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. 2023 May 1;63(10):2992–3004. doi: 10.1021/acs.jcim.2c01468

Quantum Mechanical Prediction of Dissociation Constants for Thiazol-2-imine Derivatives

Evrim Arslan †, Zeynep Pinar Haslak †,‡, Gérald Monard §, Ilknur Dogan †,*, Viktorya Aviyente †,*
PMCID: PMC10207282  PMID: 37126823

Abstract

graphic file with name ci2c01468_0015.jpg

As weak acids or bases, in solution, drug molecules are in either their ionized or nonionized states. A high degree of ionization is essential for good water solubility of a drug molecule and is required for drug–receptor interactions, whereas the nonionized form improves a drug’s lipophilicity, allowing the ligand to cross the cell membrane. The penetration of a drug ligand through cell membranes is mainly governed by the pKa of the drug molecule and the membrane environment. In this study, with the aim of predicting the acetonitrile pKa’s (pKa(MeCN)) of eight drug-like thiazol-2-imine derivatives, we propose a very accurate and computationally affordable protocol by using several quantum mechanical approaches. Benchmark studies were conducted on a set of training molecules, which were selected from the literature with known pKa(water) and pKa(MeCN). Highly well-correlated pKa values were obtained when the calculations were performed with the isodesmic method at the M062X/6-31G** level of theory in conjunction with SMD solvation model for nitrogen-containing heterocycles. Finally, experimentally unknown pKa(MeCN) values of eight thiazol-2-imine structures, which were previously synthesized by some of us, are proposed.

1. Introduction

The physicochemical features of a drug molecule, such as solubility, partition coefficient, hydrogen-bonding ability, degree of ionization, and protein binding affinity, are directly related to its therapeutic action. Among these properties, ionization degree (pKa) plays a significant role in the design of smart drug delivery systems. A high degree of ionization of a drug ligand is a prerequisite for good water solubility and therefore high hydrophilicity, which is required for drug–receptor interactions.

The nonionized form of the ligand improves the lipophilicity of a drug, and therefore, it helps the drug molecule to cross the nonpolar cell membrane.1−4 Thus, the penetration of a drug ligand through the cell membranes is mainly governed by the pKa of the drug molecule and the membrane environment. On the other hand, since the reactivity and stability of a molecule are highly dependent on its pKa, the strength of acidity or basicity of a molecule in any solvent determines the mechanisms of chemical reactions involving synthesis, catalysis, oxidation–reduction, and decomposition. In eq 1, the general monoprotic acid (HA) dissociation equilibrium reaction and the deprotonation products (H+, A–) are shown. The pKa of the given equilibrium is the negative logarithm of the equilibrium constant (Ka), as shown in eq 2. The standard free-energy difference between the reactants and products of the dissociation reaction given in eq 1 is related to Ka and pKa as shown in eqs 3 and 4

1. 1
1. 2
1. 3
1. 4

Accurate and fast pKa predictions by computational methods are crucial for more efficient drug design. Quantum chemical approaches have been extensively used for the prediction of pKa’s of the ligands.5−16 Most of the methods differ in the calculation of the dissociation free energies (ΔGaq) of a given deprotonation reaction (eq 3). The most straightforward theoretical approach is based on the direct calculation of the Gibbs free energies of the equilibrium reaction of the acid in solution (eq 1). This method, the so-called direct method, faces significant errors arising from the calculation of the free energy of H+. In the thermodynamic cycle approaches, TC1 (Scheme 1) and TC2 (Scheme 2), the free energy of solvation, desolvation, and deprotonation of the acid species HA is considered, where ΔGaq values can be calculated by

1. 5

Scheme 1. Thermodynamic Cycle 1 (TC1) Where the Acid HA Is Dissociated in Its Conjugate Base A– and a Proton H+.

Scheme 1

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ΔGsoln and ΔGgas are the free energies of deprotonation in solution and gas phases, whereas ΔGsolv is the free energy of solvation.

Scheme 2. Thermodynamic Cycle 2 (TC2) Where the Acid HA Donates Its Proton H+ to the Water Molecule to Yield Its Conjugate Base A– and Hydronium Cation H3O+.

Scheme 2

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ΔGsoln and ΔGgas are the free energies of deprotonation in solution and gas phases, whereas ΔGsolv is the free energy of solvation.

