Calculating the Partition Coefficients of Organic Solvents in Octanol

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Computational Chemistry

Calculating the Partition Coefficients of Organic Solvents in Octanol/Water and Octanol/Air Miroslava Nedyalkova, Sergio Madurga, Marek Tobiszewski, and Vasil Simeonov J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.9b00212 • Publication Date (Web): 01 May 2019 Downloaded from http://pubs.acs.org on May 6, 2019

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Journal of Chemical Information and Modeling

Calculating the Partition Coefficients of Organic Solvents in Octanol/Water and Octanol/Air

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Miroslava A. Nedyalkova*†, Sergio Madurga‡, Marek Tobiszewski §, Vasil Simeonov ⊥

†

Inorganic Chemistry Department, Faculty of Chemistry and Pharmacy, University of Sofia, Sofia 1164, Bulgaria ‡ Departament de Ciència de Materials i Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, 08028 Barcelona, Catalonia, Spain § Department of Analytical Chemistry, Faculty of Chemistry, Gdańsk University of Technology (GUT), 80-233 Gdańsk, Poland ⊥ Analytical Chemistry Department, Faculty of Chemistry and Pharmacy, University of Sofia, Sofia 1164, Bulgaria ABSTRACT Partition coefficients define how a solute is distributed between two immiscible phases at

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equilibrium. The experimental estimation of partition coefficients in a complex system can be an

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expensive, difficult and time-consuming process. Here, a computational strategy is presented to

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predict the distribution of a set of solutes in two relevant phase equilibria. The octanol/water and

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octanol/air partition coefficients are predicted for a group of polar solvents using density functional

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calculations in combination with a solvation model based on density (SMD) and are in excellent

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agreement with experimental data. Thus, the use of quantum chemical calculations to predict

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partition coefficients from free energies should be a valuable alternative for unknown solvents.

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The obtained results indicate that the SMD continuum model in conjunction with any of the three

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DFT functionals (B3LYP, M06-2X and M11) agrees with the observed experimental values. The

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highest correlation to experimental data for the octanol/water partition coefficients was reached by

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the M11 functional; for the octanol/air partition coefficient, the M06-2X functional yielded the

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best performance. To the best of our knowledge, this is the first computational approach for the

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prediction of octanol/air partition coefficients by DFT calculations, which has remarkable

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accuracy and precision.

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INTRODUCTION

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Physical properties of molecules can be used, for example, to make predictions about the

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environmental fate of unknown solvents. The lack of physical property data may be resolved by

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the development of different computational methodologies for the prediction of the appropriate

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physicochemical properties. In particular, a variety of methods have been developed to predict

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partition coefficients from a chemical structure.1-9 One of the most important prediction methods

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is based on the quantitative structure-property relationship (QSPR).10-12 Various algorithms and

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online platforms based on QSPR, such as AlogPs, ADMET predictor, and ACD/logD, have been

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developed. The main approach of these methods is based on finding the appropriate set of

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molecular descriptors that allow the precise reproduction of a given physical property using a large

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database of available experimental data. Accurate QSPR models are obtained when this method is

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applied to molecules that resemble the ones in the database used to build the model. Thus, the

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weakness of QSPR models is related to the prediction of properties of molecules that vary slightly

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from those used in the database.13-15

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Alternatively, partition coefficients can be predicted by taking into account that this property is

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related to the free energy difference of a solute in different solvents. In the work of Bannan et al.16,

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the computational scheme that was used consisted of molecular dynamics simulations with explicit

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solvent molecules to obtain transfer free energies between the solvents, which in turn were used

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to calculate their partition coefficients. The partition coefficients between octanol/water and

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cyclohexane/water were obtained using the generalized AMBER force field (GAFF) and the

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dielectric corrected GAFF (GAFF-DC).


