Chapter 3. Computational Details
3.1 Information of Quantum Chemical Calculations
The Amsterdam Density Functional (ADF) software [69-71] is used to perform all QM calculations. The equilibrium geometry of a molecule is obtained using the GGA Becke Perdew functional and TZP basis set. The spatial distribution of the electrostatic potential is then calculated (using the “densf” utility) on Cartesian grids with medium resolution.
A local minimum in the MESP is determined by comparing the value at a grid point (located at the center of a local 3×3×3 grid) with its 26 neighboring grid points. Each of the local minima found is regarded as a lone pair site. The COSMO [72] calculation is then performed to obtain screening segment charge density on the molecular surface. For neutral species, the results of COSMO calculations have been done according to ADFCRS-2010 database [73-75] and we adopt the results inside the database. The calculation procedure for the activity coefficient is the same as that in the previous work [12].
In order to evaluate the performance of the COSMO-SAC model among different quantum calculation methods, it is necessary to re-optimize the parameters in COSMO-SAC. As in our previous work [15], fpol is the first parameter to optimize based on internal consistency for the averaging process. Second, we optimized the parameters in COSMO-SAC 2002, aeff and Chb, to fit VLE data for 1118 binary systems. Third, the five parameters in COSMO-SAC 2010, AES and BES, were fitted to LLE of 71 non-HB binary systems, and the HB interaction parameters, COH-OH, COT-OT and COH-OT were fitted to 309,
mixtures that contain hydrogen bond interactions (e.g. water, alcohols and amines). The objective function to be minimized, based on root mean square (RMS) errors for the VLE data, is given in Eq. 3.1-1 below.
RMSVLE = 1
M[∑ (yMi=1 icalc-yiexpt)2]
0.5+ 1
M[∑ (picalc-pi
expt piexpt )
2
Mi=1 ]
0.5
(3.1-1)
where y and p are the mole fraction and pressure in the vapor phase respectively, the superscript expt and calc stand for experimental data and calculated values, and M is the number of data points.
The re-optimized parameters for different variations of the COSMO-SAC model are summarized in Table 3.1-1.
Finally, the liquid-liquid equilibrium (LLE), the infinite dilution activity coefficients (IDAC) and octanol-water partition coefficients (Kow) are used to assess the predictive ability of the two types of COSMO-SAC (DHB) models. The experimental data for VLE, LLE and IDAC were obtained from the DECHEMA Chemistry Data Series [76] while the Kow data were obtained from the CRC handbook [77].
Table 3.1-1 Parameters in different COSMO-SAC models considered in this work.
3.2 Three Schemes for Degree of Dissociation of ILs
In this work, we examine three possible schemes of IL dissociation, as shown in Table 3.2-1, in the following discussion.
Table 3.2-1 The three schemes discussed in this work.
Scheme Dissociation Extent (α)
Number of components
Components involved
Non-dissociation 0 2 Solvent, IL ion pair
Full dissociation 1 3 Solvent, cation, anion
Partial dissociation determined based on Eq. 2.5-2 with α0 = 0.35
4 Solvent, cation, anion, IL ion pair
3.3 Combination of COSMO Files for Ion Pairs
For generating COSMO file of ion pairs, instead of directly calculating the ion pair structures in quantum mechanical calculation, we chose to first calculate the σ-profile of both the anion and the cation respective, and then combine them to represent the ion pair, as shown in Figure 3.3-1. This approach allows us to lower the computational cost in DFT, and was proven to be feasible in previous work by Lee and Lin [54].
Figure 3.3-1 Combination of σ-profiles of cation and anion for ion pairs
Chapter 4. Improved Directional Hydrogen Bonding Interactions for the COSMO-SAC Model for Prediction of Activity Coefficients
4.1 Comparison of Thermodynamic Properties from COSMO-SAC (DHB) Using MESP versus VSEPR
The VLE is commonly used to examine the performance of different models over the entire concentration range. The accuracy of VLE is evaluated by the average absolute relative deviation in vapor pressure (AARD-P) and average absolute deviation in mole fraction in the vapor phase (AAD-y). Eqs. 4.1-1 and 4.1-2 show the definition of AARD-P and AAD-y, respectively.
AARD-P = ∑ N1(M1
i∑Mj=1i |pcalcp- pexpexpt|) × 100%
Ni=1 (4.1-1)
AAD-y = ∑ N1(M1
i∑ |yMj=1i icalc - yiexpt|) × 100%
Ni=1 (4.1-2)
where N is number of VLE mixtures and Mi is the number of data points in the ith mixture.
The results are summarized in Table 4.1-1.
Table 4.1-1 Prediction accuracy of COSMO-SAC models for VLE, LLE, IDAC and Kow
The performance in VLE from different models falls in the order COSMO-SAC (DHB) based on MESP, COSMO-SAC 2010, COSMO-SAC (DHB) based on VSEPR, and COSMO-SAC 2002. The overall AARD-P from COSMO-SAC (DHB)/MESP is improved by 26.8%, 4.61% and 7.35% compared to COSMO-SAC 2002, COSMO-SAC 2010 and COSMO-SAC (DHB)/ VSEPR, respectively. As for AAD-y, it is reduced by 17.32% in comparison with COSMO-SAC 2002 and 5.24% in MESP compared with both COSMO-SAC 2010 and COSMO-SAC (DHB)/VSEPR. There is a substantial improvement in AARD-P, which indicates that COSMO-SAC (DHB)/MESP is much more successful in predicting vapor pressures.