ΔGgas and ΔΔGsolv terms are calculated by ab initio or density functional theory (DFT) methods by adapting the expressions to the thermodynamic cycle constructed. According to the TC1 (Scheme 1), the most commonly implemented thermodynamic cycle, these terms are

1. 5a
1. 5b

In TC1 ΔGsolv(H+), values vary between −265.9 and −270.3 kcal mol–1 and this brings large uncertainties to the predicted values.17 The large uncertainties coming from the ΔGsolv(H+) values in TC1 can be prevented by substituting the proton H+ with the H2O/H3O+ pair in TC2 (Scheme 2), in which the ΔGgas and ΔΔGsolv are calculated as given in eqs 5c and 5d

1. 5c
1. 5d

Note that in these reactions the H2O is the base and signifies a water cluster, whereas H(aq)+ and H3O(aq)+ represent the hydrated proton product.18 Even though the former is claimed to be simpler and truer than the latter, both models are widely used for pKa calculations.

The isodesmic reaction scheme for pKa calculations is based on a reaction between an acid (HA) and the conjugate base of a reference molecule (B–) with an experimentally known pKa as shown in Scheme 3, whose equilibrium constant is described in eq 6. In the isodesmic reactions, the types of bonds that are made to form the products are the same as those that are broken in the reactant. The pKa of acid HA relative to pKa of reference molecule HB is calculated by eq 7. Since in the isodesmic method, only the free energies of the reactants and products in solution are calculated, the errors due to the gas-phase calculations are cancelled and as a result more accurate pKa’s are obtained. The protonation/deprotonation process occurs in similar environments in molecules A and B.

Scheme 3. Isodesmic Reaction Scheme Where the Acid HA Donates Its Proton H+ to the Base B– to Yield Its Conjugate Base A– and Conjugate Acid HB.

Scheme 3

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ΔGsoln is the free energy of deprotonation in solution.

With significant biological activities, thiazol-2-imine derivatives are commonly used in organic, synthetic, pharmaceutical, and medicinal chemistry areas due to their anti-inflammatory, analgesic,19 antibacterial,20 antifungal,21 antiviral,22 and kinase inhibition activities.19 These molecules possess chiral centers; thus, the synthesis of thiazol-2-imine derivatives as single enantiomers is of great interest. Moreover, these thiazol-2-imine derivatives that are present as single enantiomers can be used in asymmetric chemistry such as catalysts in converting olefins to primary amines,23 asymmetric hydrogenations,24 and generating chiral α-aminonitriles.25 Recently, Tuncel and Dogan have synthesized single enantiomer thiazol-2-imines (5RR, 6RR, 7RR, 8RR) by water elimination reactions from the corresponding 2-iminothiazolidine-4-ones (1RR, 2RR, 3RR, 4RR) (Figure 1).26 The synthesized molecules are insoluble in water, and their pKa’s have been predicted in acetonitrile (MeCN). Due to its relatively lower polarity compared to water, MeCN is a widely used solvent in the pharmaceutical industry since it can mimic the membrane environment.27,28 As pKa values are strongly dependent on the environment, water pKa’s may lead to improper conclusions about the degree of ionization of a molecule within the membrane. As an aprotic solvent with a pKa of 25, MeCN is a poor H-bond acceptor and a weak base; thus, when it is used as a solvent, it increases the pKa values of the solutes, such that acidic compounds act as weaker acids and basic compounds act as stronger bases in MeCN compared to water. Note also that nonaqueous pKa data are highly important in many fields since the available experimental data are less abundant than desirable.29 Several solvents, including dimethyl sulfoxide, MeCN, and tetrahydrofuran (THF), have found wide application as media for studies of strong bases. MeCN has some advantages over other aprotic solvents: it is a very weakly basic aprotic solvent with a high dielectric constant (36.016) and hence favors the dissociation of ion pairs into free ions. MeCN solvates ions more weakly than water, being a weak electron-pair donor solvates cations better than anions.4,30 Compounds 1RR-8RR, in addition to being drug-like molecules, are expected to be strong chiral organic bases as well because of the amidine conjugation in their structures (Figure 2). Since they are anticipated to be stronger bases than their amine precursors, their pKa values are worth determining in different media.

Figure 1.

Figure 1

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Two-dimensional (2D) representations of the single enantiomer thiazol-2-imines synthesized by Tuncel and Dogan.26

Figure 2.

Figure 2

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Amidine conjugation in thiazol-2-imine compounds.

In this study, the acetonitrile and water pKa’s of thiazol-2-imine derivatives will be predicted by employing the isodesmic reaction scheme based on the previously reported success of the method.14,31−35 With this purpose, by using several quantum mechanical approaches, we propose a very accurate protocol. In the first part, the methodology to be employed throughout the study is identified from a benchmark study, where several DFT functionals and solvent models are examined together with TC1 and TC2 schemes, for reproducing the experimentally known water pKa of the reference molecule to be used in the isodesmic reaction. In the second and third parts, the proposed methodology is validated on two sets of test molecules whose water and acetonitrile pKa’s are experimentally known. In the fourth part, pKa(MeCN) of the reference molecule to be used in the isodesmic reaction is calculated by the established methodology, and finally, pKa(MeCN)’s of thiazol-2-imines are calculated by using the isodesmic reaction scheme. The protocol proposed in this study can be used with confidence to predict the water and acetonitrile pKa’s of thiazol-2-imine derivatives.

