Evaluation Test of the Most Popular Models of Methanol Using Selected Thermodynamic, Dynamic and Structural Properties. Abdalla Obeidat1, 2 2 Dept. of Physics, Jordan University of Science and Technology, Irbid, 22110, Jordan ABSTRACT Molecular dynamic simulation has been carried out to examine the possibility of eight models of liquid methanol in reproducing the have been carried out using eight intermolecular potential models for methanol: J1, J2, H1, L1, Gromos, TraPEE-UA and OPLSAA. Selected thermodynamic, dynamic and structural data were used and compared with experimental results to appear the relative merits of the mentioned potential models. No single methanol potential model could be found to provide the best agreement between the experiment and simulation. Keywords: Force fields, Surface tension, liquid density, diffusion coefficients, Einstein relation, Green-Kubo, radial distribution function. 1. INTRODUCTION In view of the importance of methanol in numerous engineering, industrial, medical and biological applications[1, 2] it will continue to be an essential subject for molecular dynamics simulations. It is one of the simplest polar fluids, due to its simplicity and availability; many scientists investigate this fluid in macro level system. The success of these investigations depends on the availability of the potential model to produce the proper properties of methanol. For methanol, a variety of potential models of methanol have been proposed and tested to be used in molecular dynamic simulations. In the present work findings of nine different potential models of methanol have been investigated and compared including J1, J2, H1, B3, L1, TraPPE-UA, OPLSAA and Gromos. The mentioned models appears different degree of complicity, ranging from three site models with one interacting site for methyl group(CH3 ), another site on the oxygen atom, and a third site on the hydrogen of the hydroxyl group(OH), to six site model taking into account the flexibility and polarizability effects. The J1, J2, H1, B3, van L1, and TraPPE-UA were built on three-site atom due to its low computational cost, and the other two models (i.e. OPLS-AA and Gromos). Difference between these models reside in the values Lennard-Jones parameters and the charges on each interacting sites. The geometrical parameters as well as the values of Lennard-Jones parameters for all models are given in Table 1. Molecular dynamics have been carried out on quite good range of low temperature; from 200K to 300K with an interval of 10K. The quantities. Molecular dynamics have been carried out for methanol on quite good range of low temperature; from 200K to 300K with an interval of 10K. The quantities have been investigated in this work are: surface tension, density and its correlated properties such as t10-90 and roughness of the vapor-liquid interface, dipole moment, diffusion coefficients and structural analysis. Based on the analysis, we were able to judge the best methanol model one might use as a simple fluid or when mixed with other polar fluid such as water. One good reason of simulating the methanol at low temperature is due to its importance in studying nucleation which occurs at these low temperatures. Since nucleation is very sensitive to the surface tension (πΎ 3 ), hence, the estimation of surface energy is crucial in understanding the vapor-liquid embryo.Since calculating the surface tension requires a vapor-liquid interface which by return requires long simulation time to equilibrate. Table 1 show all the intermolecular potential studied in this work. The organization of this paper is as follows: immediately after this brief introduction, simulation details ,…., followed by Even though simulating the liquid density doesn’t require long time, but for the interface to equilibrate, long run simulations have been done especially for calculating the surface tension which depends on the pressure which fluctuates tremendously. So, to calculate the diffusion coefficients, we are obliged to use Einstein relation since it works well for long time run where the Green-Kubo fails to produce the correct value. Even though the dipole moment shouldn’t