Quantum chemical predictions of water–octanol partition coefficients applied to the SAMPL6 logP blind challenge

Abstract

Theoretical approaches for predicting physicochemical properties are valuable tools for accelerating the drug discovery process. In this work, quantum chemical methods are used to predict water–octanol partition coefficients as a part of the SAMPL6 blind challenge. The SMD continuum solvent model was employed with MP2 and eight DFT functionals in conjunction with correlation consistent basis sets to determine the water–octanol transfer free energy. Several tactics towards improving the predictions of the partition coefficient were examined, including increasing the quality of basis sets, considering tautomerization, and accounting for inhomogeneities in the water and n-octanol phases. Evaluation of these various schemes highlights the impact of modeling approaches across different methods. With the inclusion of tautomers and adjustments to the permittivity constants, the best predictions were obtained with smaller basis sets and the O3LYP functional, which yielded an RMSE of 0.79 logP units. The results presented correspond to the SAMPL6 logP submission IDs: DYXBT, O7DJK, and AHMTF.

Introduction

Forecasting molecular reactivity in complex environments is a familiar challenge in research and development across many industries, including agriculture, pharmaceutical, biotechnology, and material science/engineering. In silico modeling can serve as valuable tools for determining anticipated interactions and profiling molecules, allowing for a detailed resolution at the molecular level. As a popular approach for quantifying the association of a molecule’s chemical feature to in situ observations, quantitative structure–property relationship (QSPR) or quantitative structure–activity relationship (QSAR) modeling techniques can be used to predict physical and chemical properties or reactivity towards efforts in establishing a molecular profile [1–7]. Through the use of numerical descriptors, these mathematical models incorporate various dimensions of chemical information to formulate a prediction and may vary in complexity across different models. While many QSAR/QSPR models have been developed for predicting various properties, including ionization and solubility, such approaches lack applicability as the accuracy is limited by the quality and quantity of the preexisting experimental data used to parameterize the model [8].

Alternatively, physical-based approaches serve as a less empirical approach for extracting microscopic relationships that correlate to the macroscopic target (relate microscopic properties to macroscopic observations). Molecular mechanics (MM) and quantum mechanical (QM) approaches have demonstrated success in predicting physical and chemical properties. For properties in solution, physical methods are more advantageous as interactions of the solute with the environment can be modeled and measured directly. Although various modeling techniques exist, best practices applicable for drug discovery tools are not readily discernible as the performance of the various methods is often evaluated on different datasets.

SAMPL challenges offer a unique platform that promotes both the development of new methods and the assessment of current methods for the prediction of relevant properties in drug design, in which challenges are issued with the omission of experimental data to encourage unbiased predictions [9–15]. Previous challenges have focused on predicting various properties, including solvation free energies, binding affinities, acid dissociation constants (pK_a), and distribution coefficients (logD), and have been useful in revealing limitations to methods, highlighting inadequacies encountered by modeling approaches and areas for improvement.

The previous SAMPL5 blind challenge on water–cyclohexane distribution coefficients presented obstacles for many approaches, highlighting the importance of considering pK_a, tautomerization, as well as self-aggregation propensities [16]. In this challenge, a variety of MM and QM approaches were used [17–20]; however, the better-performing methods were those from quantum chemical calculations. The SAMPL6 challenge for physical properties was released in two parts. Part I of the SAMPL6 challenge entailed the prediction of the pK_a for 24 small molecules that resembled drug-like fragments, requiring detailed consideration of microstates due to ionization and tautomerization in solution for the prediction of both microscopic and macroscopic pK_a values for 24 drug-like molecules [21].

In this work, quantum chemical methods are employed on a subset of the SAMPL6 Part I pK_a molecule set to predict the water–octanol partition coefficients (logP) as Part II of the SAMPL6 challenge. Building upon lessons learned from the SAMPL5 logD challenge, several modeling approaches are investigated. The performance of nine electronic structure methods employed is assessed. For each method, we explore potential improvements to the model accuracy by (1) increasing the quality of the basis sets; (2) considering potential tautomers and geometric isomers; and (3) tuning parameters in the solvent model to account for salt effects and water-saturation of the organic phase. This paper presents the methods and results for the SAMPL6 logP submission IDs: DYXBT, O7DJK, and AHMTF.