2. Computational Methodology

A systematic conformational search was conducted for all of the molecules employing the semiempirical PM3 method36 by using the SPARTAN14 software.37 Free rotations around single bonds were taken into account, and all of the geometries corresponding to stationary points have been reoptimized by using the Gaussian16 program suite.37 For the benchmarking study of the DFT method, combinations of a hybrid-GGA exchange–correlation functional (B3LYP),38 a hybrid meta-GGA functional (M062X),39 and a hybrid-GGA exchange–correlation functional (ωB97XD)40 with 6-31+G*, 6-31G**, 6-31+G**, 6-31++G**, and 6-311++G** basis sets were tested. The universal solvent model (SMD)41 and the conductor-like polarizable continuum model (CPCM)42 were employed to mimic the aqueous solvent environment. The partial atomic charges were derived from Natural Population Analysis (NPA),43 Charge Model 5 (CM5),44 and Hirshfeld Analysis.45 root-mean-square error (RMSE), mean absolute deviation (MAD), and MD (mean deviation) were calculated to compare the efficiency of our predictions.

3. Results and Discussion

Since thiazol-2-imines synthesized by Tuncel and Dogan26 in Figure 1 are water-insoluble molecules, their pKa’s are predicted in an acetonitrile environment by employing the isodesmic reaction scheme. With this respect, several quantum chemical approaches were utilized. In the first place, in order to propose a methodology that describes the system best, the experimentally known water pKa of the reference molecule to be used in the isodesmic reaction was estimated, employing the TC1 and TC2 schemes with a set of different DFT functionals and solvent models. In the second part of the study, the proposed methodology was validated on a set of 2-(phenylimino)imidazolidine derivatives, and then in the third part the verification of the methodology in an acetonitrile environment was performed for a set of nitrogen-containing heterocyclic compounds. The successful applications of the proposed methodology allowed us to predict the pKa(MeCN) of the reference molecule, 2-imino-thiazolidinone. And finally, with the predicted acetonitrile pKa of the reference molecule, the pKa(MeCN)’s of thiazol-2-imines in Figure 1 were calculated by employing the isodesmic reaction scheme.

3.1. Identification of the Methodology

As the reference molecule to be used in the isodesmic reaction scheme for the prediction of pKa(MeCN)’s of thiazol-2-imines, structurally resembling 2-imino-thiazolidinone (Figure 3) with the experimental water pKa of 11.7046 is used. Since the experimental pKa(MeCN) of the reference molecule is not known, a 3-step protocol is followed to predict its pKa(MeCN). As well as the calculation scheme to be applied, the accuracy of the prediction is directly related to the quality of the QM method and the solvation model employed to describe the system’s electronic nature and solute–solvent interactions. Therefore, the computational methodology to be used is identified by employing TC1 and TC2 schemes with a set of different DFT functionals, basis sets, and solvation models for the estimation of the water pKa of the reference molecule. The reference molecule has two conformers: hydrogen on 2-imine N being either up (toward S) or down (toward N3). “Hydrogen up” conformation, which was calculated to be 0.76 kcal/mol more stable than the “down” conformation, is further considered in our calculations.

Figure 3.

Figure 3

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2D representation of the reference molecule 2-imino-thiazolidinone.

As there are two protonation sites in the reference molecule (N3 and 2-imino N), NPA, CM5, and Hirschfeld charge analysis were performed for the identification of the dominant protonation/deprotonation site. The computed charges with all methodologies were found to give the same trend, with 2-imino N having a higher electron density (qN(NPA) = −0.628e) compared to N3 (qN3(NPA) = −0.521e). Thus, the reported partial atomic charges of neutral and protonated (on 2-imino N) 2-imino-thiazolidinone are based on NPA calculations in the rest of the manuscript. First, the TC1 scheme displayed in Scheme 1 was employed with several levels of theory in order to predict the water pKa of the reference molecule. Two ΔGsolv(H+) values (−265.9 kcal/mol and −270.3 kcal/mol) were used for each trial, and the results presented in Table 1 show that the TC1 scheme predicts much lower pKa’s than that of the experimental value, which indicates the presence of a systematic error. TC1 seems to fail in the prediction of 2-imino-thiazolidinone pKa with a very high ΔpKa (the difference between the predicted and experimental pKa) range (2.56 ≤ |ΔpKa| ≤ 10.43) irrespective of the level of theory used. When ΔGsolv(H+) is taken as −270.3 kcal/mol, the calculated 2-imino-thiazolidinone pKa values (calculated pKa2) with respect to different levels of theory are observed to deviate more from the experimental value compared to calculations performed with ΔGsolv(H+) = −265.9 kcal/mol (calculated pKa1).

