Predicting Limiting Activity Coefficients and Phase Behavior from

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Predicting Limiting Activity Coefficients and Phase Behavior from Molecular Structure: Expanding MOSCED to Alkanediols Using Group Contribution Methods and Electronic Structure Calculations Pratik Dhakal, Sydnee N. Roese, Maria A. Lucas, and Andrew S. Paluch* Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, Ohio 45056, United States S Supporting Information *

ABSTRACT: The modified separation of cohesive energy density (MOSCED) is a powerful tool for early stage process conceptualization and design. It is capable of making quantitative phase-equilibrium calculations, and more importantly may be used to qualitatively understand the underlying molecular level details of a system for intuitive process design. Unfortunately, its use is limited in that parameters must first be known before predictions may be made. Here we explore the use of group contribution methods (GCMOSCED) and electronic structure calculations in the solvation model based on density (SMD) and SM8 continuum solvation models to calculate missing parameters. We demonstrate the use of GC-MOSCED to expand MOSCED using limited data, and the ability of electronic structure calculations to calculate parameters devoid of experimental data. While GC-MOSCED performs best, we demonstrate that good predictions may be made using electronic structure calculations with the SMD continuum solvation model. Application is demonstrated for limiting activity coefficients and binary isobaric azeotropic vapor−liquid equilibrium with 1,2ethanediol.

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coefficients,14,15 and a range of vapor−liquid equilibria properties15 has been demonstrated. As compared to UNIFAC, MOSCED characterizes a molecule using pure component, molecular descriptors. The use of molecular descriptors allows for the differentiation of isomers and the inclusion of (intramolecular) neighboring effects. More important, MOSCED is not restricted to making quantitative predictions, but as a solubility parameter-based method, it can be used to qualitatively understand the underlying molecular level details for intuitive solvent selection, formulation, and process design.15,16 Unfortunately, MOSCED is limited to making predictions only for systems in which parameters exist. If parameters are not available, they may be found by fitting to reference data. In the recent (2005) reparameterization, parameters were regressed for 130 organic solvents using 6441 reference limiting (or infinite dilution) activity coefficients.12 The set of reference data was obtained after the literature was carefully surveyed and the data were vetted. MOSCED may be expanded to cover additional compounds using a limited amount of data involving the 130 organic solvents for which parameters exist.

INTRODUCTION Knowledge of the phase-equilibrium of mixtures is crucial for the design of separation processes, both industrial and laboratory scale. Phase-equilibrium is additionally central to understanding the transport of environmental pollutants and for drug delivery applications. Unfortunately, phase-equilibrium data are often unavailable for a system of interest and its measurement requires extensive effort. This is particularly problematic for feasibility and comparative process studies where time and resources are limited, and for early stage process conceptualization and design. For this reason the availability of accurate methods to predict phase-equilibrium is of utmost importance.1 The universal functional group activity coefficient (UNIFAC) method2−4 and its modification by Gmehling and coworkers (mod-UNIFAC)5−10 have long been established and used to predict phase-equilibrium. However, in general, UNIFAC and mod-UNIFAC do not take into account structural information, and therefore in many cases are not able to distinguish between isomers nor account for (intramolecular) neighboring effects of functional groups.1,11 Additionally, functional groups are often lacking for novel molecules and for multifunctional compounds typically encountered in the fine-chemicals industry.1 Recently, the parameter matrix for the modified separation of cohesive energy density (MOSCED) has been refreshed,12 and its use to predict limiting activity coefficients,12 solubility of nonelectrolyte solids in pure and mixed solvents,12,13 partition © XXXX American Chemical Society

Special Issue: Emerging Investigators Received: December 12, 2017 Accepted: February 26, 2018

A

DOI: 10.1021/acs.jced.7b01080 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

ln γ2∞ = ln γ2∞,RES + ln γ2∞,COMB

The recent work of our group has been focused on developing strategies to calculate MOSCED parameters with

ln γ2∞,RES =

limited, or in the absence of, experimental reference data. In this effort we have recently developed a group contribution (GC-MOSCED) model.17 GC-MOSCED adopts groups directly from Gani and co-workers,18,19 which includes second-

⎛ v ⎞aa2 ⎛ v ⎞aa2 ln γ2∞,COMB = ln⎜ 2 ⎟ + 1 − ⎜ 2 ⎟ ⎝ v1 ⎠ ⎝ v1 ⎠

and third-order groups to provide additional structural information and to distinguish between isomers. We have

aa 2 = 0.953 − 0.002314[(τ2(T ))2 + α2(T )β2(T )]

additionally used electronic structure calculations in the SMD20

⎛ 293K ⎞0.8 (T ) ⎛ 293K ⎞0.8 (T ) ⎛ 293K ⎞0.4 ⎟ ⎟ ⎟ αi(T ) = αi⎜ , βi = βi ⎜ , τi = τi⎜ ⎝ T ⎠ ⎝ T ⎠ ⎝ T ⎠

and SM821 continuum solvents to generate reference data to regress parameters devoid of experimental data for nonelectrolyte solids.

22−26

ψ1 = POL + 0.002629α1(T )β1(T )

Alongside this work we are developing

ξ1 = 0.68(POL − 1) 2 + [3.4 − 2.4 exp(− 0.002687(α1β1)1.5 )](293K/ T )

a suite of freely available tools to facilitate the use of MOSCED and GC-MOSCED to make phase-equilibrium calcula-

POL = q14[1.15 − 1.15 exp(− 0.002337(τ1(T ))3 )] + 1

tions.15,17,27 Recently too, Gnap and Elliott28 have demon-

(1)

