On Some Origins of Tautomeric Preferences in Neutral Creatinine in Vacuo: Search for Analogies and Differences in Cyclic Azoles and Azines

Abstract

In order to look for the origins of tautomeric preferences in neutral creatinine in vacuo, we examined prototropic conversions for model azoles, namely mono-hydroxy and mono-amino imidazoles, and also for their selected 1-methyl derivatives. All possible isomeric forms of creatinine and model compounds, resulting from intramolecular proton transfer (prototropy), conformational isomerism about –OH, and configurational isomerism about =NH, were studied in the gas phase (model of non-polar environment) by means of quantum-chemical methods. Because the bond-length alternation is a consequence of the resonance phenomenon, it was measured for all DFT-optimized structures by means of the harmonic oscillator model of electron delocalization (HOMED) index. Important HOMED analogies were discussed for investigated azoles and compared with those for previously studied cyclic azines, including pyrimidine nucleic acid bases. The internal effects were taken into account, and the stabilities of the investigated tautomers-rotamers were analyzed. Significant conclusions on the favored factors that can dictate the tautomeric preferences in creatinine were derived.

1. Introduction

Numerous biomolecules containing heteroatoms (such as N and/or O), and also π- and n-electrons exhibit a particular case of constitutional isomerism of functional groups called prototropic tautomerism [1,2,3,4]. Creatinine (Crea: C₄H₇N₃O, preferred IUPAC name: 2-amino-1-methyl-5H-imidazol-4-one) is one of them. Possessing a heterocyclic structure, in which the acylguanidine part is included in the five-membered ring, Crea belongs to the family of glycocyamidines [5,6]. This lactam compound is spontaneously formed in vertebrates from the acyclic nitrogenous organic acid creatine {C₄H₉N₃O₂, IUPAC name: 2-[carbamimidoyl(methyl)amino]acetic acid, also called as methylguanidoacetic acid} (Figure 1) [7,8,9,10]. The two biomolecules, acyclic creatine and its cyclic anhydride creatinine, possess different isomeric forms, such as prototropic tautomers, and also conformational and configurational isomers [5,11,12,13,14]. They play a principal role in the metabolism of proteins [7,9,15]. As the end product of this process, Crea is always present in the urine and blood of healthy human organisms in almost constant concentrations that mainly depend on their body weight [9]. Its abnormal level indicates various disease states of muscles and/or kidneys. For detection of renal dysfunction, determination of Crea-concentration in urine seems to be a more valuable analysis than that of urea [16].

Already in the 19th century, the significance of creatine and creatinine in the human life has been well recognized [7,17]. This encouraged many chemists and biochemists to undertake various experimental and theoretical studies on their structure and physicochemical, chemical, and biochemical properties (see for example refs [5,6,7,8,9,11,18,19,20,21,22,23,24,25,26,27,28]). The two derivatives continue attracting the particular attention of researchers even in the 21st century (see for example articles on structural studies [12,13,14,29,30,31,32]). An interesting article was published in 2021 by Léon et al. [14], who discussed spectroscopic and computational results for the favored tautomeric forms of creatinine in the solid state, polar solvents, and gas phase.

Two important tautomers (showed in Figure 1) were detected for Crea. The amino-oxo-form is present in the solid state [14,18,26,27,31] as well as in the polar solvents [13,14,22,27,28,29,32]. The imino-oxo isomer is favored in the gas phase [13,14,22,27,32]. Note that the two tautomers of neutral Crea exceptionally possess a C-sp³ atom in the five-membered ring. This means that delocalization of π- and n-electrons in the cycle is incomplete, and the two isomers do not display an aromatic character. In the case of heterocompounds with the six-membered cycle, such as mono-hydroxy and mono-amino pyridines and pyrimidines, as well as di-substituted pyrimidine nucleic acid bases, tautomers containing the C-sp³ atom in the ring can only be classified to the family of rare, and even exceptionally rare forms, similarly as those for phenol and aniline [33]. For neutral cyclic azine-derivatives, these tautomers have never been experimentally identified. They could be studied only theoretically using quantum-chemical methods. Tautomeric mixtures of pyrimidine nucleic acid bases and their model azines consist mainly of tautomers possessing tautomeric protons at heteroatoms. For example, isocytosine (iC) contains the –NH₂/=NH group at 2-position and the –OH/=O group at 4-position in the ring; similarly with Crea, however, these groups in iC are linked to carbons of the six-membered pyrimidine ring, whereas in Crea they are attached to carbons of the five-membered imidazole ring. Moreover, the N1-sp³ atom in Crea cannot participate in tautomeric conversions and cannot change into N-sp². It contains the Me group that eliminates prototropy. In iC, the N1-sp² atom can attach the labile proton and can change its character from =N− (base) to –NH− (acid). These structural differences involve dramatic changes in tautomeric preferences. In the gas phase, iC prefers the aromatic amino-hydroxy tautomer [34,35], whereas Crea favors the non-aromatic imino-oxo form [13,14,22,28,32].

