Prediction of experimental properties of CO 2 , improving actual force fields
aa r X i v : . [ phy s i c s . a t o m - ph ] M a y Prediction of experimental properties of CO , improving actual force fields .Ra´ul Fuentes-Azcatl and Hector Dom´ınguez ∗ Instituto de Investigaciones en Materiales, Universidad Nacional Aut´onoma de M´exico,M´exico, D.F. 04510 [email protected] [email protected] S1bstractMost of the existing classical CO models fail to reproduce some or many experimentalproperties such as surface tension, vapor pressure, density and dielectric constant at differencethermodynamic conditions. Therfore, it is proposed a new computational model to capturebetter structural, dynamical and thermodynamic properties for CO . By scaling the LennardJones parameters and point charges; three target properties, static dielectric constant, surfacetension and density, were used to fit actual experimental data. Moreover, by constructing aflexible model, effects of polarization might be included by variations of the dipole moment.Several tests were carried out in terms of the vapour-liquid equilibria, surface tensions andsaturated pressures showing good agreement with experiments. Dynamical properties werealso studied, such as diffusion coefficients and viscosities at different pressures, and goodtrends were obtained with experimental data. I. Introduction CO is the major waste contribution of the energy production and the most important green-house gas leading to global climate change. Since the Industrial Revolution anthropogenicemissions, primarily from fossil fuels and deforestation, have rapidly increased their concen-tration in the atmosphere, driving to global warming. Therefore, capture and retention ofCO became matter of several studies, not only for scientist but also for engineers. Fromthe experimental point of view several techniques have been developed,
1, 2 however theoreticalapproaches have been used, such as computer simulations, as alternatives to study the phe-nomena. Therefore, from the computer simulations perspective is important to have realiblemodels to produce good result compared with experimental data.Nowadays, there are several CO models, i.e. force fields, described in the literature.Murthy et al. developed two- and three-site force fields with Lennard Jones (LJ) interac-tions that included a point-quadrupole moment located at the center of mass of the molecule.M¨oller and Fischer presented a force field with two interacting LJ sites with a point-quadrupole,with parameters that fit experimental data of vapour-liquid equilibrium coexistence (VLEC).Vrabec et al. reparametrized the model to improve VLEC. The EPM and EPM2 (elementaryphysical models), developed by Harris and Yung, are CO force fields widely used with LJsites and point charges in every atom. The Lennard Jones parameters of EPM model wereobtained through the production of the internal energy and pressure at temperature of T =239 K whereas the parameters of the EPM2 were obtained to reproduce the critical properties.The TraPPE F lex model developed by Potoff and Siepmann was obtained to fit the VLEC ofthe CO - propane mixture. Another common CO force field, proposed by Potoff et al., wasobtained by modifying the parameters in the attractive term of the interaction potential andit included point charges to adjust the VLEC data.On the other hand, Zhang and Duan developed a force field with three LJ sites andpoint charges
10, 11 and Merker et al. reported a force field with three LJ sites with a point-quadrupole represented by three point charges. That model was optimized for VLEC datato obtain 0.4% deviation from the experiments in the saturated liquid density and 1.8% inS2he vapour pressure. Persson developed a ”One-Center” force field with a quadrupole for theCO with parameters adjusted to the VLEC data. ab initio methods have been also usedto construct CO force fields, for instance Bock et al. proposed an intermolecular potentialwith 5 interacting sites and Bukowski et al. proposed an intermolecular potential from aperturbation theory, however, Bratschi et al. concluded that the VLEC behavior is notaccurately represented with those models.Despite the fact that CO is quite polarizable, polarizability effects are not expected in thethermophysical properties of