strated the ability to predict MOSCED parameters using

where ln γ 2∞,RES and ln γ 2∞,COMB are the residual and combinatorial contribution to ln γ∞ 2 , vi is the (liquid) molar volume, λi, τi, αi, and βi are the solubility parameters due to dispersion, polarity, and hydrogen bond acidity and basicity, respectively, where i = {1, 2}, and the induction parameter, qi, reflects the ability of the nonpolar part of a molecule to interact with a polar part. The terms ψ1 and ξ1 are empirical (solvent dependent) asymmetry terms to modify the residual contribution for polar and hydrogen bonding interactions, and aa2 is an empirical (solute dependent) term to modify the size dissimilarity in the combinatorial contribution for polar and hydrogen-bonding interactions. These additional empirical terms are not adjustable but are functions of the other parameters (τi, αi, βi, and qi). For all cases aa2 ≤ 0.953, effectively reducing the size dissimilarity and magnitude of the combinatorial contribution, with the value smaller for polar and associating compounds. R is the molar gas constant and T is the absolute temperature. The superscript (T) is used to indicate temperature dependent parameters, where the temperature dependence is computed using the empirical correlations provided in eq 1. As suggested by the equations, MOSCED adopts a reference temperature of 293 K (20 °C). An equivalent expression for the limiting activity coefficient for component 1 in 2 (γ∞ 1 ) can be written by switching the subscript indices. MOSCED may not be used directly to predict composition-dependent activity coefficients; however, γ∞ 1 and γ∞ 2 may be used to calculate binary interaction parameters for an excess Gibbs free energy model, such as Wilson’s equation, nonrandom two liquid (NRTL), or universal quasichemical (UNIQUAC), which in turn can be used to predict composition-dependent activity coefficients.39,40 Likewise, the ability to use MOSCED to predict binary interaction parameters for an excess Gibbs free energy model allows for the ability to model mixtures of three or more components. MOSCED is based on the theory that the cohesive energy (ΔUcoh) may be separated into individual contributions (due to specific intermolecular interactions) which are additive.39,41−44 On the basisof the work of ref 44, we recently demonstrated the utility of the following expression:

surface charge densities (σ-profiles) from electronic structure calculations. In the present study, we assess the use of these strategies to compute MOSCED parameters for the alkanediols: 1,2ethanediol, 1,2-propanediol, 1,3-propanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, 1,9-nonanediol, and 3-chloro1,2-ethanediol. The parameterization of MOSCED for alkanediols is of great practical interest.29,30 1,2-Ethanediol (or ethylene glycol) is the simplest alkanediol (or glycol), and has a wide range of uses from the manufacture of polyesters to use as an automobile antifreeze and airplane deicing fluid.29,30 1,2-Propanediol (or propylene glycol) is unique in that it is safe for human consumption, and has a lower environmental toxicity as compared to 1,2-ethanediol.29,30 This has encouraged its use in the food, drug, cosmetic, and liquid detergents industry.30 The study of alkanediols is additionally interesting from a method development perspective. The conformational isomers of 1,2-ethanediol remain a contemporary area of research31−38 making it an excellent assessment of the proposed methods. Application is demonstrated for limiting activity coefficients and binary isobaric azeotropic vapor−liquid equilibrium with 1,2-ethanediol.

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⎡ q 2q 2(τ1(T ) − τ2(T ))2 v2 ⎢ (λ1 − λ 2)2 + 1 2 ψ1 RT ⎢⎣ (α1(T ) − α2(T ))(β1(T ) − β2(T )) ⎤⎥ + ⎥⎦ ξ1

METHODOLOGY

The limiting activity coefficient for component 2 in 1 (γ∞ 2 ) is calculated using MOSCED via the following series of equations:12,16 B


Journal of Chemical & Engineering Data ΔU coh = v(λ 2 + a1τ 2 + a 2αβ)

Article 2 ⎛ ln γ2,∞i ,MOSCED ⎞ ⎜ ⎟ OBJ = ∑ ⎜1 − ln γ2,∞i ,ref ⎟⎠ i=1 ⎝

(2)

N

where a1 = 2.8373 and a2 = 3.1152, and were introduced as a result of the empirical asymmetry terms. Assuming the vaporphase is an ideal gas and that the molar volume of the vaporphase is much greater than the liquid-phase, the cohesive energy may be related to the enthalpy of vaporization (ΔHvap) as39,41 ΔH vap = ΔU coh + RT

(4)

ln γ∞ 2,i

the square of the relative error between computed using MOSCED and the reference (“‘ref’”) value, as indicated by the superscript, where the summation is over all N = 24 reference values. Doing so, we obtain the following MOSCED parameters, all in units of MPa1/2 or (J/cm3)1/2: λ = 16.521, τ = 8.599, α = 21.629, and β = 20.205. The agreement between MOSCED and the reference data is quantified by computing the average absolute relative error (AARE) in γ∞ 2 and the average absolute error (AAE) in ln γ∞ 2 :

(3)

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PARAMETER REGRESSION A major limitation of MOSCED is that it is not truly predictive. Before calculations may be made for a component of interest, MOSCED parameters must be known. Here we use our recently developed group-contribution model (GCMOSCED)17 and electronic structure calculations in a continuum solvent to predict MOSCED parameters devoid of experimental data. To assess these predictive flavors of MOSCED, we will predict parameters for alkanediols. In the recent 2005 MOSCED parameterization, no alkanediols were parameterized.12 Parts 1 to 6 of DECHEMA’s ‘‘Activity Coefficients at Infinite Dilution’’ collection were surveyed to identify all alkanediols for which experimental limiting activity coefficients were available.45−50 We were able to identify seven compounds: 1,2-ethanediol, 1,2-propanediol, 1,3-propanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol and 1,9-nonanediol. We add to this set the single halogen-substituted alkanediol found, 3-chloro-1,2-propanediol. We take the existence of data for this set of compounds to indicate their relevance, which we will adopt as the test set for this study. The data for 1,2-ethanediol was additionally supplemented with freely available data from the Dortmund Data Bank (DDB).51

AARE % =

AAE =

1 N

1 N

N

∑

|γ2,∞i ,ref − γ2,∞i ,MOSCED| γ2,∞i ,ref

i=1

100 (5)

N

∑ |ln γ2,∞i ,ref − ln γ2,∞i ,MOSCED|

(6)

i=1

γ∞ 2

ln γ∞ 2

We obtain an AARE in of 8.4%, and an AAE in of 0.093 log units. Using eqs 2 and 3 we predict ΔHvap = 105.25 kJ/mol at 293 K. Comparing to the reference value of ΔHvap = 69.34 kJ/mol from ref 53, we find that ΔHvap is largely over predicted by approximately 36 kJ/mol or 52%. Given the ability of eqs 2 and 3 to well model the 130 organic compounds for which MOSCED was originally parameterized, we attribute the shortcoming to an inadequacy of the reference set used to regress MOSCED parameters. To overcome this limitation, we modified OBJ to include the relative error in the predicted value of ΔHvap: 2 ⎛ lnγ2,∞i ,MOSCED ⎞ ⎟ OBJ = ∑ ⎜⎜1 − lnγ2,∞i ,ref ⎟⎠ i=1 ⎝ N

