Computer Simulation of Methanol Exchange Dynamics around

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Computer Simulation of Methanol Exchange Dynamics Around Cations and Anions Santanu Roy, and Liem Xuan Dang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b04174 • Publication Date (Web): 18 Jun 2015 Downloaded from http://pubs.acs.org on June 22, 2015

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The Journal of Physical Chemistry

Computer Simulation of Methanol Exchange Dynamics around Cations and Anions Santanu Roy and Liem X Dang* Physical Sciences Division Pacific Northwest National Laboratory Richland, Washington 99352, United States *Phone: 509-375-2557; email:[email protected]

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ABSTRACT In this paper, we present the first computer simulation of methanol exchange dynamics between the first and second solvation shells around different cations and anions. After water, methanol is the most frequently used solvent for ions. Methanol has different structural and dynamical properties than water, so its ion solvation process is different. To this end, we performed molecular dynamics simulations using polarizable potential models to describe methanol-methanol and ion-methanol interactions.

In particular, we computed methanol

exchange rates by employing the transition state theory, the Impey-Madden-McDonald method, the reactive flux approach, and the Grote-Hynes theory. We observed that methanol exchange occurs at a nanosecond time scale for Na+ and at a picosecond time scale for Cs+, Cl-, and I-. We also observed a trend in which, for like charges, the exchange rate is slower for smaller ions because they are more strongly bound to methanol.

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I. INTRODUCTION Methanol is a non-aqueous solvent used extensively in laboratories to study many chemical processes such as ion solvation.

A methanol molecule (MeOH) is the simplest

amphiphile with the hydrophobic part Me and the hydrophilic part OH. In the liquid phase, these molecules bind to each other through hydrogen-bonding and form linear chains that seldom bifurcate.1-3

This is different from liquid water in which tetrahedral hydrogen-bonded

geometries are found.4 The hydrogen-bonding lifetime for liquid methanol is longer than that of liquid water.5-6 Furthermore, the methanol dielectric constant is slightly less than half of the water dielectric constant.7 These dissimilarities between water and methanol as solvents clearly convey that ion solvation in liquid methanol driven by electrostatics and hydrogen bonding is expected to be different than in liquid water.

In efforts to understand the structural and

dynamical properties of methanol1, 3, 8-12 and their effects on ion solvation,13-17 a large number of experiments and molecular dynamics (MD) simulations have been carried out.

However,

solvation dynamics of methanol around ions with different charges and sizes is less clear, and a thorough investigation is needed to gain detailed insight into that area. In this paper, we report on our study of exchange dynamics of methanol between the first and second solvation shells of cations and anions. The choices of oppositely charged ions allow us to examine the charge effects on the nature of solvation structure and dynamics. The ions considered here are Na+, Cs+, Cl-, and I-, which are in ascending order of ionic radius. Therefore, we are able to reveal how the solvation structure and dynamics depend on the size of the ions. The solvent exchange process can simply be represented by the following equation: ( ) + = ( ) + .


(1)


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Here, X is the Na+, Cs+, Cl-, or I- ion, and methanol molecules in the first and second solvation shells are denoted by and , respectively. The number of methanol molecules that bind to an ion in the first solvation shell (i.e., the coordination number of an ion) is denoted by n. Our goal is to determine the structure of the reactants and products of Eq. 1 and the time scale of the transition from the reactant state to the product state. It is challenging to determine solvent exchange time scales using experimental techniques because the reactants and the products are identical.18-22 To this end, we use MD simulations that allow us to distinguish between structures of molecules at the atomic level and track their interconversion over time. Our model accounts for explicit polarization effects on ion-solvent and solvent-solvent interactions, thereby providing a more accurate description than ordinary MD simulations based on force fields.