Methodology

The structures of the 11 molecules were generated from the SMILES strings issued with the SAMPL6 logP challenge [22] using Open Babel 2.4.1 [23] (Fig. 1). As this only represents a single reference state per the molecule, additional structures representing potential tautomers and geometric isomers were generated manually (Figures S1 and S2). All calculations were performed in Gaussian 16 (Rev. B.01) [24]. Gas-phase geometry optimizations were performed on the initial structures using MP2 [25–28] in conjunction with cc-pVDZ basis sets to account for dispersion. Frequencies were examined to confirm that equilibrium stationary points were obtained. To determine the solvation free energies, single-point energy calculations using double and triple zeta correlation consistent basis sets were considered [29, 30]. The respective tight d augmented basis sets, cc-pV(n + d)Z [31], were used for chlorine atoms. All single point calculations were performed using the SMD implicit solvation model [32]. To probe the utility of DFT functionals for the prediction of partition coefficients, additional single-point energy calculations were carried out with 8 different DFT functionals (B3LYP [33–35], B3PW91 [33, 36], O3LYP [34, 37], PBE0 [38], M11 [39], B97D [40], ωB97 [41], and ωB97X-D [42]), using an ultrafine integration grid. As the SMD model uses several parameters to define solvents, including the index of refraction and dielectric constant, the relative permittivity or dielectric constant (ε) was modified to account for potential inhomogeneities in the water and n-octanol phases. Inhomogeneities in the solvent were modeled by modifying the dielectric constants for water and n-octanol. The defined dielectric constant for water within the SMD model is (ε = 78.3553). To account for an ionic strength of 0.15 M KCl used within the experiment, the dielectric constant was set to ε = 76.8553, as salt in water is known to shift the dielectric constant [43, 44]. For n-octanol, in addition to the dielectric constant parameterized for use with the SMD (ε = 9.8629), dielectric constants for dry (ε = 10.01) and water-saturated n-octanol (ε = 8.1) were considered [45, 46]. Using the standard and adjusted dielectric constants, six schemes were used to determine the water-octanol transfer free energies (Table 1). The partition coefficient is determined by the transfer free energy, expressed as the free energy difference of the solute in water and n-octanol,

$$\log P=\log \left(\frac{{[\text{solute}]}_{\text{octanol}}}{{[\text{solute}]}_{\text{water}}}\right)=\left(\mathrm{\Delta }{G}_{\text{water}}-\mathrm{\Delta }{G}_{\text{octanol}}\right)\frac{{\log }_{10}e}{kT}$$

where e is Euler’s number, k is Boltzmann’s constant, and T is temperature.

Fig. 1.

Structures of the 11 molecules in the SAMPL6 logP challenge

Table 1.

Calculation schemes used for determining the logP

Scheme	Aqueous phase	Organic phase	εaq	εorg
1	Wat0	Oct0	78.3553	9.8629
2	Wat0	Oct-dry	78.3553	10.01
3	Wat0	Oct-wet	78.3553	8.1
4	Wat1	Oct0	76.8553	9.8629
5	Wat1	Oct-dry	76.8553	10.01
6	Wat1	Oct-wet	76.8553	8.1

Results and discussion

For the 11 challenge molecules, several modeling approaches were considered for the prediction of logP. As an initial approach, only a single conformation of the molecules representing the reference state of the molecule was used to estimate the transfer free energy. Using the dielectric constants of water and n-octanol defined for the SMD model as a reference, nine quantum chemistry methods were employed to estimate the partition coefficient. As shown in Table 2 using a double-zeta basis set, most methods underestimate the logP, with respect to the experiment. From the considered functionals, B97D yields the lowest mean absolute deviation (MAD) of 0.95 logP units with respect to experiment and is similar to partition coefficients determined with MP2 (MAD = 0.94 logP units), whereas the M11 functional yielded in the greatest underestimations of logP (MAD = 1.25). For molecules SM07 and SM14, most methods were able to predict within 0.5 logP units of the experiment.

Table 2.