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2 ⎛ ΔH vap,MOSCED ⎞ + w ⎜1 − ⎟ ⎝ ΔH vap,ref ⎠

EXPERIMENTAL MOSCED PARAMETERS In the 2005 MOSCED parameterization, the reference data was extensively vetted. In general, limiting activity coefficients measured using liquid chromatography techniques were excluded because of its disagreement with data obtained from other techniques and known experimental uncertainties in the data measured using this technique.12,52 We therefore discarded limiting activity coefficients measured using liquid chromatography. We additionally excluded indirectly measured limiting activity coefficients, and restricted the data to only that involving the 130 organic solvents for which MOSCED is parameterized. Unfortunately, this eliminated nearly all of the data from DECHEMA and DDB, which would explain why MOSCED parameters were previously not regressed for these systems. We were left only with a limited data set for 1,2-ethanediol. For this system 24 limiting activity coefficients are available for 7 organic solutes. The solutes are methanol, ethanol, 2propanol, benzene, hexadecane, hexane, and cyclohexane. Unfortunately, the solutes show limited variety in their chemical functionality. We adopted the molar volume of 1,2ethanediol from ref 53, fixed q = 1, and regressed the remaining MOSCED parameters (λ, τ, α, and β) by minimizing the following objective function (OBJ) using the differential evolution (global) optimization technique as implement in GNU Octave:54,55

(7)

where w is a weight factor taken to be 2N, and is used to balance the contributions to OBJ. Using this updated OBJ, we obtain the following MOSCED parameters, all in units of MPa1/2 or (J/cm3)1/2: λ = 10.118, τ = 7.576, α = 14.155, and β = 21.125. We find that λ, τ, and α all decrease, while β increases. While previously we had α > β, in this new set of parameters we have α < β. This result is consistent with the linear solvation energy relationship (LSER) molecular descriptors for acidity and basicity for 1,2-ethanediol.56,57 ∞ This results in an AARE in γ∞ 2 of 18.5% and an AAE in ln γ2 of ∞ 0.157 log units. While the errors in γ2 increase slightly, we now predict ΔHvap = 69.16 kJ/mol, which is in much closer agreement with the reference data. A parity plot of ln γ∞ 2 computed using MOSCED versus the reference data is provided in Figure 1, which demonstrates the ability of MOSCED to well correlate the data. We were unable to regress parameters for any of the other compounds in our test set due to the unavailability of reliable reference data. Note that in eq 4 we sum squared relative errors in ln γ2∞. On the other hand, in the 2005 MOSCED parameterization, sum squared errors in ln γ∞ 2 were used. We found this choice to have an insignificant effect on the regressed MOSCED parameters. In the present study we use relative errors so that when ΔHvap is incorporated into the OBJ the C



Article

(This includes all compounds containing an aromatic group.) For alkenes, q, is computed as 1 minus the number of double bonds (or in general, the degrees of unsaturation) divided by twice the number of carbon atoms. First, consider 1,2-ethanediol, 1,2-propanediol, and 3-chloro1,2-propanediol. While first-order groups are available, we are missing the second-order group CHm(OH)CHn(OH) (m,n in 0...2) suggested by Gani and co-workers.18,19 The inclusion of this second order group is very important. The importance may be understood using the physical basis of MOSCED combined with the physical interpretation of the first-, second-, and thirdorder groups. For alkanes, vτ2 = 1 − q = v1/2α = v1/2β = 0. As a result, when parameterizing GC-MOSCED, all alkane group weights were assigned a value of zero in the calculation of yGC = {vτ2, 1 − q, v1/2α, v1/2β}. Ethanol is modeled using only firstorder groups, with only the OH (hydroxyl) group contributing to the cohesive energy due to polar and association interactions. The MOSCED parameters τ, α, and β are related to the charge distribution of a molecule, and are therefore directly related to the local and overall dipole moments. In this picture then we are assuming we have a single bond dipole on the OH group which is therefore equal to the overall molecular dipole. If we were to model 1,2-ethanediol using only first-order groups, only the two OH groups would contribute to the cohesive energy due to polar and association interactions. For this case then we are assuming that we have two bond dipoles, one on each OH group, which are additive. However, the additivity will be dependent on the conformation and the resulting orientation of the OH groups relative to each other. If we were to use only first order groups, we would overpredict ΔHvap by approximately 40.9 kJ/mol or 58.8%, suggesting that the modeled intermolecular interactions are too strong.53 The unique structure of 1,2-ethanediol is well-known. UNIFAC and mod-UNIFAC both represent molecules using only first-order groups, and both model 1,2-ethanediol using a 1,2-ethanediol specific main group “DOH”.3,6,58 The study of the conformational isomers of 1,2-ethanediol remains a contemporary area of research, involving experimental and advanced theoretical treatments.31−38 1,2-Ethanediol is challenging as the terminal hydroxyl groups allow for the potential of intramolecular hydrogen bonding. While in the gas phase the prominent conformations involve intramolecular hydrogen bonding, in solution with an associating species, we expect a competition between intra- and intermolecular hydrogen bonding.34,38 This interesting behavior necessitates the use of a 1,2-ethanediol specific main group. Here, we obtain the second-order group CHm(OH)CHn(OH) (m,n in 0...2) by matching the experimentally regressed MOSCED parameters for 1,2-ethanediol. In doing so, we find that the group weights for yGC = {vλ2, v1/2α, v1/2β} are all negative. This is in stark contrast to the parameterization of GC-MOSCED wherein all group weights were assumed to be greater than or equal to zero.17 As a result, we have reregressed the matrix of GC-MOSCED weights wherein first-order groups are greater than or equal to zero, but negative second- and third-order group weights are allowed. Details and the updated parameter matrix are provided in the Supporting Information. Overall, by allowing negative groups, the accuracy of the regression has improved. With this new set of GC-MOSCED weights, we obtain the second order group CHm(OH)CHn(OH) (m,n in 0...2) by matching the experimentally regressed MOSCED parameters for 1,2-ethanediol, and these may be found in Table 1.

