Ionic liquids are a special class of electrolytes that are characterized by remarkable properties such as low volatility, high thermal stability, wide electrochemical window, and excellent solvation strength. [1,2] Such favorable properties have enabled their usage in diversity of applications ranging from energy storage [3,4], reaction media [5,6], battery electrolytes [7,8,9], electroplating [10,11], solar cells [12,13,14], to gas separation processes. [15,16,17,18] One of the most attractive features of these fluids is that a large number of ionic liquids with desired properties can be envisioned through cation-anion combinations. [19] Another avenue for increasing the number of ionic liquids is through blending two ionic liquids to precisely tune properties required for a particular application. [20,21,22,23] Although conceptually a simple and promising approach, the myriad of ionic liquids makes it virtually impossible to experimentally screen ionic liquids for their properties. To address this, molecular simulations have been carried out as a complementary to experiments in understanding structure-property relationships, estimate properties, and understand molecular level mechanisms responsible for various phenomena over the last two decades.
The predictive capability of classical molecular simulation-based methods critically depends on an accurate description of intramolecular and intermolecular interactions in ionic liquids. Towards this end, a lot of effort has been expended to parametrize various classical non-polarizable force field models for estimating pure component thermophysical properties. Notable examples of all-atom force fields for imidazolium-based ionic liquids include those published by Canongia Lopes and Pádua [24,25,26,27], Acevedo and co-workers [28,29,30], Ludwig and coworkers [31,32] and Maginn and co-workers. [33,34,35,36,37] The first generation of ionic liquid force fields were derived based on placing integer charges on the ionic liquid ions. Transport properties of ionic liquids obtained with these force fields were found to be lower than the corresponding experimental measurements. In order to remedy this situation, the application of scaled charge models has received increasing attention as a way to account for the polarization in ionic liquids. Adoption of this approach has been demonstrated to considerably improve the agreement between simulation and experimental results for transport properties.
Although ionic liquid force fields have been routinely refined to reproduce their thermophysical properties, the testing of these force fields for phase equilibria properties is not fully developed. This is surprising given that a large number of ionic liquid applications necessitate the knowledge of phase equilibria. For example, in the seminal paper, Blanchard and Brennecke demonstrated the ability of the ionic liquid 1-n-butyl-3-methylimidazolium [C 4 mim] hexafluorophosphate [PF 6 ] to dissolve high amounts of CO 2 . [38] Since then ionic liquids have been under intense scrutiny for their applications as gas separating agents with numerous experimental measurements of solubility of various gases being carried out. For example, the solubility of CO 2 [39,40,41], SO 2 [42,43,44], H 2 [39,41], O 2 [45,40], H 2 S [46,47], NH 3 [48,49,43,50], CH 4 [15,40,41], C 2 H 6 [15,40,41] in ionic liquids has been extensively studied over the past few years. A comprehensive set of experimental data related to the gas solubility in ionic liquids was published by Chen and co-workers. [18] Molecular simulations have also been conducted to predict solubility of CO 2 [51,52,53,54,55,56,57,58], CH 4 [56,52,51,56,57,58], NH 3 [59,60], and SO 2 [54,58] in ionic liquids. The phase equilibria properties of gases in these studies were computed by a combination of an ionic liquid force field and available interaction potential for the gases. Despite these studies, the information on how the choice of an ionic liquid force field affects the phase equilibria predictions is far from known. We are aware of only one simulation study by MarinRimoldi et al. [61] in which a critical evaluation of several popular force fields was undertaken for three ionic liquids [C 4 mim] chloride Cl, [C 4 mim][PF 6 ], and [C 4 mim] bis(trifluoromethanesulfonyl)imide [NTf 2 ] for computing water solubility. The authors concluded that the experimentally measured absorption isotherms could not be satisfactorily reproduced by any of the force fields examined and force fields taking into account the polarization and charge transfer are necessary. Similar studies are desirable for identifying a suitable ionic liquid force field for their ability to accurately describe ionic liquid-solute interactions.