Comparison of the predicted partition coefficients using a standard approach

ID	logP	B3LYP		B3PW91		B97D		M11		O3LYP		PBE0		ωB97		ωB97X-D		MP2
	Expt.	DZa	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ
SM02	4.09	2.77	2.62	2.71	2.61	2.82	2.69	2.59	2.48	2.77	2.66	2.69	2.59	2.69	2.57	2.68	2.58	2.81	2.68
SM04	3.98	2.18	2.06	2.06	1.99	2.22	2.11	1.90	1.81	2.14	2.07	2.03	1.96	2.05	1.95	2.04	1.96	2.24	2.08
SM07	3.21	2.84	2.73	2.74	2.66	2.88	2.78	2.59	2.51	2.82	2.73	2.70	2.63	2.73	2.63	2.72	2.63	2.87	2.74
SM08	3.10	2.13	2.03	2.04	1.98	2.29	2.18	1.79	1.73	2.20	2.12	2.01	1.96	2.05	1.97	1.96	1.90	2.39	2.29
SM09	3.03	1.86	1.74	1.78	1.70	1.93	1.82	1.63	1.53	1.86	1.78	1.75	1.68	1.75	1.65	1.74	1.66	1.88	1.75
SM11	2.10	1.05	0.92	0.98	0.88	1.10	0.98	0.85	0.75	1.05	0.96	0.95	0.86	0.95	0.82	0.94	0.84	1.13	1.00
SM12	3.83	2.59	2.46	2.52	2.44	2.63	2.51	2.41	2.32	2.58	2.49	2.50	2.41	2.50	2.39	2.50	2.41	2.63	2.50
SM13	2.92	2.14	2.02	2.06	1.99	2.22	2.11	1.90	1.79	2.16	2.08	2.04	1.97	2.03	1.93	2.01	1.94	2.17	2.06
SM14	1.95	1.95	1.81	1.85	1.75	2.00	1.88	1.68	1.59	1.93	1.82	1.81	1.72	1.82	1.70	1.81	1.71	1.94	1.79
SM15	3.07	1.88	1.77	1.79	1.73	1.96	1.86	1.60	1.54	1.88	1.81	1.75	1.70	1.75	1.67	1.74	1.68	1.87	1.77
SM16	2.62	1.47	1.31	1.41	1.29	1.57	1.42	1.24	1.11	1.50	1.39	1.38	1.28	1.40	1.26	1.35	1.24	1.59	1.43
	MSDb	−1.00	−1.13	−1.09	−1.17	−0.94	−1.05	−1.25	−1.34	−1.00	−1.09	−1.12	−1.20	−1.11	−1.21	−1.13	−1.21	−0.94	−1.07
	MAD	1.00	1.13	1.09	1.17	0.95	1.05	1.25	1.34	1.00	1.09	1.12	1.20	1.11	1.21	1.13	1.21	0.94	1.07
	RSME	1.10	1.22	1.18	1.26	1.04	1.15	1.33	1.42	1.10	1.18	1.21	1.28	1.20	1.30	1.22	1.30	1.05	1.17

^aThe columns labeled DZ and TZ correspond to the cc-pVDZ and cc-pVTZ basis sets

^bThe mean signed deviation (MSD), mean absolute deviation (MAD), and root mean square error (RMSE) of the predicted logP is with respect to experiment

The SMD model was optimized over six electronic structure methods and parametrized against large datasets of solvation free energies and transfer free energies in a variety of solvents to yield solvation free energies that can be obtained with smaller basis sets [32]. Previous studies have illustrated that improving the quality of the basis sets can improve the prediction of solvation free energies [18, 47, 48]. By employing a triple-zeta basis set, all methods further underestimate the logP by an average of 0.10 logP units. Comparing the overall performance, a few notable trends were observed amongst the different methods that were consistent between basis sets. Predictions of logP determined with B97D and MP2, although closer to experiment than the other methods, are inconsistent. For example, using double-zeta basis sets with B97D achieves the lowest error for 8 of the 11 molecules, with respect to experiment; however, when using triple-zeta basis sets, MP2 yields better results for 5 of the 11 molecules although the differences are less than 0.1 logP units. Predictions obtained using B3LYP and O3LYP, irrespective of the basis set, are fairly similar, yielding MADs of 1.0 and 1.1 logP units with double-zeta and triple-zeta basis sets, respectively. Similarly, logP values determined with PBE0 are consistently more hydrophilic than those of B3PW91. For the ωB97 and ωB97X-D functionals with the double-zeta basis sets, ωB97 yields predictions marginally less hydrophilic than ωB97X-D, however, this trend reverses with triple-zeta basis sets. By assuming this isomeric state is the most representative state of the molecule in solution, the best performing methods are B97D, MP2, and B3LYP.

