Predicting the Aqueous Solubility of Neutral Organic Compounds by Reversed‐Phase Liquid Chromatography

ABSTRACT

Accurate estimation of water solubility is crucial for chemical screening, yet traditional predictive tools such as the General Solubility Equation (GSE) require melting point and octanol‐water partition coefficient data and often struggle with weak electrolytes. This study presents two highly efficient reversed‐phase liquid chromatography (RPLC) correlation strategies evaluated, comprising 49 binary solvent systems on three stationary phases. First, simple, melting point, octanol‐water partition coefficient, and descriptor‐free, isocratic models were explored to estimate the water solubility of neutral organic compounds using RPLC retention as the sole input. This approach demonstrated superior predictive accuracy of 0.307 log units and a more uniform error distribution across both non‐electrolytes and weak electrolytes than the more conventional GSE. Second, to improve the predictive accuracy of estimating water solubility, RPLC retention and melting point data were explored. Predictive accuracy improved notably at higher organic volume fractions (50%–70% v/v) across all evaluated stationary phases. The correlation model comprising 70% (v/v) acetonitrile on an XTerra MS C18 stationary phase yielded a coefficient of determination of 0.962, a standard deviation of the model fit of 0.276, and an average absolute error value of 0.222. Together, these complementary chromatographic modelling strategies offer powerful, high‐throughput alternatives for rapid solubility screening: providing either a direct, descriptor‐free approach for compounds lacking structural information or a highly precise RPLC model approach combining retention and melting point data that minimizes prediction errors below 0.3 log units.

Two reversed‐phase liquid chromatography (RPLC) model approaches to predict water solubility without descriptors were developed in this study, and RPLC correlation models outperform the General Solubility Equation model. Integrating RPLC retention with the term [MP‐25] reduces prediction error. The XTerra C18 phase with 70% acetonitrile has the lowest prediction of 0.222 log units.

1. Introduction

The water solubility of neutral organic compounds (S_w ) is a critical physicochemical property in a wide range of scientific disciplines, such as drug discovery, environmental toxicity assessment, chemical formulation, and the development of advanced materials [1, 2]. There are two main experimental approaches for determining water solubility: the shake‐flask method is used for neutral organic compounds that are soluble in water at levels above 0.1 g/L, and the column elution method is used for compounds that are soluble in water at levels below 0.1 g/L [3, 4, 5]. When experimentally determining the solubility of neutral organic compounds in water, analytes are required in high purity, as various impurities can influence experimental solubility determination [3]. Experimental methods for the determination of the solubility of neutral organic compounds in water are laborious, time‐consuming, and require high sample quantities in high purity [6, 7]. Therefore, methods for estimating the water solubility of neutral organic compounds are preferable over experimental methods [8, 9, 10].

The development of methods to estimate the water solubility of neutral organic compounds has been an active area of research for several decades [6, 7, 8, 11, 12, 13, 14]. Arguably, the most preferred method for estimating the water solubility of organic non‐electrolytes is the General Solubility Equation (GSE) developed by Yalkowsky and co‐workers [11, 15, 16, 17]. The GSE requires only two inputs, the octanol‐water partition coefficient (log P_o/w ) and melting point data for solid compounds as described in Equation (1) [15].

$$logSw=0.5-0.01\left(MP-25\right)-\log P_{O/W}$$ (1)

In the above Equation (1), MP is the melting point of neutral organic compounds in Celsius, and S_w is in units of moles per litre [15, 16, 17]. For a liquid compound where the melting point value is below 25°C, the term “MP‐25” is set to zero. The GSE is a widely adopted water solubility estimation approach due to its simplicity, with a typical average absolute error (AAE) of 0.4–0.6, while the errors are even higher for drugs up to 0.8 log units [15, 16, 17]. Despite the wide applicability and popularity of the GSE, there are several drawbacks of this estimation method: the requirement of prior knowledge of an accurate value for the log P_o/w and the omission of hydrogen bond and dipole‐type interactions, which are important, especially for weak electrolytes.

Over the years, several methods have been proposed to estimate water solubility using various molecular descriptors [12, 18, 19], as well as group‐contribution [20] and machine learning approaches [21]. Although many of these approaches can reasonably estimate the water solubility of neutral organic compounds, these methods often require molecular descriptors that are difficult to obtain for compounds with limited structural information. Despite the development of numerous models for water solubility estimation over the past 30 years, prediction accuracy has not significantly improved; the standard error remains in the range of 0.5 to 1 log units.