Looking for the reasons of particular stability of Crea-tautomers containing the C-sp³ atom in the five-membered ring, we examined in vacuo, first, the complete tautomeric mixtures for hydroxy- and amino-substituted azoles (2AIm, 4AIM, 2A1MIm, 2OIm, 4OIm, and 4O1MIm, Figure 2), and next, the complete tautomeric mixture for creatinine (Figure 1). In the literature, one can find some partial results for isolated tautomeric-azoles [2,3,36,37,38,39], but no general conclusions can be derived. For our examination, we used the same quantum-chemical methods as applied previously for pyrimidine nucleic acid bases and their model aromatic azines [33]. We estimated the stabilities of all possible isomers on the basis of their relative thermochemical parameters. We also measured the power of resonance in individual isomers by means of the geometry-based descriptor, harmonic oscillator model of electron delocalization (HOMED) index [40]. The use of the same methods for geometry optimization and quantitative analysis of the structural and energetic parameters for individual Crea-isomers as well as for their model azoles gives us the possibility to find some reasons for particular stability of Crea-tautomers containing the endo-C-sp³ atom. It also makes it possible to compare the computational results for creatinine and the model azoles with those for the previously studied pyrimidine nucleic acid bases and model azines. The comparison of geometric and energetic parameters shows interesting similarities and differences for tautomeric heterocycles possessing the five- and six-membered rings.

2. Methodology

It should be mentioned here that chemists have frequently considered experimental techniques as exceptionally important methods in investigation of structural phenomena for organic compounds of biological activity. However, for the majority of isomeric systems, only the major and some minor isomers can be detected by means of spectroscopic methods (UV, IR, Raman, MW, MS, NMR, etc.), particularly in the gas phase or solution [1,2,3,4,14,33,36]. Most of the minor isomers cannot be distinguished from the background, and rare isomers are usually undetectable. Additionally, isomeric transformations are very fast and reversible processes, and single isomers can be difficult to isolate experimentally. Isomeric equilibria are also very sensitive to their environment, e.g., the presence of other molecule(s), ion(s), and radical(s), as well as changes in phase, solvent, pH, and even the method of vaporization. Fortunately, the complete isomeric mixtures containing major, minor, rare, and exceptionally rare forms can be investigated theoretically by means of quantum-chemical methods.

2.1. Computational Details

Among various theoretical methods employed in acid-base chemistry, particularly for investigation of proton transfer equilibria, we chose the density functional theory (DFT) method [41] with the three-parameter hybrid exchange functional of Becke [42] and the correlation functional of Lee, Yang, and Parr (B3LYP) [43], and larger basis sets with the diffuse and polarization functions [44] as previously described for tautomeric nucleic acid bases and their model compounds [33,45]. The DFT(B3LYP)/6-311+G(d,p) level of theory has been considered as sufficient to describe quantitatively proton-transfer reactions [46,47]. It is also appropriate for analyzes of structural and energetic parameters for other tautomeric compounds containing heteroatoms [45,48].

All possible prototropic tautomers were taken into account in quantum-chemical calculations for Crea and model azoles 2AIm, 4AIM, 2A1MIm, 2OIm, 4OIm, and 4O1MIm. Additionally, two zwitterionic forms were considered, one for 4O1MIm and the other one for Crea. The structures of all possible isomers considered here for investigated compounds are shown in Figures S1–S5 (Supplementary Materials). Their geometries were fully optimized at their ground states without symmetry constraints using the DFT(B3LYP)/6-311+G(d,p) level of theory. Only two hydroxy isomers, one of 2OIM and the other one of 4OIm, are not found. Structures of all the other isomers of Crea and model azoles are stable at the DFT level.

For selected major and minor isomers of 4OIm, we also applied the Gaussian (G) theories {G2 and G2(MP2)} [49,50], which take considerably more computational time than the DFT methods, but they reproduce sound experimental results. They are recommended for calculations of energetic parameters of the proton-transfer reactions [51]. The Gn methods were already used for tautomeric organic compounds containing amino and/or hydroxy groups linked to C atoms of the six-membered ring, e.g., mono-hydroxy azines [52] and isocytosine [35]. In most of cases, the DFT and Gn methods led to analogous relative Gibbs energies and isomeric preferences. Some discrepancies occurred for hydroxy- and oxo-tautomers of azines for which the relative Gibbs energies are close to zero [33,52]. Employing the G-theories to 4OIm, we were able to verify the application of the selected level of theory for tautomeric prediction. For all quantum-chemical calculations, the Gaussian 03 series of programs [53] were applied.

2.2. Structural Descriptor of Electron Delocalization

The geometry-based HOMED index, recently extended to acyclic and cyclic heterocompounds, properly measure any type of electron delocalization, σ-π hyperconjugation, n-π and π-π conjugation, aromaticity, as well as their various mixtures [40]. Its procedure is analogous to that of the original harmonic oscillator model of aromaticity (HOMA) index [54,55]. The HOMED index for investigated derivatives can be estimated using the same Equation (1) as that proposed earlier for the HOMA index [56] reformulated for homo- and heteroaromatics:

HOMED = 1 − {α(CC)Σ[R_o(CC) − R_i(CC)]² + α(CN)Σ[R_o(CN) − R_i(CN)]² + α(CO)Σ[R_o(CO) − R_i(CO)]²}/n

(1)

In this equation, α(CC), α(CN) and α(CO) are the normalization constants, R_o(CC), R_o(CN) and R_o(CO) are the optimum bond lengths for the reference molecules, R_i(CC), R_i(CN) and R_i(CO) are the calculated bond lengths in the studied structures, and n is the number of bonds taken into account in the HOMED estimation. Only the values of the α and R_o parameters are different in the HOMED [40] and HOMA procedure reformulated in 1993 [56]. Parameterization of the HOMED index is based on that of the original HOMA index proposed in 1972 for aromatic hydrocarbons [54] and in 1974 for aromatic heterocycles [55]. For more details on the HOMED parameterization and differences between the HOMED and reformulated HOMA indices, see in the refs [40].

The values of R_o(CC), R_o(CN), and R_o(CO) applied for the optimum CC, CN, and CO bond lengths in the reference molecules (benzene, 1,3,5-triazine, and protonated carbonic acid, respectively) and the values of the corresponding normalization α(CC), α(CN) and α(CO) constants for the odd and even number of bonds considered in the HOMED procedure are summarized in

Table 1. HOMED parameters employed in this work (taken from Ref. [40]).

