benzoic+acid+derivatives

Comparing the accuracy of measured Abraham descriptors, model001, and the modified Platts fragment method

 * media type="custom" key="7905373" ||
 * benzoic acid ||
 * media type="custom" key="7905417" || media type="custom" key="7905503" || media type="custom" key="7905523" || media type="custom" key="7905543" || media type="custom" key="7905559" ||
 * 2-chloro-5-nitrobenzoic acid || 2-methoxybenzoic acid || 2-methylbenzoic acid || 4-acetamidobenzoic acid || 4-aminobenzoic acid ||
 * media type="custom" key="7905599" || media type="custom" key="7905605" || media type="custom" key="7905609" || media type="custom" key="7905615" || media type="custom" key="7905631" ||
 * 4-chloro-3-nitrobenzoic acid || 4-fluorobenzoic acid || 4-hydroxybenzoic acid || 4-methoxybenzoic acid || 4-nitrobenzoic acid ||

Researcher
Andrew Lang

Objective
To compare the accuracy of the modified Platts fragment method (MPFM), model001, and measured Abraham Descriptors (measuredAD) to predict the solubilities of benzoic acid derivatives in organic solvents.
 * compound || SMILES || CSID || E || S || A || B || V || data pts ||
 * benzoic acid || c1ccc(cc1)C(=O)O || 238 || 0.921 || 0.849 || 0.314 || 0.422 || 0.932 || 25 ||
 * 2-chloro-5-nitrobenzoic acid || O=C(O)c1cc(ccc1Cl)[N+]([O-])=O || 16359 || 1.407 || 1.409 || 0.487 || 0.674 || 1.228 || 20 ||
 * 2-methoxybenzoic acid || O=C(O)c1ccccc1OC || 10892 || 0.903 || 1.346 || 0.436 || 0.640 || 1.131 || 22 ||
 * 2-methylbenzoic acid || O=C(O)c1ccccc1C || 8070 || 0.936 || 0.785 || 0.271 || 0.475 || 1.073 || 20 ||
 * 4-acetamidobenzoic acid || O=C(Nc1ccc(cc1)C(=O)O)C || 18177 || 1.433 || 1.360 || 0.788 || 0.930 || 1.329 || 4 ||
 * 4-aminobenzoic acid || O=C(O)c1ccc(N)cc1 || 953 || 1.308 || 1.079 || 0.498 || 0.745 || 1.031 || 24 ||
 * 4-chloro-3-nitrobenzoic acid || O=[N+]([O-])c1cc(ccc1Cl)C(=O)O || 7044 || 1.407 || 1.414 || 0.514 || 0.536 || 1.228 || 20 ||
 * 4-fluorobenzoic acid || O=C(O)c1ccc(F)cc1 || 9579 || 0.805 || 0.946 || 0.367 || 0.393 || 0.949 || 5 ||
 * 4-hydroxybenzoic acid || c1cc(ccc1C(=O)O)O || 132 || 1.183 || 0.860 || 0.922 || 0.591 || 0.990 || 18 ||
 * 4-methoxybenzoic acid || COc1ccc(cc1)C(O)=O || 10181338 || 0.903 || 1.306 || 0.436 || 0.560 || 1.131 || 18 ||
 * 4-nitrobenzoic acid || O=[N+]([O-])c1ccc(C(=O)O)cc1 || 5882 || 1.254 || 1.412 || 0.525 || 0.445 || 1.106 || 21 ||

Background
The Abraham descriptors of solutes can be calculated by regressing known solubility values against Abraham's general solvation equations; and with these descriptors it is possible to predict the solubility of the solute in over seventy different organic solvents[Abraham99]. If solubility data is unavailable, then Abraham descriptors can be approximated from models; either by summing fragment contributions[Platts99] or via a QSAR model - such as model001. A third way to approximate Abraham descriptors for a compound is to start with the known Abraham descriptors of a structurally similar compound and modify them by converting to compound with known Abraham descriptors into the compound with unknown Abraham descriptors fragment by fragment, keeping track of how the Abraham descriptors change according to Platts' values for the fragments - in effect a modified Platts fragment method (MPFM). We have used this method to calculate the Abraham descriptors for 1,2,4-triazole derivatives from the known Abraham descriptors of 1,2,4-triazole and also for @boc-protected amino acids from the known Abraham descriptors for boc-glycine. However, the accuracy of this method for both the 1,2,4-triazole derivatives and the boc-protected amino acids can only be determined by confirming the predictions by actual measurement of solubility values - something that is in progress at the time of writing (2010-12-29), see @Exp194 and @Exp195.

To better understand the reliability of the MPFM, we can use it to approximate the Abraham descriptors of certain benzoic acid derivatives, ones that already have measured Abraham descriptors (measuredAD), from the known Abraham descriptors of benzoic acid. We can then compare the solubility predictions against measured solubility values of all the methods: measuredAD, model001, the Platts fragment method, and the MPFM. We shall also compare how the accuracy is affected by using a VCC predicted aqueous solubility value in the solvation equations instead of a measured aqueous solubility value.

Calculating the Abraham Descriptors
The measured Abraham descriptors of benzoic acid and the benzoic acid derivatives are given in the table above. These values were calculated by regressing measured solubility values against Abraham's general solvation equations, excluding measurements in non-polar solvents (alkanes, 1,4-dioxane, benzene, carbon disulfide, carbon tetrachloride, and toluene) to avoid any possible issues with potential dimerization. The number of data points used in the regression can be found in the table above. From these values, we can calculate the MPFM Abraham descriptors (S, A, & B. E & V can always be calculated from structure) of the benzoic acid derivatives by converting benzoic acid into the derivatives fragment-wise and keeping track of the changes using the values for the fragments given in Platts' paper. Computations can be aided by the PaDEL-Descriptor software.