Table 1. Benchmark Study for the Prediction of Water pKa of the Reference Molecule 2-Imino-thiazolidinone (Experimental pKa = 11.70) by Employing the TC1 Schemea,b.

level of theory calculated pKa1 ΔpKa1 calculated pKa2 ΔpKa2
B3LYP/6-31+G* CPCM 2.13 –9.57 0.27 –10.43
B3LYP/6-31+G** CPCM 2.45 –9.25 0.59 –10.11
B3LYP/6-31G** CPCM 7.68 –4.02 5.82 –5.88
B3LYP/6-31++G** CPCM 3.65 –8.05 1.79 –9.91
B3LYP/6-31++G**//B3LYP/6-31+G* CPCM 3.63 –8.07 1.77 –9.93
B3LYP/6-31++G**//B3LYP6-31G** CPCM 3.62 –8.08 1.76 –9.94
B3LYP/6-31+G* SMD 6.55 –5.15 4.68 –7.02
B3LYP/6-31+G** SMD 6.60 –5.10 4.74 –6.96
B3LYP/6-31G** SMD 5.57 –5.13 3.83 –7.87
B3LYP/6-31++G** SMD 6.67 –5.03 4.40 –7.30
B3LYP/6-31++G**//B3LYP/6-31+G* SMD 6.02 –5.68 3.90 –7.80
B3LYP/6-31++G**//B3LYP6-31G** SMD 6.14 –5.56 4.48 –7.22
ωB97XD/6-31+G* CPCM 3.75 –7.95 1.89 –9.81
ωB97XD/6-31+G** CPCM 5.62 –6.08 4.70 –7.00
ωB97XD/6-31G** CPCM 8.49 –3.21 6.63 –5.07
ωB97XD/6-31++G** CPCM 5.15 –6.55 3.29 –8.41
ωB97XD/6-31++G**//ωB97XD/6-31+G* CPCM 5.14 –6.56 3.28 –8.42
ωB97XD/6-31++G**//ωB97XD/6-31G** CPCM 5.15 –6.55 2.29 –9.41
ωB97XD/6-31+G* SMD 7.59 –4.11 6.02 –5.68
ωB97XD/6-31+G** SMD 8.00 –3.70 6.14 –5.56
ωB97XD/6-31G** SMD 7.43 –4.27 5.49 –6.21
ωB97XD/6-31++G** SMD 8.45 –3.25 6.72 –4.98
ωB97XD/6-31++G**//ωB97XD/6-31+G* SMD 6.43 –5.27 4.58 –7.12
ωB97XD/6-31++G**//ωB97XD/6-31G** SMD 7.00 –4.70 5.92 –5.78
M062X/6-31+G* CPCM 5.55 –6.15 4.68 –7.02
M062X/6-31+G** CPCM 5.69 –6.01 4.23 –7.47
M062X/6-31G** CPCM 8.01 –3.69 6.75 –4.95
M062X/6-31++G** CPCM 5.59 –6.11 4.02 –7.68
M062X/6-31++G**//M062X/6-31+G* CPCM 5.52 –6.18 3.69 –8.01
M062X/6-31++G**//M062X/6-31G** CPCM 5.01 –6.69 3.53 –8.17
M062X/6-31+G* SMD 4.59 –7.11 2.73 –8.97
M062X/6-31+G** SMD 4.70 –7.00 2.84 –8.86
M062X/6-31G** SMD 9.14 –2.56 7.28 –4.42
M062X/6-31++G** SMD 6.04 –5.66 4.18 –7.52
M062X/6-31++G**//M062X/6-31+G* SMD 6.01 –5.69 4.15 –7.55
M062X/6-31++G**//M062X/6-31G** SMD 5.95 –5.75 4.09 –7.61
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a

Calculated pKa1: ΔGsolv (H+) value is taken as −265.9 kcal/mol.

b

Calculated pKa2: ΔGsolv (H+) value is taken as −270.3 kcal/mol.

As an attempt to prevent the large uncertainties arising from the ΔGsolv(H+) values in TC1, the proton H+ was substituted by the H2O/H3O+ pair in TC2 (Scheme 2), and the calculated water pKa values of 2-imino-thiazolidinone with different levels of theory are presented in Table 2. The differences between the predicted and experimental pKa (ΔpKa) have been calculated for each level of theory and are represented in Figure 4. In the TC2 scheme, a lower ΔpKa range (0.77 ≤ |ΔpKa| ≤ 6.06) is observed compared to the TC1 scheme. As seen from Figure 4, with the CPCM solvation model, the M062X functional behaves better than the others except for the 6-31G** basis set; on the other hand, with the SMD solvation model, the 6-31G** basis set where polarization function yields the smallest ΔpKa value.