Bond	Reference Molecule	Ro (Å)	α5	α7	α6
CC	C6H6	1.3943	78.34	80.90	88.09
CN	C3N3H3	1.3342	81.98	84.52	91.60
CO	C(OH)3+	1.2811	67.84	69.74	75.00

. All of them were estimated by employing the same level of theory (DFT(B3LYP/6-311+G(d,p)) [40] as that used for the isomers of the investigated model azoles and creatinine. The use of the same quantum-chemical method for determination of the HOMED parameters and for analyzes of electron delocalization in the conjugated tautomeric systems minimize computational errors to the minimum.

For all stable isomers of creatinine and for all stable isomers of model azines, the DFT-calculated bond lengths in the optimized structures have been used for quantitative description of electron delocalization measured by the HOMED index. This descriptor was calculated for the five-membered ring (five bonds, n = 5), as well as for the entire conjugated molecule-fragment containing the exo-heterogroups (six bonds in 2AIm, 4AIM, 2A1MIm, 2OIm, 4OIm, and 4O1MIm, n = 6; and seven bonds in Crea, n = 7). We used the following abbreviations in this work for the estimated geometry-based index: HOMED5, HOMED6, and HOMED7, respectively. Note that the CH₃ group linked to the endo-N1 atom in 2A1MIm, 4O1MIm, and Crea does not participate in prototropy. Being a non-conjugated group with tautomeric sites, the H₃C–C bond was not taken into account in the HOMED estimations. However, the lone-pair of n-electrons on N1 can be conjugated with other labile electrons. Hence, the C2N1 and C5N1 bonds were considered in the HOMED5 estimations together with other bonds of the five-membered ring, C2N3, C4N3, C4C5. For the HOMED6 and HOMED7 estimations, the exo-bonds (CN and/or CO) were additionally included. The HOMED values estimated for all isomers possessing the stable DFT-structures are included in Figures S1–S5 (Supplementary Materials).

2.3. Thermochemical Quantities

Thermochemical quantities can be employed for quantitative description of isomeric equilibria, and also for estimation of isomeric mixture compositions. They have been estimated for all isomers after their geometry optimization. For each stable structure, vibrational frequencies and thermochemical quantities such as the electronic energy (E), zero-point energy (ZPE), enthalpy (H, Equation (2)), entropy (S), and Gibbs energy (G, Equation (3) for T = 298.15 K) were calculated using the same level of theory (DFT(B3LYP/6-311+G(d,p)) as that applied for the geometry optimization. All positive frequencies found for stable isomers prove that their optimized structures are true minima.

H = (E + ZPE) + pV

(2)

G = H − TS

(3)

The relative thermochemical quantities (ΔE, ΔH, TΔS, and ΔG) and equilibrium constants (K, Equation (4)) have been also estimated. The ΔG values include changes in E, ZPE, and thermal corrections to the energy and entropy (vibrational, rotational, and translational contributions). The calculated ΔE, ΔH, TΔS, and ΔG, and K values quantitatively describe all considered intramolecular transformation: prototropy, conformational and configurational isomerism [1,2,33,36]. Constitutions of the investigated isomeric mixtures have been found on the basis of the estimated Ks. Using their values, the mole fractions (x_i, Equation (5), where n is the number of considered isomers) have been determined for all stable isomers (major, minor, rare, and even, exceptionally rare forms) considered in the isomeric mixtures. The estimated values of ΔE, ΔH, TΔS, ΔG, K, and x_i for all stable isomers are compared with the HOMED indices in Tables S1–S3 (Supplementary Materials).

K = exp(−ΔG/RT)

(4)

x_i = K_i/(Σ₁ⁿK_i

(5)

3. Results and Discussion

3.1. Possible Tautomers-Rotamers for Model Azoles and Creatinine

For mono-substituted imidazoles containing one exo-NH₂ or OH group in the aromatic forms (2AIm, 4AIm, 2OIm, and 4OIm given in Figure 2), two tautomeric protons, one attached to the exo-heteroatom and the other one to the endo-N atom, can move between six conjugated tautomeric sites (N1, C2, N3, C4, C5, and X6). According to the IUPAC prototropy definition [57], 1,3-, 1,5- and/or 1,7-proton shifts are always accompanied by delocalization of π-electrons. Consequently, eight tautomers are possible for each derivative. Their structures are shown in Figure 3. To distinguish the eight tautomers of 2AIm, 4AIm, 2OIm, and 4OIm, we use the following abbreviations here: 16, 26, 36, 46, 56, 13, 15, and 34. They refer to the numbers of two heavy atoms possessing the tautomeric protons. For example, tautomer 16 contains the labile protons at the endo-N1 and exo-X6 atoms. Note that for 2AIm and 2OIm, three pairs of tautomers 16 and 36, 46 and 56, and also 15 and 34 have identical constitutions. Thus, the number of tautomers, considered in the DFT calculations, is reduced to five. In the case of 4AIm and 4OIm, all eight tautomers possess different constitutions, and all of them have been taken into account in the DFT calculations.

The 1-methyl derivatives 2A1MIm and 4O1MIm contain only one tautomeric proton linked to the exo-heteroatom in the aromatic forms (Figure 2). It can move between three and two conjugated sites, respectively. The presence of Me at the endo-N1 atom reduces prototropic equilibria in the imidazole ring. Some of those that are possible for mono-substituted imidazoles (Figure 3) are impossible for 1-methyl derivatives (Figure 4). Consequently, the tautomeric mixture of 2A1MIm consists of three tautomers (6, 3, and 5), while only two tautomers (6 and 5) are possible for 4O1MIm. All of them possess different constitutions.