Applications of reversed‐phase liquid chromatography (RPLC) to estimate physicochemical properties offer distinct advantages, including widespread instrument availability, operational simplicity, automated workflows, and, most importantly, RPLC bypasses the need for high sample quantities or chemical purities [22, 23, 24]. Despite these benefits, a systematic strategy leveraging RPLC retention data to overcome the inherent accuracy limitations of the most widely used GSE remains largely undeveloped. In this work, we address this gap by establishing RPLC as a high‐throughput, descriptor‐free alternative for predicting the water solubility of neutral organic compounds. First, we establish a direct, simplified correlation between RPLC retention and water solubility that eliminates the need for complex molecular descriptors or pre‐determined log P_o/w values. Second, we integrate RPLC retention with melting point data to develop a novel correlation modelling approach that significantly enhances prediction accuracy beyond the stagnation point of current models. Ultimately, this work provides a rapid, accurate, and accessible analytical framework that streamlines solubility screening applications, for example, early‐stage drug discovery and environmental hazard assessment.

2. Materials and Methods

2.1. Data Sources and Calculations

To identify the direct correlation between RPLC retention and the water solubility of neutral organic compounds, we obtained solvation parameter model system constants for the stationary phases XTerra MS C18, Discovery HS F5, and Sunfire C18 from several published sources [25, 26, 27]. Isocratic retention data for XTerra MS C18, Discovery HS F5, and Sunfire C18 stationary phases comprising binary solvent systems acetonitrile‐water, methanol‐water, and tetrahydrofuran‐water were taken from an in‐house database [25, 26, 27]. All isocratic retention data were measured at 45°C, corrected for extra‐column contributions [28], and utilized a standard protocol and quality control procedures for consistency [29, 30]. Stationary phases used to explore correlation models: XTerra MS C18 (50 mm × 4.6 mm × 125 nm, dp = 5 µm) [25], Discovery HS F5 (100 mm × 4.6 mm × 12 nm, dp = 5 µm) [26], and Sunfire C18 (50 mm × 4.6 mm × 10 nm, dp = 3.5 µm) [27] all were obtained from Waters Corporation (Milford, MA, USA). RPLC mobile phase modifiers tetrahydrofuran, methanol, water, and acetonitrile were high‐performance LC grade from Sigma‐Aldrich (St. Louis, MO, USA). All water solubility at 25°C, melting point, and log P_o/w data used in this study are provided in Tables S1–S3, respectively.

2.2. Theory

2.2.1. The Solvation Parameter Model

There are two general forms of the Abraham solvation parameter model, one for transfer processes from a condensed phase to a gas phase and the second for transfer processes from a condensed phase to another condensed phase; the latter is given in Equation (2) below [31].

$$\log \mathrm{SP}=c+e\mathrm{E}+s\mathrm{S}+a\mathrm{A}+b\mathrm{B}+v\mathrm{V}$$ (2)

In the above Equation (2), the term “SP” is a free‐energy‐related property, for example, the logarithmic retention factor (log k) of an RPLC system [32, 33] or log S_w [12]. The solvation parameter model intercept is denoted by “c” and does not contain any chemical information and is not considered a system constant. The remaining lower‐case letters “e”, “s”, “a”, “b”, and “v” are system constants of the solvation parameter model. These systems contain chemical information for a specific biphasic system. Uppercase letters “E”, “S”, “A”, “B”, and “V” represent properties of a particular solute, for example, excess molar refraction (E), hydrogen‐bond acidity (A), dipolarity/polarizability (S), hydrogen‐bond basicity (B), and McGowan's characteristic volume (V) [31].

2.2.2. Comparison of Models Using the D‐parameter

Similarity between two biphasic systems can be compared using five solvation parameter model system constants, "e," "s," "a," "b," and "v," and screening tools. In this work, we used the most reliable screening parameter to our knowledge, the d‐parameter, first proposed by Lazaro et al. [34]. The d‐parameter is outlined in Equation (3) below.

$$d-Parameter=\sqrt{[{\left(e_{u1}-e_{u2}\right)}^2+{\left(s_{u1}-s_{u2}\right)}^2+{\left(a_{u1}-a_{u2}\right)}^2+{\left(b_{u1}-b_{u2}\right)}^2+{\left(v_{u1}-v_{u2}\right)}^2]}$$ (3)

In the above Equation (3), the terms “e_u ,” “s_u ,” “a_u ,” “b_u ,” and “v_u ” represent normalized system constants. Normalized constants are calculated by dividing each system by the vector length (l), where l is ${(e^2+s^2+a^2+b^2+v^2)}^{1/2}$.