Figure 1. A parity plot of the log limiting activity coefficient (ln γ∞ 2 ) predicted using MOSCED versus the reference value for our reference set of organic solutes in 1,2-ethanediol.45−51 Predictions are made using MOSCED with GC-MOSCED estimated parameters, and using parameters regressed using SMD and SM8 generated reference data for 1,2-ethanediol. Note that the GC-MOSCED parameters for 1,2ethanediol are equivalent to the parameters regressed using the reference set plus enthalpy of vaporization. The vertical dotted lines are drawn for reference to separate the solutes, where to the left of the first line we have the alcohols, the right of the second line we have the alkanes, and in between we have benzene.

term is dimensionless, and the error in ln γ∞ 2 is computed in a consistent fashion.

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GC-MOSCED Recently we have proposed a group-contribution (GC) method for estimating MOSCED parameters, GC-MOSCED.17 Having demonstrated the ability of eq 2 to correlate MOSCED parameters, the method further assumes that the contributions to the cohesive energy are group additive. Parameters are calculated using the general equation: yGC =

∑ niwi i

(8)

where wi is the contribution (or weight) of group i that occurs ni times in the molecule of interest, and yGC is the groupcontribution estimated property, where yGC = {v, vλ2, vτ2, 1 − q, v1/2α, v1/2β}. Groups were adopted directly from the work of Gani and co-workers,18,19 which includes second- and thirdorder groups to provide additional structural information and to distinguish between isomers, information not contained in traditional first-order groups. We emphasize that GCMOSCED is based on the assumption of group additivity of the contributions to the cohesive energy. Therefore, for example, τ is computed as τ=

∑i ni(vτ 2)i ∑i ni(v)i

(9)

2

where (vτ )i and (v)i correspond to the weight of group i in the GC model for vτ2 and v, respectively. The GC calculation of 1 − q in general is not necessary, but was introduced to facilitate automatic parameterization. One may calculate q using the suggestions of the original MOSCED publications.12,16 For saturated molecules q = 1, and for aromatic compounds q = 0.9. D



Article

Table 1. Second- and Third-Order Groups Necessary To Model Alkanediols and Their Weighta

a

group

v

vλ2

vτ2

1−q

v1/2α

v1/2β

CHm(OH)CHn(OH) (m,n in 0...2) OH-(CHn)m−OH (m > 2, n in 0...2)

2.6978 2.6978

−5.3535 −5.3535

2.4738 2.4738

0 0

−2.1511 −2.1511

−1.2864 −1.2864

The units of v are cm3/mol, 1 − q is dimensionless, the units of the vλ2 and vτ2 are kJ/mol, and the units of v1/2α and v1/2β are (kJ/mol)1/2.

Table 2. MOSCED Parameters for the Studied Alkanediols As Computed Using GC-MOSCED17, and Regressed Using SMD and SM8 Generated Reference Dataa CASRN

method

v2

λ2

τ2

q2

α2

β2

1,2-ethanediol

107-21-1

3-chloro-1,2-propanediol

96-24-2

1,2-propanediol

57-55-6

1,3-propanediol

504-63-2

1,4-butanediol

110-63-4

1,5-pentanediol

111-29-5

1,6-hexanediol

629-11-8

1,9-nonanediol

3937-56-2

GC SMD SM8 GC SMD SM8 GC SMD SM8 GC SMD SM8 GC SMD SM8 GC SMD SM8 GC SMD SM8 GC SMD SM8

55.750 59.33 59.33 61.957 83.04 83.04 72.738 75.51 75.51 72.575 68.65 68.65 89.400 85.17 85.17 106.225 101.68 101.68 123.050 118.19 118.19 173.525 167.72 167.72

10.118 8.939 15.201 11.339 9.917 15.411 10.041 9.360 15.023 11.792 9.083 15.226 12.724 9.794 15.059 13.324 10.166 14.827 13.744 10.515 14.855 14.482 10.597 15.062

7.576 2.616 0.000 8.950 3.115 0.000 6.633 2.381 0.000 6.640 3.413 0.543 5.983 2.726 0.487 5.489 2.626 0.893 5.100 2.260 0.704 4.294 2.573 0.223

1 1 1 0.973 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

14.155 10.615 20.067 14.865 8.656 13.694 12.392 8.156 14.798 12.406 9.287 16.980 11.178 7.328 12.782 10.255 5.285 8.994 9.528 4.857 8.134 8.023 4.702 7.978

21.125 23.543 12.454 20.955 17.625 9.731 18.494 21.582 12.185 18.515 21.445 12.997 16.682 21.117 13.541 15.304 17.406 12.397 14.219 17.586 11.792 11.974 15.918 10.584

compound

a

v2 has units of cm3/mol, q2 is dimensionless, and λ2, τ2, α2, and β2 all have units of MPa1/2 or (J/cm3)1/2.

1,5-pentanediol at 298.15 K. In that work the authors find that ΔHvap at 298.15 K shows a strong linear correlation with the number of carbon atoms, with a rate of increase of 7 kJ/mol per CH2 group. The authors additionally find that comparing ΔHvap to that of an alkane with the same number of carbon atoms gives a mean difference of 47 kJ/mol, or approximately 23.5 kJ/mol per OH group. In ref 59 ΔHvap at 298.15 K was determined from vapor pressure data measured using torsionand Knudsen-effusion methods for 1,n-alkanediols with a carbon chain length of n = {6, 8, 10, 12, 14, 16}. The authors likewise found that ΔHvap at 298.15 K shows a linear correlation with the number of carbon atoms with a rate of increase of approximately 5.5 kJ/mol. A comparison of the ΔHvap to that of an alkane with the same number of carbons shows the mean difference to be 56 kJ/mol, or approximately 28 kJ/mol per OH group. While this contribution computed in ref 59 is slightly larger than that in ref 60, we note that the 1,nalkanediols with a chain length of n = {6, 8, 10, 12, 14, 16} are solid at 298.15 K and thus the results are based on extrapolations from elevated temperatures. Nonetheless, it is suggested that ΔHvap scales linearly with the number of carbon atoms, and the effect of the addition of an OH group in the 1 and n position is constant. This is in exact agreement with GC-MOSCED. For the homologous series, the change of ΔHvap with respect to the number of carbon atoms is exactly equal to the (vλ2) weight of