In this article, we attempt to bridge the gap in the knowledge by investigating four all-atom ionic liquid classical force fields, (i) one developed by Canongia and Padua -designated as CL&P, [26] and (ii) three put forth by Acevedo and co-workers -represented as (a) OPLS2009, [28] (b) OPLS2009 0.8 (with scaled charges) [29] and (c) Virtual site [30]. We present gas solubilities in the form of Henry's constant for four gases: (i) nonpolar CH 4 ; (ii) quadrupolar and acidic CO 2 ; (iii) polar and basic NH 3 ; (d) polar and acidic SO 2 . The selection of these gases is driven by various intermolecular forces that are responsible for their dissolution in ionic liquids. Furthermore, their solubilities range from high (NH 3 and SO 2 ), moderate (CO 2 ), and low (CH 4 ). The four ionic liquids considered in this work contain the common cation [C 4 mim] + and different anions Cl -, methylsulfate [MeSO 4 ] -, dicyanamide [DCA] -, and [NTf 2 ] -. These ionic liquids are characterized by various hydrogen bonding strengths between the cation and anion in the order Cl [62,63] The Henry's constants were evaluated by computing the infinite dilute excess chemical potential of gases 333, 353, and 373 K. A comparison between predicted values for the Henry's constants, heat of absorption, and entropy of absorption obtained in this work and experimental/simulation literature values is also included. The literature values are either directly obtained from the studies, whenever available, or are extrapolated from the temperature dependent data. All the relevant data are also listed in the supporting information.
In general, in an all-atom classical force field, the total energy of the system is represented as the combination of intermolecular energies (electrostatic and van der Waals interactions), and intramolecular energies, i.e., bond stretching, angle bending, torsion (both proper and improper). The force field generally assumes the following functional form:
where the adjustable parameters k r,i j , k θ,i jk , k m,i jkl , σ and have the usual meaning and are unique for different force fields.
Four ionic liquids containing cation 1-n-butyl-3-methylimidazolium [C 4 mim] + combined with anions chloride Cl -, methylsulfate [MeSO 4 ] -, bis(trifluoromethanesulfonyl)imide [NTf 2 ] -, and dicynamide [DCA] -were modeled with the following force fields: (1) Simulations using force field parameters of Canongia Lopes-Pádua [26,27] will be abbreviated as CL&P and black color will be used to represent the results in graph; (2) Since CL&P force field was parameterized based on the OPLS-AA force field, simulations were also conducted using OPLS2009 force fields, [28] represented by green color in the graphs. It is to be noted that total charge on an ion is ±1 for these force fields;
(3) It is well established that use of non-integer charges on ions can be used as an effective strategy to improve the dynamical property predictions as it can, in part, account for the polarizability. Therefore, in order to evaluate the effect of scaled charges on the calculated properties simulations using OPLS2009 0.8 with ion charges scaled to ±0.8 were conducted, [29] blue color will be used to represent the results graphically; (4) Recently, Acevedo and co-workers [30] refined their OPLS-AA force fields for imidazolium-based ionic liquids by placing a virtual site at the bisector of two ring nitrogens, which was able to predict properties such as experimental densities, heat of vaporizations, heat capacities, viscosities, surface tensions, and self-diffusivities along with cation-anion hydrogen bonding and π-π cation-cation stacking with a high degree of accuracy. The total charge on the ion is ±0.8. Simulations with this force field will be abbreviated as VSIL and be displayed in red color on the graph. For all the four force fields, the unlike Lennard-Jones interactions were computed by the geometric-mean combining rule for both the Lennard-Jones interaction parameters. The intramolecular 1-4 nonbonded interactions (Lennard-Jones and electrostatics) were reduced by a factor of 2, while these interactions were not computed for atoms involved in bonded interactions (bonds and angles). The force field parameters for CO 2 , SO 2 and NH 3 were obtained from the respective works of Shi and
Maginn [64,65,59], while TraPPE-UA parameters were used to model CH 4 . [66] M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
Molecular dynamics (MD) simulations, using GROMACS 5.1.5 package [67,68], were carried out at a pressure of 1 bar and three different temperatures 333, 353, and 373 K. Gas solubility of CH 4 , CO 2 , NH 3 and SO 2 the ionic liquids was expressed in terms of the Henry's constant, which was evaluated using four different classical force fields (see Force Field section). As these gases dissolve in ionic liquids via physical absorption mechanism, the use of Henry's constant is justified. Further, the Henry's constants provide direct information on the solute-solvent interactions.
