Introduction

Tautomeric equilibria play fundamental roles in many organic and biochemical reactions, in structural assignments, and in the biochemical activities of amino acids, sugars, and nucleic acids [1–5]. Tautomerism is an interconversion between isomeric forms that involves proton transportation and a double-bond (π-electron) shift. Keto–enol, thione–thiol, enamine–imine, acinitro–nitro, nitroso–oxime, and amide–iminole transformations can be considered the most common types of tautomerism [6]. Among these, keto–enol tautomerism plays a crucial role in compounds with a carbonyl group. Investigations of the tautomeric equilibria associated with carbonyl compounds are very important for rationalizing their biological activities and for understanding the biochemical processes in which they take part [7–17].

One of the most important interactions that influences the arrangement of molecules in crystals is the hydrogen bond [18, 19]. Hydrogen bonds are commonly encountered in both chemistry and biochemistry [19–21]. Perhaps the most important application of hydrogen-bonding interactions is in the interactions that determine the shapes of proteins and the genetic code information in DNA and RNA [22–24].

One important class of compounds that exhibit keto–enol tautomerism are the carbonyl derivatives of 1,2,4-triazole. 1,2,4-Triazoles are well known to have various types of biological activities, such as anti-inflammatory [25, 26], antiviral [27], analgesic [28], antimicrobial [29], anticonvulsant [30], anticancer [31], antioxidant [32], antitumoral [33], and antidepressant [34] activities. It has also been reported that some coordination complexes with 1,2,4-triazole as a ligand possess interesting structures and magnetic properties [35–38]. To carry out structure–activity or molecular docking studies of such systems, knowledge of the relative stabilities of the keto and enol tautomers involved is required, since the interactions of compounds with bacterial enzymes can change in the presence of a hydroxyl or a carbonyl group [7]. Moreover, knowing how the tautomerization energies change in different solvents affords insight into the influence of solvents on molecular stability and reactivity.

In the work reported in this paper, we investigated the mechanism of keto–enol tautomerism and intermolecular H-bonding interactions for the title compound using density functional theory (DFT). Single-point energy calculations were also performed at the MP2 level for the tautomeric mechanism. The effect of solvent on the tautomerism was studied by applying the polarizable continuum model (PCM) and directly involving the solvent molecules.

Computational details

The structures at the local minimum or the transition state (TS) were optimized using the Berny algorithm [39] and default cutoffs. The minimum-energy or transition-state nature of the stationary points was verified from frequency analysis. The stable structures only exhibited positive frequencies, whereas the TSs each possessed one imaginary frequency. All calculations were performed via the GaussView molecular visualization program [40] and the Gaussian 03W package [41]. The three-parameter hybrid density functional (B3LYP) [42, 43] and the 6-311++G(d,p) basis set [44, 45] were selected for the calculations. We also performed single-point energy calculations at the MP2 (second-order Møller–Plesset perturbation theory) level of theory [46] with the 6-311++G(d,p) basis set for B3LYP/6-311++G(d,p) geometries. DFT and MP2 levels of theory have been successfully used to study similar systems recently, and have been shown to give accurate normal-mode frequencies, barrier heights, characteristics of intra- and intermolecular H-bonds, and geometries [14, 15]. To connect the transition states to their respective minima, the reaction pathway was followed in both the forward and reverse directions from each TS using the intrinsic reaction coordinate (IRC) procedure [47, 48]. The binding energies of the intermolecular H-bonding interactions were obtained using the supermolecule approach [49, 50], and were corrected for basis set superposition error (BSSE) via the standard counterpoise method [51]. Solvent effects in chloroform, methanol, and water were calculated by means of the PCM method [52–55] at the B3LYP/6-311++G(d,p) level. The thermodynamic parameters were obtained from the frequency analyses of the optimized structures, and were computed using the thermodynamic equations and ΔG = ΔH – TΔS [56, 57].

Results and discussion

Theoretical structures

We determined the solid-state structure of the compound (Fig. 1a) in a previous work [58]. The molecular structure was optimized by the density functional theory (DFT) method with the 6-311++G(d,p) basis set (Fig. 1b). Some of the experimental and theoretical geometric parameters calculated in the gas phase and in solution are collected in Table 1.