S: the solute dipolarity/polarizability
Graphing the difference between the values of S for each derivative and the value of S for benzoic acid using all three methods, we see that both the Platts method and model001 correctly predict the direction that S should change, with comparable accuracy. The absolute accuracy of the MPFM for predicting S is not significantly different from that of the Platts model. This is because the Platts model predicts the core benzoic acid value for S with good accuracy (0.934 as compared to 0.849, a difference of only 0.085).
 * compound || S-measuredAD || S-MPFM || S-Platts || S-model001 ||
 * benzoic acid || 0.849 || N/A || 0.934 || 1.127 ||
 * 2-chloro-5-nitrobenzoic acid || 1.409 || 1.172 || 1.257 || 1.739 ||
 * 2-methoxybenzoic acid || 1.346 || 1.010 || 1.095 || 1.153 ||
 * 2-methylbenzoic acid || 0.785 || 0.825 || 0.910 || 1.070 ||
 * 4-acetamidobenzoic acid || 1.360 || 1.782 || 1.867 || 1.644 ||
 * 4-aminobenzoic acid || 1.079 || 1.283 || 1.368 || 1.223 ||
 * 4-chloro-3-nitrobenzoic acid || 1.414 || 1.129 || 1.214 || 1.738 ||
 * 4-fluorobenzoic acid || 0.946 || 0.900 || 0.985 || 1.145 ||
 * 4-hydroxybenzoic acid || 0.860 || 1.147 || 1.232 || 1.145 ||
 * 4-methoxybenzoic acid || 1.306 || 1.010 || 1.095 || 1.153 ||
 * 4-nitrobenzoic acid || 1.412 || 1.039 || 1.124 || 1.720 ||
 * AAE || N/A || 0.253 || 0.243 || 0.251 ||
 * RMSE || N/A || 0.280 || 0.274 || 0.259 ||

A: the hydrogen bond acidity
Graphing the difference between the values of A for each derivative and the value of A for benzoic acid using all three methods, we can see how both the Platts method and model001 predict the change in A. We see that the Platts method predicts the correct sign for the change (or no change) in A except for 4-acetamidobenzoic acid whereas model001 predicts the correct sign for the change in A except for 4-aminobenzoic acid; and both 2-methoxybenzoic acid and 4-methoxybenzoic acid. Examining the table above, we see that the MPFM does better (interestingly, model001 does well here too) than the Platts model in predicting the values of A. This is because the Platts model does well in predicting the change in A but doesn't do so well in predicting the initial value of A for benzoic acid (0.591 as compared to 0.314, a difference of 0.277).
 * compound || A-measuredAD || A-MPFM || A-Platts || A-model001 ||
 * benzoic acid || 0.314 || N/A || 0.591 || 0.496 ||
 * 2-chloro-5-nitrobenzoic acid || 0.487 || 0.399 || 0.676 || 0.594 ||
 * 2-methoxybenzoic acid || 0.436 || 0.314 || 0.591 || 0.256 ||
 * 2-methylbenzoic acid || 0.271 || 0.314 || 0.591 || 0.397 ||
 * 4-acetamidobenzoic acid || 0.788 || 0.223 || 0.500 || 0.697 ||
 * 4-aminobenzoic acid || 0.498 || 0.561 || 0.838 || 0.486 ||
 * 4-chloro-3-nitrobenzoic acid || 0.514 || 0.454 || 0.731 || 0.590 ||
 * 4-fluorobenzoic acid || 0.367 || 0.369 || 0.646 || 0.520 ||
 * 4-hydroxybenzoic acid || 0.922 || 0.953 || 1.230 || 0.684 ||
 * 4-methoxybenzoic acid || 0.436 || 0.314 || 0.591 || 0.312 ||
 * 4-nitrobenzoic acid || 0.525 || 0.369 || 0.646 || 0.612 ||
 * AAE || N/A || 0.125 || 0.237 || 0.119 ||
 * RMSE || N/A || 0.198 || 0.249 || 0.133 ||

B: the hydrogen bond basicity
Graphing the difference between the values of B for each derivative and the value of B for benzoic acid using all three methods, we can see how both the Platts method and model001 predict the change in B. We see that the Platts method predicts the correct sign (with good accuracy) for the change in B except for 2-methylbenzoic acid and the three nitro-derivative compounds: 2-chloro-5-nitrobenzoic acid, 4-chloro-3-nitrobenzoic acid, and 4-nitrobenzoic aicd. This is because Platts gives a large negative value (-0.525) to the -NO2 fragment, fragment 24 in table 2 in Platts paper. model001 predicts the correct sign for the change in B except for 4-fluorobenzoic acid. Examining the table above, we see that the accuracy of the MPFM for predicting B is not significantly different from that of the Platts model. This is because the Platts model predicts the core benzoic acid value for B with good accuracy (0.459 as compared to 0.422, a difference of only 0.037). model001 does very well in predicting the value of B with an AAE of 0.075 and RMSE of 0.092.