depend on the temperature, but we found out by increasing the temperature, the dipole moment decreases slowly. It is well known also the NPT system doesn’t give the right structure, for this reason all the simulations were run using the NVT system, also it was shown by others that the diffusion coefficients doesn’t vary with pressure especially at low temperature. For the first maxima in calculating the pair distribution function, we found that it changes linearly with temperature, and the result will be published soon for alcohol (methanol, ethanol and propanol) and water. Table 1. Lennard-Jones Parameters and geometry for potential models used. Model ππͺπΆ ππΆπ― β‘πͺπΆπ― ππΆ ππͺ πΊπΆ πΊπͺ ππΆ ππͺ J1 J2 H1 B3 L1 GROMOS96 TraPPE-UA OPLS-AA 0.1425 0.1425 0.1425 0.1530 0.1425 0.1360 0.1430 0.1410 0.0945 0.0945 0.0945 0.1000 0.0945 0.1000 0.0945 0.0945 108.53 108.53 108.53 108.50 108.53 108.53 108.50 108.50 0.3083 0.3071 0.3083 0.3180 0.3030 0.3143 0.3020 0.3120 0.38610 0.37750 0.38610 0.36000 0.37400 0.35525 0.37500 0.35000 0.73200 0.71100 0.73200 0.55200 0.71900 0.67850 0.77324 0.71128 0.78500 0.86600 0.75800 1.01700 0.87500 1.10380 0.81500 0.27614 -0.685 -0.700 -0.728 -0.674 -0.700 -0.574 -0.700 -0.683 0.285 0.265 0.297 0.266 0.265 0.176 0.265 0.145 I. ππ― 0.400 0.435 0.431 0.408 0.435 0.398 0.435 0.418 SIMULATION DETAILS Our system consists of 400 molecules of methanol confined in a box of 3.5x3.5x3.5 ππ3 , the methanol molecules distributed randomly in this box, then placed at the middle of empty box of 3x3x12 ππ3 to ensure vacuum-liquid interface. Before performing the dynamics, it must ensure that the system has no gaps or unfitting geometry. The structure is relaxed through a process called energy minimization (EM). In this work, maximum steps of 50000 energy minimization with 2×10−5 KJ/mol energy step using particle mesh Ewald (PME) grid method of a spherical cut-off radius of 1.0 nm of Leonard-Jones short-range interaction and Coulomb longrange interaction were used to minimize the energy. To begin real dynamics, the molecules must equilibrate. Equilibration is often directed in two steps. The first one is pressure equilibration, which conducted under an NPT ensemble, the mean goal of this step is to change the box size to reach the best look like realistic case in order to obtain an accurate value of density at the desired temperature. The temperature was controlled by Nose-Hoover thermostat. It is well known also the NPT system does not give the right structure, also it was shown by others that the diffusion coefficients do not vary with pressure especially at low temperature, for this reason, all the simulations were followed by using the NVT system, the temperature of the system should reach a plateau at the desired value. If the temperature has not yet stabilized, additional time is required. In this work a total time of 2 ns has applied to NPT, and 2 ns for NVT followed by production run of 100ps for collecting the data. Gromacs 4.6.5 package has been used for a set of temperatures: 200-300K. Periodic boundary conditions were applied in our simulations in all directions. The spherical cut-off radius of 1.1nm has been used simultaneously for the Leonard-Jones short range interaction and the PME Coulomb long range interaction as stated in the previous paper (~1.25nm), except for TraPPE where a cutoff radius of 1.4nm is used as recommended by their inventors. 2 II. RESULTS AND DISCUSSIONS 1. Thermodynamic Results The first focus of the paper is on the thermodynamic properties of methanol over entire range of temperature 200-300K. The thermodynamic properties were reported for all models considered for methanol, such as Density, t10−90 and Surface Roughness and surface tension. 