The theories and methods that we combine with MD

simulations to determine solvent exchange rates are the transition state theory (TST),23-25 the Grote-Hynes (GH) method,25-28 the reactive flux (RF) method,23, 26, 29 and the Impey-MaddenMcDonald (IMM) method.30-31 Previously, our group successfully applied these methods to investigate water exchange mechanisms and rates around ions.32 The remainder of the paper is organized as follows. In Section II, we describe the rate theories and the protocols for applying these theories to MD trajectories of the methanol-ion systems. Results and their interpretation are presented in Section III. Finally, we conclude and discuss possible future direction of this research in Section IV. II. METHODS AND SIMULATIONS A. Potential of mean force To calculate methanol exchange rate around an ion, we first need to determine a potential of mean force (PMF) between the ion and a selected methanol as a function of a reaction


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coordinate. We choose the center of mass separation (COM) between the ion and the methanol molecule as the reaction coordinate. This choice of reaction coordinate is simple, but it provides a good description of solvent exchange rates and mechanisms around ions.32 The PMF () can be expressed as follows:23-25

() = − ( ) .

(2)

Here, is the reaction coordinate, and is the mean force between the ion and the methanol molecule. The terms ion and MeOH are, respectively, the forces exerted on the ion and the methanol molecule by the solvent (other methanol molecules). The mean force () can be computed using the following equation:

() = < ̂ . (ion − MeOH ) >

(3)

where, ̂ is the unit vector pointing to the methanol molecule from the ion. B. Solvent exchange rates Employing TST, the methanol exchange rate (ktst) around an ion at a particular temperature (T) can be calculated using PMF, as given by the following equation:23-25

$tst =

) ( ) )* + ,-.(/ )

% &'( /) * + ,-.(/)

.

(4)

/

where r† is the position of the barrier top of the PMF and r0 is equal to 0. The terms kB, β, and µ are the Boltzmann constant, inverse of thermal energy (1/kBT), and the ion-methanol reduced mass, respectively. According to the TST assumption, during the time evolution of the reaction coordinate once the methanol-ion system reaches the barrier top from the reactant state, it immediately goes to the product state. There is no accounting for barrier recrossing induced by solvent fluctuations; therefore, the estimated ktst is greater than the actual rate. The GH and RF



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methods are used to account for barrier recrossing by determining the transmission coefficient ҡ. The actual rate then turns out to be k = 1ktst. According to the GH method,25-28 the static potential at the barrier top can be modeled with an inverted parabola; the corresponding force can be expressed as 2 = µ32 r, where 32 is the barrier frequency. Then, the dynamics along the reaction coordinate r at the barrier top can be described with a generalized Langevin equation (Eq. 5). 4

5

(6) = 2 (6) − 8 6 7(6 ) 9(6 − 6 ) + : (6).

(5)

Here, v(t) is the velocity of the ion-methanol reduced mass 4 that experiences fluctuating forces : (6) from the solvent. The term ξ(t) denotes the friction, which is a time correlation function of force fluctuations as given by Eq. 6:

7(6) = (;

B
)( † (6)−< † (6) >) >.

(6)

Now, by adapting an iterative approach, the transmission coefficient using the GH method 1GH can be determined as follows: B

1GH = (1GH + @ 8 6 7(6) @ACGH ) .

(7)

A

The transmission coefficient using the RF method23, 26, 29 is obtained from the plateau value of the time-dependent transmission coefficient (1RF (6)):

1RF (6) =

D(5.̂ )E(5.̂ )FG ) HIEG( ),) HEJ( )K) LMN D(5.̂ )E(5.̂ )F( ) )N

.

(8)

To determine 1RF (6), the ion-methanol system has to start at the transition state indicated by O( − : ), followed by a time evolution in either the forward or backward direction (r(t) or r(−t)). The term 9. ̂ represents the initial ion-methanol velocity and P(9. ̂ ) is the Heaviside


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function to account for only positive velocities. The term ±: = : ± ∂r, where ∂r is a positive infinitesimal quantity introduced to make sure that 1RF (6) starts at 1. C. The IMM method The IMM method allows the residence time of a solvent molecule in the first solvation shell of an ion to be calculated.30-31 It is determined from the normalized time-correlation function of for the population of methanol molecules in the first solvation shell of an ion, as given in Eq. 9. T(6) = < UV (6W , 6Y, 6 ∗ ) >/< UV (6W , 6W, 6 ∗ ) >V, \