 * compound || B-measuredAD || B-MPFM || B-Platts || B-model001 ||
 * benzoic acid || 0.422 || N/A || 0.459 || 0.524 ||
 * 2-chloro-5-nitrobenzoic acid || 0.674 || 0.163 || 0.200 || 0.641 ||
 * 2-methoxybenzoic acid || 0.640 || 0.629 || 0.666 || 0.665 ||
 * 2-methylbenzoic acid || 0.475 || 0.418 || 0.455 || 0.547 ||
 * 4-acetamidobenzoic acid || 0.930 || 0.880 || 0.917 || 0.985 ||
 * 4-aminobenzoic acid || 0.745 || 0.686 || 0.723 || 0.746 ||
 * 4-chloro-3-nitrobenzoic acid || 0.536 || 0.240 || 0.277 || 0.645 ||
 * 4-fluorobenzoic acid || 0.393 || 0.411 || 0.448 || 0.549 ||
 * 4-hydroxybenzoic acid || 0.591 || 0.718 || 0.755 || 0.543 ||
 * 4-methoxybenzoic acid || 0.560 || 0.629 || 0.666 || 0.643 ||
 * 4-nitrobenzoic acid || 0.445 || 0.220 || 0.257 || 0.616 ||
 * AAE || N/A || 0.142 || 0.133 || 0.075 ||
 * RMSE || N/A || 0.207 || 0.192 || 0.092 ||

Calculating the Solubilities
The solubilities of the benzoic acid derivatives were calculated using the solubility from Abraham descriptors webservice for each of the methods for estimating the Abraham descriptors: measuredAD (calculated using linear regression), MPFM (modified Platts fragment model - adding and subtracting fragment values from the core benzoic acid measuredAD values), Platts (ab initio fragment method - calculated using PaDEL-Explorer), model001 (ab initio model using CDK descriptors). Columns without the suffix VCC use a measured aqueous solubility value and columns with the suffix VCC use a predicted aqueous solubility value provided by VCC.
 * Solute || Solvent || measured || measuredAD || MPFM || MPFM-VCC || Platts || Platss-VCC || model001 || model001-VCC ||
 * 2-chloro-5-nitrobenzoic acid || 1-butanol || 0.78 || 0.68 || 7.96 || 7.96 || 7.96 || 4.93 || 0.43 || 0.03 ||
 * 2-chloro-5-nitrobenzoic acid || 1-decanol || 0.39 || 0.59 || 7.96 || 7.96 || 7.96 || 5.34 || 0.30 || 0.02 ||
 * 2-chloro-5-nitrobenzoic acid || 1-heptanol || 0.54 || 0.61 || 7.96 || 7.96 || 7.96 || 5.74 || 0.36 || 0.02 ||
 * 2-chloro-5-nitrobenzoic acid || 1-hexanol || 0.64 || 0.73 || 7.96 || 7.96 || 7.96 || 6.02 || 0.47 || 0.03 ||
 * 2-chloro-5-nitrobenzoic acid || 1-octanol || 0.48 || 0.57 || 7.96 || 7.96 || 7.96 || 5.24 || 0.39 || 0.02 ||
 * 2-chloro-5-nitrobenzoic acid || 1-pentanol || 0.74 || 0.76 || 7.96 || 7.96 || 7.96 || 5.95 || 0.45 || 0.03 ||
 * 2-chloro-5-nitrobenzoic acid || 1-propanol || 0.95 || 0.98 || 7.96 || 7.96 || 7.96 || 7.64 || 0.70 || 0.04 ||
 * 2-chloro-5-nitrobenzoic acid || 2-butanol || 0.91 || 0.95 || 7.96 || 6.94 || 7.96 || 4.61 || 0.70 || 0.04 ||
 * 2-chloro-5-nitrobenzoic acid || 2-methyl-1-propanol || 0.63 || 0.71 || 7.96 || 6.68 || 7.96 || 4.41 || 0.49 || 0.03 ||
 * 2-chloro-5-nitrobenzoic acid || 2-methyl-2-propanol || 1.21 || 0.69 || 7.96 || 7.86 || 7.96 || 5.71 || 0.57 || 0.03 ||
 * 2-chloro-5-nitrobenzoic acid || 2-pentanol || 0.76 || 0.74 || 7.96 || 7.71 || 7.96 || 4.93 || 0.42 || 0.02 ||
 * 2-chloro-5-nitrobenzoic acid || 2-propanol || 1.13 || 0.91 || 7.96 || 7.96 || 7.96 || 7.10 || 0.71 || 0.04 ||
 * 2-chloro-5-nitrobenzoic acid || 3-methyl-1-butanol || 0.68 || 0.64 || 7.96 || 6.74 || 7.96 || 4.02 || 0.37 || 0.02 ||
 * 2-chloro-5-nitrobenzoic acid || butyl acetate || 0.46 || 0.61 || 7.96 || 7.96 || 7.96 || 7.19 || 0.54 || 0.03 ||
 * 2-chloro-5-nitrobenzoic acid || dibutyl ether || 0.10 || 0.06 || 7.96 || 5.29 || 7.96 || 1.07 || 0.04 || 0.00 ||
 * 2-chloro-5-nitrobenzoic acid || diethyl ether || 0.57 || 0.56 || 7.96 || 7.96 || 7.96 || 7.96 || 0.43 || 0.03 ||