For 2A1MIm and 4O1MIm, the tautomer abbreviation correspond to the number of heavy atom possessing the labile proton. The zwitterionic form 3 (possible for 4O1MIm) with separation of the positive and negative charge, like in amino acids, also has a different constitution. It can be formed from 6 or 5 during intramolecular proton transfer from the exo-O6H or endo-C5H group to the endo-N3 atom. According to the IUPAC prototropy definition [57], the zwitterionic form 3 cannot be considered as a prototropic tautomer, because the acid (O6H and C5H) and base (N3) sites, participating in this internal neutralization reaction, are not conjugated.

Since conformational isomerism about –O6H can additionally takes place in the hydroxy tautomers, two extreme rotational isomers (a and b) can be considered for 16, 26, 36, 46, and 56 in the isomeric mixtures of 2OIm and 4OIm, and also for 6 in the isomeric mixture of 4O1MIm. For the imino forms, configurational isomerism about =N6H can also lead to two extreme geometric isomers (a and b). They are possible for 13, 15, and 34 in the 2AIm mixture, for 23, 15, and 35 in the 4AIm mixture, and also for 3 and 5 in the 2A1MIm mixture. In consequence, the following numbers of tautomers-rotamers have been considered in the DFT calculations for the model azoles: six for 2AIm, eleven for 4AIm, eight for 2OIm, thirteen for 4OIm, five for 2A1MIm, and three for 4O1MIm (see structures in Figures S1–S4, Supplementary Materials).

We found that only two tautomers-rotamers of mono-hydroxy-imidazoles (2OIM-16a/36b and 4OIm-36a) do not possess stable structures. The repulsion between the endo >N1H or >N3H and exo –O6H groups possible in 2OIm-16a/36b and 4OIm-36a is so high that −O6H rotates about C–O during the geometry optimization to the other, more stable conformer (2OIm-16b/36a and 4OIm-36b, respectively). Structures of all other tautomers-rotamers of the model azoles are stable at the DFT level. In the literature, isomers containing the C-sp³ atom in the five-membered ring have been frequently neglected for azoles. To our knowledge, there are only a few documents discussing their stability for unsubstituted imidazole and for some its derivatives (see refs [3,36,45,48,58,59,60]).

Creatinine (Crea) can be considered as derivative of 1-methyl-imidazole containing two tautomeric exo-groups, NH₂ and OH at the 2- and 4-position (see amino-hydroxy form 67 in Figure 5). It possesses two tautomeric protons, but only four conjugated tautomeric sites (N3, C5, N6, and O7). Thus, according to the IUPAC prototropy definition [57], the two labile protons of the exo-groups can move to the conjugated tautomeric sites at the 3- and 5-positions together with migration of π-electrons, and we can additionally write four prototropic tautomers (one amino-oxo 56, two imino-hydroxy 37 and 57, and one imino-oxo form 35) that result from the biomolecule internal property, keto-enol, amine-imine (amidine), enamine-imine, and amide-iminol transformations. Intramolecular proton transfer (acid-base reaction) in Crea can also form the zwitterionic form (36). For abbreviations of creatinine tautomers, we used the numbers of atoms to which the tautomeric protons are linked, like for model azoles. Additionally, the =N6H and –O7H groups can take two extreme configurations (a and b) and two extreme conformations (a and b), respectively. Consequently, two isomers (a and b) are possible for tautomers 67 and 35, whereas four isomers (aa, ab, ba, and bb) can be considered for 37 and 57. Hence, thirteen tautomers-rotamers and one zwitterionic form 36 (see structures in Figure S5, Supplementary Materials) were taken into account in our DFT calculations.

In the literature, mainly the amino-oxo and imino-oxo tautomers have been considered in theoretical and experimental investigations [11,21,22,27,28,29,30,31,32]. Recently, Valadbeigi and coworkers [13], employing quantum-chemical methods, investigated nine isomers of creatinine, including some amino-hydroxy and imino-hydroxy tautomers-rotamers, and even the zwitterionic form. However, no complete information can be derived from their investigation on the stability order of all thirteen possible Crea-isomers. It is true that Léon et al. [14] analyzed all tautomers-rotamers for creatinine, but finally they neglected all hydroxy isomers in spectral studies and considered only the amino-oxo (56) and imino-oxo isomers (35a and 35b). Note that the zwitterionic form (36) has not been considered in aqueous solution [14].

3.2. Variations of Structural-Descriptor HOMED for Isomers of Investigated Derivatives

The first perusal of the HOMED indices calculated at the DFT level for all stable isomers of 2AIm, 4AIm, 2OIm, 4OIm, 2A1MIm, and 4O1MIm (Figures S1–S4 in Supplementary Materials) shows that the HOMED values are between 0.8 and 1.0 for aromatic forms containing the amino or hydroxy group (2AIm-16/36, 4AIM-16, 4AIM-36, 2OIm-16b/36a, 4OIm-16a, 4OIm-16b, 4OIm-36b, 2A1MIm-6, 4O1MIm-6a, and 4O1MIm-6b). Generally, HOMEDs for the aromatic forms are higher for the 4- compared to the 2-substituted derivatives. Additionally, HOMED5s describing electron delocalization in the five-membered ring are higher than HOMED6s referring to the entire delocalized system. The imidazole ring contains six labile electrons (four π-electrons and two n-electrons) and it is aromatic, like in other azoles [40], whereas the entire delocalized system consisting of the imidazole ring and the exo N6H₂ or O6H group possesses eight labile electrons, i.e., extra two n-electrons of N6 or O6. This cross n-π and π-π conjugation of the eight labile electrons in the entire conjugated system leads to weaker electron delocalization compared to the conjugation of the six labile electrons in the aromatic ring.