Assuming infinite dilution limit of the solute, the Henry's constants, k H , were obtained by the following expression:
where ρ is the molar density of the solvent without the solute dissolved in it, and T is the temperature of interest.
The symbols R and k B refer to the universal gas constant and the Boltzmann's constant, respectively. The excess chemical potential µ ex was determined using Bennett's Acceptance Ratio (BAR) [69] approach. In this approach, the solute-solvent interaction strength was varied via a coupling parameter λ and an independent MD simulation was conducted at each λ point. Then, the free energy change between subsequent λ's was evaluated using GMX BAR utility of GROMACS, and the total change in free energy was determined by taking the sum over all λ values.
For CO 2 , SO 2 , and NH 3 , a two-stage strategy was adopted. In the first stage, only the Lennard-Jones interactions were scaled from the ideal gas state to a solute with Lennard-Jones parameters identical to those given by the force field. The transformation was accomplished in 11 λ points evenly spaced between 0 and 1. The next step involved coupling electrostatic interactions of the gases to the ionic liquid system in eight stages (λ = 0.1, 0.2, 0.4, 0.6, 0.7, 0.8, 0.9 and 1.0) holding the Lennard-Jones parameters fixed. For CH 4 , a single-stage scheme of coupling the Lennard-Jones interactions was followed as the united-atom TraPPE force field for CH 4 does not contain charges.
The initial configurations were generated using PACKMOL [70] by inserting 1 molecule of gas and 256 ion pairs for an ionic liquid in a cubic box with periodic boundary conditions. The initial box sizes were estimated based on experimental densities of pure ionic liquids. These initial configurations were subjected to a steepest descent minimization followed by a 2 ns annealing scheme in which the temperature was iteratively raised to a temperature 200 K above the desired temperature before bringing it back to the target temperature. Using langevin dynamics integrator, additional relaxation of each system was achieved by simulating the systems in canonical (NVT ) and isothermalisobaric (NPT ) ensembles for 5 ns and 20 ns respectively. This was followed by a production run of 20 ns in the NPT ensemble. All the simulations were performed with a time step of 1 fs. During production run, the temperature and pressure were controlled using Nosé-Hoover thermostat and Parrinello-Rahman barostat, respectively, with coupling time constants of τ T = 0.4 ps and τ P = 2.0 ps. Appropriate tail corrections were applied for the nonbonded Lennard-Jones interactions while electrostatic interactions were handled using Particle mesh Ewald (PME) method, each with a potential cutoff of 16 Å. Statistical uncertainties were estimated from three independent simulations initiated from different starting configurations.
The primary goal of the present work is to test the performance of four different force fields for phase equilibria property predictions of various gases with solubilities ranging over several orders of mangitude in different ionic liquids. From equation 2 it is clear that, at a given temperature, the value of Henry's constant primarily depends on two factors: (i) density of the pure solvent (ionic liquid in this work), and (ii) excess chemical potential of the gas dissolved in ionic liquid at infinite dilution. Therefore, accurate reproduction of liquid phase densities of pure ionic liquids can be used as a test to assess the performance of a force field model. Figure S1 of the supporting information shows the temperature dependent variation of densities obtained for
and [C 4 mim][NTf 2 ] ionic liquids using four different classical force fields examined in this work. A direct comparison of the predicted values with the experimental and simulation-based literature data indicates that, in general, all the force fields are able to estimate the liquid densities with good accuracy with maximum deviation of ∼3 % considering the statistical uncertainties. Given the generality and transferability of the force field models considered here, accuracy within ±3 % deviation can be considered reasonable. In fact, Canongia Lopes and Pádua [24,25,26,27],
and Acevedo and co-workers [28,29,30] reported densities of these ionic liquids with similar accuracies. However, a closer inspection suggests that force fields with scaled charge models (VSIL and OPLS2009 0.8) leads to better predictions of the temperature dependent-density trends.