 * 2-chloro-5-nitrobenzoic acid || ethanol || 1.40 || 1.40 || 7.96 || 7.96 || 7.96 || 7.24 || 1.04 || 0.06 ||
 * 2-chloro-5-nitrobenzoic acid || ethyl acetate || 0.75 || 0.84 || 7.96 || 7.96 || 7.96 || 7.96 || 0.82 || 0.05 ||
 * 2-chloro-5-nitrobenzoic acid || methyl acetate || 0.89 || 1.08 || 7.96 || 7.96 || 7.96 || 6.46 || 1.17 || 0.07 ||
 * 2-chloro-5-nitrobenzoic acid || THF || 2.97 || 2.86 || 7.96 || 7.96 || 7.96 || 7.96 || 3.24 || 0.19 ||
 * 2-methoxybenzoic acid || 1-butanol || 0.57 || 0.41 || 1.16 || 0.77 || 0.70 || 0.47 || 0.56 || 0.37 ||
 * 2-methoxybenzoic acid || 1-decanol || 0.22 || 0.25 || 0.89 || 0.59 || 0.49 || 0.33 || 0.39 || 0.26 ||
 * 2-methoxybenzoic acid || 1-heptanol || 0.34 || 0.33 || 1.04 || 0.69 || 0.58 || 0.39 || 0.48 || 0.32 ||
 * 2-methoxybenzoic acid || 1-hexanol || 0.37 || 0.41 || 1.15 || 0.77 || 0.69 || 0.46 || 0.56 || 0.37 ||
 * 2-methoxybenzoic acid || 1-octanol || 0.30 || 0.32 || 0.85 || 0.57 || 0.48 || 0.32 || 0.43 || 0.28 ||
 * 2-methoxybenzoic acid || 1-pentanol || 0.47 || 0.40 || 1.23 || 0.82 || 0.78 || 0.52 || 0.53 || 0.37 ||
 * 2-methoxybenzoic acid || 1-propanol || 0.76 || 0.57 || 1.41 || 0.94 || 1.05 || 0.70 || 0.67 || 0.45 ||
 * 2-methoxybenzoic acid || 1,4-dioxane || 1.53 || 1.38 || 2.08 || 1.38 || 0.95 || 0.63 || 1.45 || 0.97 ||
 * 2-methoxybenzoic acid || 2-butanol || 0.50 || 0.61 || 1.44 || 0.96 || 0.95 || 0.64 || 0.76 || 0.51 ||
 * 2-methoxybenzoic acid || 2-methyl-1-propanol || 0.41 || 0.48 || 1.24 || 0.82 || 0.82 || 0.54 || 0.62 || 0.41 ||
 * 2-methoxybenzoic acid || 2-methyl-2-propanol || 0.53 || 0.56 || 1.23 || 0.82 || 0.89 || 0.59 || 0.62 || 0.41 ||
 * 2-methoxybenzoic acid || 2-pentanol || 0.39 || 0.42 || 1.32 || 0.88 || 0.84 || 0.56 || 0.61 || 0.40 ||
 * 2-methoxybenzoic acid || 2-propanol || 0.59 || 0.59 || 1.32 || 0.88 || 1.09 || 0.73 || 0.64 || 0.42 ||
 * 2-methoxybenzoic acid || 3-methyl-1-butanol || 0.36 || 0.40 || 1.22 || 0.81 || 0.72 || 0.48 || 0.58 || 0.39 ||
 * 2-methoxybenzoic acid || butyl acetate || 0.34 || 0.42 || 0.96 || 0.64 || 0.33 || 0.22 || 0.61 || 0.40 ||
 * 2-methoxybenzoic acid || chloroform || 0.46 || 0.36 || 1.38 || 0.92 || 0.13 || 0.09 || 1.36 || 0.91 ||
 * 2-methoxybenzoic acid || dibutyl ether || 0.04 || 0.05 || 0.19 || 0.12 || 0.04 || 0.03 || 0.11 || 0.07 ||
 * 2-methoxybenzoic acid || diethyl ether || 0.24 || 0.36 || 0.94 || 0.62 || 0.39 || 0.26 || 0.50 || 0.34 ||
 * 2-methoxybenzoic acid || ethanol || 1.19 || 0.84 || 1.98 || 1.31 || 1.35 || 0.90 || 1.04 || 0.69 ||
 * 2-methoxybenzoic acid || ethyl acetate || 0.66 || 0.58 || 1.20 || 0.80 || 0.46 || 0.31 || 0.75 || 0.50 ||
 * 2-methoxybenzoic acid || methanol || 1.82 || 0.96 || 1.84 || 1.23 || 1.27 || 0.86 || 1.10 || 0.73 ||
 * 2-methoxybenzoic acid || methyl acetate || 0.86 || 0.88 || 1.58 || 1.05 || 0.54 || 0.36 || 1.18 || 0.79 ||
 * 2-methoxybenzoic acid || THF || 2.02 || 1.71 || 3.00 || 2.00 || 1.57 || 1.05 || 1.80 || 1.20 ||
 * 2-methylbenzoic acid || 1-heptanol || 1.28 || 1.48 || 2.54 || 5.70 || 1.43 || 3.20 || 0.37 || 0.82 ||
 * 2-methylbenzoic acid || 1-hexanol || 1.38 || 1.53 || 2.63 || 5.90 || 1.57 || 3.51 || 0.42 || 0.94 ||
 * 2-methylbenzoic acid || 1-octanol || 1.16 || 1.16 || 2.04 || 4.56 || 1.14 || 2.52 || 0.32 || 0.72 ||
 * 2-methylbenzoic acid || 1-pentanol || 1.49 || 1.65 || 2.79 || 6.25 || 1.77 || 3.97 || 0.44 || 0.98 ||
 * 2-methylbenzoic acid || 1-propanol || 1.77 || 1.71 || 2.98 || 6.67 || 2.21 || 4.95 || 0.52 || 1.22 ||
 * 2-methylbenzoic acid || 2-butanol || 1.75 || 1.53 || 2.55 || 5.70 || 1.69 || 3.79 || 0.52 || 1.17 ||