The GC-MOSCED predicted parameters for 1,2-ethanediol, 1,2-propanediol, and 3-chloro-1,2-propanediol may be found in Table 2. By construction, the GC-MOSCED parameters for 1,2-ethanediol are equivalent to the experimentally regressed parameters. However, 1,2-propanediol and 3-chloro-1,2-propanediol may be viewed as predictions. The enthalpy of vaporization at 293.15 K is available for 1,2-propanediol, which we find GC-MOSCED under-predicts by just 0.3 kJ/mol or 0.4%.53 Next, we consider the homologous series of the 1,nalkanediols: 1,3-propanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, and 1,9-nonanediol. For 1,3-propanediol and longer chains in the homologous series, UNIFAC and modUNIFAC represent the molecules as a sum of the same CH2 and OH groups used to model linear alcohols.58 On the other hand, Gani and co-workers18,19 suggest that for 1,3-propanediol and longer chains the third-order group OH-(CHn)m−OH (m > 2, n in 0...2) be used. The inclusion of this third-order group is important as already discussed in the context of 1,2ethanediol. Following the work of refs 59 and 60 we assume the thirdorder group OH-(CHn)m−OH (m > 2, n in 0...2) weights are identical to the second-order group CHm(OH)CHn(OH) (m,n in 0...2) weights which we obtained from 1,2-ethanediol. In ref 60, detailed vaporization calorimetry studies were performed on the series 1,2-ethanediol, 1,3-propanediol, 1,4-butanediol, and E



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Article

ELECTRONIC STRUCTURE CALCULATIONS Using electronic structure calculations in a continuum solvent (or molecular simulation free energy calculations) one may calculate the solvation free energy of a solute (component 2) in a solvent (component 1), ΔGsolv 2,1 , or equivalently the residual chemical potential at infinite dilution.63−65 Here, we define the solvation free energy as the change in free energy of taking a solute from an ideal gas to solution at the same molecular density (or concentration). We have shown previously that 15,22,66−68 ∞ ΔGsolv 2,1 may be related to γ2 as

a CH2 group. Also by assuming the parameters for the thirdorder group OH-(CHn)m−OH (m > 2, n in 0...2) and the second-order group CHm(OH)CHn(OH) (m,n in 0...2) are the same, ΔHvap relative to that of an alkane with the same number of carbon atoms is a constant 54.7 or 27.35 kJ/mol per OH group. As noted in the development of GC-MOSCED, for all homologous series with a repeating CH2 unit, GC-MOSCED will predict that the rate of increases of ΔHvap with respect to the carbon number is exactly equal to the (vλ2) weight of a CH2 group, 4.38 kJ/mol.17 Reference 59 finds that the linear homologous series of alkanes, methyl ethers, alkane-1-ols, alkane-1-thiols, and 1,n-alkanedithiols all show a linear dependence on the number of carbon atoms with a rate of increase of approximately 5 kJ/mol. This is in agreement with the recent work of Costa et al.61 who suggest a rate of increase of 4.95 kJ/mol for n-alkanes and their monosubstituted derivatives. The rate of increase for 1,n-alkanediols is either greater than or less than this value depending on the data set. For example, the data of ref 62 gives a rate of approximately 4.1 kJ/mol. While not pursued in the present study, if desired, the rate of increase in ΔHvap with respect to the carbon number could be used to obtain vλ2 weights of CH2 that are unique to a particular chemical family for improved predictions. This was not pursued here because of the variation in available reference data and the desire to keep the model as simple as possible. The data from refs 59,60, and 62 are plotted alongside the GC-MOSCED predictions in Figure 2. The GC-MOSCED

v (T , p ) 1 solv (T , p) = ln γ2∞(T , p) + ln 1 ΔG2,1 RT v2(T , p) 1 + ΔG2self (T , p) RT

(10)

ΔGself 2

where is the solute “‘self’”-solvation free energy. ΔGself 2 , v1, and v2 are all pure component properties. It stands that using electronic structure calculations in a continuum solvent we can compute ln γ∞ 2 within a solute dependent constant, ΔGself . This presents a route wherein electronic structure 2 calculations in a continuum solvent may be used to generate reference data to regress MOSCED parameters. Namely, if calculations are performed for a solute in a range of solvents for which MOSCED parameters exist, the results may be used to regress the necessary MOSCED parameters and ΔGself 2 . The solute molar volume, v2, in general is not regressed. In the present study its value is adopted from the group-contribution method of Hukkerikar et al.19 Likewise, q2 need not be regressed. If it is desirable to optimize q2 for best fit, we recommend restricting its value to the range of 0.9 to 1. This practice was adopted in the present study, and in all cases we obtain q2 = 1. Electronic structure calculations were performed for all eight compounds in our test set, and were performed in a similar manner as in our recent work to use electronic structure calculation to paramaterize MOSCED for nonelectrolyte solids.23−26 The point of departure from our previous work is on the generation of the molecular structures. As already mentioned, for the molecules in our test set, the molecular conformation is very important. We therefore performed a detailed conformer search and geometry optimization using molecular mechanics with MMFF94 using Avogadro.69−71 In all cases, the lowest energy conformer was found to involve intramolecular hydrogen bonding between the two hydroxyl groups.72 We then took the lowest energy conformer and optimized the geometry in vacuum at the M06-2X/6-31G(d) level of theory/basis set.64,73 Using this geometry, single point energy calculations were performed at the M06-2X/6-31G(d) level of theory/basis set in vacuum and in a self-consistent reaction field (SCRF) using the SMD20 or SM821 universal solvation model for each solvent of interest; both SMD and SM8 are parameterized with the goal of reproducing experimental solvation and transfer free energies at 298.15 K. The single point energy calculation in each solvent combined with the single point energy calculation in vacuum is used to calculate ΔGsolv 2,1 . The calculations involving SMD were all performed with Gaussian 09,74 and the calculations involving SM8 were all performed with Q-Chem 4.0.1.75 Calculations were performed in 72 organic solvents at 298.15 K. The solvents were chosen because they were contained in the SMD parameter database in Gaussian 09, the SM8 parameter database in Q-Chem 4.0.1, and in MOSCED. All

Figure 2. Enthalpy of vaporization (ΔHvap) versus the number of carbon atoms (NC) in the homologous series of the 1,n-alkanediols. Reference data are provided from Piacente et al.,59 Knauth and Sabbah,60 and Gardner and Hussain62 at 298.15 K, and from Yaws53 at 293.15 K. Predictions are made at 293.15 K using MOSCED with GCMOSCED estimated parameters, and using parameters regressed using SMD and SM8 generated reference data.

