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Predicting Abraham Model Solvent Coefficients Jean-Claude Bradley1, Michael H Abraham2, William E Acree Jr3 and Andrew SID Lang4*

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Predicting Abraham Model Solvent Coefficients Jean-Claude Bradley1, Michael H Abraham2, William E Acree Jr3 and Andrew SID Lang4* Bradley et al. Chemistry Central Journal (2015) 9:12 DOI 10.1186/s13065-015-0085-4 RESEARCH ARTICLE Open Access Predicting Abraham model solvent coefficients Jean-Claude Bradley1, Michael H Abraham2, William E Acree Jr3 and Andrew SID Lang4* Abstract Background: The Abraham general solvation model can be used in a broad set of scenarios involving partitioning and solubility, yet is limited to a set of solvents with measured Abraham coefficients. Here we extend the range of applicability of Abraham’s model by creating open models that can be used to predict the solvent coefficients for all organic solvents. Results: We created open random forest models for the solvent coefficients e, s, a, b, and v that had out-of-bag R2 values of 0.31, 0.77, 0.92, 0.47, and 0.63 respectively. The models were used to suggest sustainable solvent replacements for commonly used solvents. For example, our models predict that propylene glycol may be used as a general sustainable solvent replacement for methanol. Conclusion: The solvent coefficient models extend the range of applicability of the Abraham general solvation equations to all organic solvents. The models were developed under Open Notebook Science conditions which makes them open, reproducible, and as useful as possible. Keywords: Abraham general solvation model, Solvent coefficients, Sustainable solvents, Solvent replacement, Partition coefficients, Solubility Background and (E, S, A, B, V) are the solute descriptors: E is the The Abraham model was developed and is widely used solute excess molar refractivity in units of (cm^3/mol)/ to predict partition coefficients for both conventional or- 10, S is the solute dipolarity/polarizability, A and B are ganic solvents [1-11] and ionic liquid solvents [12,13], the overall or summation hydrogen bond acidity and for the partitioning of drug molecules between blood basicity, and V is the McGowan characteristic volume in and select body organs [14-18], and for partitioning into units of (cm^3/mol)/100. micelles [19] and for prediction of enthalpies of solv- The solvent coefficients are obtained by linear regres- ation in organic solvents [20] and ionic organic liquids sion using experimentally determined partitions and sol- [21]. The Abraham model is based on the linear free en- ubilities of solutes with known Abraham descriptors. ergy relationship (LFER) Traditionally, the intercept c is allowed to float and is assumed to encode information not characterized by the ¼ þ þ þ þ þ ð Þ log P c eE sS aA bB vV 1 other solvent-solute interaction terms. However, for where logP is the solvent/water partition coefficient. some partitioning systems the value of c can vary greatly Under reasonable conditions, this model can also be depending upon the training-set used [23]. This makes it used to predict the solubility of organic compounds in difficult to directly compare different solvents by exam- organic solvents [22] as follows ining their solvent coefficients. Van Noort has even sug- gested that the c-coefficient be derived directly from ¼ þ þ þ þ þ þ ð Þ log Ss log Sw c eE sS aA bB vV 2 structure before the other coefficients are determined [24]. A problem with this suggestion is that the c-coefficient de- where S is the molar concentration of the solute in the s pends on the standard state. Partition coefficients can be organic solvent, S is the molar concentration of the sol- w expressed in concentration units of molarity and mole ute in water, (c, e, s, a, b) are the solvent coefficients, fractions, and the numerical value of the c-coefficient will * Correspondence: [email protected] be different for each concentration unit. Abraham model 4Department of Computing and Mathematics, Oral Roberts University, 7777 correlations considered in this study have partition coeffi- S. Lewis Avenue, Tulsa, OK 74171, USA cients expressed in concentration units of