Acevedo and co-workers [29] reported that although OPLS2009 can predict properties such as heat of vaporizations, heat capacities, viscosities, surface tensions, and self-diffusivities reasonably well, a charge scaling improves reproduction of not only the bulk-solvent properties but also the local ion-ion intermolecular interactions such as cation-anion hydrogen bonding and π-π cation-cation stacking, in imidazolium-based ionic liquids, with maximum absolute error ranging between 10-15 %, as was observed in OPLS2009 0.8. Furthermore, presence of a virtual-site, in VSIL model, dramatically improves the above mentioned macroscopic with a high degree of accuracy with maximum absolute error of < 3.5 % for all except self-diffusion coefficients where deviation was ∼10 %. [30] Structural properties were also commensurate with those calculated from ab initio calculations. Thus, overall the four force fields considered here can predict the structural and macroscopic properties of pure ionic liquids with good accuracy.
Before delving into the comparison, it is worth mentioning some general apparent trends. (i) For a given gas and an ionic liquid, the Henry's constants increase with increasing temperature, implying that the solubility of the gas decreases. (ii) At a particular temperature, for the same ionic liquid the solubility follows the order: SO 2 > NH 3 > CO 2 > CH 4 . This trend is consistent with previously reported trend. [18] These trends are well-reproduced irrespective of the choice of force field model. However, important differences between the performances of the force fields, in terms of the level of agreement reached with the experimental data, will be discussed in the following sections. The following subsections are organized in the increasing order of gas solubilities.
The variation in Henry's constants of CH 4 for the ionic liquids and force fields considered in this work is given in Figures 1 (a) -(d). These predictions have been compared with the published experimental data. To our knowledge, a complete set of data for the imidazolium-based ionic liquid containing butyl side chain throughout the temperature range of 333-373 K is not available for the current set of anions. Hence, comparison is made at discrete temperature levels. As remarked earlier, CH 4 is the least soluble in ionic liquids amongst all the gases examined in this work. This is clearly reflected in the calculations performed, where k H,CH4 is an order of magnitude higher than the Henry's constants for CO 2 , NH 3 and SO 2 .
For [C 4 mim]Cl ionic liquid, significant difference in the predictions using different force fields are observed at 333 K. The Henry's constants of CH 4 calculated with the OPLS2009 and CL&P force fields are lower by a factor of 4 when compared with those computed with the force fields with scaled charges (VSIL and OPLS2009 0.8). In general, the Henry's constants for methane are similar when scaled charge force fields are employed and are higher than those obtained with the force fields developed with integer charges. Our calculations (not shown) of the Henry's constant of CH 4 in [C 4 mim]Cl using a united-atom force field with ionic charges of ±0.8 also indicate solubilities similar to
those obtained with the OPLS2009 0.8 and VSIL force fields. At the highest temperatures, all the force fields yield similar values within the statistical uncertainties. Interestingly, the OPLS2009 0.8 and VSIL force field show almost no variations in the Henry's constants. We will revert to this point below when discussing the heat of absorption for various systems.
The force field performance is qualitatively different for the [C 4 mim][MeSO 4 ] ionic liquid. In terms of matching the Henry's constant with experimental results (Figure 1(b)), the CL&P and OPLS2009 force field outperform the OPLS2009 0.8 and VSIL at 333 K. At a temperature of 353 K, the Henry's constant computed with the OPLS2009 force field is in better agreement with the experimental results, while the scaled charge force fields are to be preferred at 373 K. In terms of the temperature variation, the OPLS2009 0.8 and VSIL force fields reproduce the experimental trend. Similar to the observation for [C 4 mim]Cl, the Henry's constants predicted with the OPLS2009 0.8 and VSIL force fields are nearly indistinguishable, especially at 333 and 353 K. The Henry's constants for [C 4 mim][DCA] are presented in Figure 1(c). When a comparison is made between various force fields, the OPLS2009 0.8 force field predicts values that are the lowest at all the temperatures, implying the largest solubility with the Henry's constants ∼ 1100 bar. The VSIL force field yields values that are nearly independent of the temperature (∼ 1750 bar). The higher values for the Henry's constant in the case of the VSIL force field may be related to a higher density obtained for the pure ionic liquid than that with the OPLS2009 0.8 force field. It is interesting to note that the Henry's constants estimated by fitting the soft-SAFT equation of state to the experimental data and determining the slope as the solubility approaches zero [71] fall between the predictions by the OPLS2009 0.8 and VSIL force fields. Additionally, the weak temperature dependence of the Henry's constants for CH 4 is well described by the two force fields. The CL&P and OPLS2009 force field overestimate the Henry's constants over the three temperatures in comparison to those experimentally derived and calculated from the scaled charge models. It is noteworthy that the OPLS2009 force field is able to reproduce the temperature invariance of the Henry's constants. According to our calculations, an incorrect temperature trend of the Henry's constant is likely to be obtained with the CL&P force field.