 * 2-methylbenzoic acid || 2-methyl-1-propanol || 1.28 || 1.43 || 2.41 || 5.40 || 1.60 || 3.57 || 0.45 || 1.00 ||
 * 2-methylbenzoic acid || 2-methyl-2-propanol || 2.19 || 1.38 || 2.48 || 5.55 || 1.80 || 4.03 || 0.48 || 1.07 ||
 * 2-methylbenzoic acid || 2-pentanol || 1.68 || 1.71 || 2.81 || 6.28 || 1.79 || 4.01 || 0.45 || 1.02 ||
 * 2-methylbenzoic acid || 2-propanol || 1.95 || 1.49 || 2.64 || 5.92 || 2.19 || 4.89 || 0.52 || 1.17 ||
 * 2-methylbenzoic acid || 3-methyl-1-butanol || 1.34 || 1.53 || 2.51 || 5.63 || 1.50 || 2.35 || 0.41 || 0.92 ||
 * 2-methylbenzoic acid || butyl acetate || 1.17 || 1.36 || 2.56 || 5.74 || 0.88 || 1.96 || 0.38 || 0.84 ||
 * 2-methylbenzoic acid || dibutyl ether || 0.58 || 0.40 || 0.73 || 1.63 || 0.15 || 0.33 || 0.06 || 0.14 ||
 * 2-methylbenzoic acid || diethyl ether || 1.65 || 1.49 || 2.83 || 6.33 || 1.18 || 2.64 || 0.38 || 0.84 ||
 * 2-methylbenzoic acid || ethanol || 2.08 || 2.10 || 3.53 || 7.90 || 2.42 || 5.41 || 0.72 || 1.62 ||
 * 2-methylbenzoic acid || ethyl acetate || 1.49 || 1.61 || 3.07 || 6.87 || 1.19 || 2.65 || 0.49 || 1.09 ||
 * 2-methylbenzoic acid || methyl acetate || 1.51 || 1.67 || 3.01 || 6.75 || 1.03 || 2.30 || 0.59 || 1.33 ||
 * 2-methylbenzoic acid || THF || 2.92 || 3.65 || 7.33 || 8.46 || 3.84 || 8.46 || 1.30 || 2.92 ||
 * 4-aminobenzoic acid || 1-heptanol || 0.16 || 0.23 || 0.21 || 0.17 || 0.12 || 0.10 || 0.14 || 0.11 ||
 * 4-aminobenzoic acid || 1-hexanol || 0.21 || 0.28 || 0.27 || 0.22 || 0.16 || 0.13 || 0.18 || 0.14 ||
 * 4-aminobenzoic acid || 1-octanol || 0.12 || 0.20 || 0.20 || 0.16 || 0.11 || 0.09 || 0.13 || 0.10 ||
 * 4-aminobenzoic acid || 1-pentanol || 0.23 || 0.34 || 0.30 || 0.24 || 0.19 || 0.16 || 0.20 || 0.16 ||
 * 4-aminobenzoic acid || 2-butanol || 0.30 || 0.42 || 0.42 || 0.34 || 0.28 || 0.23 || 0.28 || 0.23 ||
 * 4-aminobenzoic acid || 2-methyl-1-propanol || 0.19 || 0.31 || 0.30 || 0.24 || 0.20 || 0.16 || 0.20 || 0.16 ||
 * 4-aminobenzoic acid || 2-propanol || 0.42 || 0.38 || 0.40 || 0.33 || 0.33 || 0.27 || 0.25 || 0.20 ||
 * 4-aminobenzoic acid || 3-methyl-1-butanol || 0.18 || 0.29 || 0.25 || 0.20 || 0.15 || 0.12 || 0.18 || 0.14 ||
 * 4-aminobenzoic acid || acetone || 0.69 || 0.28 || 0.43 || 0.35 || 0.19 || 0.15 || 0.25 || 0.20 ||
 * 4-aminobenzoic acid || benzene || 0.00 || 0.03 || 0.02 || 0.02 || 0.00 || 0.00 || 0.02 || 0.02 ||
 * 4-aminobenzoic acid || chlorobenzene || 0.01 || 0.02 || 0.02 || 0.01 || 0.00 || 0.00 || 0.02 || 0.01 ||
 * 4-aminobenzoic acid || chloroform || 0.14 || 0.08 || 0.06 || 0.05 || 0.01 || 0.01 || 0.07 || 0.06 ||
 * 4-aminobenzoic acid || cyclohexane || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 ||
 * 4-aminobenzoic acid || diethyl ether || 0.13 || 0.14 || 0.16 || 0.13 || 0.07 || 0.06 || 0.10 || 0.08 ||
 * 4-aminobenzoic acid || DMF || 0.56 || 0.63 || 1.42 || 1.15 || 1.26 || 1.02 || 0.65 || 0.52 ||
 * 4-aminobenzoic acid || ethanol || 0.80 || 0.59 || 0.59 || 0.48 || 0.40 || 0.33 || 0.39 || 0.32 ||
 * 4-aminobenzoic acid || ethyl acetate || 0.58 || 0.17 || 0.23 || 0.19 || 0.09 || 0.07 || 0.14 || 0.11 ||
 * 4-aminobenzoic acid || ethylene glycol || 1.16 || 0.80 || 0.84 || 0.68 || 0.95 || 0.77 || 0.58 || 0.47 ||
 * 4-aminobenzoic acid || formamide || 0.26 || 0.22 || 0.39 || 0.32 || 0.47 || 0.38 || 0.22 || 0.18 ||
 * 4-aminobenzoic acid || heptane || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 ||
 * 4-aminobenzoic acid || methanol || 1.23 || 0.58 || 0.64 || 0.52 || 0.44 || 0.36 || 0.43 || 0.35 ||
 * 4-chloro-3-nitrobenzoic acid || 1-heptanol || 0.25 || 0.25 || 7.96 || 5.45 || 5.45 || 3.06 || 0.04 || 0.02 ||