Figure 4.1-1 demonstrates the VLE of a few binary mixtures: (a) ethanol (1) – water (2) at 348.15K (b) 2-methyl-1-propanol – DMSO at 353.15K (c) difluoro methane – hydrogen fluoride at 283.15K. Species that cannot be evaluated from VSEPR theory are marked in bold face. In general, COSMO-SAC (DHB)/MESP performs better than the other models, as seen in Figure 4.1-1 (a) and (b). As for case (c), COSMO-SAC 2010 performs the best, perhaps because of the use of variation in hydrogen bond interaction.
It is also worth mentioning that the VSEPR method is not applicable for DMSO, difluoro methane and hydrogen fluoride. Although COSMO-SAC (DHB)/MESP may not always be the best choice for individual systems, it does give the overall best results.
(a)
1E+04 2E+04 3E+04 4E+04 5E+04 6E+04 7E+04 8E+04 9E+04 1E+05
P(Pa)
(b)
(c)
Figure 4.1-1 Comparison of predicted phase diagrams of example VLE binary systems:
(a) ethanol (1) – water (2) at 348.15K (b) 2-methyl-1-propanol (1) – DMSO (2) at 353.15K (c) difluoro methane (1) – hydrogen fluoride (2) at 283.15K. The black
The LLE can be used to assess the predictive performance for equilibria between the two fluids in the two rich phases. The performance for LLE can be evaluated in several ways.
One is to count the number of converged and phase separated points, which is denoted as computable data points, and the second measure is the root mean square error.
RMSLLE = (1
𝑁∑𝑁𝑖=1(𝑥𝑖𝑐𝑎𝑙𝑐 − 𝑥𝑖𝑒𝑥𝑝)2)0.5 (4.1-3)
where N is the number of computable data points in the LLE mixture. In most cases, although there is a slight improvement of RMS in MESP (0.0932 compared to 0.0933), the performance based on VSEPR and MESP are very similar. An apparent progress has been made in the water-3-methyl-1-butanol binary, as shown in Figure 4.1-2(a). MESP is able to determine more data points (2393 compared to 2345) and systems (167 compared to 164) that exhibit phase separation, indicating the effectiveness of using the MESP in orientational constraints for identifying and characterizing hydrogen bonds. Figure 4.1-2(b) presents an example where correct phase separation is predicted only with COSMO-SAC (DHB)/MESP.
(a)
(b)
Figure 4.1-2 LLE of (a) water (1) - 3-methyl-1-butanol (2) (b) water(1) - succinonitrile
The IDAC is useful to examine the solvation behavior of a solute in a solvent. The predictive performance for IDAC is evaluated by the root mean square error
RMSIDAC = [1
N∑ (lnγNi=1 icalc - lnγiexpt)2]
0.5 (4.1-4)
For IDAC, a greater deviation occurs when water is infinitely dilute in alkanes. In MESP, this kind of deviation is more apparent than that in VSEPR. Therefore, the overall RMS of IDAC in MESP is higher than that in VSEPR. However, MESP is more accurate than VSEPR for predicting IDAC after excluding such types of systems, indicating that MESP still performs better in general. Table 4.1-2 illustrates the RMS of IDAC for infinite dilution of water in alkane systems and for the other systems. The scatter plot of comparison between VSEPR and MESP of a total of 431 datapoints is also provided in Figure 4.1-3.
Table 4.1-2 RMS error of IDAC by VSEPR and MESP methods for different systems RMSIDAC
Figure 4.1-3 The relationship between predicted and experimental data [76] for the infinite dilution activity coefficient from COSMO-SAC (DHB) (square: MESP circle:
VSEPR)
Kow is another useful property to examine the solvation behavior of a solute in another solvent. The performance in Kow is evaluated by the root mean square error
RMSlog Kow = [1
𝑁∑𝑁𝑖=1(log 𝐾𝑜𝑤𝑐𝑎𝑙𝑐 − log 𝐾𝑜𝑤𝑒𝑥𝑝𝑡)2]0.5 (4.1-5)
For Kow, MESP also performs better than VSEPR and makes a 3.8% improvement in RMS (0.462 compared to 0.480). Figure 4.1-4 shows the results of Kow from VSEPR and
-5 0 5 10 15 20 25
-5 5 15 25
Calculated ln γi
Experimental ln γi
DHB (VSEPR) DHB (MESP)
Figure 4.1-4 The relationship between predicted and experimental data [77] for the octanol-water partition coefficient from COSMO-SAC (DHB) (square: MESP circle:
VSEPR).
-2 0 2 4 6 8 10
-2 0 2 4 6 8 10
Calculated log(Kow)
Experimental log(Kow)