For the [C 4 mim][NTf 2 ] ionic liquid, OPLS2009 0.8 force field is in very good agreement with the available experimental results [72] and group contribution [73] predictions by Yu and co-workers at 333 and 353 K and is observed to perform the best in comparison to other force fields. At 333 K, the Henry's constant of 497 ± 17 bar obtained from this force field is also comparable to Henry's constant of 524 bar reported by Ramdin and co-workers [57] from Monte Carlo simulations and 549 bar from experiments by Peters and co-workers. [74] On the other hand, Budhathoki et al. [51] determined the Henry's constant of CH 4 to be 331 ± 11 bar from Monte Carlo simulations, the value which is quantitatively obtained with the VSIL force field (339 ± 7 bar). The VSIL force field consistently yield the highest solubilities for CH 4 followed by OPLS2009 0.8. For these two force fields, the Henry's constants are within a factor of 2 at all the temperatures. The CL&P force field also appears to capture the solubility trend with the temperature.
Overall, based on the available data and our predictions, for [C 4 mim] + system, the CH 4 solubility order can be expressed as
force fields. The overall trends for the CO 2 solubility is consistent with the hydrogen-bond acceptor ability of the anions when they are combined with the same cation. [62,63] This result was expected as it is well established fact that solubility mechanism of CO 2 in ionic liquids is highly dependent on the interaction between CO 2 and anion and
the size with weakly coordinating anion possessing greater absorption capacity. [18] For [C 4 mim]Cl (Figure 2 (a)), it is evident that the Henry's constant predictions are similar for all the force fields when statistical uncertainty are taken into account. Moreover, the agreement with the experimental data [75] is also good. It is noteworthy that the Henry's constants obtained with the OPLS2009, OPLS2009 0.8 and VSIL force fields are in excellent agreement with the calculations performed with a united-atom model with scaled charges. [76] At 333 K, the Henry's constants calculations with VSIL and OPLS2009 0.8 are show a good level of agreement with experimentally measured Henry's constant, while the CL&P and OPLS2009 predictions are lower by approximately 50 %. This is probably attributable to the fact that melting temperature of [C 4 mim]Cl is ∼ 340 K, making it a super-cooled liquid at 333 K. In addition, the high viscosity of the ionic liquid makes it challenging to measure CO 2 solubility. At the highest temperature (373 K), all the force fields converge around the experimental measurement.
In Jacquemin et al. [39] and Hiraga et al. [82]. While values predicted by CL&P and OPLS2009 are in agreement with those reported by Raeissi et al. [83]. One possible explanation for the difference in experimentally determined values may be related to the presence of impurities such as Cl -and water. [84] Also, the use of different experimental methods/protocols can produced different values. [18] The predictions with the VSIL force field compare well with the values determined by Kapoor and Shah [76] who used a united-atom model force field proposed by Liu et al. [85] Further, these values also correspond well to those reported by Budhathoki et al. [51] and Singh et al. [52] who employed a Generalized Amber Force Field for their Monte Carlo simulations. Although the predicted values of Henry's constants are different, we concluded that, significantly lower statistical uncertainties and excellent agreement with most of the experimental and simulation-based studies indicate that the recently proposed VSIL force field is a reliable force filed for determining CO 2 solubility in [C 4 mim][NTf 2 ].