Abraham et al. have developed several models over the years to estimate log S_w using the solvation parameter model [12, 18]. For water solubility estimation, a modified solvation parameter model that includes the A*B term, as shown in Equation (4), is typically used. In Equation (4), N represents the number of compounds in the model, r ² is the coefficient of determination, SD is the standard deviation, and F is the model's F‐statistic. In retention modelling for RPLC systems, the general form of the solvation parameter model in Equation (2), which does not include the A*B term, is used [27, 32, 33].

$$\begin{array}{ccc}\hfill log{S}_W& =& 0.394-0.954E+0.318S+1.1157A+3.255B\hfill \\ & & -3.329V-0.786A\ast B\hfill \end{array}$$ (4)

N = 1071, r ² = 0.888, SD = 0.670, F = 1401

For screening purposes to identify the correlation between log S_w and log k in RPLC systems we explored in this study, we used the general form of the solvation parameter model proposed by Abraham and Le, Equation (5) [12].

$$log{S}_W=0.849-1.061E+0.851S+0.646A+3.279B-4.050V$$ (5)

N = 594, r ² = 0.895, SD = 0.630, F = 1004, AAE = 0.470

Next, we multiplied both sides of Equation (5) by ‐1 to yield Equation (6) below; this is to make RPLC system constants comparable for screening purposes.

$$-log{S}_W=-0.849+1.061E-0.851S-0.646A-3.279B+4.050V$$ (6)

3. Results and Discussion

3.1. Direct Correlation Between Water Solubility and RPLC Retention

In our screening process, we used the solvation parameter model described in Equation (6) as the target to identify similarities among 49 binary solvent systems evaluated in this study. These systems include acetonitrile‐water (14 systems), methanol‐water (21 systems), and tetrahydrofuran‐water (14 systems), on three stationary phases: XTerra MS C18, Discovery HS F5, and Sunfire C18. Details of the binary solvent compositions, stationary phases, and d‐parameter values are provided in Table S4. In general, a lower d‐parameter value would mean the two compared biphasic systems have greater similarity and a promising potential to correlate [23, 24]. We used the selection criterion that the d‐parameter is ≤ 0.150 to identify potential chromatographic correlation models to estimate the water solubility [35].

Of the 49 binary solvent systems evaluated in this study, 8 RPLC systems satisfied the screening criterion. These selected RPLC systems were subsequently modelled using the correlation in Equation (7), where “p” represents the slope and “q” denotes the intercept. The relationships between log S_w and log k, along with the corresponding model statistics, are summarized in Table 1 for these systems.

$$log{S}_W=q+p.\log k$$ (7)

TABLE 1.

Shortlisted reversed‐phase liquid chromatography models for estimating solubility of organic compounds in water.

Reversed‐phase liquid chromatography system	Correlation model		Model statistics
	p	q	r 2	SD	AAE	F	N
XTerra MS C18, 10% of acetonitrile (v/v) and 90% water (v/v)	−1.549	0.353	0.810	0.553	0.423	145	36
XTerra MS C18, 20% of acetonitrile (v/v) and 80% water (v/v)	−1.571	−0.245	0.781	0.592	0.446	139	41
XTerra MS C18, 10% of methanol (v/v) and 90% water (v/v)	−1.637	0.694	0.638	0.631	0.454	60	36
XTerra MS C18, 20% of methanol (v/v) and 80% water (v/v)	−1.518	0.194	0.828	0.440	0.325	175	38
XTerra MS C18, 30% of methanol (v/v) and 70% water (v/v)	−1.468	−0.254	0.807	0.475	0.365	167	42
Discovery HS F5, 30% of methanol (v/v) and 70% water (v/v)	−1.947	0.541	0.912	0.382	0.307	416	42
Discovery HS F5, 40% of methanol (v/v) and 60% water (v/v)	−2.233	0.136	0.897	0.415	0.315	349	42
Discovery HS F5, 50% of methanol (v/v) and 50% water (v/v)	−2.483	−0.456	0.900	0.409	0.316	361	42

p is the slope and q is the intercept of the log S_w and log k correlation model. AAE is the average absolute error, N represents the number of compounds in the model, r ² is the coefficient of determination, SD is the standard deviation of the model fit, and F is the model's F‐statistic.

For the eight shortlisted RPLC correlation models, the SD ranged from 0.380 to 0.631, and the AAE ranged from 0.307 to 0.454. Among these models, the most promising results were obtained with 30%–50% (v/v) methanol isocratic mobile phases on a Discovery HS F5 stationary phase, as described in Equations (8)–(10).

$$\begin{array}{c}\hfill \log S_W=0.541\left(0.126\right)-1.947\left(0.095\right)\log {\mathrm{k}}_{\left(\mathrm{Discovery}\mathrm{HS}\mathrm{F}5,30\%\mathrm{methanol}\right)}\end{array}$$ (8)

N = 42, r ² = 0.912, SD = 0.382, F = 416, AAE = 0.307, PRESS = 6.584

$$\begin{array}{c}\hfill \log S_W=0.136\left(0.119\right)-2.233\left(0.119\right)\log {\mathrm{k}}_{\left(\mathrm{Discovery}\mathrm{HS}\mathrm{F}5,40\%\mathrm{methanol}\right)}\end{array}$$ (9)