 * 4-chloro-3-nitrobenzoic acid || 1-hexanol || 0.27 || 0.29 || 7.96 || 5.45 || 5.79 || 3.25 || 0.05 || 0.03 ||
 * 4-chloro-3-nitrobenzoic acid || 1-octanol || 0.23 || 0.24 || 7.96 || 4.78 || 4.77 || 2.67 || 0.04 || 0.02 ||
 * 4-chloro-3-nitrobenzoic acid || 1-pentanol || 0.27 || 0.29 || 7.96 || 5.34 || 6.05 || 3.39 || 0.04 || 0.02 ||
 * 4-chloro-3-nitrobenzoic acid || 1-propanol || 0.37 || 0.38 || 7.96 || 5.91 || 7.82 || 4.39 || 0.07 || 0.04 ||
 * 4-chloro-3-nitrobenzoic acid || 2-butanol || 0.32 || 0.33 || 7.13 || 4.00 || 4.74 || 2.66 || 0.07 || 0.04 ||
 * 4-chloro-3-nitrobenzoic acid || 2-methyl-1-propanol || 0.19 || 0.26 || 6.78 || 3.80 || 4.48 || 2.51 || 0.05 || 0.03 ||
 * 4-chloro-3-nitrobenzoic acid || 2-methyl-2-propanol || 0.38 || 0.28 || 7.64 || 4.29 || 5.55 || 3.11 || 0.05 || 0.03 ||
 * 4-chloro-3-nitrobenzoic acid || 2-pentanol || 0.30 || 0.27 || 7.96 || 4.54 || 5.17 || 2.90 || 0.04 || 0.02 ||
 * 4-chloro-3-nitrobenzoic acid || 2-propanol || 0.39 || 0.35 || 7.96 || 5.00 || 7.38 || 4.14 || 0.07 || 0.04 ||
 * 4-chloro-3-nitrobenzoic acid || 3-methyl-1-butanol || 0.24 || 0.23 || 6.86 || 3.85 || 4.08 || 2.29 || 0.04 || 0.02 ||
 * 4-chloro-3-nitrobenzoic acid || butyl acetate || 0.23 || 0.31 || 7.96 || 7.96 || 4.89 || 2.74 || 0.05 || 0.03 ||
 * 4-chloro-3-nitrobenzoic acid || dibutyl ether || 0.05 || 0.03 || 3.20 || 1.80 || 0.65 || 0.36 || 0.00 || 0.00 ||
 * 4-chloro-3-nitrobenzoic acid || diethyl ether || 0.24 || 0.29 || 7.96 || 7.96 || 6.39 || 3.59 || 0.04 || 0.02 ||
 * 4-chloro-3-nitrobenzoic acid || ethanol || 0.55 || 0.50 || 7.96 || 6.10 || 7.44 || 4.17 || 0.10 || 0.06 ||
 * 4-chloro-3-nitrobenzoic acid || ethyl acetate || 0.36 || 0.42 || 7.96 || 7.96 || 6.83 || 3.83 || 0.08 || 0.04 ||
 * 4-chloro-3-nitrobenzoic acid || methyl acetate || 0.44 || 0.47 || 7.96 || 7.38 || 4.49 || 2.52 || 0.11 || 0.06 ||
 * 4-chloro-3-nitrobenzoic acid || THF || 1.95 || 1.49 || 7.96 || 7.96 || 7.96 || 7.96 || 0.31 || 0.17 ||
 * 4-fluorobenzoic acid || acetonitrile || 0.39 || 0.43 || 0.38 || 1.12 || 0.10 || 0.30 || 0.07 || 0.19 ||
 * 4-fluorobenzoic acid || DMSO || 4.19 || 4.38 || 3.72 || 9.43 || 6.60 || 9.43 || 2.14 || 6.30 ||
 * 4-fluorobenzoic acid || ethanol || 0.80 || 0.89 || 0.94 || 2.78 || 0.64 || 1.90 || 0.18 || 0.54 ||
 * 4-fluorobenzoic acid || methanol || 0.76 || 0.83 || 0.86 || 2.55 || 0.60 || 1.76 || 0.21 || 0.61 ||
 * 4-fluorobenzoic acid || THF || 2.49 || 1.94 || 1.82 || 5.38 || 0.95 || 2.82 || 0.28 || 0.83 ||
 * 4-fluorobenzoic acid || toluene || 0.07 || 0.14 || 0.14 || 0.41 || 0.01 || 0.03 || 0.01 || 0.02 ||
 * 4-hydroxybenzoic acid || 1-hexanol || 0.95 || 1.15 || 0.18 || 0.39 || 0.11 || 0.23 || 0.88 || 1.91 ||
 * 4-hydroxybenzoic acid || 1-octanol || 0.68 || 0.73 || 0.12 || 0.25 || 0.06 || 0.14 || 0.65 || 1.41 ||
 * 4-hydroxybenzoic acid || 1-pentanol || 0.84 || 1.58 || 0.24 || 0.51 || 0.15 || 0.33 || 1.01 || 2.20 ||
 * 4-hydroxybenzoic acid || 1-propanol || 1.40 || 2.19 || 0.38 || 0.82 || 0.28 || 0.61 || 1.44 || 3.13 ||
 * 4-hydroxybenzoic acid || 2-methyl-1-propanol || 1.40 || 1.30 || 0.23 || 0.51 || 0.15 || 0.34 || 0.96 || 2.09 ||
 * 4-hydroxybenzoic acid || 2-propanol || 1.76 || 2.26 || 0.42 || 0.91 || 0.35 || 0.76 || 1.44 || 3.14 ||
 * 4-hydroxybenzoic acid || acetone || 1.54 || 0.48 || 0.11 || 0.25 || 0.05 || 0.11 || 1.13 || 2.46 ||
 * 4-hydroxybenzoic acid || benzene || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.03 || 0.07 ||
 * 4-hydroxybenzoic acid || butyl acetate || 0.45 || 0.20 || 0.04 || 0.08 || 0.01 || 0.03 || 0.44 || 0.96 ||