1. Density Measuring density is essential to determine the characteristics of materials, here the effect of temperature on the density was examined for the eight models considered for methanol and compared to experiment. It is clear from Figure 1 that the density of methanol follows the experimental trend regardless of the model used, but the, L1, TraPPE and OPLS-AA best fit the experimental data as stated by their inventor who cared about the density of vapor-liquid interface for temperatures up to the critical point. The vapor and liquid densities of vapor-liquid interface can be calculated after fitting the density profile to 1 1 z − z0 ρ(z) = (ρl + ρv ) − (ρl − ρv )tanhβ‘( ) 2 2 d Where ππ , ππ£ are the bulk densities of the liquid and vapour respectively, π§0 is the place of the Gibbs dividing surface and π is the width of the interface Since we are simulating methanol at low temperatures, the vapor density is set to zero, π§0 is the place of Gibbs dividing surface, and π is related to the π‘10−90 (the width of the interface) by πππ’ππ‘πππ, the width also is very important in determining the roughness of the surface, it is given by ππππππππ. Figure 2 and 3 show the variation of the thickness and the roughness of the surface, the figures show that both quantities vary linearly with temperature. Comparing the roughness with the experimental value measured at 300K; a value of 0.48, we notice that the best model estimates the roughness is the Gromos force field followed by L1, B3 and TraPPE-UA (it is clear the last value is not right!) Figure1.Thedensity (π) of all methanol force fields as a function of temperature (T) compared to experimental data[3] 3 Figure2. The roughness of all methanol force fields as a function of temperature. Figure3. The roughness of all methanol force fields as a function of temperature. 2. Surface Tension The temperature effect on the surface tension were investigated for all models presented for methanol. To estimate the surface tension, a 10ns run time have been simulated since the surface tension depends on pressure which fluctuates heavily, the surface tension has been calculated using the following relation followed by the tail correction 1 ∞ ππ₯π₯ + ππ¦π¦ πΏπ§ ππ 3π 3 − π πΎ = (ππ§π§ − ) + 12πππ 6 (ππ − ππ£ )2 ∫ ππ ∫ coth ( ) β‘ππ 2 2 π π3 0 ππ Where Lz is the box length on z direction,β‘Pαα is the αα component of the pressure tensor, rc is the cutoff radius andβ‘Ο΅ and σ are the Lennard-Jones parameters Figure 4 shows the variation of surface tension with temperature, the relation as expected is inversely linear. The best models which estimate the correct value are OPLS-AA and Gromos, unfortunately, both models are built on six-site model which require high computational cost. For the three-site model, the best models are L1 and TraPPE-UA. 4 Figure 4. Temperature dependence of the surface tension liquid methanol. The MD results are shown for all methanol models compared to experimental data (β)[4] II. DIFFUSION COEFFICIENT In this section, we turn to focus on studying translational mobility of molecules of methanol at constant pressure in the temperature range from 200 to 300 K through calculating the self-diffusion coefficient. Figure 6 shows the diffusion coefficient of methanol obtained by Green-Kubo formalism[5] for the present models which is given by 1 ∞ π·π = ∫ ππ‘ ⟨ππ (t). ππ (0)⟩ 3ππ 0 Where ππ (t) is the center of mass velocity vector of molecules at some time t, ππ (0) is the same but at time π‘ = 0,⟨… . . ⟩ denotes the ensemble average, and ππ is the total number of molecules of type π. In figure 5 the temperature dependence of diffusion coefficient for each of the models considered in this is presented together with the NMR experimental results obtained from previous study[6-8]. It is clear that the diffusion coefficient is well produced by GROMOS96 and J2 models over the entire temperature range spanned by the NMR experimental results. While the J1 model gave the worst results with values much higher than the experimental values, the B3 model gave good results at low temperature range, but the results gradually moved away below the experimental values with the increase in temperatures. Models J2, H1, and OPLSAA shows a very good match and smooth. TraPPE-UA and L1 Models gave excellent results for the first half of the temperature but moved away slightly and gradually as the temperature increases It is believed that the self-diffusion coefficient follows an Arrhenius- like relation with temperature The relationship is π· = π·0 π ΔπΈ ππ΅ π − , 5 Figure 5. Temperature dependence of the diffusion coefficient of liquid methanol. The MD results are shown for all methanol models compered to experimental data (β)[9] As seen from figure 10 and 11, the diffusion coefficient of methanol obeys the Arrhenius equation; the calculated apparent activation energies(E) of diffusion are listed in table2. 