For the imino and oxo tautomers-rotamers without C-sp³ in the ring (2AIm-13, 2OIM-13, 2A1MIm-3a, and 2A1MIm-3b), HOMEDs are also slightly higher for the five-membered ring than for the entire conjugated part. Generally, they are close to 0.7. Analogous HOMEDs (close to 0.7) are found for the zwitterionic form 4O1MIm-3. However, in this case, the value for HOMED5 is slightly lower than that for HOMED6 (without N1−Me bond), suggesting that the separation of the delocalized positive and negative charges in the zwitterion system containing the exo-heterogroups increases the alternation of bond lengths in comparison to that in the five-membered ring. All the imino, oxo, and zwitterionic forms (without endo-C-sp³) can be considered as moderately delocalized isomers in comparison to the aromatic ones. As could be expected, the other isomers (possessing endo-C-sp³) completely lose an aromatic character of the ring. Owing to the cross σ-π hiperconjugation with n-π and π-π conjugations, all of them have weakly delocalized structures. Their HOMED5 and HOMED6 values are not higher than 0.4.

Analogous variations of the HOMED indices (HOMED6 and HOMED7) have been observed previously for tautomeric mono-amino and mono-hydroxy pyrimidines (azines) containing the six-membered ring with N included at the 1- and/or 3-positions [33]. However, the HOMED values are slightly higher than those for azoles. They are close to unity for the aromatic forms (>0.9), for which the six-membered ring contains six labile π-electrons. Usually, aromatic derivatives with only π-electrons are better delocalized than those possessing a mixture of n- and π-electrons in the ring, like aromatic azoles [40]. For the imino and oxo forms of azines without C-sp³ in the ring, the HOMED values are between 0.7 and 0.8, and for those containing the endo-C-sp³ atom are lower than 0.5. Slightly higher HOMEDs for isomers of azines are a consequence of higher numbers of π-electrons and lower numbers of n-electrons in the conjugated parts than in the case of investigated isomers of azoles. This tendency is in accord with the general rules of resonance that are well recognized in organic chemistry. The resonance structures with a separation of positive and negative charge are less important in the resonance hybrid of n-π and π-π conjugated parts than those without separation of charge in only π-π conjugated systems. More important resonance structures in the resonance hybrid involve stronger electron delocalization in the conjugated system.

However, independently on the type and power of conjugation, the HOMED variations for isomers of 2-amino imidazoles are parallel to those for the corresponding isomers of 2-hydroxy derivatives. In the other words, analogous intramolecular proton transfers (1,3-, 1,5-, or 1,7-proton shifts) involve analogous electron delocalization in 2AIm and 2OIm. The same is true for 4AIm and 4OIm. Changes of the HOMED5 and HOMED6 values are symmetric (see Figures S6 and S7, Supplementary Materials). Thus, general linear relationships (Figure 6) exist between HOMED5s, and separately, between HOMED6s estimated for all stable isomers of mono-amino (AIm) and mono-hydroxy imidazoles (OIm).

The correlation coefficients (R ≥ 0.98) and slopes of linear regressions (a ≥ 0.95) between HOMEDs of AIm and OIm are close to unity. Slight deviations of some hydroxy and imino isomers (a and b) from the linear relationships can be a consequence of different favorable and unfavorable interactions between exo- and endo-groups. The change of these interactions when going from a to b slightly affects electron delocalization and also HOMEDs. Similar linear relationships with analogous correlation coefficients and slopes exist between HOMEDs for isomers of mono-amino and mono-hydroxy azines [33,52], as well as between HOMEDs for isomers of di-substituted pyrimidine nucleic acid bases [33]. These relations between HOMED6s corresponding to the six-membered ring are also included in Figure 6. The HOMED6 data for pyrimidine bases and their model azines were taken from ref. [33]. All these linear relationships between HOMEDs for analogous tautomeric systems containing the five- and six-membered rings quantitatively confirm significant relation between electron delocalization and intramolecular proton transfers.

When HOMEDs for isomers of 1-methyl derivatives (2A1MIm and 4O1MIm) are compared to those of imidazoles (2AIm and 4OIm), interesting effects of the Me group on electron delocalization in the five-membered ring, as well as in the entire delocalized fragment, containing the exo-heterogroup, can be observed. The Me group is not conjugated with the imidazole ring. In the gas phase, it can mainly act by its polarizability and inductive (field) effects.

Table 2. Me effects ^a on the HOMED5 and HOMED6 indices in mono-substituted azoles ^b.

Isomer of X1MIm	Isomers of XIm	Presence of C-sp3 in the Ring	ΔHOMED5	ΔHOMED6
2A1MIm-6	2AIm-16	no	0.010	0.001
2A1MIm-3a	2AIm-13	no	0.007	0.010
2A1MIm-3b	2AIm-13	no	0.005	0.009
2A1MIm-5a	2AIm-15a	yes	0.025	0.028
2A1MIm-5b	2AIm-15b	yes	0.026	0.030
4O1MIm-6a	4OIm-16a	no	0.004	0.003
4O1MIm-6b	4OIm-16b	no	0.004	0.003
4O1MIm-5	4OIm-15	yes	0.014	0.015

^a Estimated as ΔHOMED = HOMED(X1MIm) − HOMED(XIm), where X corresponds to 2-amino (2A) or 4-hydroxy (4O). HOMEDs taken from Figures S1 and S4 (Supplementary Materials). ^b All isomer abbreviations are in bold like in the text.

summarizes variations in electron delocalization measured by means of the HOMED5 and HOMED6 values when proceeding from the corresponding isomers of 2AIm to 2A1MIm and also from isomers of 4OIm to 4O1MIm. For tautomers-rotamers without C-sp³ in the five-membered ring, changes of the HOMED values are not very large (ΔHOMED ≤ 0.01). However, stronger Me effects take place for isomers containing the endo-C-sp³ atom (ΔHOMED > 0.01). These variations suggest that the Me group affects the bond lengths alternation in the non-aromatic systems with endo-C-sp³ considerably stronger than in already well or moderately delocalized isomers without C-sp³ in the ring.