(9)

The value of nα is assigned to 1 if a methanol molecule is found in the first solvation shell at both the initial (ti) time and the final (tf) time, and it does not leave the shell for a continuous period of time longer than t* = 2 ps. To ignore the transient escapes from the first solvation shell, t* is used. The function < ⋯ >V, \ in Eq. 9 indicates averaging over methanol molecules (^) and initial times (6W ). P(t) is approximated as the exponential function exp(−t/τp) such that the residence time _p can be determined as follows: B

B

_p = 8 T(6) 6 = 8 exp (−6/_p ) 6.

(10)

D. MD simulation To determine the methanol exchange rates using the methods described above, we performed MD simulations of the Na+-methanol, Cs+-methanol, Cl--methanol, and I--methanol systems using a modified version of AMBER9. The polarizable force field parameters for these systems used in the simulations have been published previously, and the parameters are summarized in Table 1.9,

33-34

Each system is composed of a cubic box of 499 methanol

molecules and one of these ions. The time step used in the MD simulations was 2 fs, and the



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long range electrostatic interactions were treated with the Ewald summation technique.35 The internal molecular geometry was kept constrained using the SHAKE algorithm.36 All systems were equilibrated in NPT ensemble at room temperature and at a pressure of 1 atmosphere. The equilibrated average cubic box length was the same (32 Å) for all the systems. In the PMF calculations for all the ion-methanol systems, we performed a series of constrained MD simulations (each for 5 ns) in the NVT ensemble at 300 K using the equilibrated cubic boxes as the starting configurations.

In each simulation, a different, but fixed, ion-

methanol COM separation was maintained and other degrees of freedom were sampled. Then, using Eq. 3 and Eq. 2, we calculated the mean force and the corresponding potential. For the GH method, 10-ns MD simulations of all the ion-methanol system in the NVT ensemble at 300 K were carried out, constraining the systems at the transition state and saving the force F†(t) every 2 fs. Then the friction 7(6) (Eq. 6) and the transmission coefficient 1GH (Eq. 7) were calculated. In this MD simulation, snapshots were saved every 4 ps, providing 2500 conformations at the transition state. We used these conformations for the RF method as follows. MD simulations starting with these conformations were carried out in both the forward and the backward directions over time. The constraint that the systems were in the transition state was released, and the systems were subjected to time evolution for 2 ps in the NVE ensemble, using a time step of 1 fs.

We used five different initial velocities for each

conformation, and the RF results (Eq. 8) were averaged over these five sets of data. This approach helped to minimize statistical errors. For the IMM calculations, 5-ns MD simulation of the Cs+-methanol, Cl--methanol, and I--methanol systems in the NVT ensemble at 300 K were performed. We needed a 10-ns MD trajectory for the Na+-methanol system such that T(6) ~ 0 well before the final time.


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III. RESULTS and DISCUSSION The PMFs obtained for the Na+-methanol, Cs+-methanol, Cl--methanol, and I--methanol systems are shown in Figure 1. In this figure, the top panel shows PMFs for Na+ (black) and Cs+ (red) and the bottom panel shows PMFs for Cl- (green) and I- (blue). There are three distinct features in each PMF, indicating three different states of the systems. The first minimum represents the contact-ion-methanol-pair (CIMP) state, where the ion and the methanol molecule are in direct contact through electrostatic interaction.

Figure 1: Computed PMFs for different ion-methanol systems as a function of the ion-methanol COM separation. Top panel is for Na+ (black) and Cs+ (red), and the bottom panel is for Cl(green) and I- (blue). The second minimum is the solvent-separated-ion-methanol-pair (SSIMP) state, where solvent molecules screen the electrostatic force between the ion and the methanol molecule. The third



feature is the barrier top (r = r†), which represents the transition state. The position and the height of the barrier top are listed in Table 2. From this information, we learned that two ions with similar charges could have different PMF profiles if they have different ionic radii. The ion with the larger ionic radius has the smaller barrier height and has the larger COM separation from the methanol molecule corresponding to the CIMP state. This means that the smaller ion has stronger electrostatic binding to the methanol molecule. In general, barrier height decreases if ionic radius increases. The distributions of methanol molecules in the CIMP and SSIMP states are represented in Figure 2. In this figure, the left column is for the CIMP and the SSIMP is the right column.

