The 4(5)-methylimidazole System in the gas phase: Insights from helium droplet experiment vs. quantum chemistry

Two of the 21 proteogenic amino acids feature an aromatic heterocycle, with histidine (Fig. 1) being one of them. Its imidazole ring consists of five atoms, two of which are non-equivalent nitrogen atoms, allowing neutral histidine to exist in two tautomeric forms. The equilibrium between these tautomers is influenced by the biological environment and is quantified by the tautomeric constant, $K T$⁠. Specifically, histidine’s behavior in proton transfer mechanisms varies depending on the pH of the environment,¹ a distinctive property shared by only a few biological molecules.

This tautomerism arises from the structure of the imidazole ring, where one nitrogen atom is covalently bound to a hydrogen atom while the other nitrogen carries a lone pair of electrons. Under different environmental conditions, a hydrogen atom can preferentially bind to either nitrogen, resulting in the two tautomers and explaining the potential formation of a cation when both nitrogen are protonated. However, studying only the imidazole molecule to understand histidine’s tautomerization is insufficient, as imidazole itself has two equivalent tautomers, which does not reflect the case with histidine due to the presence of the carbon chain. Histidine’s side chain, 4(5)-methylimidazole (Fig. 1), exhibits two tautomers that are no longer equivalent, making it a more relevant model for studying histidine tautomerization.

The tautomerization of imidazole and its derivatives has been extensively studied, but most of these studies—whether theoretical or experimental—have focused on the condensed phase. These studies often provide ambiguous results regarding the tautomeric equilibrium. For 4(5)-MeIm, whose pKa is 7.52,² reported values of K_T range from 0.45 to 1.5^3–5 depending on the solutions. In aqueous solution and at low pH, 5-MeIm is the preferred tautomer due to its higher dipole moment compared to 4-MeIm, resulting in stronger stabilization through interactions with water. In contrast, quantum chemistry calculations estimate $K T$ to range from 0.18 to 3.4 in the gas phase and from 0.14 to 3.39 in aqueous solution, depending on the theory level^6–8 [6-31G* to 6-311++G** across MP2, MP3, MP4, and DFT methods (BLYP, B3LYP, B3PW91)] and the models used for the solvation.

This dispersion on the K_T value highlight the inherent difficulty in accurately estimating this tautomeric constant and studying tautomerization in a specific environment may not fully capture the intrinsic processes involved. Moreover, quantum chemistry (QC) calculations of this constant when the tautomers are in solution are a challenge. Consequently, examining 4(5)-MeIm in the gas phase could offer a more effective approach for gaining fundamental insights into the tautomeric equilibrium, free from the complexity of condensed phase interactions.

The initial assumption of this work is that this tautomeric equilibrium is supposed to be determined solely by the intrinsic properties of the tautomers and their relative energies. Next, the idea is to use helium droplets (0.4 K) to capture and almost instantaneously freeze all the internal degrees of freedom of 4(5)-MeIm. The tautomers are then identified by infrared spectroscopy of NH stretch using the HENDI (HElium NanoDroplet Isolation) technique developed by Scoles’ group.^9,10 Tautomer populations are proportional to the area of these bands once corrected for relative intrinsic band intensities (obtained by QC). This procedure follows the pioneering work of Choi et al.¹¹ on guanine tautomers. Various QC calculations were also performed, as they are essential for data analysis and interpretation.

The first part of this work describes the theoretical and experimental methods, and the results are presented in the second part. Finally, the value of the tautomeric constant is discussed in the context of QC calculations and other experimental data.

The quantum chemistry program package Turbomole V7.0¹² was used to obtain energetic and structural data for MeIm. The dispersion-corrected density functional theory (DFT-D) method, previously applied to biological molecules,^13–16 was employed in this study. Specifically, the B97-D3(BJ-abc) exchange-correlation functional,^17,18 incorporating corrections for two- and three-body dispersion (semi-empirical terms), was chosen in combination with the def2-TZVPPD triple-zeta valence orbital basis set.¹⁹ To optimize the balance between accuracy and computational time, the resolution of identity approximation (RI-DFT) was applied,²⁰ using an m4 grid for numerical integration of exchange-correlation terms, an electronic density convergence criterion of 10^–8 hartree (≈0.3⋅10^–6 eV) and a geometry convergence criterion of 10^–5 a.u. (≈0.53 fm). At this stage, the structures, the enthalpy at 0 K, and the Gibbs free energy at 315 K were determined for the two tautomers. Additionally, the vibrational frequencies of the normal modes using the harmonic approximation and their oscillator strengths, rotational constants, and inertia principal for the two tautomers were calculated. For comparison with experimental data, the raw vibrational frequencies were scaled according to the procedure described in Appendix 3.