 * 4-hydroxybenzoic acid || chloroform || 0.00 || 0.01 || 0.00 || 0.01 || 0.00 || 0.00 || 0.06 || 0.13 ||
 * 4-hydroxybenzoic acid || diethyl ether || 0.52 || 0.40 || 0.06 || 0.12 || 0.02 || 0.05 || 0.56 || 1.22 ||
 * 4-hydroxybenzoic acid || DMF || 2.48 || 2.43 || 0.82 || 1.78 || 0.73 || 1.58 || 4.66 || 9.96 ||
 * 4-hydroxybenzoic acid || DMSO || 4.61 || 9.96 || 9.35 || 9.96 || 9.96 || 9.96 || 9.96 || 9.96 ||
 * 4-hydroxybenzoic acid || ethanol || 1.98 || 2.19 || 0.44 || 0.96 || 0.30 || 0.66 || 1.71 || 3.73 ||
 * 4-hydroxybenzoic acid || ethyl acetate || 0.74 || 0.33 || 0.06 || 0.13 || 0.02 || 0.05 || 0.67 || 1.45 ||
 * 4-hydroxybenzoic acid || ethylene glycol || 1.86 || 2.92 || 1.06 || 2.30 || 1.20 || 2.62 || 1.78 || 3.88 ||
 * 4-hydroxybenzoic acid || hexane || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 ||
 * 4-hydroxybenzoic acid || methanol || 2.46 || 1.66 || 0.43 || 0.94 || 0.30 || 0.65 || 1.62 || 3.53 ||
 * 4-hydroxybenzoic acid || toluene || 0.01 || 0.00 || 0.00 || 0.00 || 0.00 || 0.00 || 0.02 || 0.05 ||
 * 4-methoxybenzoic acid || 1-heptanol || 0.09 || 0.09 || 0.10 || 0.46 || 0.06 || 0.26 || 0.06 || 0.26 ||
 * 4-methoxybenzoic acid || 1-hexanol || 0.10 || 0.10 || 0.12 || 0.51 || 0.07 || 0.30 || 0.07 || 0.30 ||
 * 4-methoxybenzoic acid || 1-octanol || 0.08 || 0.08 || 0.09 || 0.37 || 0.05 || 0.21 || 0.05 || 0.23 ||
 * 4-methoxybenzoic acid || 1-pentanol || 0.10 || 0.10 || 0.12 || 0.54 || 0.08 || 0.34 || 0.07 || 0.31 ||
 * 4-methoxybenzoic acid || 1-propanol || 0.13 || 0.14 || 0.14 || 0.62 || 0.10 || 0.46 || 0.09 || 0.38 ||
 * 4-methoxybenzoic acid || 2-butanol || 0.13 || 0.14 || 0.14 || 0.63 || 0.10 || 0.42 || 0.09 || 0.41 ||
 * 4-methoxybenzoic acid || 2-methyl-1-propanol || 0.08 || 0.11 || 0.12 || 0.54 || 0.08 || 0.36 || 0.08 || 0.34 ||
 * 4-methoxybenzoic acid || 2-methyl-2-propanol || 0.17 || 0.14 || 0.12 || 0.54 || 0.09 || 0.39 || 0.08 || 0.35 ||
 * 4-methoxybenzoic acid || 2-propanol || 0.14 || 0.14 || 0.13 || 0.58 || 0.11 || 0.48 || 0.08 || 0.37 ||
 * 4-methoxybenzoic acid || 3-methyl-1-butanol || 0.08 || 0.10 || 0.12 || 0.53 || 0.07 || 0.32 || 0.07 || 0.31 ||
 * 4-methoxybenzoic acid || butyl acetate || 0.08 || 0.12 || 0.10 || 0.42 || 0.03 || 0.14 || 0.07 || 0.31 ||
 * 4-methoxybenzoic acid || dibutyl ether || 0.02 || 0.02 || 0.02 || 0.08 || 0.00 || 0.02 || 0.01 || 0.05 ||
 * 4-methoxybenzoic acid || diethyl ether || 0.09 || 0.10 || 0.09 || 0.41 || 0.04 || 0.17 || 0.06 || 0.27 ||
 * 4-methoxybenzoic acid || ethanol || 0.20 || 0.19 || 0.20 || 0.87 || 0.14 || 0.59 || 0.13 || 0.56 ||
 * 4-methoxybenzoic acid || ethyl acetate || 0.13 || 0.16 || 0.12 || 0.53 || 0.05 || 0.20 || 0.09 || 0.39 ||
 * 4-methoxybenzoic acid || THF || 0.70 || 0.47 || 0.30 || 1.32 || 0.16 || 0.69 || 0.23 || 0.99 ||
 * 4-nitrobenzoic acid || 1-heptanol || 0.08 || 0.07 || 1.84 || 8.79 || 1.03 || 7.81 || 0.01 || 0.05 ||
 * 4-nitrobenzoic acid || 1-hexanol || 0.08 || 0.09 || 1.87 || 8.79 || 1.12 || 8.46 || 0.01 || 0.06 ||
 * 4-nitrobenzoic acid || 1-octanol || 0.06 || 0.07 || 1.65 || 8.79 || 0.93 || 7.02 || 0.01 || 0.05 ||
 * 4-nitrobenzoic acid || 1-pentanol || 0.09 || 0.09 || 1.82 || 8.79 || 1.15 || 8.76 || 0.01 || 0.06 ||
 * 4-nitrobenzoic acid || 1-propanol || 0.11 || 0.12 || 2.02 || 8.79 || 1.50 || 8.79 || 0.01 || 0.10 ||
 * 4-nitrobenzoic acid || 2-butanol || 0.10 || 0.11 || 1.48 || 8.79 || 0.97 || 7.48 || 0.01 || 0.10 ||
 * 4-nitrobenzoic acid || 2-methyl-1-propanol || 0.07 || 0.08 || 1.39 || 8.79 || 0.92 || 6.99 || 0.01 || 0.07 ||