Table 2. Benchmark Study for the Prediction of Water pKa of the Reference Molecule 2-Imino-thiazolidinone (Experimental pKa = 11.70) by Employing the TC2 Scheme.

level of theory calculated pKa ΔpKa
B3LYP/6-31+G* CPCM 8.17 –3.00
B3LYP/6-31+G** CPCM 7.65 –4.05
B3LYP/6-31G** CPCM 7.55 –4.15
B3LYP/6-31++G** CPCM 5.69 –6.01
B3LYP/6-31++G**//B3LYP/6-31+G* CPCM 7.20 –4.50
B3LYP/6-31++G**//B3LYP/6-31G** CPCM 8.42 –3.28
B3LYP/6-31+G* SMD 9.21 –2.49
B3LYP/6-31+G** SMD 9.12 –2.58
B3LYP/6-31G** SMD 9.08 –2.62
B3LYP/6-31++G** SMD 8.05 –3.65
B3LYP/6-31++G**//B3LYP/6-31+G* SMD 7.80 –2.90
B3LYP/6-31++G**//B3LYP/6-31G** SMD 8.69 –3.01
ωB97XD/6-31+G* CPCM 5.64 –6.06
ωB97XD/6-31+G** CPCM 5.01 –6.69
ωB97XD/6-31G** CPCM 9.68 –2.02
ωB97XD/6-31++G** CPCM 7.90 –3.80
ωB97XD/6-31++G**//ωB97XD/6-31+G* CPCM 6.50 –5.20
ωB97XD/6-31++G**//ωB97XD/6-31G** CPCM 6.12 –5.58
ωB97XD/6-31+G* SMD 9.64 –2.06
ωB97XD/6-31+G** SMD 9.12 –2.58
ωB97XD/6-31G** SMD 8.55 –3.15
ωB97XD/6-31++G** SMD 9.05 –2.65
ωB97XD/6-31++G**//ωB97XD/6-31+G* SMD 7.43 –4.27
ωB97XD/6-31++G**//ωB97XD/6-31G** SMD 7.01 –4.69
M062X/6-31+G* CPCM 9.68 –2.02
M062X/6-31+G** CPCM 8.56 –3.14
M062X/6-31G** CPCM 7.98 –3.02
M062X/6-31++G** CPCM 9.02 –2.68
M062X/6-31++G**//M062X/6-31+G* CPCM 9.13 –2.57
M062X/6-31++G**//M062X/6-31G** CPCM 9.27 –2.43
M062X/6-31+G* SMD 6.87 –4.83
M062X/6-31+G** SMD 10.00 –1.70
M062X/6-31G** SMD 12.47 0.77
M062X/6-31++G** SMD 8.45 –3.25
M062X/6-31++G**//M062X/6-31+G* SMD 8.70 –3.00
M062X/6-31++G**//M062X/6-31G** SMD 7.32 –4.38
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Figure 4.

Figure 4

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Differences between the predicted and experimental pKa (ΔpKa) for three different DFT functionals and six different basis sets considered in this study. Geometry optimizations were performed using the (a) CPCM model and (b) SMD model.

When the M062X/6-31G** level of theory is used in the presence of the SMD solvation model, the calculated pKa of 2-imino-thiazolidinone by employing the TC2 scheme is 12.47, for which the |ΔpKa| is 0.77 unit. Therefore, in order to predict the pKa(MeCN) of the reference molecule, further verification of the established methodology is performed on a set of test molecules.

3.2. Validation of the Methodology for Water Environment

For the validation of the methodology established, a set of molecules with experimentally known water pKa were collected from the literature. The selected 10 2-(phenylimino)-imidazolidine derivatives share common scaffolds with our target molecules, thiazol-2-imines, as displayed in Figures 5 and S1, and the pKa’s of these molecules vary between 9.08 and 10.78.47 The methodology proposed in the previous section is applied to the molecules in Figure 5 in order to predict their pKa’s in water. Initially, NPA charges on the N atoms were calculated for all of the structures and the most electron-rich N atom was selected as the first protonation site. For each molecule, the electron density around imine N was observed to be the highest and that their pKa’s are directly related to the electron density around the N atom. For example, ph6 has the highest pKa value (10.78) and the computed NPA charge on imine N for ph6 is the lowest (qN = −0.781e), whereas ph10 has the lowest pKa (9.08) with the highest NPA charge (qN = −0.362e) among the ph molecules. The presence of electron-withdrawing groups such as carbonyl moieties in the structures of ph8, ph9, and ph10 makes the imine N more electron-deficient compared to ph1–7 and as a result less basic. To estimate the water pKa’s of the 10 molecules displayed in Figure 5, the TC2 scheme with the M062X/6-31G** level of theory in conjunction with the SMD solvation model using water as a solvent was applied by protonating the imine N.