6 Figure 6. Arrhenius plot for the logarithm of self-diffusion (D) as a function of temperature (T) inverse compared to experimental data (β). The MD results are shown for all methanol models. Model J1 J2 H1 B3 L1 π«π 17.46 16.45 16.84 18.55 16.92 OPLSAA 17 GROMOS 15.82 TraPPEUA 16.6 EXP 13.75 It was shown by Jorgensen that the activation energy of H2 model is ~8. II. DIPOLE MOMENT The experimental value of the dipole moment of methanol is ~1.7 D, the models studied in this work predicts the following values: J1(2.24), J2(2.26), H1(), B3(2.42), L1(2.26), OPLS-AA (2.37), Gromos (1.91) and TraPPE-U A (2.26). Clearly, the best model which produces the closest value to experimental one is the Gromos force field, which overestimates the liquid density! Generally speaking, the dipole moment shouldn’t depend greatly on temperature, our results show a small change of dipole moment by decreasing the temperature in the third digit as in figure 6. 7 Figure 7. Temperature dependence of the dipole moment of B3 model of methanol. 8 I. RADIAL DISTRIBUTION FUNCTION (RDF) The structure of liquids is ordinarily expressed in terms of radial distribution functions. in particular, the most structured and interesting RDF for liquid methanol corresponds to O-O, O-H, and H-H radial distribution functions, they played an important role in assessing the quality of methanol models. In Figures 8 and 9 the πππ and πππ» RDFs is plotted and compared to experimental neutron diffraction RDFs published by Yamaguchi et al [10] for the eight models of methanol. The most essential features of these functions are, the position and the height of the ο¬rst peak, as well as, the position of the first minimum, they have been listed in Table 3 and 4. The hydrogen bonding of O-O, O-H, and H-H RDFs show excellent match with the positions of the first maximum and minimum peaks, but their corresponding O-O and O-H g(r)s much higher than the experimental ND maxima and lower than the minima. The best matches with experimental peaks positions are O-O and H-H for GROMOS96 model and O-H for the L1 model. For g(r)s value, J1 have the best O-H and O-O matches, and GROMOS96 for H-H. Figure 8. O-O RDFs for methanol models compared to experimented ND RDF 9 4 4 J1 Exp. 2 2 1 2 1 0 0.0 5 0.5 r (nm) 1.0 1.5 B3 Exp. 4 1 0 0.0 5 0.5 r (nm) 1.0 1.5 vLS Exp. 4 2 1 r (nm) 1.0 1.5 TraPPE Exp. 4 0 0.0 4 0.5 r (nm) 1.0 1.5 0.5 r (nm) 1.0 1.5 0.5 r (nm) 1.0 1.5 3 2 1 0 0.0 0 0.0 4 Exp. OPLS Exp. 3 1 Gromos Exp. 1 2 2 1.5 2 g (rOH) g (rOH) 3 1.0 g (rOH) 0.5 r (nm) 4 1 0 0.0 5 0.5 g (rOH) 2 0 0.0 5 3 g (rOH) 3 g (rOH) 3 H1 Exp. 3 g (rOH) 3 g (rOH) g (rOH) 3 4 J2 Exp. 1 0 0.0 0.5 r (nm) 1.0 1.5 0 0.0 0.5 r (nm) 1.0 1.5 Figure 1: O-H RDFs for methanol models compared to experimented ND RDF As a summary of the previous figures, Table 4 shows the positions of the first maxima for each model alongside their corresponding values, furthermore, the coordination numbers are shown in Table 5 with the corresponding values of the first minima. The most important coordination number values to describe the hydrogen bonding is for O-O and H-H in which give a value ranged approximately about 2 for all models, these values are in agreement with the experimental coordination number value of ND. Table 3. The position of first maxima and its value compared to experimental data. Model J1 J2 H1 B3 Gromos OPLS-AA TraPPE-UA L1 EXP C-C 4.28,1.753 4.20,1.779 4.32,1.138 4.04,1.585 4.08,1.795 4.08,1.755 4.18,1.100 4.28,1.779 4.00,2.108 C-H 3.02,0.949 2.84,1.070 2.90,0.644 2.82,1.030 2.64,1.125 2.76,0.896 2.78,1.100 2.80,1.114 2.80,0.900 C-O H-H 3.58,1.722 3.54,1.870 3.56,1.137 3.54,1.947 3.44,1.892 3.5,1.796 3.50,1.920 3.48,1.915 3.54,1.715 10 2.50,2.470 2.46,3.450 2.44,3.230 2.48,3.679 2.40,3.290 2.52,3.030 2.42,3.700 2.40,3.710 2.34,2.750 O-H 1.90,3.570 1.80,5.110 1.86,4.380 1.76,6.350 1.68,4.193 1.88,4.190 