As the initial approach was useful for screening which methods are stronger for use as a quick approach for predicting partition coefficients, as well as for highlighting trends amongst the different functionals, it relies on the approximation that the molecule remains static in both solutions. To capture potential conformations and states, three to six additional isomers were considered for each molecule, with the exclusion of SM14 and SM15 (Tables S1–S4). For some molecules, including SM07, SM08, and SM11, the initial reference structure is the most stable species in water and n-octanol. Using the lowest energy state per molecule in the respective solvent, in general, improved predictions for all methods. As shown in Table 3, the trends observed in the previous approach change per method. For example, in the initial approach utilizing double-zeta basis sets, only two methods achieved an MAD less than 1.0 logP unit, whereas, with the inclusion of isomers, seven methods yield an MAD of less than a logP unit.

Table 3.

Comparison of the predicted partition coefficients using tautomers

ID	logP	B3LYP		B3PW91		B97D		M11		O3LYP		PBE0		ωB97		ωB97X-D		MP2
	Expt.	DZa	TZ	DZ	TZc	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ
SM02	4.09	3.24	3.11	3.18	3.09	3.11	2.78	3.00	2.91	3.26	3.16	3.15	3.06	3.12	3.01	2.92	2.77	2.81	2.68
SM04	3.98	2.18	2.06	2.06	1.99	2.22	2.11	1.90	1.81	2.76	2.53	2.03	1.96	2.05	1.95	2.04	1.96	2.24	2.08
SM07	3.21	2.84	2.73	2.74	2.66	2.88	2.78	2.59	2.51	2.82	2.73	2.70	2.63	2.73	2.63	2.72	2.63	2.87	2.74
SM08	3.10	2.13	2.03	2.04	1.98	2.29	2.18	1.79	1.73	2.20	2.12	2.01	1.96	2.05	1.97	1.96	1.90	2.39	2.29
SM09	3.03	2.35	2.23	2.26	2.20	2.04	1.82	2.06	1.90	2.36	2.30	2.23	2.17	2.20	2.02	1.74	1.66	1.88	1.75
SM11	2.10	1.05	0.92	0.98	0.88	1.10	0.98	0.85	0.75	1.05	0.96	0.95	0.86	0.95	0.82	0.94	0.84	1.13	1.00
SM12	3.83	3.08	2.96	3.01	2.93	2.84	2.52	2.85	2.77	3.08	3.01	2.98	2.91	2.95	2.85	2.66	2.51	2.63	2.50
SM13	2.92	2.67	2.56	2.58	2.52	2.22	2.11	1.90	1.79	2.70	2.65	2.31	2.18	2.03	1.93	2.01	1.94	2.17	2.06
SM14	1.95	1.95	1.81	1.85	1.75	2.00	1.88	1.68	1.59	1.93	1.82	1.81	1.72	1.82	1.70	1.81	1.71	1.94	1.79
SM15	3.07	1.88	1.77	1.79	1.73	1.96	1.86	1.60	1.54	1.88	1.81	1.75	1.70	1.75	1.67	1.74	1.68	1.87	1.77
SM16	2.62	1.80	1.63	1.75	1.63	1.89	1.74	1.61	1.47	1.84	1.71	1.73	1.61	1.74	1.59	1.70	1.57	1.59	1.68
	MSDb	−0.79	−0.92	−0.88	−0.96	−0.85	−1.01	−1.10	−1.19	−0.73	−0.83	−0.93	−1.01	−0.96	−1.07	−1.06	−1.16	−0.94	−1.05
	MAD	0.79	0.92	0.88	0.96	0.86	1.01	1.10	1.19	0.73	0.83	0.93	1.01	0.96	1.07	1.06	1.16	0.94	1.05
	RSME	0.92	1.03	0.99	1.06	0.96	1.11	1.18	1.27	0.82	0.91	1.04	1.11	1.05	1.15	1.15	1.24	1.05	1.15

^aThe columns labeled DZ and TZ correspond to the cc-pVDZ and cc-pVTZ basis sets

^bThe mean signed deviation (MSD), mean absolute deviation (MAD), and root mean square error (RMSE) of the predicted logP is with respect to experiment