Figure 5.

Figure 5

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2D representations of 2-(phenylimino)imidazolidine derivatives with computed NPA charges on the heteroatoms (the most negative one is colored with red) (M062X/6-31G**//SMD = water, pop = npa) (experimental pKa’s are given in blue).

The results presented in Table S1 show that the predicted pKa’s of 2-(phenylimino) imidazolidine derivatives are very close to their experimentally determined values with a strong correlation (R2 = 0.96; Figure 6). This impacts the success of the proposed methodology with a high accuracy of MAD and ΔpKa values (MAD = 0.12 and 0.05 ≤ |ΔpKa | ≤ 0.21). We additionally assessed the prediction power of our method by comparing the assigned pKa’s on imine N of 2-(phenylimino) imidazolidine derivatives with ChemAxon,48 which is a commercial pKa prediction tool widely used in drug development processes. ChemAxon uses the empirically calculated partial atomic charges in molecules as parameters to identify the micro pKa’s. The predicted pKa’s by ChemAxon listed in Table S1 are mostly found to be in good agreement with the experimental values except ph8 and ph9, which deviate more than 1 unit. However, the correlation between the predicted and experimental pKa’s are observed to be weaker (R2 = 0.31; Figure S2) with a higher MAD value (0.57) compared to the methodology developed in this study.

Figure 6.

Figure 6

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Linear regression of experimental vs calculated pKa values of 2-(phenylimino)-imidazolidine derivatives (M062X/6-31G**/SMD = water).

3.3. Validation of the Methodology for Acetonitrile Environment

Following the validation of the proposed methodology in water environment, the applicability of the methodology was tested for a set of molecules for which there are experimentally determined pKa(MeCN)’s. The selected 17 molecules are nitrogen-containing heterocycles as displayed in Figures 7 and S3. Since some of the molecules possess more than one N atom in their structures, calculated NPA atomic charges on the N atoms allowed us to determine the most electron-rich N to identify the first protonation site. For the molecules that possess a -NH2 functional group (3, 5, 6, 7, 8, 9, 11, 12, 14), the highest electron density is observed to be located on the N atom of the amino substituent. Then, imine N and N on the -N(CH3)2 substituent were calculated to have more electron density in molecules 2 and 4, respectively. The lack of amidine conjugation in 10, 13, 15, 16, and 17 makes these molecules less basic compared to that of 1, as predicted by the calculated partial charges on N atoms. TC2 scheme was employed with the M062X/6-31G** level of theory in conjunction with the SMD solvation model using acetonitrile as a solvent for the prediction of pKa(MeCN)’s of nitrogen-containing heterocycles.

Figure 7.

Figure 7

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2D representations of selected nitrogen-containing heterocycles with NPA charges on the heteroatoms (the most negative one is colored with red) (M062X/6-31G**/SMD = MeCN, pop = NPA).

The experimental and predicted pKa’s of N-containing aromatic compounds are presented in Table 3. The maximum deviation of the predicted pKa(MeCN)’s from experimental pKa(MeCN)’s is found to be 0.77 unit, and a very good agreement between calculated and experimental values was obtained with R2 = 0.98 (Figure S4). Moreover, a small MAD value calculated (0.33) demonstrates the applicability of the proposed methodology to the acetonitrile environment. In addition to the pKa(MeCN) calculations, the water pKa’s of the molecules in Figure 7 are calculated with the proposed methodology and the results are presented in Table 3. Among the 17 selected molecules, experimental pKa(water)’s were collected from the literature for 14 of them. A very good correlation is obtained between the calculated and the experimental pKa’s with a maximum deviation of 0.53 units. MeCN is a polar aprotic solvent with a polarized C≡N triple bond. Unlike water, it does not donate hydrogens to anions, and therefore, when used as a solvent, the ionization of the molecules in MeCN is more difficult compared to that of water, which in turn results in higher pKa’s and thus stronger basicity’s in MeCN environment. The pKa for these molecules in MeCN ranges between 24.77 and 12.56, whereas in water it is between 13.50 and 5.23.30

Table 3. Calculated and Experimental pKa’s of Nitrogen-Containing Small Aromatic Compounds Displayed in Figure 7 (M062X/6-31G**/SMD = MeCN/Water).