To validate the method, the obtained energetics were compared with those calculated using a more advanced approach, such as CCSD(T)^21,22 with the quantum chemistry program package Gaussian 16.0 Revision A.03²³ with the same basis set as for DFT-D calculation but also with QZPPD. The convergence thresholds chosen were 10^–8 for the electronic density (SCF), 10^–7 for energy (CCSD) and for geometry, a maximum gradient of 4.5⋅10^–4 a.u. (RMS: 3⋅10^–4) and maximum displacement of 1.8⋅10^–3 a.u. (RMS: 1.2⋅10^–3). This comparison aimed to assess the impact of methods, basis sets, and the number of correlated electrons on the optimization of 4(5)-MeIm geometries and energy convergence. The most precise single-reference methods, coupled cluster (CC) with single (S), double (D), and triple (T) substitutions, along with increasingly larger basis sets, were employed. Some calculations involved freezing the core electrons, excluding excitations from core orbitals to virtual orbitals. For MeIm, core electrons refer to those in the 1 s orbitals of the carbon and nitrogen atoms. The comparison, presented in Table I of the results section, demonstrated that DFT-D is a suitable method for describing the energies and properties of 4(5)-MeIm, offering a significant reduction in computational cost without a loss of accuracy.

The tautomerization process of 4(5)-MeIm in the condensed phase involves partner molecules and the exchange of a proton between them. However, in the gas phase or within a helium droplet, where 4(5)-MeIm is isolated, this exchange involving partners does not occur. Instead, for tautomerization to occur, the same proton must be transferred from one nitrogen atom to the other. Since this process differs from that in the condensed phase, it is more accurately described as isomerization. To investigate this phenomenon, and in particular, to obtain a rough estimate of the isomerization barrier, simple QC calculations were carried out.

The coordinate system used to describe the 5-MeIm $← →$ 4-MeIm reaction pathway is illustrated in Fig. 2. Atoms are numbered, and two artificial points $P 1$⁠, $P 2$ are indicated. $P 2$ is located at the midpoint between N(1) and N(3), with the axis [ $P 1$⁠, $P 2$] being perpendicular to the molecular plane formed by the atoms N(1), C(2), N(3), C(4), C(5), and C(8). Each atom in the molecule is defined by intrinsic coordinates: a distance, an angle, and a dihedral angle, all of which are defined relative to either $P 1$ and $P 2$⁠, or the atoms within the molecule itself. The H(6) proton is the one involved in isomerization. To track this labile proton along the reaction path, it proved efficient to reference its position relative to $P 2$⁠, C(2) and N(1) by defining three coordinates: the distance H(6)– $P 2$⁠, the angle $H(6) – P 2 – ^ C(2)$ and the dihedral angle $Φ$ between the two planes H(6)– $P 2$–C(2) and $P 2$–C(2)–N(1). Similarly, each other atom is defined by its distance, angle, and dihedral angle relative to $P 1$ and $P 2$⁠.

The quantum chemistry program package Molpro 2010.1²⁴ was employed for these calculations. The first step involved optimizing the geometry of 5-MeIm as a starting point to determine the reaction coordinate. The energy minimization was performed using a CASSCF calculation.^25,26 Due to problems of convergence of the geometry of the molecule along the reaction coordinate, only the orbitals involved in isomerization were included in the active space. Specifically, 4 electrons were distributed within the 4 orbitals, which correspond to HOMO-1, HOMO, LUMO, and LUMO+1 at the RHF level of calculation. All calculations employed the aug-cc-pVDZ basis set. It should be noted that taking into account all the $π$ electrons in the cycle would lead to a much more time-consuming calculation, beyond the scope of a simple estimation of the isomerization barrier, and certainly to a lower, but non-zero, barrier.

The subsequent steps were integrated into a calculation loop that sampled the dihedral angle $Φ$ from 0 to 180° in increments of 3.6. Each step included two geometry optimizations performed at the CAS(4,4)/aug-cc-pVDZ level using Molpro’s built-in automatic geometry optimization program (OPTG). In the first optimization, the coordinates defining the methyl group and the position of H(7) were blocked. The second optimization used the geometry obtained from the first step and freed these previously constrained coordinates. Throughout both optimizations, the dihedral angle Φ, as well as the coordinates defining points P₁ and P₂ and the plane N(1)–C(2)–N(3), were held fixed. This two-step optimization strategy aimed to reduce, though not entirely eliminate, scenarios where the migrating proton was placed in unrealistic positions.