^cThe predictions correspond to the submission ID: DYXBT

For most molecules, the O3LYP and B3LYP functionals paired with double-zeta basis sets yield the lowest errors with MADs of 0.73 and 0.79, with respect to experiment, which contrasts with the initial approach as the top two methods were B97D and MP2. Similar to observations in the initial approach, predictions with ωB97 and ωB97X-D are fairly similar for most molecules, in which ωB97 yields a lower RMSE than ωB97X-D. Additionally, all predictions obtained using B3PW91 are within 0.04 logP units of those obtained by PBE0, with the exception of SM13 in which B3PW91 was more accurate by 0.27 logP units. Parallel to initial observations, employing triple-zeta basis sets result in more hydrophilic predictions by an average of 0.1 logP units for most methods. While functionals such as B3PW91, PBE0, and B3LYP yielded consistent underestimations across the 11 challenge molecules, predictions with B97D were more sensitive to the larger basis set (differences of 0.3 logP units for some molecules).

To further probe modeling approaches to improve predictions, five additional schemes were considered for determining the water-octanol transfer free energies. It is known that the solvent structure of the biphasic mixture of water and n-octanol is not completely uniform, as octanol is amphiphilic and may have dilute concentrations of water in the octanol phase at equilibrium [49–55]. Previous studies have shown that the difference in solvation free energies measured in anhydrous n-octanol and water-saturated n-octanol is small, ranging from 0.1 to 1.1 kcal/mol (0.1 to 0.8 logP units) for small organic molecules [56, 57]. While the optimized parameters within the SMD model may implicitly incorporate for experimental uncertainties, such as the presence of water in n-octanol mixtures, the parameter for relative permittivity was modified to distinguish between dry and water-saturated −n-octanol. Anhydrous and water-saturated n-octanol were modeled using dielectric constants of 10.01 and 8.1, respectively. As shown in Table 4, modeling dry n-octanol using double zeta basis sets resulted in an improvement to the predictions of logP by an average of 0.02 logP units, ranging from 0.02–0.04 logP units across all methods, while modeling wet-octanol yielded partition coefficients significantly more hydrophilic ranging from 0.3 to 0.5 logP units (or 0.28–0.54 logP units). While the trends for dry n-octanol were consistent across methods, some functionals, including M11 and PBE0, were more greatly impacted by changing the dielectric constant to model wet-octanol.

Table 4.

Partition coefficients determined using dielectric constants for anhydrous and water-saturated n-octanol

ID	B3LYP		B3PW91		B97D		M11		O3LYP		PBE0		ωB97		ωB97X-D		MP2
	εoct-drya	εoct-wet	εoct-dry	εoct-wet	εoct-dry	εoct-wet	εoct-dry	εoct-wet	εoct-dry	εoct-wet	εoct-dry	εoct-wet	εoct-dry	εoct-wet	εoct-dry	εoct-wet	εoct-dry	εoct-wet
SM02	3.26	2.93	3.20	2.85	3.13	2.81	3.03	2.64	3.28	2.95	3.17	2.81	3.15	2.78	2.95	2.58	2.82	2.56
SM04	2.20	1.88	2.09	1.74	2.24	1.92	1.93	1.54	2.78	2.44	2.05	1.69	2.07	1.72	2.06	1.70	2.26	1.94
SM07	2.86	2.55	2.76	2.42	2.90	2.59	2.61	2.23	2.84	2.52	2.73	2.38	2.75	2.40	2.74	2.39	2.89	2.58
SM08	2.17	1.65	2.08	1.55	2.32	1.83	1.83	1.25	2.23	1.72	2.04	1.50	2.08	1.55	1.99	1.45	2.42	1.94
SM09	2.37	2.02	2.29	1.91	2.06	1.72	2.09	1.67	2.39	2.03	2.25	1.87	2.22	1.83	1.76	1.43	1.90	1.60
SM11	1.07	0.74	1.00	0.65	1.12	0.79	0.88	0.50	1.07	0.74	0.97	0.61	0.97	0.61	0.97	0.61	1.15	0.84
SM12	3.10	2.78	3.03	2.70	2.86	2.56	2.87	2.50	3.10	2.79	3.00	2.66	2.97	2.63	2.68	2.34	2.65	2.40
SM13	2.70	2.30	2.61	2.18	2.24	1.91	1.93	1.53	2.73	2.33	2.34	1.90	2.05	1.68	2.04	1.66	2.19	1.85
SM14	1.98	1.62	1.87	1.49	2.03	1.68	1.71	1.28	1.95	1.59	1.83	1.44	1.84	1.45	1.84	1.45	1.96	1.60
SM15	1.90	1.53	1.81	1.41	1.98	1.62	1.62	1.18	1.90	1.52	1.78	1.37	1.78	1.37	1.77	1.36	1.89	1.52
SM16	1.82	1.44	1.78	1.39	1.92	1.56	1.63	1.21	1.86	1.49	1.76	1.36	1.77	1.37	1.73	1.33	1.59	1.59
MSDb	−0.77	−1.13	−0.85	−1.24	−0.83	−1.17	−1.07	−1.49	−0.71	−1.07	−0.91	−1.30	−0.93	−1.32	−1.04	−1.42	−0.92	−1.23
MAD	0.77	1.13	0.85	1.24	0.84	1.17	1.07	1.49	0.71	1.07	0.91	1.30	0.93	1.32	1.04	1.42	0.93	1.23
RMSE	0.90	1.23	0.97	1.32	0.94	1.25	1.16	1.55	0.79	1.13	1.01	1.38	1.03	1.39	1.13	1.49	1.03	1.30