The HOMED5 and HOMED7 values estimated for the creatinine isomers and included in Figure S5 (Supplementary Materials) vary in analogous way to that for the model azoles. For the aromatic amino-hydroxy isomers (Crea-67a and Crea-67b), they are higher than 0.8. For the imino-hydroxy isomers without endo-C-sp³ (Crea-37aa, Crea-37ab, Crea-37ba, and Crea-37bb) and zwitterion (Crea-36), they are close to 0.7. For isomers containing endo-C-sp³, such as the amino-oxo (Crea-56), imino-hydroxy (Crea-57aa, Crea-57ab, Crea-57ba, and Crea-57bb), and imino-oxo forms (Crea-35a and Crea-35b), HOMED5 and HOMED 7 are close to 0.3 and 0.4, respectively.

Analogous differences in electron delocalization were observed previously for the pyrimidine base isocytosine (iC), constitutional isomer of cytosine, being a structural part of guanine [34]. Isocytosine (C₄H₅N₃O) contains the two endo-N atoms included in the six-membered ring at 1- and 3-positions and the two exo-heterogroups, NH₂ at 2-position and OH at 4-position, like Crea. Among twenty-one isomers possible for iC, we selected the fourteen structures (Figure S8, Supplementary Materials) analogous to those of Crea-isomers (Figure S5, Supplementary Materials). Their HOMED6 and HOMED8 indices estimated for the six-membered ring and for the entire molecule, respectively, are also included in Figure S8. Although Crea (azole with the five-membered ring, seven H atoms, six labile n- electrons, and four labile π-electrons) is structurally different from iC (azine with the six-membered ring, five H atoms, four labile n-electrons, and six labile π-electrons), the HOMEDs variations in Crea-isomers seem to be parallel to those in the corresponding iC-isomers.

Figure 7 illustrates a good linear trend between HOMED5s of Crea-isomers and HOMED6s of iC-isomers estimated for the five- and six-membered rings, respectively, as well as another linear trend between their HOMEDs7 and HOMED8s estimated for the entire conjugated part, containing the ring and exo-heterogroups. The linear relationships with correlation coefficients R higher than 0.98 additionally confirm strong quantitative dependence between electron delocalization and intramolecular proton transfers for analogous tautomeric systems not only between derivatives possessing the six-, or separately, five-membered rings (Figure 6), but also between compounds containing various rings (Figure 7). Note that HOMEDs referring to the tautomer iC-37 and zwitterion Crea-36 fit well the linear relationships. The slopes of the regression lines (0.82 and 0.74) are considerably lower than unity, indicating some important differences in electron delocalization in the series of cyclic azole- and azine-isomers.

Although variations of electron delocalization are parallel in analogous isomeric mixtures of cyclic azoles and azines, no linear trends exist between their energetic parameters (see in the next section). Consequently, there are no linear trends between the geometric and energetic parameters. This suggests that electron delocalization, being a pivotal factor associated with prototropy, is a less important structural phenomenon in the prediction of the tautomeric preferences for the heterocycles containing the exo NH₂ and OH groups. Analogous schemes of intramolecular proton-transfers and electron delocalization seem to characterize mainly the geometric relations of the tautomeric systems. Aromaticity seems to act as a secondary factor on the composition of tautomeric mixtures.

3.3. Thermochemistry of Isomeric Conversions for Title Compounds

Electron delocalization in the tautomeric systems depends on the number of conjugated sites, the number and type of labile electrons, and the positions of labile protons, whereas tautomeric equilibria and tautomeric preferences depend mainly on acid-base properties of the tautomeric sites. Since electronegativity of C, N, and O atoms significantly differ, acid-base properties of –CH₂/=CH, –NH₂/=NH, and –OH/=O sites also differ in the cyclic azoles (2AIm, 4AIm, 2OIm, 4OIm, 2A1MIm, 4O1MIm, and Crea) as well as in the cyclic azines including the pyrimidine bases [33,34,52]. Consequently, we do not observe parallel changes between the geometric and energetic parameters for the investigated isomers included in Figures S1–S5 and S8 (Supplementary Materials). When the relative Gibbs energies for the isomers of mono-amino imidazoles (AIm) are plotted against those for the isomers of mono-hydroxy imidazoles (OIm), and the HOMED7 indices are plotted against the relative Gibbs energies for isomers of 2AIm, 4AIm, 2OIm, and 4OIm, we obtain scatter plots in all cases (Figure S9 in Supplementary Materials). The same is true when ΔGs of Crea-isomers are plotted against ΔGs of iC-isomers, and also when HOMEDs of Crea-isomers are plotted against their ΔGs (Figure 8). There are no linear trends between the geometric and energetic parameters. This confirms our suggestion that electron delocalization cannot be treated as the main factor that dictates tautomeric preferences in creatinine.