results are in good agreement with the results of ref 62. It is interesting to note that the data of refs 60 and 62 are in excellent agreement for 1,2-ethanediol, but predict a different rate of increase of ΔHvap with respect to carbon number (7 vs 4.1 kJ/mol, respectively). Data is also shown from ref 53 at 20 °C. The data show great agreement for 1,2-ethanediol, but then exhibit noticeable scatter. F



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Table 3. Vapor Pressure (psat) of the Studied 1,n-Alkanediols in Units of Pa Predicted When Regressing MOSCED Parameters Using SMD and SM8 Generated Reference Data, along with Reference Dataa from Yaws77 and Knauth and Sabbah60,78

of the solvent molar volumes at 298.15 K (v1) were taken directly as the molar volume at 293 K contained in the current MOSCED (2005) database. This was motivated by our desire to parameterize MOSCED devoid of experimental data while striving to keep the proposed method as simple as possible. The required single point energy calculations are computationally inexpensive, so no attempt was made to reduce/optimize the solvent set. With this set of N = 72 reference (ref) values of ΔGsolv 2,1 , MOSCED parameters and ΔGself were regressed by minimizing 2 the following objective function (OBJ-E) using the differential evolution (global) optimization technique as implement in GNU Octave:54,55 ⎛ ⎞2 ΔG2,solv,MOSCED i ⎟ OBJ‐E = ∑ ⎜⎜1 − ⎟ ΔG2,solv,ref ⎠ i i=1 ⎝

SM8

Yaws77

1,2-ethanediol 1,3-propanediol 1,4-butanediol 1,5-pentanediol 1,6-hexanediol 1,9-nonanediol

63.148 19.332 9.148 28.135 7.064 0.02725

100.370 20.642 10.523 24.613 12.174 0.10217

8.7893 5.0388 1.3982 0.99994 0.10354 0.1022

Knauth and Sabbah60,78 13.332 2.6664 0.39997 0.039997 0.0053329

The MOSCED predicted values and the data from Yaws are at 293.15 K, while the data from Knauth and Sabbah is at 298.15 K.

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which is analogous to eq 4. The resulting MOSCED parameters are provided in Table 2, and ΔHvap values computed using eqs 2 and 3 are shown in Figure 2. We find that with the SMD and SM8 regressed parameters, ΔHvap is underpredicted. The disagreement with the reference data is the least for 1,2ethanediol, and increases with the number of carbon atoms. This suggests that SMD and SM8 underestimate the selfinteraction energy. Comparing the SMD regressed parameters to GC-MOSCED, for all cases λ2, τ2, and the self-association (α2β2) predicted using SMD is less than that predicted using GC-MOSCED. SMD does, however, predict that β2 > α2 in agreement with GC-MOSCED and LSER molecular descriptors for acidity and basicity for 1,2-ethanediol.56,57 For all cases, SM8 predicts τ2 = 0. The polarity parameter (τ2) is related to the fixed dipole moment of a molecule in solution, and in the recent 2005 MOSCED parameterization of organic solvents, only the alkanes had values of τ2 = 0. This value is therefore questionable. We additionally find that for 1,2-ethanediol, 3chloro-1,2-propanediol, 1,2-propanediol, and 1,3-propanediol, SM8 predicts β2 < α2, in disagreement with GC-MOSCED, the SMD regressed parameters, and LSER molecular descriptors for acidity and basicity.56,57,76 In addition to regressing MOSCED parameters via eq 11, we 0 additionally regress ΔGself 2 . The pure liquid fugacity, f 2, may be 22 self related to ΔG2 as v (T , p) 1 ΔG2self (T , p) − ln 2 RT RT

SMD

a

N

ln f 20 (T , p) =

compound

ization scheme. In doing so, we are implicitly including reference experimental data in the parameterization. Our previous work has shown that this results in improved quantitative predictions compared to using electronic structure calculations alone.23 For the case of 1,2-ethanediol, SMD and SM8 solvent parameters exist, allowing ΔGself 2 to be computed directly. In doing so, we compute ΔGself 2 /(RT) to be −12.62 and −14.49 for SMD and SM8, respectively. This corresponds to psat 2 of 138.09 and 21.28 Pa, respectively. The agreement with the reference data decreases with SMD, but improves with SM8. By computing ΔGself 2 , we could directly compute values of ln γ∞ 2 that could be used to parameterize MOSCED. However, we found this did not have a significant effect on the regressed MOSCED parameters, and in the general case, SMD and SM8 solvent parameters are not expected to be available. As an additional test, we repeated the SMD and SM8 solvation free energy calculations for 1,2-ethanediol in the 72 organic solvents wherein the geometry was reoptimized in each solvent. This was found to have an insignificant effect on the regressed MOSCED parameters. Using the reference set of limiting activity coefficients for organic solutes in 1,2-ethanediol, we obtain an AARE in γ∞ 2 of of 0.362 and 1.370 log 51.5% and 76.9%, and an AAE in ln γ∞ 2 units for the SMD and SM8 regressed parameters, respectively. As seen in Figure 1, we find that the SMD predictions are in good agreement with the reference data and GC-MOSCED. This is especially encouraging as the SMD results are pure predictions whereas the GC-MOSCED parameters for 1,2ethanediol include the data in its parameterization, and the reference values of γ∞ 2 span 4 orders of magnitude. Moreover, while SMD appeared to underestimate the self-interaction energy, we can nonetheless make an accurate prediction of γ∞ 2 . We additionally point out that the reference set is for organic solutes in 1,2-ethanediol, while the SMD and SM8 generated reference data used to regress parameters is for when 1,2ethanediol is the solute. The largest disagreement between the predictions made using the SMD regressed parameters and the reference set is for 2-propanol. Data are available at 313 and 323 K, and the AARE in γ∞ 2 for these two points is 256%. Excluding these two points, the AARE in γ∞ 2 decreases from 51.5 to 32.9%. On the other hand, the predicted trend using the SM8 regressed parameters is noticeably different. For all cases except 2-propanol, γ∞ 2 is underpredicted.