molarity. Full list of author information is available at the end of the article © 2015 Bradley et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Bradley et al. Chemistry Central Journal (2015) 9:12 Page 2 of 10 Table 1 Solvent coefficients c e s a b v Solvent e0 s0 a0 b0 v0 0.351 0.223 −0.150 −1.035 −4.527 3.972 methyl acetate 0.195 −0.068 −0.924 −4.571 4.152 0.328 0.369 −0.446 −0.700 −4.904 4.150 ethyl acetate 0.343 −0.369 −0.597 −4.945 4.319 0.248 0.356 −0.501 −0.867 −4.973 4.281 butyl acetate 0.336 −0.443 −0.788 −5.005 4.409 −0.605 0.930 −1.153 −1.682 −4.093 4.249 isopropyl myristate 0.977 −1.295 −1.870 −4.018 3.939 0.090 0.205 −0.172 1.305 −4.589 3.833 N-methylacetamide 0.197 −0.151 1.335 −4.601 3.880 0.284 0.128 −0.442 1.180 −4.728 3.856 N-ethylacetamide 0.105 −0.375 1.269 −4.764 4.002 −0.271 0.084 0.209 0.915 −5.003 4.557 dimethylacetamide 0.105 0.145 0.832 −4.970 4.419 0.213 0.034 0.089 1.342 −5.084 4.088 N,N-diethylacetamide 0.017 0.139 1.409 −5.111 4.198 −0.171 0.070 0.308 0.589 −3.152 2.432 formamide 0.083 0.268 0.537 −3.132 2.345 0.114 0.407 −0.287 0.542 −4.085 3.471 N-methylformamide 0.398 −0.260 0.579 −4.100 3.530 0.220 0.034 −0.166 0.935 −4.589 3.730 N-ethylformamide 0.016 −0.114 1.005 −4.617 3.843 −0.305 −0.058 0.343 0.358 −4.865 4.486 DMF −0.034 0.271 0.264 −4.828 4.330 0.332 0.302 −0.436 0.358 −4.902 3.952 dibutylformamide 0.275 −0.358 0.462 −4.944 4.123 0.276 0.334 −0.714 0.243 −3.320 3.549 methanol 0.312 −0.649 0.330 −3.355 3.691 0.222 0.471 −1.035 0.326 −3.596 3.857 ethanol 0.453 −0.983 0.396 −3.623 3.971 0.243 0.213 −0.575 0.262 −3.450 3.545 ethanol/water(90:10)vol 0.193 −0.518 0.339 −3.481 3.670 0.172 0.175 −0.465 0.260 −3.212 3.323 ethanol/water(80:20)vol 0.161 −0.424 0.314 −3.233 3.411 0.063 0.085 −0.368 0.311 −2.936 3.102 ethanol/water(70:30)vol 0.079 −0.353 0.331 −2.944 3.134 −0.040 0.138 −0.335 0.293 −2.675 2.812 ethanol/water(60:40)vol 0.141 −0.344 0.281 −2.670 2.792 −0.142 0.124 −0.252 0.251 −2.275 2.415 ethanol/water(50:50)vol 0.135 −0.285 0.207 −2.257 2.342 −0.221 0.131 −0.159 0.171 −1.809 1.918 ethanol/water(40:60)vol 0.148 −0.211 0.103 −1.782 1.805 −0.269 0.107 −0.098 0.133 −1.316 1.414 ethanol/water(30:70)vol 0.128 −0.161 0.049 −1.283 1.276 −0.252 0.043 −0.040 0.096 −0.832 0.916 ethanol/water(20:80)vol 0.063 −0.099 0.017 −0.801 0.787 −0.173 −0.023 −0.001 0.065 −0.372 0.454 ethanol/water(10:90)vol −0.009 −0.042 0.011 −0.350 0.365 0.000 0.000 0.000 0.000 0.000 0.000 water 0.000 0.000 0.000 0.000 0.000 0.139 0.405 −1.029 0.247 −3.767 3.986 1-propanol 0.393 −0.996 0.291 −3.785 4.058 0.099 0.343 −1.049 0.406 −3.827 4.033 2-propanol 0.335 −1.026 0.438 −3.839 4.084 0.188 0.354 −1.127 0.016 −3.568 3.968 2-methyl-1-propanol 0.339 −1.083 0.076 −3.592 4.065 0.211 0.171 −0.947 0.331 −4.085 4.109 2-methyl-2-propanol 0.154 −0.897 0.398 −4.112 4.218 0.165 0.401 −1.011 0.056 −3.958 4.044 1-butanol 0.388 −0.972 0.108 −3.979 4.129 0.127 0.253 −0.976 0.158 −3.882 4.114 2-butanol 0.242 −0.946 0.199 −3.898 4.179 0.073 0.360 −1.273 0.090 −3.770 4.399 3-methyl-1-butanol 0.354 −1.256 0.113 −3.779 4.437 0.150 0.536 −1.229 0.141 −3.864 4.077 1-pentanol 0.524 −1.194 0.188 −3.883 4.154 0.115 0.455 −1.331 0.206 −3.745 4.201 2-pentanol 0.445 −1.304 0.243 −3.759 4.260 0.115 0.492 −1.164 0.054 −3.978 4.131 1-hexanol 0.483 −1.137 0.091 −3.993 4.191 0.035 0.398 −1.063 0.002 −4.342 4.317 1-heptanol 0.395 −1.055 0.014 −4.347 4.335 −0.034 0.489 −1.044 −0.024 −4.235 4.218 1-octanol 0.491 −1.052 −0.034 −4.231 4.201 −0.058 0.616 −1.319 0.026 −4.153 4.279 1-decanol 0.620 −1.333 0.009 −4.146 4.250 −0.096 0.148 −0.841 −0.438 −4.040 4.125 octadecanol 0.155 −0.864 −0.467 −4.028 4.076 0.369 0.386 −1.568 −3.535 −5.215 4.514 pentane 0.357 −1.481 −3.419 −5.261 4.704 0.333 0.560 −1.710 −3.578 −4.939 4.463 hexane 0.533 −1.632 −3.473 −4.981 4.634 0.297 0.643 −1.755 −3.571 −4.946 4.488 heptane 0.619 −1.685 −3.477 −4.983 4.641 0.231 0.738 −1.840 −3.585 −4.907 4.502 octane 0.719 −1.786 −3.512 −4.936 4.621 0.240 0.619 −1.713 −3.532 −4.921 4.482 nonane 0.600 −1.657 −3.457 −4.951 4.606 0.186 0.722 −1.741 −3.449 −4.970 4.476 decane 0.707 −1.697 −3.390 −4.993 4.572 0.058 0.603 −1.661 −3.421 −5.120 4.619 undecane 0.598 −1.647 −3.402 −5.128 4.649 Bradley et al.
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