Once the optimal geometry was obtained, the CAS(4,4)/aug-cc-pVDZ calculation, accounting only for static electronic correlation, was supplemented by RS2C²⁷ and MRCI^28,29 calculations to include dynamic correlation effects. These RS2C and MRCI calculations were incorporated into the loop sampling the $Φ$ angle.

To address convergence issues, two sets of calculations were performed. The first followed the procedure described above to explore the reaction coordinate from 5- to 4-MeIm. The second reversed the sampling direction, exploring the coordinate from 4- to 5-MeIm by varying $Φ$ from 180 to 0°. Ideally, for the same $Φ$ value, both calculations would yield identical energy values. However, discrepancies of up to a few hundredths of a hartree were observed for certain $Φ$ values. These differences were not due to a lack of convergence in energy calculations but instead highlighted limitations in achieving fully optimized geometries.

The results presented in the Subsection 3.1.2. “Estimation of the isomerization barrier” were constructed by selecting, the calculation yielding the lowest energy for each $Φ$ value, corresponding to the most accurately optimized geometry.

The experimental setup, previously described in detail,³⁰ is briefly summarized here. It consists of three vacuum chambers, as shown in Fig. 3.

In the first chamber, a helium cluster beam is generated by the condensation of helium gas in a supersonic expansion. The helium gas (P₀ ≈ 10 bars, T₀ ≈ 10.7 K) is expanded through a 5 μm diameter nozzle, producing clusters with an average size of a few thousand atoms. The central part of the beam is extracted by a 1 mm diameter skimmer and directed into the second, or “pick-up”, chamber.

In this chamber, the helium clusters are doped using the well-known pick-up technique.³¹ Home-made pure pellets of 4(5)-MeIm (powder from Sigma-Aldrich) are heated in an oven (T_f ≈ 315 K), causing the molecules to evaporate into the gas phase. By controlling the oven temperature (Appendix 1), the pressure of the evaporated molecules can be adjusted, allowing for variation in the average number of molecules captured by the clusters. Under typical experimental conditions, less than one 4(5)-MeIm molecule is captured per cluster on average.

The doped clusters then enter the final chamber, where the HENDI technique is used to perform infrared spectroscopy of the dopants. The clusters pass through a multi-pass optical cell, where an infrared laser beam (Lockheed-Martin Aculight ARGOS 2400-SF-15, tunable around σ = 3300 cm^–1, Δσ = 1 MHz) is reflected multiple times. Depending on the laser wavelength, part or all of the helium cluster may evaporate. The depletion of the helium cluster beam is measured using a quadrupole mass spectrometer (Extrel, MAX 500HT). By recording this depletion as a function of the laser wavelength, a HENDI spectrum is obtained, which is an action spectrum that, over and above the traditional rovibrational spectroscopic information, also contains information on the interaction between helium and the dopant.

As introduced in the previous section, the RI-B97-D3(BJ-abc) method chosen for this study has been compared to more sophisticated methods. While prior studies^14,15 have demonstrated that this method is well-suited for this type of system, additional validation was required because Li et al.⁸ reported significant variations in enthalpy and Gibbs free energy depending on the method, level of theory, and basis set used. In their work, the authors employed extended basis sets ranging from 6-31G* to 6-311++G** across MP2, MP3, MP4, and DFT methods (BLYP, B3LYP, B3PW91).

The values compared in Table I reveal a minimal difference in enthalpy (0.1 kJ⋅mol^–1) and Gibbs free energy (0.2 kJ⋅mol^–1), confirming the reliability of the chosen method for describing 4(5)-MeIm. Table I also shows that 4-MeIm is the most stable tautomer, with a zero-point energy (ZPE)-corrected enthalpy at 0 K approximately 2 kJ⋅mol^–1 lower than that of 5-MeIm.

At 315 K, the Gibbs free energy difference (ΔG_5–4) between the two tautomers is 2.4 kJ⋅mol^–1, further confirming that 4-MeIm is the most stable tautomer in the gas phase. Considering the commonly accepted error bars for quantum chemical calculations,³² the Gibbs free energy is estimated as ΔG_5–4 (315 K) ≈ (2.4 ± 2) kJ⋅mol^–1.