Fig. 1
figure 1

a Experimental structure of the title compound, along with the atom-numbering scheme used in this work [42]. b Theoretical structure of the title compound. c Superposition of the experimental (black) and calculated (red) structures. Hydrogen atoms are omitted for clarity

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Table 1 Experimental and optimized structural parameters of the keto–enol tautomers and transition state of the title compound
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As can be seen in Table 1, the optimized structures closely resemble the experimental one. X-ray study reveals that the triazole ring makes dihedral angles of 2.95(14)° and 16.43(12)° with the planes of the chlorophenyl and benzene rings, respectively. These angles were calculated as 4.13° and 23.48° in the gas phase, 2.62° and 31.72° in chloroform, 1.66° and 33.99° in methanol, and 1.44° and 34.31° in water, respectively. In addition, the dihedral angle between the chlorophenyl and benzene rings was found to be 19.29(11)° experimentally, while it was determined theoretically as 19.97°, 31.34°, 33.57°, and 33.86° in the gas phase, chloroform, methanol, and in water. When the optimized and experimental structures of the molecule were compared by overlaying them using a least-squares algorithm that minimizes the distances between the corresponding non-hydrogen atoms, as shown in Fig. 1c, the resulting RMSEs were 0.179, 0.151, 0.169, and 0.172 Å, respectively, in the gas phase, chloroform, methanol, and in water (Fig. 1c). So, these results show that the level of theory adequately describes the experimental geometry and can be used to study the reaction mechanism of the keto–enol tautomerism displayed by the title compound.

In order to prove that the structure presented in this work is the global minimum, a preliminary search of low-energy structures was performed using the B3LYP/6-311++G(d,p) computations as a one-dimensional scan by varying the φ 1(N2–N1–C7–C6) and φ 2(N2–C9–C10–C15) torsion angles from −180° to 180° in steps of 10°. Molecular energy profiles with respect to rotations around the N1–C7 and C9–C10 bonds are presented in Fig. 2. It can be seen from the figure that the lowest-energy domain is located at −170° for φ 1(N2–N1–C7–C6) and at 160° for φ 2(N2–C9–C10–C15), which are in agreement with the optimized values of −171° and 157°.

Fig. 2
figure 2

Molecular energy profiles of the title compound for selected degrees of torsional freedom

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Direct keto–enol tautomerism

As can be seen in Fig. 3, there are two possible tautomeric forms for the compound: keto and enol; the former has an exocyclic C8=O1 double bond and the latter has an endocyclic C8=N3 double bond. The geometric parameters for the keto and enol and the corresponding TS geometries of the compound are also collected in Table 1, while their energetic parameters are given in Table 2. The imaginary frequency at the transition state was found to be 1915i cm−1 in the gas phase, 1945i cm−1 in chloroform, 1958i cm−1 in methanol, and 1960i cm−1 in water.

Fig. 3
figure 3

Schematic representation of possible tautomers of the title compound

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Table 2 Energies of the keto and enol forms of the title 1,2,4-triazole compound in hartrees, and energy differences, activation energies, and thermodynamic parameters in kJ mol−1
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The keto and enol tautomers can transform into each other via an intramolecular proton-transfer reaction. Because of the migration of a hydrogen atom from atom N3 to atom O1, some changes are observed in the structure. The distance between atoms O1 and H3 decreases upon the proton transfer associated with keto → TS → enol. It can be concluded that the N3–H3 bond is broken and an O1–H3 bond (0.967 Å in the gas phase and 0.968 Å in all solvent media) is formed during the intramolecular proton-transfer process in the compound. On going from the keto to the enol monomer, the N3–C8 bond length is reduced by 0.072 Å in the gas phase, 0.065 Å in chloroform, and 0.061 Å in methanol and water, while the O1–C8 distance is increased by 0.125 Å in the gas phase, 0.113 Å in chloroform, and 0.108 Å in methanol and water. This is consistent with scission of the C=O double bond and the corresponding formation of a C=N double bond. In addition, a lengthening of the N3―N4 bond and a shortening of the N2―C8 bond are observed. Among the bond angles, the C8–N2–C9, C8–N3–N4, O1–C8–N3, O1–C8–N2, and N4–C9–N2 angles contract while the C8–N2–N1, C9–N4–N3, and N3–C8–N2 angles expand. The N3···H3 and O1···H3 lengths in the TS structure were computed to be 1.340 and 1.402 Å in the gas phase, 1.338 and 1.401 Å in chloroform, and 1.336 and 1.401 Å in methanol and water, respectively.

It should be mentioned here that the molecule is soft and has low-lying vibrational modes in its vibrational spectrum related to the torsion angles φ 1(N2–N1–C7–C6) and φ 2(N2–C9–C10–C15). It has been shown that the deformation of the molecule at the transition state from the isolated state or solution or crystal can be fully explained by its softness [59].