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At low pressures we may assume the vapor phase in equilibrium with the liquid phase at T is an ideal gas (so that the fugacity coefficient is unity) and the Poynting correction is negligible sat such that f L2 ≈ psat 2 , where p2 is the (pure component) liquid 39 saturation pressure. In Table 3 we compare psat 2 at 298.15 K obtained in our regression of parameters using both SMD and SM8 data as compared to reference data from ref 77 and from refs 60 and 78 in which the later data was measured directly at 298.15 K using Knudsen effusion. We find that the predicted values of psat 2 are in reasonable agreement with the reference data given the small magnitude of the values. We find that for all cases the value of psat 2 predicted using SMD and SM8 is greater than the reference data, further confirming that the selfinteraction energies appear to be underestimated. The value of ΔGself 2 regressed is dependent not only on the SMD and SM8 reference data, but additionally we include the MOSCED parameters for 72 organic solvents in the parameterG



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Table 4. MOSCED Parameters for Naphthalene As Computed Using GC-MOSCED,17 and Regressed Using SMD and SM8 Generated Reference Dataa in Our Previous Work25

a

compound

CASRN

method

v2

λ2

τ2

q2

α2

β2

naphthalene

91-20-3

GC SMD SM8

129.07 136.4 136.4

17.09 15.10 15.94

4.97 5.23 4.279

0.92 0.9 0.9

1.32 0.076 0.0008

1.33 0.68 1.210

v2 has units of cm3/mol, q2 is dimensionless, and λ2, τ2, α2, and β2 all have units of MPa1/2 or (J/cm3)1/2.

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VAPOR−LIQUID EQUILIBRIUM As a final assessment of the predictive flavors of MOSCED, we will use them to predict binary isobaric (Txy) azeotropic vapor−liquid equilibrium (VLE). Azeotropic VLE results from deviations from ideality, with either favorable or unfavorable cross interactions. Additionally, the prediction of isobaric VLE offers the additional challenge of accurately calculating temperature-dependent activity coefficients. A survey of parts 1, 2a, 2b, 2h, and 7 of the DECHEMA ‘‘Vapor−Liquid Equilibrium Data Collection’’,79−83 the DECHEMA ‘‘Recommended Data of Selected Compounds and Binary Mixtures’’,84 and the freely available data from DDB51 shows that the only candidate system identified was 1,2-ethanediol and naphthalene at 99.99 kPa.51,85 MOSCED parameters for naphthalene were estimated using GC-MOSCED for use with the GC-MOSCED 1,2-ethanediol parameters, where the necessary third-order group AROM.FUSED[2] was previously fit using only data for quinoline.17 Parameters for naphthalene for use with the SMD and SM8 regressed 1,2-ethanediol parameters were adopted directly from our previous work to use SMD and SM8 to regress MOSCED parameters for nonelectrolyte solids.25 The parameters are summarized in Table 4. For all VLE calculations, the pure component vapor pressure of 1,2-ethanediol and naphthalene were computed using the Antoine equation parameters from ref 77. While MOSCED may not be used directly to predict composition-dependent ∞ activity coefficients, γ∞ 1 and γ2 may be used to calculate binary interaction parameters (BIPs) for an excess Gibbs free energy model, such as Wilson’s equation, NRTL, or UNIQUAC.39,40,86 The parameterized model may then be used to predict composition-dependent activity coefficients. Experimentally, 1,2-ethanediol and naphthalene exhibit a heterogeneous azeotrope. We therefore adopted the NRTL equation with a fixed value of α12 = 0.3.15,39,40 Using each parameter set, MOSCED calculations were performed at 10 equally spaced temperatures between the saturation temperature of each ∞ component. At each temperature, ln γ∞ 1 and ln γ2 were used to solve for the BIPs in the NRTL equation. While the NRTL equation contains a temperature dependence, we performed a linear correlation of the temperature dependent BIPs (i.e., a12 = c0+c1T). The parameterized NRTL equation is able to compute temperature and composition dependent values of γ1 and γ2. The “‘modified’”-Raoult’s law (γ−ϕ approach) was used to model VLE. Reference calculations were additionally performed with mod-UNIFAC.5−10 using CHEMCAD 7.1.0.9402.87 The VLE predictions were analyzed following the recommendation of Mathias.88 In Figure 3 we compare the predicted volatility of 1,2-ethanediol (K1) and naphthalene (K2), where Ki =

yi xi

= γi

Figure 3. Relative volatility (α1,2) and volatility of 1,2-ethanediol (K1) and naphthalene (K2) as a function of 1,2-ethanediol liquid mole fraction (x1) at isobaric vapor−liquid equilibrium at 99.99 kPa. Reference (ref) values are provided51,85 along with predictions made using mod-UNIFAC5−10 and using MOSCED with GC-MOSCED estimated parameters, and using parameters regressed using SMD and SM8 generated reference data (for both components). The average absolute relative error (AARE) is computed for K1 and K2 in the dilute region, x1 ≤ 0.25 and x2 ≤ 0.25, respectively, as indicated by the vertical dotted line drawn as a reference.

where psat i is the pure component vapor pressure of species i, and we compare the relative volatility, α1,2 = K1/K2. At the azeotrope, α1,2 = 1. We find that all of the methods correctly predict the presence of an azeotrope in good quantitative agreement. To assess the ability of the methods to predict VLE, we focus on the prediction of K1 and K2 when 1,2-ethanediol and naphthalene are dilute, respectively, where here we take dilute to be when x1 and x2 ≤ 0.25. In the dilute region the error is largest. The error in quantified using the average absolute relative error (AARE) in the volatility, computed as AARE =

Kpred i

N

∑ i=1

|K ipred − K iref | K iref

(14)

Kref i

where and are the predicted and reference volatility, respectively, and the summation is over all N reference compositions in the dilute region. Considering the volatility of 1,2-ethanediol, K1, all of the methods overpredict K1 in the dilute region, with SM8 performing best, followed by modUNIFAC, and SMD and GC-MOSCED which are in excellent agreement. Considering the volatility of naphthalene, K2, using mod-UNIFAC, GC-MOSCED, and MOSCED with SMD predicted parameters, K2 is likewise overpredicted in the dilute region. For this case, GC-MOSCED performs best, followed by MOSCED with SMD predicted parameters. If we were to average the error of K1 and K2 in the dilute region, GCMOSCED would perform best, closely followed by SMD, and then mod-UNIFAC. Using MOSCED with SM8 predicted

pisat P

1 N

(13) H



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7.1.0.9402.87 The CHEMCAD recommended data uses the NRTL equation fit to reference data. (Results using UNIQUAC instead of NRTL were found to be indistinguishable.) We see that the predictions made with GC-MOSCED and MOSCED with SMD predicted parameters compare favorably to the CHEMCAD recommended data. Also, while we use the NRTL equation with α12 = 0.3 with the MOSCED predictions, CHEMCAD uses α12 = 0.103. This value of α12 would have been regressed along with the BIPs. We find that if we use this value of α12 with our MOSCED predictions, the change is insignificant. In Figure 6 we additionally provide plots of the percent relative error (%RE) in the volatility as a function of composition, where

parameters, K2 is underpredicted. Of all of the predictions, the overall error in K1 and K2 is smallest with the SM8 predicted parameters. However, the improvement over GC-MOSCED and MOSCED with SMD predicted parameters is not great for this single test case. In Figure 4 we additionally provide a Txy