SSIMP

Cl --MeOH Cs +-MeOH Na+-MeOH

CIMP

I --MeOH

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Figure 2: Distribution of methanol molecules from MD snapshots around Na+, Cs+, Cl-, and Iions in the CIMP and SSIMP solvation states. The yellow-colored methanol molecules show its presence in both the solvation states. 10 ACS Paragon Plus Environment

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The OH group of methanol molecules point towards the anions and away from the cations in the CIMP state. The average coordination number of Na+, Cs+, Cl-, and I- are 4.0, 6.0, 4.6, and 4.0, respectively. The methanol exchange rate around ions using the TST method (Eq. 4) displays a trend in which the exchange becomes faster as the ionic radius increases (see Table 2 for the exchange time scale τtst = 1/ktst). However, as demonstrated earlier, TST only provide us with a partial understanding of methanol exchange around ions. The exchange rates need to be corrected with transmission coefficients obtained using the GH and RF methods. In the GH method, we obtained the friction ξ(t) to determine the transmission coefficient 1GH . The computed friction ξ(t) for the four ions is showed in Figure 3. In this figure, the top panel shows ξ(t) for Na+ (black) and Cs+ (red) and the bottom panel shows ξ(t) for Cl- (green) and I- (blue). The term ξ(t) has two distinguishable components for all the ion-methanol systems: a sharp initial drop at t ~ 50-60 ps, followed by a slow decay on a picosecond time scale. We found that, in the case of the cation-methanol or the anion-methanol systems, the value of ξ(t) is larger for the smaller ion. Observations are similar for the barrier frequencies:

the values of 32 are 26 and 6 ps-1,

respectively, for the Na+/Cs+-methanol and 19 and 13 ps-1, respectively, for the Cl-/I--methanol systems. The transmission coefficients 1GH are 1.9 × 10-1, 2.8 × 10-2, 8.6 × 10-3, and 8.0 × 10-3, respectively, for Na+-methanol, Cs+-methanol, Cl--methanol, and I--methanol systems. These rather low values indicate that methanol exchanges are very slow around these ions as demonstrated by the exchange time scales _GH = 1/kGH in Table 2. However, these values may not be accurate because of the assumption of the GH method that the barrier top is an inverted parabola. The results of this method are very sensitive to the computed values of the barrier frequency 32 and the friction kernel ξ(t). 11 ACS Paragon Plus Environment


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Figure 3: The time-dependent friction (Eq. 6) used in the GH method for the ion-methanol systems. In this figure, the top panel shows ξ(t) for Na+ (black) and Cs+ (red) and the bottom panel shows ξ(t) for Cl- (green) and I- (blue). The RF method allows the transmission coefficient from MD trajectories to be determined. The term 1RF (6)), as depicted in Figure 4, has two components for all the ionmethanol systems. In this figure, the top panel shows κ(t) for Na+ (black) and Cs+ (red) and the bottom panel shows κ(t) for Cl- (green) and I- (blue).


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Figure 4: Time-dependent transmission coefficient (Eq. 8) obtained from the RF method for the ion-methanol systems. Top panel is for Na+ (black) and Cs+ (red), and the bottom panel is for Cl(green) and I- (blue). The first component rapidly decays at t > 500 fs to the second component, which is a plateau. For both the cation (top panel, Figure 4) and anion (bottom panel, Figure 4) cases, 1RF (6) is systematically larger for the larger ion. We consider the last 500 fs to obtain the average value of the transmission coefficient 1RF (6).

Again, we find the transmission

coefficients 4.2 x 10-2/8.4 x 10-2 and 5.3 x 10-2/6.1 x 10-2 for the Na+/Cs+-methanol and Cl-/I-methanol systems, respectively.