The structures, optimized at RI-B97-D3(BJ-abc) level of theory, are presented in Fig. 4, with interatomic distances labeled. The ring of the molecule, its hydrogen atoms, and the β-carbon of the methyl group form a plane. One hydrogen atom of the methyl group lies in a plane perpendicular to the ring, passing through the β- and α-carbon atoms, while the other two hydrogen atoms are symmetrically arranged relative to this plane. All the structural results are in good agreement with each other and, in particular, with those of the highest theoretical level. As shown in Table I, the same remark can be made with the energetics, so much so that DFT-D is used next. It should be noted that these structural findings are in relatively good agreement with previous theoretical results (6-31 + G*, 6-311 + G*, 6-311++G** basis sets at simple MP2 and DFT levels, the best calculations of Ref. 8 and 6-31G force fields and optimized geometries.³³ 

The tautomeric constant, $K T$⁠, describing the tautomeric equilibrium illustrated in Fig. 1, is expressed by Eq. (1). Based on the Gibbs free energy difference determined previously, the theoretical gas phase tautomeric constant at 315 K is $K T= 2.5 − 1.3 + 3.1$ taking into account the error bars of ΔG. It is important to note that even slight variations in ΔG can result in significant changes to $K T$ due to the exponential nature of the relationship.

These calculations predict that in the gas phase, following vaporization in an oven at 315 K, the 4-MeIm tautomer will predominate over 5-MeIm. At this temperature, the population of 4-MeIm is expected to be approximately twice that of 5-MeIm.

Harmonic frequency calculations, corrected as described in Appendix 3, were also performed at the RI-B97-D3(BJ-abc) level of theory. The results for the two tautomers are presented in Table II. These calculations allow to determine the spectral region to scan, which lies between 3500 and 3530 cm^–1.

The QC calculations performed to estimate the isomerization barrier were conducted for the conversion of 5-MeIm to 4-MeIm and vice versa (see Subsection 2.1). Regardless of the theoretical method used (CAS(4,4), RS2C, or MRCI), 4-MeIm always proved to be the most stable tautomer, with an enthalpy around 2 kJ⋅mol^–1 lower than that of 5-MeIm, consistent with the results presented in the previous section. The optimized geometries obtained from these calculations are in excellent agreement with those of the previous section.

The results of the reaction for the 5-MeIm $← →$ 4-MeIm isomerization and its associated energetics are summarized in Fig. 5. The horizontal axis, shared across all three panels of the figure, represents the dihedral angle $Φ$ as defined in Fig. 2. The middle panel illustrates the variation of the angle $H(6) – P 2 – ^ C(2)$⁠, while the bottom panel shows the distance H(6)– $P 2$⁠, both plotted as functions of $Φ$⁠. Together, these provide a detailed depiction of the reaction coordinate from 5-MeIm (left) to 4-MeIm (right).

The top panel of Fig. 5 displays the potential energy variation along the reaction coordinate $Φ$⁠. Across all computational methods (CAS(4,4), RS2C, MRCI, and CCSD(T)), the same trend emerges: proton H(6), responsible for the isomerization reaction, moves above the molecular plane to form a high-energy reaction intermediate. This intermediate, with an energy barrier of 2.2 to 2.4 eV (depending on the computational method), involves H(6) binding to carbon C(2). Interestingly, despite the 4 valence of the C(2) carbon, the intermediate retains a planar molecular skeleton similar to that of the MeIm molecule. This intermediate is connected to 5- and 4-MeIm via two transition states, in which H(6) remains above the molecular plane, bonded to either N(1) or N(3).

The thermal energy available at 315 K is close to 27 meV. Thus, these calculations show that in the gas phase, at a temperature of 315 K, the isomerization reaction of the isolated 4(5)-MeIm molecule is highly unlikely.

The survey spectrum of methylimidazole embedded in a helium cluster is shown in Fig. 6. Two distinct bands are observed near the predicted N–H vibrational frequencies: 3517.94 and 3507.83 cm^–1. Based on QC calculations (Table II), their assignments are straightforward. The strongest band is assigned to the N–H stretching mode of 4-MeIm, while the weakest corresponds to the same stretching mode of the second tautomer. Spectra recorded at higher MeIm pressure reveal the multimer stretching modes and are presented in Appendix 2.