Henry's constants of NH 3 , as a function of temperature, the four ionic liquids and different force fields are displayed in Figures 3 (a) -(d). To the best of our knowledge, experimental and simulation-based literature data are reported for the ionic liquids examined. However, it is interesting to note that all the ionic liquids exhibit comparable Henry's constants, ranging from 10 to 50 bar at the three temperatures investigated. Such a behavior suggests that, unlike CO 2 , the anion effect on NH 3 solubility is less pronounced. This observation is consistent with the study performed by Shi and Maginn [59] in which the authors computed the radial distribution functions of NH 3 with the cation and anion of the ionic liquid ethylmethylimidazolium [C 2 mim][NTf 2 ] and concluded that the most important NH 3 interaction occurred with one of the hydrogen atoms in the imidazolium ring. Based on the activity coefficients
and vapor pressure data provided in this paper, we estimated the Henry's constants for NH 3 in [C 2 mim][NTf 2 ] to be 11.9, 22.9 and 51.0 bar at 298.1, 322.3, and 347.5 K, respectively. These values are similar to the force field predictions, but somewhat lower, presumably due to the longer alkyl chain employed in this study. Furthermore, Henry's constants data extrapolated from the available experimental measurements for [C 4 CL&P force field or OPLS2009 exhibit solubilities that are higher than the corresponding solubilities estimated by the other two force fields for these three ionic liquids. Contrary to this observation, all the force fields but OPLS2009 0.8 display very similar NH 3 solubilities in [C 4 mim][NTf 2 ]. As there is no strong dependence of the Henry's constant on the type of force field, any of the four force fields is suitable for the initial estimate. If the force fields are ranked based solely on the precision, VSIL force field is found to be superior.
The dependence of Henry's constants of SO 2 for various ionic liquids on the type of force field is illustrated in Figures 4 (a) -(d). The Henry's constants span the range from 1-20 bar, with higher values observed at higher temperatures. Across all the ionic liquids, we observe that the Henry's constants are categorized in two force field groups: The available literature data are sparse for SO 2 Henry's constant in these ionic liquids; however, comparison of experimental and other simulation data at different temperatures is performed to test the validity of the force fields.
The experiments by Lee et al. [86] show that the absorption of SO 2 is higher in [C 4 mim]Cl in comparison to that for [C 4 mim][MeSO 4 ] at 323 K (Henry's constant 0.55 bar, see below). However, the absorbed amount could not be fully recovered hinting at a chemical complex formation. The value of 0.9 bar obtained with the OPLS2009 and CL&P force fields at 333 K seem to follow this behavior. As the possibility of chemical interactions in the models is neglected, the agreement can be considered somewhat fortuitous. The Henry's constant calculations using a free energy-based molecular modeling approach by Mondal and Balasubramanian [87] also point to a value of 1.0 bar at 353 K, which is closely mimicked by the OPLS2009 and CL&P force fields for this ionic liquid. VSIL and OPLS2009 0.8 force field estimations for the Henry's constants are in line with the physical absorption mechanism for SO 2 .
Shiflett and Yokozeki [44] derived a Henry's constant of 0.04 bar for [C 4 mim][MeSO 4 ] at 298 K. The authors alluded to the chemical complexation between SO 2 and the ionic liquid. The data reported by Lee et al. [86] over the temperature range of 308-328 K show that the Henry's constant of SO 2 in this ionic liquid varies from 0.43 to 0.62 bar, indicating that the solubility of SO 2 is most likely driven by a chemical complexation mechanism. Higher temperatures and modeling the physical solubility are the main reasons that the Henry's constants predictions for SO 2 are higher than than those reported experimentally. The predictions with VSIL and OPLS2009 0.8 closely follow one another at all the temperatures with similar behavior noted for the other two force fields.
, there exists only one data point reported by Garcia et al. [88] based on COSMO-RS calculations at 298 K. Although a direct comparison is not possible due to the different modeling approaches and temperatures, the Henry's constant values determined in this work are similar. Interestingly, the accuracy of the predictions for all the force fields is remarkably similar for [C 4 mim][NTf 2 ]. The COSMO-RS calculations performed by Garcia et al. [88] at 303 K yield a value of 3.5 bar for the Henry's constant of SO 2 in [C 4 mim][NTf 2 ], which compares favorably with the data reported here. Anderson et al. [89] measured the Henry's constant of SO 2 in 1-
hexyl-3-methylimidazolium [C 6 mim][NTf 2 ] to be ∼ 4.1 bar at 333 K. Shi and Maginn [90] calculated this value to be 3.6 bar from the absorption isotherms determined from Monte Carlo simulations. Given that the effect of the alkyl chain length on the SO 2 solubility is minor [91], the Henry's constant predictions for all the force fields are in very good agreement for [C 4 mim][NTf 2 ].