N = 42, r ² = 0.897, SD = 0.415, F = 349, AAE = 0.315, PRESS = 7.739

$$\begin{array}{c}\hfill \log S_W=-0.456\left(0.098\right)-2.483\left(0.131\right)\log {\mathrm{k}}_{\left(\mathrm{Discovery}\mathrm{HS}\mathrm{F}5,50\%\mathrm{methanol}\right)}\end{array}$$ (10)

N = 42, r ² = 0.900, SD = 0.409, F = 361, AAE = 0.316, PRESS = 7.515

In the above correlations, PRESS (predicted residual error sum of squares) measures how well the model predicts log S_w. RPLC retention data to construct correlation models were taken from an in‐house database from three previous studies [25, 26, 27], and no independent external dataset was available; we used PRESS values as an internal validation measure. All three correlation models showed excellent ability to estimate the water solubility of neutral organic compounds. Notably, the model employing a mobile phase of 30% (v/v) methanol on a Discovery HS F5 stationary phase yielded the lowest PRESS value (6.584), along with an AAE of 0.307 and an SD of 0.382, making it particularly promising. Figure 1 illustrates the correlation between log S_w and log k for 30% (v/v) methanol on a Discovery HS F5 stationary phase. Table 2 presents the experimental log S_w , log k, and the predicted log S_w from the model in Equation (8).

FIGURE 1.

Correlation model plot of log S_w and log k for the reversed‐phase liquid chromatography system on Discovery HSF5 stationary phase comprising 30% (v/v) methanol.

TABLE 2.

Experimental log S_w , log k data on Discovery HS F5‐30 (v/v) methanol, Discovery HS F5‐30 (v/v) methanol model predicted log S_w , and predicted log S_w using the general solubility equation.

Compounds	log Sw	log k	Discovery HS F5‐30 (v/v) MeOH model predicted log Sw	GSE predicted log Sw
Acetanilide	−1.33	0.57	−0.57	−1.55
Acetophenone	−1.28	0.94	−1.28	−1.08
Anisole	−1.85	1.10	−1.61	−1.56
Benzene	−1.64	0.93	−1.26	−1.64
Benzonitrile	−1.00	0.91	−1.23	−1.07
Benzophenone	−3.12	1.99	−3.34	−2.92
Benzyl alcohol	−0.43	0.45	−0.33	−0.60
Biphenyl	−4.35	2.24	−3.81	−3.98
1‐Bromonaphthalene	−4.35	2.52	−4.36	−3.80
Caffeine	−0.88	0.37	−0.18	−1.54
1‐Chloronaphthalene	−3.93	2.45	−4.22	−3.58
Diethyl phthalate	−2.35	1.82	−3.01	−2.04
2,6‐Dimethylphenol	−1.29	1.23	−1.86	−2.10
Ethylbenzene	−2.77	1.66	−2.70	−2.65
Fluorene	−5.00	2.50	−4.32	−4.48
4‐Hydroxybenzaldehyde	−0.96	0.61	−0.64	−1.77
2‐Methylphenol	−0.62	0.86	−1.14	−1.51
Naphthalene	−3.60	1.88	−3.11	−3.37
1‐Naphthol	−2.22	1.56	−2.50	−3.06
2‐Naphthol	−2.28	1.48	−2.35	−3.17
2‐Nitroaniline	−1.96	1.09	−1.59	−1.81
Nitrobenzene	−1.80	1.13	−1.66	−1.38
4‐Nitrotoluene	−2.49	1.55	−2.47	−2.14
Phenol	0.00	0.52	−0.46	−1.12
Toluene	−2.21	1.32	−2.03	−2.14
1,2,3‐Trimethylbenzene	−3.20	2.04	−3.42	−3.04
Methylparaben	−1.83	1.00	−1.41	−2.46
Methyl benzoate	−1.85	1.27	−1.93	−1.62
Butan‐2‐one	0.52	0.05	0.44	0.21
Heptan‐2‐one	−1.45	1.21	−1.81	−1.48
Cyclohexanone	−0.60	0.39	−0.22	−0.36
Aniline	−0.41	0.37	−0.18	−0.40
4‐Chloroaniline	−1.66	1.05	−1.50	−1.78
N‐Ethylaniline	−1.70	1.28	−1.94	−1.66
Pyridine	0.76	0.30	−0.05	−0.15
Quinoline	−1.30	1.12	−1.64	−1.53
m‐Toluidine	−0.85	0.85	−1.12	−0.90
o‐Toluidine	−0.81	0.71	−0.84	−0.82
p‐Toluidine	−1.21	0.76	−0.94	−1.08
4‐Methylphenol	−0.70	0.85	−1.11	−1.55
2‐Phenylethanol	−0.74	0.73	−0.87	−0.86
Indole	−1.52	1.14	−1.67	−1.92

Methanol (MeOH) and General Solubility Equation (GSE).

