinity. In Figure 15b, we compare the PMFs of alkali halides consisting of cations and counteranions of different sizes or charge densities. It suggests strong ionic association between the ion pair of small ions with high charge density (i.e., LiF), whereas the ion pair consisting of a small cation and a large anion (i.e., LiI) shows large interionic separation and weak interionic contact. It is interesting to see that the ion pairs consisting of large−large (i.e., CsI) or large−small (i.e., CsF) ions have smaller interionic separation and are more stable contacts as compared to ion pairs with small−large (i.e., LiI) ions. Our results suggest that the stability of the ion pair follows the order small cation−small anion (most stable) > large cation−small anion > large cation−large anion > small cation− large anion (least stable). On the basis of mass spectrometric analysis, Megyes et al.30 have reported that the strong lithium−halide (Li+−X−) interaction leads to weak lithium−methanol (Li+−MeOH) interaction. With increasing size of the halide ion, the Li+−X− interaction decreases whereas the Li+−MeOH interaction increases. They also observed that the solvation of cations (i.e., Li+) is more favorable as compared to halide ions and the solvation of anions becomes weaker with increasing size of the anions. Our results are in agreement with the observations of Megyes et al.30 Analysis of RDFs and orientation of methanol molecules suggests strong interionic interaction between Li+

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank Department of Science and Technology, New Delhi, for the Ramanna Fellowship to S.Y. and financial support under Fast Track scheme to P.K.

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REFERENCES

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DOI: 10.1021/acs.jpcb.5b00481 J. Phys. Chem. B XXXX, XXX, XXX−XXX