Therefore, their respective methanol exchange time scales 13

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(_RF =1/$RF ) are slow (thousands of picosecond for Na+ and tens of picosecond for other ions, as shown in Table 2), but faster than those found using the GH method. This result implies that the GH method largely underestimates methanol exchange rates for the Na+-methanol system. Nevertheless, according to the RF method, the methanol exchange rate increases as the ionic radius increases in the case of like charges. Note that, as we have found, methanol exchanges around ions are slower in general than water exchanges around ions.32 In Figure 5, we show the values of P(t) obtained using the IMM method. In this figure, the top panel shows P(t) for Na+ (black) and Cs+ (red) and the bottom panel shows P(t) for Cl(green) and I- (blue). The decay of P(t) is much slower for the Na+-methanol system than for the Cs+-methanol system (also compared to other ion-methanol systems).

Between the anion-

methanol systems, the I--methanol system exhibits faster P(t) decay than the Cl--methanol system. This finding essentially means that the residence time _p for a methanol molecule in the first solvation shell of a cation (anion) depends on its size; that is, _p is smaller for the larger ion. This is justified quantitatively by integrating P(t), which provides us with _p = 1.5 ns and _p = 105 ps, respectively, for the Na+-methanol and Cs+-methanol systems and _p = 112 ps and _p = 92 ps, respectively, for the Cl--methanol and I--methanol systems. These values are significantly larger than that of methanol exchange time scales determined using the RF method. This discrepancy can be attributed to the arbitrary choice of the transient escape time t* from the first solvation shell.31 However, based on the current study, there is insufficient evidence to claim that the RF method is more accurate than the IMM method. We are interested in expanding our current study to other systems and hopefully we will be able to compare the accuracy of both methods.


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Figure 5: Normalized time-correlation function (Eq. 9) to determine the residence time of a methanol molecule in the first solvation shell of the cations and anions. Top panel is for Na+ (black) and Cs+ (red) and the bottom panel is for Cl- (green) and I- (blue). IV. CONCLUSION We have demonstrated computer simulation of the exchange dynamics of the solvent methanol around Na+, Cs+ cations and Cl-, I- anions. Barriers that separate the CIMP and SSIMP solvation states in the PMF profile decrease as the ionic radius increase. Therefore, according to the TST method, the methanol exchange rate between the first and second solvation shells increases as the ionic radius increases. However, if we correct the rates with the transmission coefficient obtained using the GH or RF methods, the trend is true for the like charges. 15 ACS Paragon Plus Environment


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However, the exchange rates are underestimated in most cases by the GH methods compared to the exchange rates obtained using the RF method. The residence times of a methanol molecule in the first solvation shell of the ions computed using the IMM method follow the same trend, but they also are significantly different from the RF results. However, based on the current study, there is insufficient evidence to claim that the RF method is more accurate than the IMM method. We are interested in expanding our current method to other systems, and hopefully, we will be able to compare the accuracy of both methods. Our investigation complements other research on water exchange dynamics around ions. In the future, it will be interesting to examine methanol-water mixtures solvating different ions. In these systems, investigating water or methanol exchange dynamics around ions and its dependency on the molar ratio between methanol and water will provide in-depth insight into ion solvation processes.


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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. The calculations were carried out using computer resources provided by the Office of Basic Energy Sciences.