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Jones et al. used ab initio calculations to predict the cyclohexane/water partition coefficient for a

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set of 53 compounds. The free energy of transfer was calculated with several DFT functionals in

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combination with the solvation model based on density implicit solvation model, obtaining a good

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estimation.17 Rayne et al. computed air-water partition coefficients for a dataset of 86 large

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polycyclic aromatic hydrocarbons and their unsaturated relatives by means of high-level theory

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G4(MP2) gas and aqueous phase calculations with the SMD, integral equation formalism variant

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(IEFPCM-UFF), and conductor-like polarizable continuum model (CPCM) solvation models.18

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The results of the three solvation models for a range of neutral and ionic compounds show accurate

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air/water partition coefficients (Kaw). Better accuracy is obtained when using higher levels of

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theory.

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In the work of Michalik19, the octanol/water partition coefficients for 27 alkane alcohols were

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predicted by quantum chemical calculations with three solvation models. The results were in rather

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good agreement with the corresponding experimental values. When comparing their results with

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other implicit solvent models (IEF-PCM or C-PCM), the authors observed deviation of the

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linearity. This mixed quantum (DFT) – QSPR analysis has been recently implemented successfully

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in the prediction of pKa values for carboxylic acids.20

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In the present work, the prediction of octanol/water and air/water partition coefficients of a set of

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55 organic solvents was carried out by means of DFT calculations. Solvation free energies were

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computed at the DFT levels of theory to estimate the partition coefficients. Good correlation

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coefficients were obtained between the calculated and experimentally measured values.

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DATASET:

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The dataset consisted of 55 molecules that were selected by a previous study.21 In that study, 150

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solvents were clustered on the basis of physicochemical properties—melting and boiling points,

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density, water solubility, vapor pressure, Henry’s law constant, logP, logKoa and surface tension.

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Molecules included in the present study belong to polar or nonpolar groups. The experimental

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values for the octanol/water and air/water partition coefficients are presented in Supporting

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information - S1. The majority of these 55 molecules have been considered to be green solvents

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in various literature reports.21 Some of the included molecules, such as ether-alcohols, are poorly

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characterized in terms of their hazards or physicochemical properties.22

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COMPUTATIONAL METHODS

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All calculations presented in this work were performed using the Gaussian 09 quantum chemistry

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package.23 Molecular structures were generated in the more extended conformation using

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GaussView 5.0. 24

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Geometries of all 55 molecules were optimized with three levels of theory using M06-2X 24, M1126

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and B3LYP27, with the 6-311+G** basis set using the continuum solvation model based on density,

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SMD28. Hessian analysis indicated no existence of imaginary frequencies, proving that all

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optimized structures were true minima. SMD can be used as a universal solvation model because

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it can be applied to any charged or uncharged solute in any type of solvent. The parameters required

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for the solvent are the dielectric constant, refractive index, bulk surface tension, and acidity and


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basicity parameters. This model divides the solvation free energy into two main contributions—

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the bulk electrostatic contribution and the cavity dispersion contribution.

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To calculate the octanol/water partition coefficient, the obtained SMD free energies in both

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solvents at 298.15 K were used to calculate the standard free energy associated with the transfer

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of the solute from the aqueous phase (w) to octanol (o):

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Δ𝐺0𝑜 𝑤 = Δ𝐺0𝑜 ― Δ𝐺0𝑤 (1) The octanol/water partition coefficient was then calculated according to ΔG0o w

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log𝑃𝑜 𝑤 = ― 2.303𝑅𝑇 (2)

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To calculate the octanol/air partition coefficient, Po/a, the SMD solvation free energy in octanol

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was obtained from the free energies of the molecule in gas phase and in octanol:

105 106

Δ𝐺0𝑠𝑜𝑙𝑣,𝑜 = Δ𝐺0𝑜 ― Δ𝐺0𝑔𝑎𝑠 (3) The octanol/air partition coefficient was then calculated according to 𝛥𝐺0𝑆𝑜𝑙𝑣,𝑜

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log𝑃𝑜 𝑎 = ― 2.303𝑅𝑇 (4)

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RESULTS

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The structures of the fifty-five (55) solvents under study are shown in Figure 1. All the

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correlation coefficients, slopes, and intercepts for all molecules are collected in Table 1 and

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Table 2. The linear correlation between the experimental and calculated values for octanol/water

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and octanol/air partition coefficients for the observed organic solvent dataset are presented

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graphically in Figure 2 and Figure 3.