The partial molar enthalpy (∆h) of absorption is useful in understanding the strength of interaction between the solute and solvent, while the partial molar entropy (∆s) of absorption provides insights into the degree of ordering in liquids associated with the dissolution of the solute. These thermodynamic quantities can be extracted from the temperature-dependent Henry's constant data using equations 3 and 4
The values of ∆h and ∆s for all the gases in different ionic liquids along with the literature data -wherever available -are collected in Tables 1 and2 respectively.
With the exception of few cases, the values of ∆h are negative as the solubility of all the gases were found to decrease with increasing temperatures. In general, all ∆h values are relatively small, irrespective of the gas and ionic liquid, indicating a physical dissolution mechanism as the absorption driven by chemical interaction would yield much larger values. [40] The interactions strengths for the gases with ionic liquids increase in the order of CH 4 < CO 2 < NH 3 < SO 2 . This observations can be explained on the basis of the type of interactions the solute is able to establish with ionic liquids. Table 3 lists the polarizabilities and dipole and quadrupole moments of the gases. This clearly suggests that the primary mode of interaction for CH 4 is van der Waals (vdW) interactions due to its nonpolar character.
In addition to the vdW interactions, CO 2 can interact through electrostatic interactions due to its large quadrupole moment. The polar nature of NH 3 and SO 2 is evident due to the presence of permanent dipole and quadrupole moments which is also reflected in the high enthalpy of absorption. The partial molar entropy of absorption follows exactly the opposite trend to that for the enthalpy. The strength of the interaction also correlates with the order of increasing gas solubility.
In line with the variation in Henry's constants with temperature, the calculated enthalpy of absorption values are negative except for [C 4 mim][DCA] ionic liquid with the CL&P force field, indicating that the solubility decreases as the temperature is raised. The enthalpies are rather low (ranging from -5 kJ/mol to 0 kJ/mol) for all the ionic liquids when computed using the VSIL and OPLS2009 0.8 force fields, implying a weak interaction with the ionic liquids and temperature dependence of solubility. The OPLS2009 force field shows such a weak dependence only 1. Comparing the enthalpy of absorption with the available literature data shows that the VSIL and OPLS2009 0.8 force fields provide a better predictive capability in comparison to the other two force fields.
All the force fields indicate that the entropic driving force is either negligible or offers resistance to the dissolution of methane in the four ionic liquids. Among the force fields, a trend identical to that observed for the enthalpies of absorption can be noted for the entropy of absorption. For example, the application of the VSIL and OPLS2009 0.8 force field leads to values that are more aligned with the experimental data across the four ionic liquids, while CL&P and OPLS2009 force fields demonstrate a varying degree of agreement with the experimental observations. When a comparison is made with other gases in Table 2, it is can be seen that methane dissolution is least affected by entropic contributions. Taken together, we recommend the use of OPLS2009 0.8 and VSIL force fields for estimating the Henry's constants of CH 4 in the investigated ionic liquids. The temperature dependence of the Henry's constants, in the form of enthalpy and entropy of absorption, is correctly reproduced when comparison is carried out with the available experimental data. Although numerical values for the Henry's constants computed with the OPLS2009 and CL&P force field show varying degrees of agreement with the experimental data, the predictions of the enthalpy and entropy of absorption for [C 4 mim][NTf 2 ] and [C 4 mim][DCA] are found to be generally reliable.
In comparison to the experimental value, the enthalpy of absorption for CO 2 in the ionic liquid [C 4 mim]Cl is overpredicted by a factor of 2-3 when using the CL&P and OPLS2009 force fields, suggesting that the interaction between CO 2 and the ionic liquids modeled in these force fields is too strong. Based on the entropy of absorption, a much higher ordering in the ionic liquid is projected to occur by these force fields. The scaling of ionic charges by 0.8 (OPLS2009 0.8) results in the values of ∆h and ∆s closely matching the experimental measurements. The placement of an additional virtual site results into values that are indistinguishable from those obtained by simply scaling the charges. Thus, for [C 4 mim]Cl, a correct temperature dependence can be expected when either the OPLS2009 0.8 or VSIL force field is applied. Given the spread in the experimental values for ∆h and ∆s, it is difficult to assess the accuracy of the simulation predictions for the ionic liquid [C 4 mim][ MeSO 4 ]. Nonetheless, it can be seen that the ∆h and ∆s predictions employing the force fields CL&P, OPLS2009 0.8, and VSIL are in very good agreement with experimental data. On the other hand, the CO 2 -ionic liquid interactions are indicated to be slightly stronger than with the OPLS2009 force field. In the case of CO 2 in the ionic liquid [C 4 mim][NTf 2 ], both ∆h and ∆s values are comparable across all the force fields and with experimental values. However, subtle differences do exist. For example, the CO 2 -ionic liquid interactions are a little stronger in the CL&P force fields, while the interactions are marginally weaker in the OPLS2009 force field as suggested by ∆h values. As a consequence of this behavior, the entropy of absorption is the most negative for the CL&P force field and the least for the OPLS2009 force field. Considering the dissolution of CO 2 in [C 4 mim][DCA], the simulation results are in quantitative agreement with the experimental value for the enthalpy and entropy of absorption of CO 2 in the ionic liquid.