 * 4-nitrobenzoic acid || 2-methyl-2-propanol || 0.15 || 0.10 || 1.56 || 8.79 || 1.14 || 8.61 || 0.01 || 0.09 ||
 * 4-nitrobenzoic acid || 2-pentanol || 0.08 || 0.08 || 1.59 || 8.79 || 1.01 || 7.69 || 0.01 || 0.06 ||
 * 4-nitrobenzoic acid || 2-propanol || 0.11 || 0.12 || 1.71 || 8.79 || 1.41 || 8.79 || 0.01 || 0.10 ||
 * 4-nitrobenzoic acid || 3-methyl-1-butanol || 0.07 || 0.07 || 1.40 || 8.79 || 0.83 || 6.30 || 0.01 || 0.05 ||
 * 4-nitrobenzoic acid || butyl acetate || 0.08 || 0.11 || 3.12 || 8.79 || 1.07 || 8.08 || 0.01 || 0.07 ||
 * 4-nitrobenzoic acid || dibutyl ether || 0.02 || 0.01 || 0.83 || 6.27 || 0.17 || 1.27 || 0.00 || 0.00 ||
 * 4-nitrobenzoic acid || diethyl ether || 0.10 || 0.10 || 3.20 || 8.79 || 1.34 || 8.79 || 0.01 || 0.06 ||
 * 4-nitrobenzoic acid || ethanol || 0.14 || 0.15 || 2.16 || 8.79 || 1.48 || 8.79 || 0.02 || 0.15 ||
 * 4-nitrobenzoic acid || ethyl acetate || 0.13 || 0.16 || 3.80 || 8.79 || 1.47 || 8.79 || 0.02 || 0.11 ||
 * 4-nitrobenzoic acid || methanol || 0.18 || 0.15 || 1.50 || 8.79 || 1.03 || 7.84 || 0.03 || 0.19 ||
 * 4-nitrobenzoic acid || methyl acetate || 0.14 || 0.18 || 3.09 || 8.79 || 1.05 || 7.99 || 0.02 || 0.17 ||
 * 4-nitrobenzoic acid || THF || 0.78 || 0.52 || 8.79 || 8.79 || 5.37 || 8.79 || 0.05 || 0.41 ||

Results
It was our premise that the MPFM would be better at predicting solubilities than both ab initio methods (Platts, model001), though not as well as the optimal method of using measuredAD descriptors. However, for benzoic acid derivatives, using the measuredAD descriptors for benzoic acid as the core values in the MPFM, this turned out not to be the case; as can be seen by a summary of average absolute error (AAE) and root mean square error (RMSE) in the table below. There are several reasons for this. Firstly, the ab inito Platts method does well in predicting the values of S and B for benzoic acid and thus the MPFM values for S and B are not significantly different than the ab initio Platts values, in fact they are slightly worse. The power of the MPFM can be seen with the A descriptor where the ab initio Platts value is not very good but the predicted changes to A are in general good, leading to good MPFM predictions for A. Secondly, the error that the Platts method makes in predicting the value of B for the nitro-substituted benzoic acid derivatives makes a big difference in the predicted solubilities for those compounds and this skews the results a little, as can be seen in the table below, where we have removed those data values. Of course, this can only be done in hindsight. Finally, we note that, as expected, using measured aqueous values instead of a predicted ones gives better solubility predictions.
 * measure || measuredAD || MPFM || MPFM-VCC || Platts || Platss-VCC || model001 || model001-VCC ||
 * AAE || 0.167 || 2.348 || 3.211 || 1.876 || 2.327 || 0.494 || 0.650 ||
 * RMSE || 0.490 || 3.694 || 4.531 || 3.203 || 3.579 || 0.698 || 0.954 ||
 * measure || measuredAD || MPFM || MPFM-VCC || Platts || Platss-VCC || model001 || model001-VCC ||
 * AAE || 0.224 || 0.615 || 1.202 || 0.415 || 0.727 || 0.620 || 0.977 ||
 * RMSE || 0.604 || 0.970 || 2.091 || 0.793 || 1.312 || 0.835 || 1.089 ||

Data Files
[|combineddataforwiki.xlsx] (combined solubility predictions spreadsheet), [|combineddataforwikiwithoutnitros.xlsx] (solubilities without nitro-substituted compounds), [|combineddescriptors.xlsx] (spreadsheet of a S,A, & B descriptor values), [|combineddescriptorsforTP.xlsx] (descriptor values formatted for Tableau Public - used to create graphs).