Table 2 presents a comparison of predicted log S_w values for 30% (v/v) methanol on a Discovery HS F5 stationary phase, obtained with the RPLC correlation model in Equation (8) and the GSE model, using the same dataset comprising 42 solutes. Figure 2 illustrates a residual plot that compares the RPLC correlation model in Equation (8) to the GSE model, with residuals plotted against log S_w . The log S_w values for compounds in this dataset range from 0.76 for pyridine to ‐5.0 for fluorene. As shown in Figure 2, residual values for the RPLC correlation model in Equation (8) were more uniform than those for the GSE model estimates. The residual values for the GSE were more uniform in the range log S_w ‐5 to 2, demonstrating high residuals for the range log S_w 2 to 0.76. Figure 3 shows the residuals for each model compound, again comparing the correlation model in Equation (8) and the GSE model. In both figures, residuals represent the difference between the experimental log S_w values and those estimated by the models. The AAE for the dataset in Table 2 for the GSE model was calculated using Equation (11) below.

$$AAE=\sum \lfloor \log S_{w_{obs}}-\log S_{w_{cal}}\rfloor /N$$ (11)

FIGURE 2.

Illustration of residual plot for the reversed‐phase liquid chromatography system on Discovery HS F5 stationary phase comprising 30% (v/v) methanol correlation model in Equation (8) and general solubility equation estimated residuals. Residual values were calculated as (experimental log S_w —model estimated log S_w ) and were plotted against log Sw.

FIGURE 3.

Illustration of residual values of each model compound compared for the reversed‐phase liquid chromatography system on Discovery HS F5 stationary phase comprising 30 % (v/v) methanol correlation model in Equation (8) and general solubility equation estimated residuals. Residual values were calculated as (experimental log S_w —model estimated log S_w ).

In Equation (11) above, log S_wobs represents the experimental water solubility, while log S_wcal is the water solubility estimated by the model. For the dataset in Table 2, the GSE model had an AAE of 0.359, slightly higher than the RPLC model's AAE of 0.307 in Equation (8). The GSE model requires two inputs, log P_o/w and melting point data, and estimates log S_w for non‐electrolytes with reasonable accuracy. However, we found that the GSE model produced larger errors for weak electrolytes such as phenol, 2‐naphthol, 2‐methylphenol, 4‐methylphenol, and 1‐naphthol. Overall, the RPLC model described in Equation (8) estimated water solubility more consistently across the compared dataset.

In this work, we identified the RPLC correlation method to predict log S_w using RPLC log k as the only input. The proposed RPLC isocratic system of 30 % (v/v) methanol on a Discovery HS F5 stationary phase demonstrated superior performance with a prediction error of 0.307 log units for the estimation of water solubility over the traditional GSE. This method eliminates the need for any solute descriptors, melting point, or log P_o/w data, with more uniform accuracy across both non‐electrolytes and weak electrolytes for rapid chemical screening of neutral organic compounds, particularly those with limited structural information.

3.2. Estimating Water Solubility of Neutral Organic Compounds Using a Combination of RPLC Retention and Melting Point Data

When estimating the water solubility of neutral organic compounds using the GSE, the model introduces the melting point term denoted as [MP‐25] [16, 17]. This term reflects the idea that water solubility partly depends on the energy required to break the solid crystal lattice before molecules can dissolve. In other words, a higher melting point indicates a stronger lattice and, therefore, lower solubility. This forms part of the thermodynamic basis of the GSE, which combines crystal‐lattice (ideal‐solubility) considerations with octanol‐water transfer effects.

Previously, in Section 3.1, we shortlisted eight RPLC systems based on the direct correlation between water solubility and RPLC retention (Table 1). To test whether integrating RPLC retention data with melting point information improves prediction accuracy beyond the limitations of current models, we modeled the eight RPLC systems in Table 1 using the relationship described in Equation (11).

$$log{S}_W=q+p.\log k+s.\left[\mathrm{MP}-25\right]$$ (12)

In Equation (12), “p” and “s” are coefficients, and “q” is the intercept in the correlation between log S_w and log k. Table 3 summarizes the models used to estimate the water solubility of neutral organic compounds, which combine RPLC retention and melting point data for the eight RPLC systems listed in Table 1. For all eight RPLC systems evaluated in Table 3, incorporating both log k and [MP‐25] terms into the correlation models resulted in lower SD and AAE values compared to the same systems in Table 1. The changes in SD and AAE values, with and without the [MP‐25] term, are summarized in Table 4. Notably, we observed a gradual increase in ΔSD (the difference in standard deviation between models without and with the melting point term) and ΔAAE (the difference in AAE between models without and with the melting point term) as the organic volume fraction of the mobile phase increased. The observations prompted us to conclude that RPLC systems with higher organic volume fractions in the mobile phase are more effective for estimating the water solubility of neutral organic compounds by combining retention and melting point data. Therefore, we investigated XTerra MS C18, 50‐70 % of acetonitrile (v/v), XTerra MS C18, 50‐70 % of methanol (v/v), and Discovery HS F5, 50‐70 % of methanol (v/v) RPLC systems integrating retention and melting point data. Nine RPLC correlation models for the estimation of water solubility having organic mobile phase compositions of 50 to 70 % (v/v) are summarized in Table 5.