pure CO . However, in CO mixtures with polar components,like water, the properties may not be exact when using non-polarizable force fields. Vlceket al. obtained new optimized parameters for a CO - H O mixture using SPC/E waterand EPM2 force field, however, the compositions of the CO -rich phase at 348 K were notadequately represented. Recently, Orozco et al. performed MC simulations in the Gibbsensemble to study the VLEC of the CO - H O mixture. It was found that non-polarizableforce fields, such as the TraPPE model, have limitations in the prediction of compositionsand densities for steam and liquid phases.It is worthy mentioning that the existing models, using molecular dynamics, reproducesome of the CO properties but they fail to reproduce others, i.e. there is not a CO modelwhich captures most of the actual experimental properties. However, the EPM2 model usingMonte Carlo methods captures several properties such as densities, VLEC and vapour pres-sures but it does not reproduce surface tension or dielectric constants. Recently a polarizablemodel proposed by Jiang et al. with gaussian charges using monte carlo methods repro-duced correctly VLEC and vapour pressures and they obtained good dynamical properties,however, they did not calculate surface tensions neither dielectric constants.In the present paper we propose a new simple flexible CO force field to reproduce betterthermodynamic, structural and dynamical experimental data. The interest of having a flexiblemodel is to study changes in the molecular geometry to search thermodynamic states due todipole moment variations. A flexible molecule can be obtained with changes in the O-C-Oangle which could modify the dipole moment and consequently producing fluctuations in thedielectric constant.The remaining of the paper goes as follows. In section 2 the new model for the CO / ε is introduced. In section 3, the methodology to obtain of the new parameters is described,section 4 shows the simulation details and the results are analysed in section 5. Conclusionsare presented in section 6. II. The CO / ε Model
Carbon dioxide, CO , is a linear and symmetric molecule with zero dipole moment. Themodel consists of intra and intermolecular potentials. In fact, in order to have a flexiblemodel an harmonic potential was included in the intramolecular interaction, see figure ?? . U ( θ ) = k θ θ − θ ) , (S.1)where θ is the angle O-C-O and θ refers to the equilibrium value, k θ is the spring constant.S3ABLE S 1: Parameters of the CO models considered in this work.model d OC k θ θ OCO ǫ O − O σ O − O ǫ C − C σ C − C q O q C ˚A kJ/mol rad deg kJ/mol ˚A kJ/mol ˚A e eCO /ε molecules, the Lennard Jones (LJ) andCoulomb interactions are used, u ( r ) = 4 ǫ αβ "(cid:18) σ αβ r (cid:19) − (cid:18) σ αβ r (cid:19) + 14 πǫ q α q β r (S.2)where r is the distance between sites α and β , q α is the electric charge of site α , ǫ is thepermitivity of vacuum, ǫ αβ is the LJ energy scale and σ αβ the repulsive diameter for an α − β pair. The cross interactions between unlike atoms are obtained using the Lorentz-Berthelotmixing rules, σ αβ = (cid:18) σ αα + σ ββ (cid:19) ; ǫ αβ = ( ǫ αα ǫ ββ ) / (S.3) III. Parametrization Approach
Using molecular dynamics (MD) simulations two CO models, TraPPE F lex (flexible) andEPM2, were initially tested to evaluate some thermodynamic properties such as the surfacetension. Then, with the method suggested by Alejandre et al. the surface tension was deter-mined, however,the computational results did not agree well with the experiments. Therefore,in order to improve the actual CO models series of molecular dynamics were conducted tofind a set of parameters of a CO flexible model to reproduce better the experiments. Theprocedure started using a CO TraPPE
F lex force field following the method of Salas et al, i.e. by modification of the ǫ and σ Lennard Jones parameters to fit the experimental surfacetension and the density. In the same procedure, as Fuentes et al. reported, the sitecharges were also scaled until the static dielectric constant was improved.The purpose of the present work is also to built a flexible model, then the harmonicpotential constant is also parametrized to increase flexibility that is linked to the polarity ofthe molecule and the dielectric constant by the dipole moment.