^aThe dielectric constants for anhydrous (ε_oct-dry = 10.01) n-octanol and water-saturated (ε_oct-wet = 8.1) n-octanol are used with the dielectric of pure water (ε_wat0 = 78.3553)

^bThe mean signed deviation (MSD), mean absolute deviation (MAD), and root mean square error (RMSE) of the predicted logP is with respect to experiment

As the ionic influence on solvent equilibria was anticipated, the dielectric constants for water were adjusted. For water, the effect of a 150 mM potassium chloride buffer was modeled by using a dielectric constant of ε = 76.8553 (or Δε = 1.5). Comparing partition coefficients determined with the standard dielectric constant for water and n-octanol, there is little to no impact by tuning the dielectric for water alone (Tables S5–S12). The RMSE, with respect to the experimental logP, per method employed with double-zeta basis sets is illustrated in Fig. 2. The magnitude of improvement is only noticeable when used with the modeling of dry octanol. Although modeling both water-saturated n-octanol and ionic strength corrected water, in theory, would serve as the more representative model, it results in the worst predictions yielding strongly hydrophilic logP values.

Fig. 2.

Effect of the ionic influence on predicting partition coefficients with double-zeta basis sets

Focusing on the O3LYP functional, as it was one of stronger performing methods, the impact on the solvation free energy as a result of tuning the dielectric constants to account for different solvent compositions is apparent and can provide further insight on the role of the basis sets. As shown in Table 5, by considering the dielectric constants parameterized for the SMD implicit solvation model as a reference, the difference between the partition coefficients determined with double-zeta and triple-zeta basis sets is nearly identical to partition coefficients determined using the dielectric constant for dry n-octanol. For this, the difference in the MAE and RMSE between basis sets is approximately 0.10 logP units, with respect to experiment. For the water-saturated n-octanol, employing triple-zeta basis sets impact the aqueous solvation free energy more, resulting in partition coefficients that are more hydrophilic, and equate to a difference in the MAE and RMSE of 0.12 logP units between the two basis sets. This is also observed for respective models that utilize the ionic strength adjusted dielectric constant for water.

Table 5.