TABLE 3.

Reversed‐phase liquid chromatography models for estimating solubility of organic compounds in water integrating retention and melting point data.

Reversed‐phase liquid chromatography system	Correlation model			Model statistics
	p	s	q	r 2	SD	AAE	F	N
XTerra MS C18, 10% of acetonitrile (v/v) and 90% water (v/v)	−1.525	−0.008	0.619	0.909	0.389	0.305	165	36
XTerra MS C18, 20% of acetonitrile (v/v) and 80% water (v/v)	−1.670	−0.010	0.183	0.935	0.327	0.253	271	41
XTerra MS C18, 10% of methanol (v/v) and 90% water (v/v)	−1.699	−0.006	1.022	0.731	0.552	0.404	45	36
XTerra MS C18, 20% of methanol (v/v) and 80% water (v/v)	−1.609	−0.006	0.453	0.888	0.360	0.270	139	38
XTerra MS C18, 30 % of methanol (v/v) and 70% water (v/v)	−1.614	−0.007	0.062	0.894	0.357	0.274	167	42
Discovery HS F5, 30% of methanol (v/v) and 70% water (v/v)	−1.952	−0.005	0.669	0.938	0.326	0.262	294	42
Discovery HS F5, 40% of methanol (v/v) and 60% water (v/v)	−2.261	−0.006	0.335	0.944	0.311	0.250	327	42
Discovery HS F5, 50% of methanol (v/v) and 50% water (v/v)	−2.488	−0.006	−0.276	0.945	0.308	0.243	333	42

p and s are coefficients, and q is the intercept of the log S_w and log k relationship in Equation (12). AAE is the average absolute error, N represents the number of compounds in the model, r ² is the coefficient of determination, SD is the standard deviation of the model fit, and F is the model's F‐statistic.

TABLE 4.

Differences in standard deviation of the model fit and average absolute error without and with the melting point term integrated in the correlation model to estimate water solubility of organic compounds.

Reversed‐phase liquid chromatography system	ΔSD	ΔAAE
XTerra MS C18, 10% of acetonitrile (v/v) and 90% water (v/v)	0.164	0.118
XTerra MS C18, 20% of acetonitrile (v/v) and 80% water (v/v)	0.265	0.193
XTerra MS C18, 10 % of methanol (v/v) and 90% water (v/v)	0.079	0.050
XTerra MS C18, 20% of methanol (v/v) and 80% water (v/v)	0.080	0.055
XTerra MS C18, 30% of methanol (v/v) and 70% water (v/v)	0.118	0.091
Discovery HS F5, 30% of methanol (v/v) and 70% water (v/v)	0.056	0.045
Discovery HS F5, 40% of methanol (v/v) and 60% water (v/v)	0.104	0.065
Discovery HS F5, 50% of methanol (v/v) and 50% water (v/v)	0.101	0.073

ΔSD = (standard deviation of the model fit without the melting point term—standard deviation of the model fit with the melting point term) and ΔAAE = (average absolute error without the melting point term—average absolute error with the melting point term).

TABLE 5.

Reversed‐phase liquid chromatography (RPLC) models for estimating solubility of organic compounds in water integrating retention and melting point data comprising organic mobile phase compositions 50%–70% (v/v).

Reversed‐phase liquid chromatography system	Correlation model			Model statistics
	p	s	q	r 2	SD	AAE	F	N
XTerra MS C18, 50% of acetonitrile (v/v) and 50% water (v/v)	−2.979	−0.014	−1.144	0.962	0.275	0.226	521	44
XTerra MS C18, 60% of acetonitrile (v/v) and 40% water (v/v)	−3.557	−0.016	−1.763	0.959	0.296	0.237	475	44
XTerra MS C18, 70% of acetonitrile (v/v) and 30% water (v/v)	−4.226	−0.016	−2.576	0.962	0.276	0.222	496	42
XTerra MS C18, 50% of methanol (v/v) and 50% water (v/v)	−2.248	−0.011	−0.904	0.930	0.368	0.298	286	46
XTerra MS C18, 60% of methanol (v/v) and 40% water (v/v)	−2.565	−0.011	−1.602	0.942	0.335	0.267	350	46
XTerra MS C18, 70% of methanol (v/v) and 30% water (v/v)	−2.903	−0.015	−2.268	0.949	0.316	0.254	387	45
Discovery HS F5, 50% of methanol (v/v) and 50% water (v/v)	−2.488	−0.006	−0.276	0.945	0.308	0.243	333	42
Discovery HS F5, 60% of methanol (v/v) and 40 % water (v/v)	−3.018	−0.006	−0.905	0.948	0.310	0.247	364	43
Discovery HS F5, 70% of methanol (v/v) and 30% water (v/v)	−3.703	−0.007	−1.868	0.952	0.313	0.252	409	44

p and s are coefficients, and q is the intercept of the log S_w and log k relationship in Equation (12). AAE is the average absolute error, N represents the number of compounds in the model, r ² is the coefficient of determination, SD is the standard deviation of the model fit, and F is the model's F‐statistic.