ID experimental pKa (MeCN) calculated pKa (MeCN) ΔpKa (MeCN) experimental pKa (water) calculated pKa (water) ΔpKa (water)
1 24.7730 24.13 –0.64 13.5049 13.02 –0.48
2 19.8330 20.60 0.77 NA 11.56  
3 19.3630 19.43 0.07 NA 11.30  
4 18.1130 17.74 –0.37 9.6050,51 9.07 –0.53
5 17.7830 17.40 –0.38 9.1752 9.02 –0.15
6 16.4430 16.70 0.26 9.3453 9.06 –0.28
7 16.0230 16.11 0.09 NA 8.76  
8 15.9630 15.87 –0.09 NA 8.45  
9 14.3230 15.03 –0.71 6.7850 6.43 –0.35
10 15.0830 14.77 –0.31 7.4351 7.70 0.27
11 13.9430 14.56 0.12 6.1350 5.85 –0.28
12 13.8830 14.26 0.38 6.8250 6.60 –0.22
13 14.0230 14.04 0.02 6.5850 7.00 0.42
14 14.3130 13.96 –0.35 6.0450 5.64 –0.40
15 13.7730 13.92 0.15 6.7250 6.32 –0.40
16 12.9830 13.11 0.13 5.8154 5.19 –0.38
17 12.5630 12.33 –0.23 5.2355 5.43 0.20
RMSE     0.39     0.27
MAD     0.33     0.21
MD     –0.05     –0.08
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3.4. Prediction of pKa(MeCN)’s of Thiazol-2-imines

In this study, the goal is to predict the pKa’s of thiazol-2-imines synthesized by Tuncel and Dogan26 in an acetonitrile environment. An accurate protocol is suggested by a two-step methodology validation. In the final step of the study, pKa(MeCN)’s of thiazol-2-imines were calculated by employing the isodesmic reaction scheme at the M062X/6-31G** level of theory in conjunction with the SMD solvation model using acetonitrile as a solvent. Scheme 4 illustrates an isodesmic reaction where the protonated 1RR is the acidic species HA+ and 2-imino-thiazolidinone is the reference species BRef.

Scheme 4. Isodesmic Reaction between an Acid Species (HA+) and a Reference Species (BRef).

Scheme 4

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To the best of our knowledge, the pKa(MeCN) of the reference molecule 2-imino-thiazolidinone is not known experimentally; its pKa(MeCN) is first predicted by employing the established methodology. The calculated pKa(MeCN) of 2-imino-thiazolidinone using acetonitrile as a solvent is 19.41 (TC2/M062X/6-31G**/SMD), and this prediction will further be used in the next step to propose pKa(MeCN)’s of thiazol-2-imine derivatives by employing the isodesmic reaction scheme.

The computed charges indicate that the protonation dominantly occurs on the imine N as presented in Table 4 and the predicted pKa’s of thiazol-2-imines are given in Table 5. We observe that 1RR, 2RR, 3RR, and 4RR have relatively lower pKa values compared to 5RR, 6RR, 7RR, and 8RR. Withdrawal of the electrons from the exocyclic imine N by the carbonyl substituents on the thiazole ring in 1RR, 2RR, 3RR, and 4RR results in less electron density around the N atom than the imine N atom of 5RR, 6RR, 7RR, and 8RR (qN = −0.582e for 1RR; qN = −0.745e for 5RR) (Table 4). The lower electron density on the protonation site makes these molecules less available for proton abstraction. Thus, 1RR, 2RR, 3RR, and 4RR were predicted to be less basic compared to 5RR, 6RR, 7RR, and 8RR. For the molecules of our interest, the pKa range in MeCN is between 17.16–10.59 and 7.42–1.77 in water.

Table 4. Computed NPAa, CM5b, and Hirshfeldc Charges of Nitrogen Atoms of Thiazol-2-imines Considered in This Study (M062X/6-31G**/SMD = MeCN).

ID imine-nitrogen ring nitrogen
1RR –0.582a –0.336a
–0.616b –0.445b
–0.602c –0.403c
2RR –0.594a –0.345a
–0.626b –0.455b
–0.612c –0.413c
3RR –0.612a –0.409a
–0.647b –0.489b
–0.625c –0.447c
4RR –0.623a –0.421a
–0.659b –0.435b
–0.646c –0.428c
5RR –0.745a –0.471a
–0.802b –0.455b
–0.767c –0.463c
6RR –0.704a –0.436a
–0.759b –0.448b
–0.738c –0.442c
7RR –0.824a –0.503a
–0.865b –0.532b
–0.847c –0.517c
8RR –0.805a –0.487a
–0.849b –0.545b
–0.836c –0.503c
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Table 5. Three-dimensional (3D) Representations of Thiazol-2-imine Derivatives and Their Predicted pKa’s in MeCNa and Waterb.

3.4.