IV. Simulation Details
Molecular dynamic simulations were performed using GROMACS software and the newCO parameters were estimated with three target properties, the static dielectric constant,the surface tension and density. For the surface tension calculations a CO slab was locatedS4n a parallelepiped cell with dimensions L x = L y = 9.269 nm and L z = 3L x , i.e. the surfacearea was large enough to avoid any finite size effects and 5324 molecules were used inthe simulations. Then, simulations in the NVT ensemble with periodic boundary conditionsapplied in all three directions were conducted. The equations of motions were solved using theleapfrog algorithm with a time step of 2 fs using the Nose-Hoover thermostat with a parameterof 1.4 and LINCS algorithm to keep bond distances. Electrostatic interactions were handledwith the particle mesh Ewald (PME) method with a grid space of 0.35 nm and a splineof order 4. The truncation potential distance was 2.6 nm. Liquid phase simulations wereperformed in the isotropic NPT ensemble with a fixed number of molecules, N=500. The LJand the real part of electrostatic interactions were truncated at 1 nm, and the PME methodwas used for the long-range electrostatic part with the following settings: a tolerance of 10 − for the real space contribution, a grid spacing of 0.12 nm and a 4-order interpolation. Theenergy and pressure corrections implemented in GROMACS were also applied due to theuse of a finite cut-off for LJ interactions. V. Results
It is already known that the important parameter to modify the surface tension is the ǫ LJ parameter. Therefore, simulations at different ǫ LJ values, by scaling all ǫ LJ parameters,were conducted until the error with the target property was less than 5.6 % with respect tothe experimental value. The average components of the pressure tensor were obtained for30 ns after an equilibration period of 5 ns. The corresponding surface tension, γ , for planarinterfaces was calculated from the mechanical definition, γ = 12 L z [ P zz −
12 ( P xx + P yy )] (S.4)where P αα are the diagonal elements of the microscopic pressure tensor. The factor 1/2 takesinto account the two symmetrical interfaces in the system.In figure 1 the surface tension results of the new CO / ε force field with other most commonmodels are shown. In the figure, it is observed that the new CO / ε force field describes betterthe experimental surface tension values at different temperatures . In general, the otherCO models fail to reproduce the experiments, only the EPM2 has good agreement withexperimental data between temperatures T = 260 K and T = 280 K whereas TraPPE F lex results are even further away from the experiments.The selection of the charges in the new model was determined by calculation of the di-electric constant obtained by the fluctuations of the total dipole moment M , ǫ = 1 + 4 π k B T V ( < M > − < M > ) (S.5)where k B is the Boltzmann constant and T is the absolute temperature. The dielectricconstant was obtained for long simulations, 40ns, using isotropic NPT ensemble. The new setof charges were obtained by variation of the original ones, of all atomic sites, until the targetS5
80 200 220 240 260 280 300Temperature / K0510152025 S u rf ace T e n s i on / m N m - ExpCO / ε EPM2 TraPPE flex
Figure 1: Surface tension as a function of temperature for the different CO models. Thesimulation results for the EPM2, TraPPE F lex and CO / ε were obtained from this work. Thecontinuous line represents the experimental data. property, the dielectric constant was about % with respect to the TraPPE f lex andit does not cause other properties to be lost. The proper evaluation of the dielectric constant needs long simulations to have the averagedipole moment of the system around zero. Results of the dielectric constant at 273.15K oftemperature at diferent pressures are show in the figure 2 where it is observed that the newforce field CO2/ ε shows better agreement with the experiments. The reproduction of the dielectric constant show that the new force field can modify theCO2 structure in order to capture the change in the dipole moment.With the new ǫ LJ and charges values the σ LJ of all atoms were also scaled to match thedensity at 50 bar and 280K of pressure and temperature repectively with errors less than 17%.The new parameters of the CO / ε model are indicated in table 1. Finally, to have a flexiblemodel the angular potential was reduced from the original one, using an angular constantof k θ = 500. This value was chosen since it reproduced better the experimental data. Forall those last calculations simulations in the NPT ensemble were carried out with differentpressures using Nose-Hoover barostat.Flexibility of the model was tested at temperature of T = 300 K and pressure of P = 1 barby measuring the average O-C-O angle over the simulation time, see table 2. From table 2 isobserved that the new model is a little more flexible than the others as a consequence of thereduction of the spring constant, k θ , in the angular potential. In fact, it is observed that thedipole moment increased with respect to the other models by improving the dielectric constant.Since fluctuations in the dipole moment are related with the instantaneous polarization thenthe factor G K (equation S.6), was introduced to calculate the differences in the polarizationS6 l og ε EPM2CO / ε ExpTraPPE/