Figure 4 shows the potential energy diagram for the keto–enol isomerization of the title compound. The energy difference between the two tautomers was calculated to be −76.15, −69.94, −66.73, and −66.33 kJ mol−1 in the gas phase, chloroform, methanol, and water, respectively. Single-point energy calculations provided slightly smaller values (−73.63, −68.02, −64.88, and −64.49 kJ mol−1, respectively). According to the ground-state energies of the enol and keto tautomers and the tautomerization energies shown in Table 2, the calculations predict the keto form to be the most stable in the gas phase and in solution. The calculated IRC profile for the direct proton-transfer reaction is presented in Fig. 5. It is clear that the investigated proton-transfer reactions involve concerted atomic movement. This means that the proton transfers happen in a single step without any intermediate.

Fig. 4
figure 4

Potential energy diagram for the direct keto–enol tautomerism of the title compound in the gas phase and in various solvents

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Fig. 5
figure 5

Profiles of the relative total energy versus the intrinsic reaction coordinate (IRC) for the direct keto–enol tautomerism of the title compound in the gas phase and in various solvents, as calculated at the B3LYP/6-311++G(d,p) level of theory

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The forward reaction barrier—encountered during proton transfer from the keto to the enol form of the compound—was computed as 262.24, 264.01, 264.22, and 264.21 kJ mol−1 in the gas phase, in chloroform, in methanol, and in water, respectively. These values show that a great deal of energy is required for the forward proton transfer to occur. For the reverse reaction, the barrier height was calculated as 186.09, 194.07, 197.49, and 197.88 kJ mol−1 in the gas phase, in chloroform, in methanol, and in water, respectively. The MP2 results predict larger barrier heights: 327.49, 329.48, 329.43, and 329.36 kJ mol−1 for the forward reaction and 253.86, 261.46, 264.55, and 264.88 kJ mol−1 for the reverse reaction, respectively. Consequently, neither the forward nor the reverse reaction appears to happen spontaneously. The standard enthalpy and free-energy changes associated with the keto ↔ enol tautomerism are also tabulated in Table 2. According to the calculated thermodynamic parameters, the single proton-transfer reaction in both directions is strongly endothermic, with large positive standard enthalpy and free-energy changes in all phases. As a result, we can deduce that the single proton-transfer reaction between the keto and enol tautomers is not a favored process.

Solvent-assisted keto–enol tautomerism

We also investigated the keto ↔ enol tautomerism in the presence of a single solvent molecule. In this case, the imaginary frequency at the transition state was found to be 235i cm−1 for chloroform, 1142i cm−1 for methanol, and 1499i cm−1 for water. The structural parameters shown in Fig. 6 display significant geometric changes as the tautomerism proceeds. Complexation with a single solvent molecule has a significant effect on the geometries of the keto and enol moieties, and mainly influences the geometric parameters in the vicinity of the intermolecular hydrogen-bonding region.

Fig. 6
figure 6

Mechanism of the solvent-assisted tautomerization between keto and enol complexes by double proton transfer. Distances are in Å and angles are in degrees

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The energies of the keto and enol forms complexed with the solvent molecules, energy differences, activation energies, and standard enthalpy and free-energy changes are given in Table 3. The energy separation between the two tautomers was found to be −68.56, −54.90, and −56.59 kJ mol−1 for B3LYP, and −89.99, −72.15, and −71.60 kJ mol−1 for MP2, in chloroform, methanol, and water, respectively. The keto form is therefore more stable than the enol form. The IRC profile for the solvent-assisted proton-transfer reaction is presented in Fig. 7. It can be seen from the figure that the proton-transfer reactions occur in a single step without any intermediates.

Table 3 Energies of the keto and enol tautomers complexed with the solvent molecules in hartrees, and energy differences, activation energies, and thermodynamic parameters in kJ mol−1
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Fig. 7
figure 7

Profiles of the relative total energy versus the intrinsic reaction coordinate (IRC) for the solvent-assisted keto–enol tautomerism of the title compound, as calculated at the B3LYP/6-311++G(d,p) level of theory

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The relative energies of the TS with respect to the keto tautomer were obtained as 219.59, 93.83, and 100.93 kJ mol−1, while the reverse reaction barriers were calculated as 151.03, 38.92, and 44.34 kJ mol−1 in chloroform, methanol, and water, respectively. The MP2 barrier heights were found to be higher than those of B3LYP: 236.21, 151.31, and 156.57 kJ mol−1 for the forward reaction and 146.22, 79.16, and 89.96 kJ mol−1 in chloroform, methanol, and water, respectively. Compared with the direct proton-transfer process in the presence of bulk solvent, it is clear that the intervention of a solvent molecule considerably reduces the energy barrier and the enthalpy and free-energy changes. However, the large positive standard enthalpy and free-energy changes as well as the tautomeric energy barrier reveal that a substantial amount of energy is still necessary for either the forward or the reverse proton transfer to occur in the presence of one solvent molecule, indicating a process that is disfavored or not spontaneous.