Overall, our analysis indicates that the OPLS2009 0.8 and VSIL force fields are to be preferred for estimating the temperature dependence of the Henry's constant of CO 2 in the four ionic liquids. We also conclude that, for CO 2 , the effect of the additional virtual site in the VSIL force field is only secondary. The reduction of the CO 2 -ionic liquid interaction by lowering the cation and anion charge to ± 0.8 is sufficient for predicting the behavior of the Henry's constant for CO 2 in these ionic liquids as a function of temperature. Another notable feature of these calculations is that the enthalpy and entropy of absorption calculated with the two force fields exhibit weak dependence on the type of ionic liquid, suggesting that the infinite dilution thermodynamics of CO 2 dissolution is similar in the four ionic liquids.
The solubility mechanism of NH 3 in ionic liquids depends on the interaction of NH 3 with cation, which we believe has a non-negligible dependence on the interaction of cation with anions. As mentioned above, solubility of NH 3 in ionic liquids studied in this work follows the order Cl
] -, at a given temperature.
The enthalpy and entropy of absorption for NH 3 determined with a given force field follows the identical order, implying that the physical mechanism underlying NH 3 solubility is captured by all the force fields. This observation ] are lower (more negative) by a factor of 2-3 than the corresponding values determined for the OPLS2009 0.8 and VSIL force fields. The data for the Henry's constant for SO 2 along with the enthalpic and entropic contributions obtained with the four force fields suggest that the application of scaled charge models leads to better predictions.
We considered four all-atom ionic liquid force fields (two with integer charges and two with scaled charges of ± 0.8) to test their accuracy in predicting the Henry's constants of solutes of varying polarity in four ionic liquids:
. The solutes of interest consisted of nonpolar CH 4 , quadrupolar and acidic CO 2 , and polar and basic NH 3 and polar and acidic SO 2 . Henry's constants were determined by evaluating excess chemical potentials using BAR approach at temperatures of 333, 353, and 373 K. Partial molar enthalpies and entropies of absorption were derived from the temperature dependent Henry's constant using the van't Hoff equation.
Our calculations indicate that all the force fields are capable of reproducing the experimentally observed gas solubility trend (SO 2 > NH 3 > CO 2 > CH 4 ) in a given ionic liquid. This is remarkable considering that the Henry's constants span over three orders of magnitude. Similarly, the force fields can be employed to correctly identify ionic liquids with high gas solubility. For example, NH 3 solubility is ranked in the order of Cl
In addition, with a few exceptions, all the force fields show that the gas solubility decreases when the temperature is raised. As a consequence of which, we find that the entropies of absorption are negative for all the ionic liquids. Consistent with the solubility trends, the partial molar enthalpy of absorption are ordered (from least negative to the most) as CH 4 < CO 2 < NH 3 < SO 2 . The partial molar entropies are also negative indicating enhanced ordering in the ionic liquids when these gases dissolve in the chosen ionic liquids.
In general, we find that the force fields with scaled charges (termed as VSIL and OPLS2009 0.8) tend to align better with experimental results in comparison to the integer charge models (OPLS2009 and CL&P). The reduction in the overall charge on the cation and anion also brings the enthalpies and entropies of absorption closer to the available literature data. As an aside, we note that the experimental data for NH 3 and SO 2 in ionic liquids are scarce when compared to those for CH 4 and CO 2 . Such measurements will assist in expanding the present study to include more ionic liquids.