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Figure 1. The chemical structures of solvents.

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Notably, a high linear correlation was obtained with the functional M11 for the LogP values. The

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statistical variety of error metrics were calculated to compare the calculated LogP and logKoa,

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values (illustrated in Tables 1 and 2) to the experimentally determined measures using root-mean-

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squared error (RMSE), Pearson’s correlation coefficient (R), mean absolute deviation (MAD),

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mean square error (MSE) and mean absolute percentage error (MAPE), along with standard errors.

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The assumed outliers observed in the first data assessment (Supporting Information – 2) were

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eliminated in the next level of linear regression by applying the 4-sigma rule30 for the detection of

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outliers. Extremely large and extremely small values for both coefficients were observed in our

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data. The 4-sigma region represents 99.99% of the values for a normal distribution and 97% for

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symmetric unimodal distributions. In our case, the outliers were adequately identified and

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excluded from further statistical treatment of the dataset. New plots were established and are

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presented below.

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These metrics allow us to make meaningful comparisons between experimental and calculated

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data with the SMD solvent model and the three functionals. As previously mentioned, the best

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results were obtained with the M11 functional with a RMSE of 0.72 and a Pearson’s correlation

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coefficient (R) of 0.99.

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The obtained statistics show a good accuracy of the computed partition coefficients when applying

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the M11 functional. In general, the sign of the calculated and experimental data were in agreement.

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Positive values indicate a preference for the organic phase, and negative values indicate a

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preference for the aqueous phase. For DFT-based SMD solvation models, this approach appears

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to be appropriate for obtaining good correlations with the experimental measurements in the

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calculation of logP. Presumably, the accuracy of the results is due to the appropriated

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parametrization of the SMD solvation model to yield accurate solvation free energies.


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Level of theory – logP DFT-M062X DFT-M11 DFTB3LYP

149 150 151 152 153 154 155 156

Slope

Intercept

R2

R

MAD

MSE

RMSE

MAPE

Standard Error

0.9498

0.020

0.9726

0.9879

0.29

0.41

0.48

0.56

0.65

0.9816

0.5398

0.9841

0.9920

0.75

0.96

0.72

0.57

0.72

1.022

0.8597

0.9609

0.9802

0.86

0.96

0.90

0.58

0.86

Table 1. Linear regression parameters obtained for the calculated logP with respect to the experimental data, and statistical error assessment of the linear regression terms based on applied computational models.

Level of theory – logKoa

Slope

Intercept

R2

R

MAD

MSE

RMSE

MAPE

DFT-M062X

1.0111

0.1806

0.9780

0.9889

0.40

0.39

0.59

0.95

Standard Error

0.3 DFT-M11 DFTB3LYP

157 158 159 160 161 162

0.9816

0.5398

0.8891

0.9428

2.18

1.45

1.20

0.90

0.8410

0.9527

0.8618

0.9339

1.78

1.92

1.33

0.63

0.6 0.75

Table 2. Linear regression parameters obtained for the calculated logKoa with respect to the experimental data, and statistical error assessment of the linear regression terms based on applied computational models.

8 Calculated B3LYP

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6 4 2 0

-2

0 -2

163 164 165

2

4

6

8

Experimentl logP


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6

M11

Calculated M11

8

4 2 0

-2

0

166 167

2

4

6

8

Experimental logP

-2 8

4

M11

Calculated M06-2X

6

2 0

-2

168 169 170 171 172 173

0

2

4

6

8

Experimental logP

-2

Figure 2. Comparison of the calculated logP to the experimental values. The upper graph shows the B3LYP model results, the middle graph shows M11, and the bottom graph shows M06-2X.