%RE =

K ipred − K iref K iref

100 (15)

Figure 4. Isobaric vapor−liquid equilibrium (Txy) of 1,2-ethanediol(1) and naphthalene(2) at 99.99 kPa. Reference (ref) values are provided51,85 along with predictions made using mod-UNIFAC5−10 and using MOSCED with GC-MOSCED estimated parameters, and using parameters regressed using SMD and SM8 generated reference data (for both components).

diagram comparing all of the methods. We notice that GCMOSCED and MOSCED with SMD predicted parameters are in excellent agreement, while MOSCED with SM8 predicted parameters predicts lower temperatures. To further illustrate the quality of the predictions made with GC-MOSCED and MOSCED with SMD predicted parameters, in Figure 5 we provide a Txy comparing predictions made in the present study to the recommended data provided by CHEMCAD

Figure 6. Percent relative error (% RE) in the predicted volatilities as compared to the reference data51,85 for 1,2-ethanediol (K1) and naphthalene (K2) at isobaric vapor−liquid equilibrium at 99.99 kPa. Predictions are made using mod-UNIFAC5−10 and using MOSCED with GC-MOSCED estimated parameters, and using parameters regressed using SMD and SM8 generated reference data (for both components).

We notice that GC-MOSCED and MOSCED with SMD predicted parameters are in very good agreement.

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CONCLUSION In the present study we assessed the use of the recently proposed group contribution method (GC-MOSCED) and electronic structure calculations in the SMD and SM8 continuum solvents to calculate MOSCED parameters with limited or no experimental reference data. Application was made to the alkanediols: 1,2-ethanediol, 1,2-propanediol, 1,3propanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, 1,9-nonanediol, and 3-chloro-1,2-ethanediol. Parts 1 to 6 of DECHEMA’s ‘‘Activity Coefficients at Infinite Dilution’’ collection were surveyed to identify experimental limiting activity coefficient data,45−50 and data for 1,2ethanediol were additionally supplemented with freely available data from the Dortmund Data Bank (DDB).51 While data were available for all of the compounds of interest, after vetting the data we were left with a limited reference set of limiting activity coefficients for seven organic solutes in 1,2-ethanediol. The

Figure 5. Isobaric vapor−liquid equilibrium (Txy) of 1,2-ethanediol(1) and naphthalene(2) at 99.99 kPa. Reference (ref) values are provided51,85 along with the recommended data provided by CHEMCAD 7.1.0.9402,87 and predictions made using MOSCED with GC-MOSCED estimated parameters, and using parameters regressed using SMD and SM8 generated reference data (for both components). I



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data set was not chemically diverse, and we were unable to calculate reasonable MOSCED parameters. However, reasonable parameters were obtained after including the enthalpy of vaporization in the fit. Using GC-MOSCED, the studied alkanediols could be described using first-order groups from our previous work.17 However, this led to an overprediction of the self-interaction energies and an overestimation of the enthalpy of vaporization. This results from the importance of the conformation of the compounds, which is captured using a second- or third-order group. We fit this missing group by matching the predicted 1,2ethanediol parameters with those calculated using experimental data. With this new group, we were able to well predict the enthalpy of vaporization for the homologous series of 1,nalkanediols. This is consistent with our previous findings in the development of GC-MOSCED for the homologous series of linear primary monocarboxylic acids.17 If MOSCED can be parameterized for a single molecule in a homologous series, GC-MOSCED can be used to predict parameters for the entire series. This provides a route wherein the MOSCED parameter matrix may efficiently be expanded using limited reference data. Using electronic structure calculations in the SMD continuum solvent to regress MOSCED parameters devoid of experimental data, the predicted limiting activity coefficients in 1,2-ethanediol were in good agreement with the calculations made using GC-MOSCED (which was fit to the reference data). On the other hand, using electronic structure calculations in the SM8 continuum solvent, we obtain the unreasonable result that the polar parameter, τ, is equal to zero, and the predictions were consistently less than the reference data. Additionally, using the SMD and SM8 based parameters to predict the enthalpy of vaporization of the homologous series of 1,n-alkanediols gave results that were not in good qualitative nor quantitative agreement with the available reference data. The predicted parameters were additionally used to model the binary isobaric vapor−liquid equilibrium (Txy) of the system 1,2-ethanediol(1)/naphthalene(2) at 99.99 kPa. All of the predictive methods were able to predict the location of the azeotrope in good agreement with experiment. On the basis of the ability to accurately predict the volatility of each species in the dilute region, we found that GC-MOSCED performs best overall, followed closely by MOSCED with SMD regressed parameters. This is consistent with the advice of ref 1 that the accuracy of the predicted phase-equilibria should decrease from using experimental data, to group contribution methods, to electronic structure calculations. When regressing parameters using SMD and SM8 generated reference data, we include the MOSCED parameters for 72 organic solvents in the parameterization scheme. In doing so, we are implicitly including reference experimental data in the parameterization. Our previous work has shown that this results in improved quantitative predictions compared to using electronic structure calculations alone.23

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (513) 529-0784. Fax: (513) 529-0761. ORCID

Andrew S. Paluch: 0000-0002-2748-0783 Funding

Acknowledgment is made to the donors of the American Chemical Society Petroleum Research Fund (56896-UNI6) for support of this research. S.N.R. is additionally thankful for financial support from the Office of Research for Undergraduates at Miami University through the Undergraduate Summer Scholars (USS) program. Computing support was provided by the Ohio Supercomputer Center. Notes

The authors declare no competing financial interest.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b01080. Updated GC-MOSCED parameter matrix and details of the fit (PDF) J



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