The differences in the acid-base properties of the conjugated tautomeric sites are well described by the relative thermochemical quantities (ΔE, ΔH, and ΔG), equilibrium constants (K), and mole fractions (x_i) [1,2,33,36]. The ΔE, ΔH, TΔS, ΔG, K, and x_i calculated at the DFT level for all stable isomers of the mono-substituted imidazoles (2AIm, 4AIm, 2OIm, and 4OIm), selected 1-methyl derivatives (2A1MIm and 4O1MIm), and creatinine (Crea) are listed in Tables S1–S3 (Supplementary Materials). A perusal of these data clearly shows important differences in the tautomeric preferences for the investigated tautomeric compounds (Figure 9). The aromatic forms (≥99.9%) predominate only for the mono-amino model azoles 2AIm, 4AIm, and 2A1MIm. For other derivatives, they belong to minor or rare tautomers. 2OIm prefers the oxo form 13 without endo-C-sp³ (100%), whereas 4OIm and 4O1MIm favor the oxo form 35 (99.8%) and 5 (100%), respectively, with C5-sp³ in the ring. Creatinine containing two exo-heterogroups at the 2- and 4-positions also favors isomers with the endo-C5-sp³ atom, two major imino-oxo isomers 35a and 35b (together 97.7%), and the minor amino-oxo form 56 (2.3%). Tautomeric preferences for isocytosine, taken from refs [34,35], are also included in Figure 9 to show the completely different composition of the tautomeric mixture for iC (derivative of azine) compared to that for Crea (derivative of azole). In the iC-mixture, the aromatic amino-hydroxy 78a (79.67%) and amino-oxo 37 (20.4%) isomers are favored in the gas phase [34]. Isomers of isocytosine containing the endo-C5-sp³ atom belong to the family of exceptionally rare forms.

Our DFT results for creatinine can be compared with some scarce literature data. In 1997, Craw et al. published an article [27], in which only two isomers of creatinine (56 and 35a) were investigated at various HF, MP2, and DFT levels, and the isomer 35a was found to be favored in the gas phase. Applying the PCM methods, a change of the tautomeric preference from 35a in the gas phase to 56 in aqueous solution was documented. Sixteen years later, Gao and coworkers investigated the same isomers of creatinine (35a and 56) in the gas phase (DFT) and aqueous solution (PCM), and they derived an analogous conclusion on the tautomeric-preference change [32]. In 2015, Valadbeigi et al. [13] considered also other tautomers, but not all possible rotamers resulting from conformational and configurational isomerism (see in Table S4, Supplementary Materials). Although calculations have been performed for isolated, micro-, and macro-solvated species at different levels of theory, the results are only partial. Some important isomers have been omitted, for example, the isomer 35b that is favored in the tautomeric mixture in the gas phase. Only Léon et al. in 2021 published an article [14] in which both experimental and theoretical data for creatinine in various phases have been reported, and they showed that three isomers (35a, 35b, and 56) can be detected for gaseous creatinine in high-resolution rotational spectra. The relative energies in vacuo have been estimated by quantum-chemical methods for the complete isomeric mixture. Our DFT results are consistent with these literature theoretical data (Table S4, Supplementary Materials).

3.4. Search for Origins of Tautomeric Preferences in Creatinine

Looking for some chemical origins of tautomeric preferences in creatinine, first we confirmed our DFT results for selected keto-enol conversions in 4-hydroxy-imidazole (4OIm). Using the G2 and G2(MP2) methods [49,50], we carried out calculations for three isomers of 4OIm possessing ΔG < 6 kcal mol⁻¹: aromatic hydroxy form 16a, and two non-aromatic oxo forms containing the C5-sp³ atom in the ring, 15 and 35. The high level Gn theories reproduce sound experimental data for proton-transfer equilibria [33,35,51,52,61,62,63,64,65]. On the basis of our G2 and G2(MP2) thermochemical data compared with those calculated at the DFT level (Table S5, Supplementary Materials), we can see that the differences in the relative energetic parameters calculated at the three levels of theory are very small and close to 1 kcal mol⁻¹. The three methods (DFT, G2, and G2(MP2)) lead to the same conclusion that the non-aromatic tautomer 35 is a favored form in the tautomeric mixture of 4OIm (99.84, 99.97, and 99.96%, respectively). Stability of the keto form 35 is considerably higher than that of the enol isomer 16a. These results confirm that the DFT method has been a good choice for investigation of prototropy in azoles. Additionally, our calculations show that aromaticity does not play an important role for tautomeric preference in 4OIm, contrary to phenol and mono-hydroxy pyridines with the six-membered ring that prefer the aromatic enol forms [33,52]. The energy of aromatic stabilization in 4OIm is probably lower than that of keto-enol conversion. Moreover, the favored tautomer 35 can be stabilized by favorable intramolecular interactions between C5H₂ and n-electrons of N1, and also between N3H and n-electrons of O6. The other keto form 15 possesses lower stability than the favored isomer 35, probably because of the intramolecular interactions that are unfavorable in the case of 15. They correspond to the repulsion of the N1H andC5H₂ groups, and also to the repulsion of the two pairs of n-electrons of N3 and O6.

In the second step, we investigated the effect of the Me group on the tautomeric conversions in 1-methyl derivatives of mono-substituted imidazoles. When going from 2AIm to 2A1MIm, the Me effects can be estimated in 2A1MIm for 1,3-proton shifts from N6 to N3 {amine-imine (amidine) prototropy} and from N3 to C5 (enamine-imine conversion), and also for direct 1,5-proton shift from N6 to C5 (mixture of the two previous prototropic transformations). Analogously, the Me effects can be analyzed in 4O1MIm for 1,3-proton shift from C5 to O6 (keto-enol rearrangement) when going from 4OIm to 4O1MIm. For analysis of these effects, the DFT-calculated relative Gibbs energies can be employed, and the Me effects estimated as differences between ΔGs of the corresponding isomers-pairs of mono-substituted 1-methyl imidazoles X1MIm and imidazoles XIm, where X denotes 2A or 4O: δG(Me) = ΔG(X1MIm) – ΔG(XIm). The Me effects, estimated in this way, are summarized in

Table 3. Me effects ^a on tautomeric equilibria in mono-substituted azoles ^b.