All nine models in Table 5 demonstrated good predictive capabilities, having AAE values less than 0.3 log units. The RPLC Model comprising XTerra MS C18, 70 % of acetonitrile (v/v) had the lowest AAE value of 0.222.

$$\begin{array}{ccc}\hfill \log S_W& =& -2.576\left(0.062\right)-4.226\left(0.144\right)\log k_{\left(\mathrm{XTerra}\mathrm{MS}\mathrm{C}18,70\%\mathrm{ACN}\right)}\hfill \\ & & -0.016(0.001\left[\mathrm{Mp}-25\right]\hfill \end{array}$$ (13)

N = 42, r ² = 0.962, SD = 0.276, F = 496, AAE = 0.222, PRESS = 3.4

Table 6 compares predicted log S_w values for 70% (v/v) acetonitrile on an XTerra MS C18 stationary phase, estimated using the RPLC correlation model in Equation (13) and the GSE model, with the same dataset comprising 42 solutes. In this dataset, the GSE model had an AAE of 0.373, which is considerably higher than the RPLC model in Equation (13) AAE of 0.222. Figure 4 illustrates a residual plot comparing the RPLC correlation model in Equation (13) to the GSE model, with residuals plotted against log S_w . The log S_w values for the dataset in Table 6 compounds range from 0.52 for butan‐2‐one to ‐5.26 for phenanthrene. As shown in Figure 4, the residuals for the RPLC correlation model in Equation (13) are considerably more uniform than those for the GSE model. Figure 5 presents the residuals for each compound, comparing the correlation model in Equation (13) to the GSE model. Overall, the RPLC model in Equation (13) estimated water solubility more consistently across the dataset.

TABLE 6.

Experimental log S_w , log k data on XTerra MS C18 70 (v/v) acetonitrile, predicted log S_w using retention data on XTerra MS C18 70 (v/v) acetonitrile integrating melting point data, and predicted log S_w using the general solubility equation.

Compounds	log Sw	log k	XTerra MS C18 acetonitrile 70% (v/v) model predicted log Sw	GSE predicted log Sw
Acetanilide	−1.33	−0.60	−1.44	−1.55
Acetophenone	−1.28	−0.35	−1.10	−1.08
Anisole	−1.85	−0.19	−1.76	−1.56
Benzamide	−0.96	−0.79	−0.86	−1.19
Benzene	−1.64	−0.15	−1.93	−1.64
Benzonitrile	−1.00	−0.36	−1.05	−1.07
Benzophenone	−3.12	−0.04	−2.80	−2.92
Benzyl alcohol	−0.43	−0.57	−0.15	−0.60
Biphenyl	−4.35	0.21	−4.15	−3.98
1‐Bromonaphthalene	−4.35	0.33	−3.95	−3.80
1‐Chloronaphthalene	−3.93	0.27	−3.72	−3.58
4‐Chlorophenol	−0.70	−0.46	−0.92	−2.07
Diethyl phthalate	−2.35	−0.18	−1.80	−2.04
Ethylbenzene	−2.77	0.12	−3.07	−2.65
Fluorene	−5.00	0.25	−5.07	−4.48
2‐Methylphenol	−0.62	−0.48	−0.63	−1.51
Naphthalene	−3.60	0.08	−3.79	−3.37
1‐Naphthol	−2.22	−0.33	−2.31	−3.06
2‐Naphthol	−2.28	−0.36	−2.56	−3.17
2‐Nitroaniline	−1.96	−0.37	−1.75	−1.81
4‐Nitroaniline	−2.37	−0.54	−2.18	−1.97
Nitrobenzene	−1.80	−0.28	−1.38	−1.38
4‐Nitrotoluene	−2.49	−0.15	−2.35	−2.14
Phenanthrene	−5.26	0.30	−5.00	−4.74
Phenol	0.00	−0.59	−0.33	−1.12
Progesterone	−4.42	0.08	−4.53	−4.29
Propylbenzene	−3.27	0.27	−3.71	−3.20
Toluene	−2.21	−0.02	−2.50	−2.14
1,2,3‐Trimethylbenzene	−3.20	0.22	−3.49	−3.04
Methylparaben	−1.83	−0.57	−1.73	−2.46
Methyl benzoate	−1.85	−0.23	−1.60	−1.62
Butan‐2‐one	0.52	−0.58	−0.12	0.21
Heptan‐2‐one	−1.45	−0.19	−1.76	−1.48
Cyclohexanone	−0.60	−0.48	−0.53	−0.36
4‐Chloroaniline	−1.66	−0.35	−1.80	−1.78
o‐Toluidine	−0.81	−0.40	−0.89	−0.82
m‐Toluidine	−0.85	−0.39	−0.92	−0.90
p‐Toluidine	−1.21	−0.42	−1.08	−1.08
3‐Bromophenol	−0.88	−0.39	−1.04	−2.21
4‐Methylphenol	−0.70	−0.48	−0.70	−1.55
2‐Phenylethanol	−0.74	−0.57	−0.18	−0.86
Indole	−1.52	−0.31	−1.71	−1.92

FIGURE 4.