1.78,5.750 1.78,5.750 1.80,1.580 O-O 2.82,3.130 2.74,4.240 2.78,3.860 2.74,4.480 2.66,4.330 2.80,3.700 2.70,4.690 2.68,4.460 2.71,1.930 Table 4. The position of first minima and its corresponding coordination number. Models HH OH J1 J2 H1 B3 GROMOS OPLS TraPPE VL&S EXP 3.520,2.630 3.220,2.450 3.380,2.440 3.220,2.530 3.180,2.560 3.460,2.660 3.280,2.560 3.180,2.500 3.300,2.150 2.700,1.170 2.580,1.260 2.600,1.128 2.600,1.320 2.680,1.260 2.680,1.260 2.540,1.300 2.540,1.300 2.620,0.810 OO 3.560,2.160 2.480,2.320 3.520,2.160 3.420,2.370 3.280,2.370 3.520,2.310 3.420,2.350 3.320,2.280 3.490,1.896 The experimental X-ray diffraction structure-function published by Narten and Habenchuss was derived from the measured scattering cross section based on a two-site model (OH and CH3) and normalized to the scattering from a single average site in a methanol molecule (29, 30). This representation of the structure-function depends, however, on the number of sites used to describe the molecule (31). In this study, the same technique used to calculate total X-ray structure functions and distinct weighted structure functions and distinct RDF functions, so that, we convert our 3-site and 6-site methanol models to 2-site model by joining the hydrogen atoms to the carbon and oxygen atoms; the only O-O, C-O and C-C RDFs are used, reweighted by using the equation πππ’ππ‘πππ The total X-ray structure functions H(k) can be calculated by including the intramolecular RDFs (are not shown in figures 1015) into account. Figure 16 shows the total weighted structure functions of methanol models compared with experimental XRD total weighted structure function (30). It is clear that the OPLS-AA model has the best match with the X-ray experiment; even though most models show a good agreement with experiment but with a shift in the results of B3. Obviously, there is a small peak in the experimental data after the first highest peak, all models fail to reproduce it, also, and for all models, when the π value increases, the height of the peaks does not correspond well with the experimental values, this might due to the approximation of the form factor to be equal to the number of atoms, and we know well this is true only for small values of π. The comparison shows that all model leads to a basically correct description of the structure of liquid methanol including intramolecular geometry. A more sensitive check of the intermolecular structure is possible by the comparison of the distinct structure functions shown in Figure 17. We note that the experimental ND values are calculated by using the XRD structure-function formula, with using the C-C, C-O and O-O ND RDFs. The distinct structure functions of all models have a good agreement with experiment except for a small phase shift at π values approximately between 2.5 and 5. 11 1.0 1.0 1.0 H1 Exp. J2 Exp. J1 Exp. KH (K) 0.5 0.0 KH (K) 0.5 KH (K) 0.5 0.0 -0.5 0 5 K(A o -1 ) 10 -0.5 15 1.0 0.0 0 5 10 K(A 1.0 o -1 15 -0.5 ) 10 1.0 -0.5 15 ) 0.0 0 5 10 K(A 1.0 o -1 15 -0.5 ) 10 o -1 o -1 -0.5 15 15 ) KH (K) 0.0 K(A 10 K(A 0.5 KH (K) KH (K) 0.0 5 5 Exp. 0.5 -0.5 0 0 1.0 OPLS Exp. T raPPE Exp. 0.5 15 ) KH (K) 0.0 o -1 o -1 0.5 KH (K) 0.0 K(A 10 K(A Gromos Exp. 0.5 KH (K) 0.5 5 5 vLS Exp. B3 Exp. -0.5 0 0 1.0 0.0 0 5 ) 10 K(A o -1 15 -0.5 0 5 ) K(A o -1 10 15 ) Figure 2: Total weighted structure functions of methanol models compared with experimental XRD total weighted structure function 0.8 0.8 J1 Ex p. XRD Ex p. ND 0.4 0.4 -0.4 4 8 K (A 0.8 12 16 ) -0.8 -0.4 0 4 K (A o -1 8 ) 12 16 B3 Exp. XRD Exp. ND VAN-B Ex p. XRD Ex p. ND 0.4 K (A o -1 ) 8 12 16 -0.8 Tra PPE Ex p. XRD Ex p. ND 0 4 K (A o -1 ) 8 12 16 -0.8 OPLS Ex p. XRD Ex p. ND KHd K (A o -1 ) 8 12 16 -0.8 16 Gromos Ex p. XRD Ex p. ND 0 4 K (A o -1 8 ) 12 16 Exp. XRD Exp. ND 0.4 -0.4 4 12 0.8 0.4 -0.4 8 ) -0.4 0.0 KHd 0.0 o -1 0.0 0.8 0.4 K (A 0.4 -0.4 0.8 4 KHd 0.0 -0.4 0 0.8 KHd KHd 0.0 4 -0.8 0.8 0.4 -0.8 0 KHd -0.4 o -1 -0.8 0 0.4 KHd -0.8 0 H1 Ex p. XRD Ex p. ND 0.0 KHd 0.0 KHd 0.0 0.8 J2 Ex p. XRD Ex p. ND 0.0 -0.4 0 4 K (A o -1 ) 8 12 16 -0.8 0 4 K (A o -1 8 ) 12 16 Figure 3. Distinct weighted structure functions of methanol models compared