Flex
Figure 2: Dielectric constant as a function of pressure at 273.15K of temperature for theCO2/ ε , EPM2 and TraPPE force fields. The continuous line represents the experimentaldata. Figure 3: Graphical representation of CO2 in gas phase at 300K and 1 bar of temperatureand pressure, respectively; According to the data reported in table 2among the different models studied in the present work, G K = < M > /N µ (S.6)where M is the total dipole moment of the system, N is the number of molecules and µ is the dipole moment of a single molecule. From the results it is depicted that G K increasefor CO / ε table 2, then the polarizations change in order to improve the dieletric constantfigure2. Based on the optimal point charge approximation of Anandakrishnan et al. described in figure 3 . We calculated the dipole and quadrupole moments, usingS.7 and S.8, that describe well these dipole and quadrupole moments of the CO molecule in this context. The values are given in table 2. µ = 2 qz (S.7)S7
00 220 240 260 280 300Temperature / K020406080 P s a t / b a r expCO / ε EPM2 TraPPE flex
Figure 4: Saturated vapour pressures at different temperatures. The simulation results forthe TraPPE
F lex , EPM2 model and CO / ε obtained from this work. The continuous linerepresents the experimental data. Q T = 3 qy It is observed that the calculated dipole and quadrupole moments of the CO / ε model are higher than those obtained with the other models. Due to the flexibilityof CO / ε model and the new parameters the electrostatic moments produce highelectrostatic moments. Even though the CO / ε dipolar moment is higher respectto the other models all values are small. On the other hand, the quadrupolemoment reported in the literature is 4.3 D˚A(1D = 0.2082 e˚A) and from table2 is noted that none of the models have good values, the TraPPE and the EPM2force fields underestimate the data with an error of 21 % and 28 %, respectivelywhereas the CO / ε overestimate the value with 42 % error. However, in order tohave similar quadrupole effects of all the models, we keep the CO / ε quadrupolemoment per charge the same as given in the other models (see last column intable2). With this approximation not only the dielectric constant is improvedbut also other thermodynamics properties remained. One important property within the chemical engineering community is the calculation ofvapour pressures. In figure 4 the results of the vapour pressure calculated with the perpen-dicular component of the pressure tensor respect to the surface are shown for different CO force fields. It is observed that the new CO / ε describes well the vapour pressure , the EPM2increases its value from 220K and overestimates the experimental value at high temperatureshowever the trappe flexible force field overestimate the experimental values.S8
200 400 600 800 1000 1200 ρ /
Kg m -3 T / K EPM2 MC expTraPPE Flex CO / ε Figure 5: Vapour - Liquid phase equilibrium. CO / ε obtained from this work and the valuesof EPM2 MC are taken from Harris et al. The continuous line represents the experimentaldata. The vapour and liquid densities were calculated with the slab method described aboveand the results are plotted in figure 5. It is noted that the liquid and vapour branches arewell described with the Monte Carlo EPM model. The CO /ε model produces good vapourbranch although the liquid line is not as good as the EPM model.S9ABLE S 2: Results at T = 300 K and P = 1 bar for the CO models considered in thiswork. θ prom G K Dipole moment | Q T | | Q T /q O | degree debye (D) D˚A D˚A/eTraPPE flex /ε / ε capture the liquid branch reasonably well at high pressures.However, at high temperatures different issues are depicted.The structure of CO is represented by the proposed CO / ε force field and plotted interms of the pair distribution function (g(r)) in figure 7. It is observed that the CO / ε captures better the first peak indicated by the experiments, i.e. at 0.319 nm very close tothe experimental data, 0.332 nm. In fact, there is a second peak around 0.434 nm closeto the experimental value of 0.405 nm, figure 8B, is noted the second peak, in theg(r), higher than the first one whereas the experiments show two peaks nearly atthe same height. Due to the flexibility of the model it is possible that the CO2molecule bents more and more attraction between O-O atoms compare with theC-O interactions could be produced by increasing the second peak of the g(r), i.ethe larger number of second nearest neighbors. At large distances the g(r) of theCO / ε looks more similar than the experimental one. Experiments of the liquid CO structure