Illustration of residual plot for the reversed‐phase liquid chromatography system on XTerra MS C18 stationary phase comprising 70% (v/v) acetonitrile correlation model in Equation (13) and general solubility equation estimated residuals. Residual values were calculated as (experimental log S_w —model estimated log S_w ) and were plotted against log Sw.

FIGURE 5.

Illustration of residual values of each model compound compared for the reversed‐phase liquid chromatography system on XTerra MS C18 stationary phase comprising 70% (v/v) acetonitrile correlation model in Equation (13) and general solubility equation estimated residuals. Residual values were calculated as (experimental log S_w —model estimated log S_w ).

3.3. General Guidelines for Estimating Water Solubility of Neutral Organic Compounds Using RPLC

Two RPLC correlation model systems can estimate water solubility: (A) the Discovery HS F5 column with 30 (v/v) methanol (Equation (8)), which does not require melting point, log P_o/w , or descriptor data; and (B) the XTerra MS C18 column with 70 (v/v) acetonitrile (Equation (13)), which does require melting point data. The main practical contribution of this work is the log S_w vs. log k correlation model (Equation (8)), as this approach avoids the need for melting point, log P _o/w, and descriptor data and is therefore more practical for estimating the water solubility of neutral organic compounds. By contrast, the correlation model in Equation (13) may improve predictive accuracy, but it requires melting point data for solid compounds and is therefore less broadly applicable when such data are unavailable. The correlation model in Equation (8) applies mainly to more polar compounds, while the correlation model in Equation (13) applies mainly to more nonpolar compounds. RPLC retention itself is a key consideration of which system should be used to estimate water solubility. As most pharmaceutical drugs are more polar compounds, the correlation model in Equation (8) can be an obvious choice. The correlation model in Equation (8) can be even more attractive as the melting point as an experimental parameter may not be available for some of the compounds in the early stages of drug discovery. Overall, the correlation model in Equation (13) is recommended as the second option if the correlation model in Equation (8) is not workable.

As both RPLC correlation models use experimentally measured log k values, their predictions may be sensitive to instrumental variation and differences between columns. This source of uncertainty was not separately quantified in the present study and should be considered when interpreting model performance. Water solubility estimations depend on crystal form for solid compounds, as polymorphs, hydrates, solvates, and amorphous forms can have different lattice energies, intermolecular interactions, and phase behavior, which change both measured and predicted solubility [36]. These aspects have not been taken into consideration when constructing RPLC correlation models in this work. It should be noted that the reported RPLC correlation models were developed for neutral compounds and are not intended for ions or strongly ionizable solutes.

4. Conclusion

This work establishes two novel and highly effective RPLC modelling strategies that significantly advance the rapid estimation of water solubility for neutral organic compounds. The main significance of this study lies in solubility prediction with good accuracy without the need for complex molecular descriptors by offering a flexible and purely experimental alternative. The first approach introduces a descriptor‐free, high‐throughput screening approach utilising a 30% (v/v) methanol mobile phase on a Discovery HS F5 stationary phase. By relying exclusively on the chromatographic retention data, this approach eliminates the need for structural descriptors, log P_o/w or melting point data. Most importantly, it demonstrates superior predictive uniformity across both non‐electrolytes and weak electrolytes, overcoming a main limitation of the traditional GSE approach. The second approach demonstrated vastly improved predictive accuracy by combining RPLC retention data with a melting point term (MP‐25). This study reveals an interesting RPLC trend: systems with higher organic volume fractions (50%–70% v/v) exhibit improved water solubility estimates when log k is combined with melting point data. Two water solubility estimation approaches identified in this work enable rapid, reliable chemical profiling of newly synthesised or poorly characterised neutral organic compounds, significantly streamlining early‐stage drug discovery and environmental risk assessments.

Author Contributions

Sanka N. Atapattu: conceptualization, investigation, methodology, visualization, writing – review and editing, writing – original draft, formal analysis, and project administration. Jianwei Li: conceptualization, investigation, methodology, writing – original draft, and writing – review and editing.

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

The authors did not receive funding for this research.

Supporting information

Supporting File: jssc70504‐sup‐0001‐SuppMat.docx.

Data Availability Statement

Data will be made available on request.