Impact of tuning dielectric constants with O3LYP

	εwat0 = 78.3553						εwat1 = 76.8553
	εoct-refa,b		εoct-dry		εoct-wet		εoct-ref		εoct-dry		εoct-wet
ID	DZc	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ	DZ	TZ
SM02	3.26	3.16	3.28	3.19	2.95	2.84	3.26	3.17	3.28	3.19	2.95	2.84
SM04	2.76	2.53	2.78	2.55	2.44	2.19	2.77	2.53	2.79	2.56	2.45	2.20
SM07	2.82	2.73	2.84	2.76	2.52	2.41	2.82	2.74	2.84	2.76	2.52	2.42
SM08	2.20	2.12	2.23	2.16	1.72	1.61	2.20	2.13	2.24	2.16	1.73	1.61
SM09	2.36	2.30	2.39	2.32	2.03	1.94	2.37	2.30	2.39	2.32	2.04	1.95
SM11	1.05	0.96	1.07	0.99	0.74	0.63	1.06	0.97	1.08	0.99	0.75	0.64
SM12	3.08	3.01	3.10	3.03	2.79	2.69	3.09	3.01	3.11	3.03	2.79	2.70
SM13	2.70	2.65	2.73	2.67	2.33	2.25	2.71	2.65	2.73	2.68	2.34	2.26
SM14	1.93	1.82	1.95	1.85	1.59	1.46	1.93	1.83	1.96	1.85	1.59	1.47
SM15	1.88	1.81	1.90	1.83	1.52	1.43	1.88	1.81	1.91	1.84	1.53	1.44
SM16	1.84	1.71	1.86	1.73	1.49	1.33	1.84	1.71	1.87	1.74	1.50	1.33
MSDd	−0.73	−0.83	−0.71	−0.80	−1.07	−1.19	−0.72	−0.82	−0.70	−0.80	−1.07	−1.19
MAD	0.73	0.83	0.71	0.80	1.07	1.19	0.72	0.82	0.70	0.80	1.07	1.19
RMSE	0.82	0.91	0.79	0.89	1.13	1.25	0.81	0.91	0.79	0.89	1.13	1.25

^aThe reference dielectric constant for n-octanol (ε = 9.8629)

^bDielectric constants for anhydrous (ε_oct-dry = 10.01) n-octanol and water-saturated (ε_oct-wet = 8.1) n-octanol

^cThe columns labeled DZ and TZ correspond to the cc-pVDZ and cc-pVTZ basis sets

^dThe mean signed deviation (MSD), mean absolute deviation (MAD), and root mean square error (RMSE) of the predicted logP is with respect to experiment

The methods submitted to the SAMPL6 challenge correspond to partition coefficients determined using B3PW91 with triple-zeta basis sets for the minimal energy tautomer and with implicit solvent parameters to model: (1) a reference method by employing SMD parameters (ID: DYXBT); (2) pure water and water-saturated n-octanol (ID: O7DJK); and (3) ionic strength adjusted water and water-saturated n-octanol (ID: AHMTF). In comparison to the predictions obtained from O3LYP with triple-zeta basis sets, the differences in error between two methods and the respective approach for modeling the solvent highlight the sensitivity of the method for predicting partition coefficients, with differences in RMSE from 0.15 to 0.17 logP units.

Regarding outliers, despite efforts for improving the solvent description, SM04, SM11, SM15 were significantly underestimated across all methods in each approach relative to other molecules in the challenge set. In contrast to molecule SM07, introducing a chlorine to SM04 results in a favoring of the water phase. Six of the challenge molecules share a 4-aminoquinazoline scaffold that primarily differs by the substituents attached to the 4-amino group. Unfortunately, with the different approaches modeled, there was not an optimal method capable of properly ranking the substituent effects, however, some methods were within 1 rank unit. With the exclusion of SM04, the M11, O3LYP, ωB97 functionals predict the relative trend of the substituent effects better than the other methods considered in this study.

Conclusion

In this study, several quantum chemical methods were used to predict the water-octanol partition coefficients of molecules as a part of the SAMPL6 logP blind challenge. Considering a simple approach to determine the transfer free energy with the SMD implicit solvent model, using a single tautomer as the initial guess, MP2 and B97D in conjunction with cc-pVDZ yielded in the best predictions of logP resulting in an MAD of 0.94 and 0.95 logP units from the experiment, respectively. Using a larger basis set did not improve the results. By considering additional isomeric and tautomeric states, the predictions of logP improved for most methods and resulted in lower RMSEs. Efforts to enhance the description of the implicit solvent model were explored by adjusting the dielectric constants per solvent. The results highlight that changes in the dielectric constants can improve the accuracy. Modeling dry n-octanol with ionic strength corrected water yielded the best results, whereas employing a dielectric constant for water-saturated n-octanol resulted in more hydrophilic predictions. The best predictions were obtained with O3LYP/cc-pVDZ and achieved an MAD of 0.70 logP units. Moving forward, these approaches can be further improved by considering alternative approaches for modeling the solvation.