were obtained from van Tricht et al. using neutrondiffraction experiments. Dynamical properties were also calculated with the new CO / ε model. In figure 8,9results of the diffusion coefficients as function of the pressure at two different temperaturesare shown. At T = 223 K the CO / ε in general reproduces better the values better than theothers models repect to the experiments. At T = 298 K the CO / ε captures well the shapeof the experimental data, in particular at low pressures, however data for all models are notgood compared with the experiments.It is important to mention that the size of the simulated system for the diffusion coefficientscalculations were big enough to avoid any size effects as indicated in previous works. Thediffusion coefficient was obtained from the long-time limit of the mean square displacementaccording to the Einstein relation, D = lim x →∞ < ( r ( t ) − r (0)) > / t (S.9)where r(t) corresponds to the position vector of the center of mass at time t and theaveraging < ... > is performed over both time origins.Finally, another dynamical property was also calculated, the viscosity ( η ), and plotted infigure 9. The viscosity was calculated with the GreenKubo formula S.10 relates the shearS10
00 400 500 600Temperature / K1000 l og d e n s it y / kg m - TraPPE
Flex vaporExp LiqExp vaporCO / ε vaporCO / ε liqEPM SCEPM LiqTraPPE Flex liq
300 400 500 6001001000300 400 500 6001001000 l og d e n s it y / kg m -
300 400 500 600Temperature / K1000
A)A) B)C) D)
Figure 6: Logarithmic of the density as a function of temperature at different pressuresA) P = 50 bar. B) P = 100 bar. C) P = 1000 bar. D) P = 2000 bar. The simulationresults for TraPPE
F lex , EPM2 and CO / ε were obtained from this work. The solid blackline represents the experimental data of the liquid phase and the solid black line with starsrepresents experimental data of the vapour phase. g (r) g CO (r)g OO (r)g CC (r) A) g (r) ExpCO / ε B) Figure 7: Figure A. The Radial distribution functions g OO , g OC and g CC for CO / ε are plotedfrom the calculation of molecular Dynamics at T = 239 K and P = 14.5 bar. Figure B. Radialdistribution functions, g(r), for CO / ε and neutron weighted pair correlation function at T= 239 K and P = 14.5 bar; experimental pair correlation function is shown in black circles. S11
500 1000 1500 2000P bar51015 D / - m s - TraPPE Exp EPM2 CO2/ ε Figure 8: Diffusion coefficients as a function of pressure at A)298 K of temperature and B)223 K of temperature. The simulation results for the TraPPE, EPM2 and CO / ε are obtainedfrom this work. The black square and solid black lines represent the experimental data. viscosity to the autocorrelation function ACF of the off-diagonal components of the stresstensor P α,β , namely, η = Vk B T Z ∞ < P αβ ( t ) P αβ ( t + t ) > t dt, (S.10)In figure 9 is observed that the CO / ε model gives the correct tendency with the experi-ments. S12
500 1000 1500 2000Pressure / bar00.050.10.150.20.250.3 η / m P a s Exp CO2/ ε TraPPE
Flex
EPM20 50 100 150 200Pressure / bar0.10.150.20.250.30.350.4A) B)
Figure 9: Shear viscosity as a function of pressure at temperature A) T = 298K and B) 223Kfor the TraPPE, EPM2 and CO / ε models are compare. The solid black line represents theexperimental data. VI. Conclusions
Comprehensive molecular dynamics simulations were conducted to built a new flexible CO molecule. Then, series of simulations were carried out to find a new set of parameters forthe CO / ε model. The proposed flexible force field captured polarization of the molecule andreproduced correctly the experimental surface tensions, vapor pressures, densities and thestatic dielectric constants. Dynamical properties were also calculated, and even though theCO / ε model was not parameterized to reproduce these transport properties, the calculationswith the new model are close to the experimental valuesVariation on the ǫ -LJ parameter influence interaction between molecules and somehowinternal energy of the system, therefore thermodynamic properties might be modified and itcould be the reason why the parameter is the one that correct the surface tension. On theother hand, σ -LJ affects the size estructure and consequently the system density. Electrostaticproperties can be altered by point charges and therefore properties such as the static dielecticconstant can be modified by adjustment of those charges. It has been shown that changesof LJ-parameters and charges can directly affect some properties, however they also mightinfluence any other by spoiling correct data and it could be the reason that in some case someproperties fits correctly whereas others fails in other force fields. In fact, by adjustingparameters is hard to reproduce all thermodynamic and dynamical properties ofthe CO2, if some properties are correctly fitted there are other properties thatmight be wrong and vice versa, therefore the best selection of parameters arethose which capture most of the properties with reasonable experimental error.