Notably, the N–H vibrational frequency of 4-MeIm closely matches the value reported for imidazole by Choi et al.,³⁴ indicating that the methyl group has minimal influence on this vibrational mode. In contrast, the N–H vibrational frequency of 5-MeIm is red-shifted by 10 cm^–1.

In this study, the measurement of the tautomeric ratio is based on a quenching hypothesis. The molecules picked up by the helium cluster are rapidly cooled due to a huge helium evaporation rate (≈10¹⁰ K⋅s^–1).³⁵ This cooling occurs so quickly that the molecules are unable to explore their conformational space, effectively “freezing” them in the conformation they held at the moment of capture (same approach as Choi et al.¹¹). As a result, the molecules cool directly to the bottom of their potential wells, with only a few rotational levels populated in their fundamental vibrational state. Consequently, the population ratio of 4- to 5-MeIm in a helium droplet is assumed to reflect the gas phase ratio after molecular evaporation in the oven.

Using experimental data and oscillator strengths from the “Theoretical tautomeric constant” section, the semi-experimental tautomeric ratio was determined as $R T$ (315 K) = 5.3 ± 0.8 confirming that 4-MeIm is the predominant conformer.

As shown, the expression for $K T$ Eq. (1) is highly sensitive to ΔG due to its exponential dependence. In contrast, the alternative expression (2) for $K T$⁠, involves a ratio, making it less sensitive to variations in its operands compared to the exponential function. In this ratio, the potential error arising from theoretical calculations of oscillator strengths is expected to be small. This is because the oscillator strengths are likely very similar, as they involve equivalent free N–H vibration in structurally comparable molecules. Moreover, it is their ratio, not the absolute values, that contributes to the calculation. For these reasons, the error bars of the experimental tautomeric ratio can be considered as smaller than those of the theoretical tautomeric constant.

A measurement of the tautomeric ratio of 4(5)-MeIm in the gas phase was also carried out recently by Antonelli et al.³⁶ using laser desorption and chirped-pulse Fourier transform microwave spectroscopy. Based on the relative intensities of the strongest tautomeric bands, the authors determined that the tautomeric ratio was 1.7. This first experimental gas phase measurement identifies 4-MeIm as the preferred tautomer, in agreement with the theoretical work of Li et al.⁸ and their calculated tautomeric constant.

The theoretical and experimental values of the tautomeric ratios and their error bars obtained in this study are summarized in Table III. Both values indicate the same trend: 4-MeIm is the predominant tautomer in the gas phase.

As shown in Table III, the tautomeric ratio measured by Antonelli et al. is close to the theoretical value of this work, although the effective temperature of the laser desorbed sample is ill-defined. It is also more than twice lower than the present experimental measurement. Although the difference of the tautomeric ratio of this work lies within the error bars, it remains significant and in disagreement with the measurement of Antonelli et al.³⁶ These discrepancies may arise from several factors: the absence of tautomeric equilibrium in our solid sample or the impossibility of achieving tautomeric equilibrium in the gas phase in contrast with laser-desorbed material process. In other words, 4(5)-MeIm would be faced with a situation where tautomeric equilibrium is no longer respected in our experiment.

To confirm the first assumption, one approach should be to measure $K T$ in the solid sample before evaporation of the tautomers into the gas phase. In the solid state, proton exchange is relatively slow compared to solution so the gas phase measurements might better reflect the initial solid state equilibrium. This approach could be particularly insightful, as the tautomeric ratio in solid samples varies with the pH of the solution from which the solid is obtained. For example, Henry et al.³⁷ demonstrated that the tautomeric ratio of lyophilized L-histidine changes with the initial solution pH. However, tautomeric ratios may also change during the vaporization of the molecules. Araujo-Andrade et al.³⁸ showed that tetrazole acetic acid (TAA) undergoes a coordinated mechanism that changes drastically its tautomeric ratio during its sublimation at 330 K. Although it is unlikely that the mechanism involved in the tautomerization of TAA occurs for 4(5)-MeIm (higher barrier to tautomerization, different arrangement in the solid), this study shows that it is not possible to definitively rule out the existence of a mechanism leading to the same consequence. Therefore, measuring $K T$ in the solid sample may not provide useful information for gas phase tautomerization measurement.