with experimental ND and XRD distinct weighted structure function 12 Figure 4.Total distinct RDF functions of methanol models compared with experimental ND and XRD Total distinct RDF functions To better comparison, the distinct RDF has been calculated by Fourier transformation from the distinct structure function. The Gd(r) from experiment ND and XRD and the models are compared in Figure18. It can be seen from the comparison that the first peak is due to O-O, and this means that the O-O first RDF peak of X-ray is higher than all the models. The distance spectrum in a range of 3-6 nm is a combination of O-O second peak and C-O and C-C first peaks. It’s clear that a reason for the phase shift distance spectrum reflected in distance spectrum by the high and position of the first and second O-O RDF. In general, OPLS-AA methanol model shows the best results compared to X-ray structure function. To better comparison, the distinct RDF has been calculated by Fourier transformation from the distinct structure function. The Gd(r) from experiment ND and XRD and the models are compared in Figure18. It can be seen from the comparison that the first peak is due to O-O, and this means that the O-O first RDF peak of X-ray is higher than all the models. The distance spectrum in a range of 3-6 nm is a combination of O-O second peak and C-O and C-C first peaks. It’s clear that a reason for the phase shift distance spectrum reflected in distance spectrum by the high and position of the first and second O-O RDF. In general, OPLS-AA methanol model shows the best results compared to X-ray structure function. 13 MD simulations were performed to study the structural and the dynamics of unary liquid methanol of J1, J2, H1, B3, L1, GROMOS96, TraPPE-UA and OPLS-AA models, and the dynamics of the binary TraPPE-UA/TIP4P, TraPPE-UA/SPCE, OPLSAA/TIP4P and OPLS-AA/SPCE mixed models in NVT ensembles. The calculated radial distribution functions of unary methanol models were compared with neutron diffraction experimental RDFs. All models show agreement with C-C, C-H, C-O and H-H neutron diffraction RDFs with a slight difference. The hydrogen bonding O-O and O-H RDFs agreed with the positions of peaks, but with a higher g(r) values, the J1 model provided the closest agreement with the height of the peak. For all models, the coordination numbers of O-O and H-H are about two, and one for O-H, these values agree with experimental ND values. Total X-ray structure functions and distinct weighted structure functions and distinct RDF functions were computed for all methanol models and compared with experimental XRD and calculated ND, a phase shift in spectrums appeared with a general agreement with experimental XRD spectrums. The phase shift in spectrums appeared because of the high and position of the first and second O-O RDF. General comparison using H(k), Hd(K) and Gd(r) spectrums, OPLS-AA have the best X-ray structure function. The diffusion constant was calculated by using Green-Kubo method for unary methanol models at different temperatures and for binary water-methanol and water-ethanol mixed models at different mixing ratios. For unary methanol, all models, except J1 and B3 models show very close values to experimental data. The GROMOS96 model shows the best match compared to other models, while OPLS-AA is the smoothest curve as the temperature changes. 14 CONCLUSION We have presented a methanol model and compared its performance for a wide range of properties to models found in the literature. To achieve this goal each model has been simulated under the same conditions for long simulation times. Our model B3 is shown to be in overall agreement with experiment and to be competitive concerning the reproduction of a variety of experimental quantities with reference models from the literature. The initial aim of getting a model that combines well with SPC water and that has a dielectric permittivity close to the experimental value is only partly fulfilled. The B3 methanol model interacts well with SPC water over the whole range of mole fractions and also reproduces well the hydration free energy. 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