Intermolecular hydrogen-bonding interactions

The geometric and energetic properties of the intermolecular hydrogen-bonding interactions of the compound were investigated at the same level of theory in the gas phase, and the results are collected in Table 4, together with the corresponding experimental values.

Table 4 Intermolecular H-bond geometries and interaction energies (kJ mol−1) in the gas phase
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In the crystal structure of the compound, two intermolecular interactions are observed, N1–H1···O1 and N3–H3···O1, which form centrosymmetric dimers characterized as R 22 (10) and R 22 (8) motifs [60], respectively. It is apparent from the table that the computed hydrogen bond lengths are 1.948 and 1.843 Å for the N1–H1···O1 and N3–H3···O1 interactions, respectively, which are shorter than those observed experimentally. Because of the hydrogen-bonding interactions, the bond lengths N1–H1 and N3–H3 were calculated to be slightly longer, by 0.174 and 0.237 Å, respectively, than those in the free keto tautomer. Although the collinear bond angle of the N1–H1···O1 interaction was found to be more linear than that of the N3–H3···O1 interaction (177° versus 163°), the remaining geometrical parameters of the two interactions are consistent with the experimental values, which demonstrate that the N3–H3···O1 interaction is stronger than the N1–H1···O1 interaction.

The computational results show that the cyclic dimer constructed via two N3–H3···O1 interactions is more thermodynamically stable than the other dimer formed via two N1–H1···O1 interactions, the difference between their total energies being −19.08 kJ mol−1. As can be seen from Table 4, the BSSE-corrected binding energies were found to be −19.00 and −30.96 kJ mol−1 for the N1–H1···O1 and N3–H3···O1 interactions, respectively.

The energies of the intermolecular H-bonds, in kcal mol−1, were also evaluated using the empirical Iogansen relationship [61]

$$ E=0.33\sqrt{\varDelta \nu -40}, $$

where Δν (cm−1) is the magnitude of the redshift (relative to the free molecule) of the stretching mode of the H-bonded groups involved in the H-bonding. According to the formula, the intermolecular N1–H1···O1 and N3–H3···O1 interactions have energies of 3.33 and 6.07 kcal mol−1, respectively. Hence, the N3–H3···O1 hydrogen bond is stronger than the N1–H1···O1 bond.

The computed Mulliken charges on the donor, hydrogen, and acceptor atoms in the two intermolecular interactions are given in Table 5; ΔQ is the change in the charge on the atoms because of the intermolecular hydrogen-bonding interactions. All of the atoms involved in the hydrogen bonding present a change in charge, and the variations in the charges on the donor, acceptor, and hydrogen atoms are not the same for the two H-bonds. In the N1–H1···O1 interaction, the nitrogen atom is more negative and the hydrogen atom is more positive, while the oxygen atom is less negative. In the N3–H3···O1 interaction, the nitrogen and oxygen atoms are more negative, while the hydrogen atom is more positive. The net charges (ΔQ donor + ΔQ hydrogen + ΔQ acceptor), which are −0.037e for the N1–H1···O1 hydrogen bond and −0.073 for the N3–H3···O1 hydrogen bond, indicate that the neighboring atoms are also included in the charge transfer.

Table 5 Calculated Mulliken charges (e) on key atoms involved in the interactions in the gas phase
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Conclusions

In this paper we have reported the results we obtained at the B3LYP/6-311++G(d,p) level of theory for the structural parameters, the direct and solvent-assisted keto–enol tautomerism, and the intermolecular hydrogen-bonding interactions in the title 1,2,4-triazole compound. When exploring the tautomeric mechanism, additional single-point energy calculations were also carried out at the MP2/6-311++G(d,p) level. The calculated values for the structural parameters of the molecule were found to be in good accord with the corresponding experimental values. It was calculated that the keto form is the predominant tautomer in all phases. Very high barrier heights were found for the keto ↔ enol tautomerization process, so this tautomerization does not occur spontaneously in the gas phase or in solution. When a single molecule of solvent participated in the proton-transfer reaction, it was found that the barrier heights decreased significantly. Even though the calculated values still suggested that the tautomerization was unfavorable, it was clear that including more solvent molecules in the proton-transfer reaction not only lowers the positive standard free energy but also greatly reduces the activation energy. According to the energy values obtained for the hydrogen-bonding interactions, the N3–H3···O1 intermolecular hydrogen bond contributes more to the stability of the crystal structure than the N1–H1···O1 hydrogen bond does.