8 Calculated B3LYP

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6 4 2 0

-2

174 175 176

0 -2

2

4

6

8

Experimental logKoa


1 1


8

4

M11

Calculated M11

6

2 0

-2

0

2

4

6

8

Experimental logKoa

-2

177 178 179 180

8 6 4 2

M11

Calculated M06-2X

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0 -2

0 -2

181 182 183 184 185 186 187 188

2

4

6

8

Experimental logKoa

Figure 3. Comparison of the calculated logKoa to the experimental values. The upper graph shows the B3LYP model results, the middle graph shows M11, and bottom graph shows M06-2X.

The predicted values for logKoa allowed us to evaluate the solvation free energy obtained with

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the SMD model. The various error statistical metrics were calculated and are depicted in Table 2.

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The best agreement between the calculated and experimental partition coefficients was obtained

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with the M06-2X functional. This indicates a good estimation of the solvation free energy using

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the M06-2X functional. These findings provide useful information for understanding the


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partitioning, and the proposed computational scheme can be applied to other unknown solvents.

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For the other functionals, the obtained results also indicate that the approach is valid.

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In all calculations, a single conformation (the more extended conformation) was used for each

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molecule in each phase. Although this conformation was verified to be a minimum in the gas phase

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and in both solvents, it is possible that multiple conformations in the gas and/or solvents should be

198

taken into account to obtain accurate descriptions.

199 200

CONCLUSIONS

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The accuracy of predicted partition coefficients, octanol/water and octanol/air were estimated

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within the framework of DFT, with three functionals represented by B3LYP, and two popular (but

203

different) meta-GGA Minnesota functionals, M06-2X and M11. The best correlation with the

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experiment data was achieved with the M11 and M06-2X functionals. The quality of the regression

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model was significantly improved after excluding points that were defined as outliers. Thus, this

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computational protocol could be used as a tool for newly synthesized solvents where there is a lack

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of data regarding the octanol/water and octanol/air partition coefficients. The methodology is

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useful for predicting missing data for envirometrics data interpretation and modeling.

209 210

Highlights

211 212 213 214 215 216 217

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Prediction of the octanol/water partition coefficient for 55 green solvents Prediction of the octanol/air partition coefficient for 55 green solvents Accurate application of DFT for logP and logKoa Cross-validation of standard error for estimated models

AUTHOR INFORMATION


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Corresponding Author

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*E-mail: [email protected]. Phone: 00359 885 76 33 98

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Author Contributions

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All authors contributed to the writing of this manuscript. All authors have approved the

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final version of the manuscript.

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Notes

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The authors declare no competing financial interests.

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ACKNOWLEDGMENTS

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The authors are thankful for the support through the project BG05M2OP001-1.001-0004-C01/28.02.2018 (2018-

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2023) and for the computational resources provided by the project HPC-EUROPA3 (INFRAIA-2016-1-730897), with

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the support of the EC Research Innovation Action under the H2020 Programme. The author Miroslava Nedyalkova

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gratefully acknowledges the computer resources and technical support provided by the HPC center - Barcelona

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Supercomputing Center-Centro Nacional de Supercomputación (BSC-CNS). The financial support from Generalitat

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de Catalunya (Grants 2017SGR1033) and the Spanish Structures of Excellence María de Maeztu program through

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grant MDM-2017–0767 is fully acknowledged.

234 235 236 237 238 239 240 241 242 243 244

SUPPORTING INFORMATION Supporting Information Available: Additional Table with the experimental values for the octanol/water and air/water partition coefficients are presented in Supporting information – S1 Additional information about the applied Evaluation Metrics: MAD, MSE, RMSE, MAPE in Supporting information – S2 Additional plots with the deviated from the linearity points in Supporting information – S2

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Calculating the Partition Coefficients of Organic Solvents in Octanol

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