S13revios works, with using polarizable models have also shown good results with actualexperiments, although they do not calculate surfacte tensions. Comparisons of the present re-sults with a polarizable model are shown in the supplementary material. There, it is observedthat our results agree with those data.On the other hand, force fields using classical potentials fail to reproduce some or manyexperimental properties such as surface tension, vapor pressure, density and dielectric constantat difference thermodynamic conditions. Therefore, in the present work, a new CO force fieldhas been proposed ; which reproduces several thermodynamics, structural and dynamicalproperties improving the present classical CO force fields.It is worthy to mention that approprite CO2 force fields can help us to perform more real-istic and reliable simulations of actual system and to understand better the behaviour of realphenomena such as CO2 capture where good models are needed to explore real experiments. VII. Conflicts of interest
There are no conflicts of interest to declare
VIII. Acknowledgments
The authors acknowledge support from DGAPA-UNAM-Mexico grant IN102017 and DGTIC-UNAM grant LANCAD-UNAM-DGTIC-238 for the supercomputer facilities. RFA thanksDGAPA-UNAM for a posdoctoral fellowship. We also acknowledge Alberto Lopez-Vivasand Alejandro Pompa for technical support. We also want to thank the reviewers for theircomments of the manuscript, they help to improve significantly the paper.
References [1] Lee, S. Y. ;Park, S. Y. Applications of Pore-Expanded Mesoporous Silicas. 3. TriamineSilane Grafting for Enhanced CO2 Adsorption.
J. Ind. Eng. Chem. , , , 111.[2] Wang, Q. ;Luo, L.; Zhong, Z. ;Borgna, A. CO2 capture by solid adsorbents and theirapplications: current status and new trends. Energy Environ.Sci. , , , 4255.[3] Li, B. ; Duan, Y. ; Luebke, D.; Morreale, B. Advances in CO2 capture technology: Apatent review. Appl. Energy, , , 1439-1447.[4] Murthy, C. S.; Singer, K.; McDonald, I. R. Interaction Site Models for Carbon Dioxide. Mol. Phys. , , 135-143.[5] M¨oller, D.; Fischer, J. Determination of An Effective Intermolecular Potential for CarbonDioxide Using Vapour-Liquid Phase Equilibria from NpT + Test Particle Simulations. Fluid Phase Equilib. , , 35-61. S146] Vrabec, J.; Stoll, J.; Hasse, H. A Set of Molecular Models for Symmetric QuadrupolarFluids. J. Phys. Chem. B , , 12126-12133.[7] Harris, J. G.; Yung, K. H. Carbon Dioxide Liquid-Vapor Coexistence Curve And CriticalProperties as Predicted by a Simple Molecular Model. J. Phys. Chem. , , 12021-12024.[8] Potoff, J. J.; Siepmann, I. J. Vapor-Liquid Equilibria of Mixtures Containing Alkanes,Carbon Dioxide, and Nitrogen. AIChE J. , ,1676-1682.[9] Potoff, J. J.; Errington, J. R.; Panagiotopoulos, A. Z. Molecular Simulation of PhaseEquilibria for Mixtures of Polar and Non-Polar Components. Mol. Phys. , , 1073-1083.[10] Zhang, Z.; Duan, Z. An Optimized Molecular Potential for Carbon Dioxide. J. Chem.Phys. , , 214507-15.[11] Merker, T.; Vrabec, J.; Hasse, H. Comment on ”An Optimized Potential for CarbonDioxide” [J. Chem. Phys. 122, 214507 (2005)]. J.Chem. Phys. , , 087101-2.[12] Merker, T.; Engin, C.; Vrabec, J.; Hasse, H. Molecular Model for Carbon Dioxide Opti-mized to Vapor-Liquid Equilibria. J. Chem. Phys. , , 234512-7.[13] Persson, R. A. X. Simple One-Center Model for Linear Molecules: Application to CarbonDioxide. J. Phys. Chem. B. , ,10073-10078.[14] Bock, S.; Bich, E.; Vogel, E. A New Intermolecular Potential Energy Surface for CarbonDioxide from ab Initio Calculations. Chem. Phys. , 257 , 147-156.[15] Bukowski, R.; Sadlej, J.; Jeziorski, B.; Jankowski, P.; Szalewicz, K.; Kucharski, S. A.;Williams, H. L.; Rice, B. M. Intermolecular Potential of Carbon Dioxide Dimer fromSymmetry-Adapted Perturbation Theory.