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15. Yamagami, M.; Wakita, H.; Yamaguchi, T. Neutron-Diffraction Study on Chloride-Ion Solvation in Water, Methanol, and N,N-Dimethylformamide. J Chem Phys 1995, 103, 81748178. 16. Varma, S.; Rempe, B. S. Structural Transitions in Ion Coordination Driven by Changes in Competition for Ligand Binding. Journal of Amer. Chem. Soc. 2008, 130, 15405–15419. 17. Cabarcos, O. M.; Weinheimer, C. J.; Martinez, T. J.; Lisy, J. M. The Solvation of Chloride by Methanol - Surface Versus Interior Cluster Ion States. J Chem Phys 1999, 110, 9516-9526. 18. Hrovat, M. I.; Wade, C. G. NMR Pulsed Gradient Diffusion Measurements .2. Residual Gradients and Lineshape Distortions. Journal of Magnetic Resonance 1981, 45, 67-80. 19. Hrovat, M. I.; Wade, C. G. Nmr Pulsed-Gradient Diffusion Measurements .1. Spin-Echo Stability and Gradient Calibration. Journal of Magnetic Resonance 1981, 44, 62-75. 20. Salmon, P. S.; Howells, W. S.; Mills, R. The Dynamics of Water Molecules in Ionic Solution 0.2. Quasi-Elastic Neutron-Scattering and Tracer Diffusion Studies of the Proton and Ion Dynamics in Concentrated Ni2+, Cu2+ and Nd3+ Aqueous-Solutions. Journal of Physics C-Solid State Physics 1987, 20, 5727-5747. 21. Teixeira, J.; Bellissentfunel, M. C.; Chen, S. H.; Dianoux, A. J. Experimental-Determination of the Nature of Diffusive Motions of Water-Molecules at Low-Temperatures. Physical Review A 1985, 31, 1913-1917. 22. Gilligan, T. J.; Atkinson, G. Ultrasonic-Absorption in Aqueous Alkali-Metal SulfateSolutions. J Phys Chem-Us 1980, 84, 208-213. 23. Rey, R.; Guardia, E. Dynamic Aspects of the Na+-Cl- Ion-Pair Association in Water. J Phys Chem-Us 1992, 96, 4712-4718. 24. Guardia, E.; Rey, R.; Padro, J. A. Potential of Mean Force by Constrained MolecularDynamics: A Sodium Chloride Ion-Pair in Water. Chemical Physics 1991, 155, 187-195. 25. Hynes, J. T. Chemical Reaction Dynamics in Solution. Annual Review of Physical Chemistry 1985, 36, 573-597. 26. Ciccotti, G.; Ferrario, M.; Hynes, J. T.; Kapral, R. Dynamics of Ion-Pair Interconversion in a Polar-Solvent. J Chem Phys 1990, 93, 7137-7147. 27. Zichi, D. A.; Hynes, J. T. A Dynamical Theory of Unimolecular Ionic Dissociation Reactions in Polar-Solvents. J Chem Phys 1988, 88, 2513-2525. 28. Grote, R. F.; Hynes, J. T. The Stable States Picture of Chemical-Reactions .2. Rate Constants for Condensed and Gas-Phase Reaction Models. J Chem Phys 1980, 73, 2715-2732.



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Table 1: Optimized potential parameters for methanol, sodium, cesium, chloride, and iodide a used in the MD simulation 3

Atom type

σ (Å)

ε (kcal/mol)

q (e)

O

3.2340

0.1825

−0.4770

α (Å ) 2.02

HO

0.0000

0.0000

0.3361

0.00

CT

3.3854

0.1300

−0.0954

0.00

HT

2.5034

0.0230

0.0787

0.00

+

2.3787

0.1000

1.0000

0.24

+

3.6972

0.1000

1.0000

2.44

-

4.1000

0.1000

−1.0000

3.69

5.2342

0.1000

−1.0000

6.90

Na Cs

Cl -

I a

σ and ε are the Lennard-Jones parameters, q is atomic charge, and α is the polarizability



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Table 2: Barrier positions and heights of the PMFs (Figure 1) for the ion-methanol systems and time scales of methanol exchange around the ions. Systems Naf -MEOH Csf -MEOH Cl -MEOH I -MEOH

Barrier height (kcal/mol) 3.4 1.5 1.4 1.0

: (Å)

_tst (ps)

_GH (ps)

_RF (ps)

_IMM (ps)

3.3 4.3 4.1 4.4

43 4 2 2

225 119 257 209

1017 40 42 28

1500 105 112 92


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TOC

SSIMP

Cl --MeOH Cs +-MeOH Na+-MeOH

CIMP

I --MeOH

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Computer Simulation of Methanol Exchange Dynamics around

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