In the studies of this work, 4(5)-MeIm is used as a solid sample, with both tautomers initially present in an unknown ratio. During evaporation, each gaseous tautomer reaches thermodynamic equilibrium with its solid counterpart. The vapor pressure of each tautomer depends on the intermolecular forces in the solid, which are influenced by the permanent dipole moment. The QC calculations, reported in Table I, indicate that the dipole moment of the 5-MeIm is significantly higher than that of 4-MeIm. This theoretical result is in agreement with other works^7,8 and is the explanation put forward to explain the predominance of 5-MeIm in aqueous solution, as seen in the introduction. Similarly, in the solid phase, 5-MeIm forms stronger interactions, making its evaporation less efficient than that of 4-MeIm. Consequently, 4-MeIm is preferentially vaporized. It should be noted that increasing the oven temperature in order to reach tautomeric equilibrium, would not have been helpful, as multimers would have formed (see Appendix 2), and also because the product would have rapidly reached its melting temperature (≈ 330 K). Once in the gas phase, as discussed in Subsection 3.1, isomerization is effectively impossible due to the barrier calculated at over 2 eV. Thus, the measurement carried out after pick-up by a helium droplet yields a gas phase tautomeric ratio, which could reflect the preferential evaporation of 4-MeIm over 5-MeIm at 315 K and is not determined solely by the intrinsic properties of the isolated tautomers as initially assumed. This may reasonably explain the difference of a factor of 2 in the observed gas phase ratio as compared to that resulting from a gas phase equilibrium.

It is noteworthy that Antonelli et al.³⁶ measured a tautomeric ratio in the gas phase close to our theoretical prediction, but using laser desorption to vaporize the molecules into the gas phase. A number of questions have been raised concerning such a measurement using this technique, including matrix, pulse energy, and photon wavelength effects.³⁹ Nevertheless, it is generally accepted that this technique can be used for thermal desorption with a high heating rate (≈10¹¹ K⋅s^–1) that allows molecules to desorb intact, although at a relatively high temperature,¹⁴ provided that some precautions are taken.^40,41 It has also been used to co-desorb different molecules without discrimination⁴² illustrating the differences in experimental conditions between their measurements and ours. It would furthermore have been interesting to know the tautomeric ratio of Antonelli et al. solid sample.

This study investigates the gas phase tautomeric ratio of the 4(5)-MeIm molecule through both experimental and theoretical approaches. Experimentally, the vaporized tautomers, initially in an unknown ratio, are trapped and frozen in a helium droplet at 0.4 K. Infrared spectroscopy performed using the HENDI technique, enables a clear identification of each tautomer and the measurement of their respective populations. The tautomeric ratio derived from these measurements is compared to values obtained from quantum chemistry calculations and those measured using other techniques. Finally, the observed discrepancies between our measurements and the various tautomeric constants are attributed to differences in the vaporization processes used to bring the molecules into the gas phase.

This work received partial funding from Agence nationale de la Recherche (ANR-14-CE06-0019—ESBODYR and ANR-06-BLAN-0314—GOUTTELIUM) and Triangle de la Physique (2010-004 T—NOSTADYNE-2). E. Mengesha acknowledges partial support from Eurotalent (2015 Project No. 259).

Under standard conditions, 4(5)-MeIm is a white powder. However, its partial pressure (approximately a few 10^–3 mbar) is too high for direct use in the oven, where the pressure typically ranges from around a few 10^–7 mbar. To address this issue, small pellets of 4(5)-MeIm were prepared and placed in a sealed container with a small hole (0.5 mm), which was then inserted directly into the oven. Vaporization occurs through the hole, effectively limiting evaporation at room temperature. The oven’s temperature controls the partial pressure inside the container and, consequently, the pressure within the oven.

In order to observe 4(5)-MeIm multimers, the effective capture cross-section of helium droplets was increased by increasing their size, i.e. the stagnation pressure $P 0$ as shown in Figs. 7 and 8.

The vibrational frequencies of the two tautomers were calculated using the same level of theory as the energetics,

DFT-D, RI-B97-D3(BJ-abc)/def2-TZVPPD, applying the harmonic approximation. To address approximations and computational errors, these frequencies were scaled using a mode-dependent procedure. The N–H stretch frequencies were adjusted with a linear function, using coefficients (a, b) = (0.8464, 472.25 cm^–1), which were derived from a fit of experimental and theoretical (obtained with the same level of theory) data for similar vibrational stretches as shown in Table IV. The molecules used for the scaling procedure are imidazole, its dimer, and its complexes with water (acceptor = Wa; donor = Wd).