J. Chem. Phys. , , 3785-3803.[16] Bratschi, C.; Huber, H.; Searles, D. J. Non-Hamiltonian Molecular Dynamics Implemen-tation of the Gibbs Ensemble Method. II. Molecular Liquid-Vapor Results for CarbonDioxide. J. Chem. Phys. , , 164105-8.[17] Vlcek, L.; Chialvo, A. A.; Cole, D. R. Optimized Unlike-Pair Interactions for Water-Carbon Dioxide Mixtures Described by the SPC/E and EPM2 Models. J. Phys. Chem.B. , , 8775-8784.[18] Orozco, G. A.; Economou, I. G.; Panagiotopoulos, A. Z. Optimization of IntermolecularPotential Parameters for the CO2/ H2O Mixture. J. Phys. Chem. B. , , 11504-11511.[19] Jiang, H.; Moultos, O. A.; Economou, I. G.; Panagiotopoulos, A. Z.. Gaussian-ChargePolarizable and Nonpolarizable Models for CO2. J. Phys. Chem. B , , 984-994S1520] Alejandre, J.; Tildesley, D. J.; Chapela, G. A.; Molecular dynamics simulation of theorthobaric densities and surface tension of water. J. Chem. Phys. , , 4574-4583.[21] Salas, F. J.; M´endez-Maldonado, G. A.; N´u˜nez-Rojas, E.; Aguilar-Pineda, G. E.;Dom´ınguez C , H.; Alejandre, J. Systematic Procedure To Parametrize Force Fieldsfor Molecular Fluids. J. Chem. Theory Comput .2015 , , 683-693.[22] Fuentes-Azcatl, R.; Barbosa, M.C.; Potassium bromide, KBr/ ε : New ForceField. J.Physica A . , 491, 480-489.[23] Fuentes-Azcatl, R.; Barbosa, M.C.; Sodium Chloride, NaCl/ ε : New Force Field. J.Phys.Chem.B. , , 2460-2470.[24] Fuentes-Azcatl R.; Alejandre, J.; Non-Polarizable Force Field of Water Based on theDielectric Constant: TIP4P/ ǫ . J. Phys. Chem. B . , , 1263-1272.[25] Fuentes-Azcatl, R. Mendoza, N.; Alejandre, J.; Improved SPC force field of water basedon the dielectric constant: SPC/ ε . J.Physica A . , 420, 116-123.[26] Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms forHighly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem.TheoryComput. , , 435447.[27] Orea, P.; L´opez-Lemus, J.; Alejandre, J. Liquid-vapour equilibrium of n-alkanes usinginterface simulations J. Chem. Phys. , ,114702.[28] Essmann, U. ; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.;Pedersen, L. G. Asmooth particle mesh Ewald method. J. Chem. Phys. , , 85778593.[29] B. M. Mognetti, L. Yelash, P. Virnau, W. Paul, K. Binder, M. Mller, and L. G. Mac-Dowell. Efficient prediction of thermodynamic properties of quadrupolar fluids from sim-ulation of a coarse-grained model: The case of carbon dioxide. J. Chem. Phys. , , 104501.[30] R. Anandakrishnan, C. Baker, S. Izadi, and A. V. Onufriev. Point Charges OptimallyPlaced to Represent the Multipole Expansion of Charge Distributions. PLoS One , ,e67715.[31] P.J. Linstrom. and W.G. Mallard. NIST Chemistry WebBook, NIST Standard ReferenceDatabase Number 69; National Institute of Standards and Technology, GaithersburgMD; http://webbook.nist. gov (retrieved January 1, 2018).[32] Neumann, M. Dipole Moment Fluctuation Formulas in Computer Simulations of PolarSystems. Mol. Phys. , , 841845.[33] Moriyoshi , T.; Kita, T.; Uosaki, Y.; Ber. Bunsen-Ges. Phys. Chem. , , 589.S1634] Glattli,A.; Daura, X.;van Gunsteren, W. F. Derivation of an improved simple pointcharge model for liquid water: SPC/A and SPC/L J. Chem. Phys., , 9811.[35] van Tricht, J. B.; Fredrikze, H.; van der Laan, J. Neutron Diffraction Study of LiquidCarbon Dioxide at Two Thermodynamic[36] Dunweg, B.; Kremer, K. Molecular dynamics simulation of a polymer chain in solution