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3.5. Applicability of the Established Methodology to Drug Compounds

We additionally tested our methodology on a small data set (due to the lack of experimental data in the literature) of drug precursors/compounds containing nitrogen heterocycles, which have experimentally determined water and MeCN pKa’s. Among heterocyclic pharmacophores, the benzimidazole ring system is quite common. Imidazole-containing molecules (benzimidazole, thiabendazole, carbendazim, imidazole) have been chosen since imidazole-based medicinal chemistry suggests the potential therapeutic values of imidazole-derived compounds for treating incurable diseases. Literature survey reveals that the various derivatives of benzimidazole have been synthesized for their pharmacological activities such as antimicrobial,56 antifungal,57 antiviral,58 analgesic,59 antiprotozoal,60 anticancer,61 anti-inflammatory,62 antihistaminic,63 and antimalarial.64 These substructures are often called “privileged” due to their wide recurrence in bioactive compounds.65

Besides the imidazole derivatives, we have also evaluated the pKa values of guanidine derivatives 1,5,7-triazabicyclo [4.4.0]dec-5-ene (TBD), N-methyl TBD (MTBD), and 1-(2-pyridyl)-1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine (2-(hpp)C5H4N). Since the Middle Ages in Europe, guanidine has been used to treat diabetes. Due to its long-term hepatotoxicity, further research for blood sugar control was suspended at first after the discovery of insulin. Later development of nontoxic, safe biguanides led to the long-used first-line diabetes control medicine metformin.66−69 We attempted to predict the pKa’s of seven drug compounds by employing the isodesmic scheme at the M062X/6-31G** level of theory with the SMD solvent model in both water and MeCN, and the results presented in Table 6 are found to be in harmony with the experimentally reported pKa’s. The reference molecule is imidazole for benzimidazole, thiabendazole, and carbendazim; benzimidazole for imidazole. TBD is a reference molecule for MTBD and 2-(hpp)C5H4N and MTBD for TBD.

Table 6. Calculated and Experimental pKa’s of Drug Precursors/Compounds Containing Nitrogen Heterocycles.

3.5.

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4. Conclusions

The pKa of a drug molecule and the membrane environment are the key factors controlling how well a drug penetrates through the cell membranes. In this study, an elaborate protocol to evaluate the pKa’s of the single enantiomers of thiazol-2-imines is proposed. Different functionals and basis set combinations were tested to evaluate the pKa(water) of a reference molecule resembling the molecules synthesized by Dogan et al.,26 2-imino-thiazolidinone, to be employed in the isodesmic reaction scheme. The M062X/6-31G** level of theory and SMD solvation model are found to be adequate for the prediction of pKa(water) of the reference molecule. In order to ensure that the constructed methodology describes the nitrogen-containing heterocyclic compounds well, a two-step validation procedure is followed. First, pKa(water) of 2-(phenylimino)imidazolidine derivatives were calculated with the proposed methodology and the predicted values were found to be very close to the experimental pKa(water)’s. Being interested in pKa calculations in a less polar medium, it was necessary to test the methodology for compounds similar to the species of interest whose pKa values in acetonitrile are experimentally known. Thus, the applicability of the method was verified on a set of nitrogen-containing heterocyclic compounds with experimentally known pKa(MeCN). With the justified methodology, the experimentally unknown pKa(MeCN) of the reference molecule, 2-imino-thiazolidinone, was calculated, and finally, isodesmic reactions between the reference molecule and thiazol-2-imine derivatives synthesized by Dogan et al. were proposed to evaluate the pKa(MeCN)’s of the latter. Moreover, we showed that the protocol established in this study is very satisfying and promising in terms of its applicability to more diverse drug data sets for future validations. The predicted pKa values of these drug-like molecules will enable the evaluation of their lipophilicity/hydrophilicity at a given pH.

Acknowledgments

Computational resources were provided by the National Center for High Performance Computing at Istanbul Technical University (UHEM) with project number (5005832018).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.2c01468.

  • 3D representations of 2-(phenylimino)imidazolidine derivatives; calculated and experimental water pKa’s of 2-(phenylimino)imidazolidine derivatives; linear regression of experimental vs ChemAxon calculated pKa values of 2-(phenylimino)-imidazolidine derivatives; 3D representations of nitrogen-containing small aromatic compounds; and linear regression of experimental vs calculated pKa values of nitrogen-containing small aromatic compounds (PDF)

Author Contributions

∥ E.A. and Z.P.H. contributed equally to this work. E.A.: investigation, methodology, software, writing—original draft, and writing—review and editing. Z.P.H.: investigation, conceptualization, methodology, writing—original draft, and writing—review and editing. G.M.: conceptualization, methodology, and writing—review and editing. V.A.: conceptualization, supervision, methodology, writing—original draft, and writing—review and editing. I.D.: conceptualization, supervision, methodology, writing—original draft, and writing—review and editing. E.A. and Z.P.H. contributed equally.

The authors declare no competing financial interest.

Supplementary Material

ci2c01468_si_001.pdf (432.6KB, pdf)

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