Pair of Isomers for Proton Transfer		Type of Proton Transfer	δG(Me)
X1MIm	XIm
2A1MIm-6→2A1MIm-3a	2AIm-16/36→2AIm-13	N6→N3	−0.5
2A1MIm-6→2A1MIm-3b	2AIm-16/36→2AIm-13	N6→N3	−1.1
2A1MIm-3a→2A1MIm-5a	2AIm-13→2AIm-15a/34b	N3→C5	0.7
2A1MIm-3b→2A1MIm-5b	2AIm-13→2AIm-15b/34a	N3→C5	0.3
2A1MIm-6→2A1MIm-5a	2AIm-16/36→2AIm-15a/34b	N6→C5	0.2
2A1MIm-6→2A1MIm-5b	2AIm-16/36→2AIm-15b/34a	N6→C5	−0.8
4O1MIm-5→4O1MIm-6a	4OIm-15→4OIm-16a	C5→O6	−0.8
4O1MIm-5→4O1MIm-6b	4OIm-15→4OIm-16b	C5→O6	−0.7

^a In kcal mol⁻¹, estimated as δG(Me)= ΔG(X1Mim) − ΔG(Xim), where X corresponds to 2-amino (2A) or 4-hydroxy (4O). ΔG taken from Figures S1 and S4 (Supplementary Materials). ^b All isomer abbreviations are in bold like in the text.

.

The Me effects are not very strong, and they slightly depend on the configuration about =N6H in the 2-imino forms of imidazoles and on conformation about –O6H in 4-hydroxy imidazoles. Generally, the Me group, structurally introduced at N1 in X1MIm, slightly influences the relative Gibbs energies for the considered intramolecular proton transfers by 0.2–1.1 kcal mol⁻¹. So small variations indicate that the Me effects cannot dictate particular stability of the amino-oxo (56) and imino-oxo forms (35a and 35b) for Crea. Note that the estimated δG(Me) values are negative or positive. They correspond to the ΔG decrease or increase between the selected pair of isomers, showing some favored or unfavored Me effects on the selected proton-transfer. The Me group slightly favors the 1,3-proton shift from N6 to N3 in 2A1MIm, in a slightly higher degree for the configuration b than a. It also favors the 1,5-proton shift from N6 to C5 for the same configuration b. In the case of 4O1MIm, only one type of proton-transfer (keto-enol) from C5 to O6 could be analyzed and Me effects estimated. For the two –O6H conformations a and b, ΔGs are lower for the Me-derivative 4O1MIm than for 4OIm, indicating that enolization is slightly favored for 4O1MIm in comparison to 4OIm.

Additionally, we analyzed the effects of the intramolecular interactions between the exo- and endo-functional groups (less or more favorable and less or more unfavorable) resulting from the rotational isomerism about –OH and the geometrical isomerism about =NH, when proceeding from the isomer a to isomer b. For isomers with less or more favorable intramolecular interactions between the exo- and endo-groups, the relative Gibbs energies are lower than for those with less or more unfavorable ones (see in Figures S1–S5 and S8, Supplementary Materials). Difference between the relative Gibbs energies of the isomers a and b can be considered as the measure of difference in the intramolecular interactions {δG(=NH) or δG(–OH) = ΔG(isomer a) – ΔG(isomer b)}. In

Table 4. Effects of intramolecular interactions ^a between the exo- and endo-groups on the stability of the isomers a and b in mono-substituted azoles and di-substituted creatinine compared to those in isocytosine ^b.

Pair of Isomers a and b	δG(=NH)	Pair of Isomers a and b	δG(–OH)
2AIm-15a/34b→2AIm-15b/34a	−3.9	2OIm-46a/56b→2OIm-46b/56a	−0.8
2A1MIm-3a→2A1MIm-3b	−0.6	4OIm-16a→4OIm-16b	3.8
2A1MIm-5a→2A1MIm-5b	−4.9	4OIm-26a→4OIm-26b	4.8
4AIm-23a→4AIm-23b	−0.6	4OIm-46a→4OIm-46b	0.6
4AIm-15a→4AIm-15b	4.4	4OIm-56a→4OIm-56b	5.1
4AIm-35a→4AIm-35b	−1.6	4O1MIm-6a→4O1MIm-6b	3.9
Crea-37aa→Crea-37ba	−0.5	Crea-67a→Crea67b	3.5
Crea-37ab→Crea-37bb	−0.7	Crea-37aa→Crea-37ab	−0.8
Crea-57aa→Crea-57ba	−4.5	Crea-37ba→Crea-37bb	−1.1
Crea-57ab→Crea-57bb	−5.2	Crea-57aa→Crea-57ab	6.3
Crea-35a→Crea-35b	−0.4	Crea-57ba→Crea-57bb	5.6
iC-38aa→iC-38ba	7.5	iC-78a→iC-78b	4.4
iC-38ab→iC-38bb	6.6	iC-38aa→iC-38ab	−2.4
iC-58aa→iC-58ba	0.6	iC-38ba→iC-38bb	−3.3
iC-58ab→iC-58bb	−0.4	iC-58aa→iC-58ab	8.0
iC-35a→iC-35b	5.1	iC-58ba→iC-58bb	7.0

^a In kcal mol⁻¹, estimated as δG(=NH) or δG(–OH) = ΔG(isomer a) − ΔG(isomer b), ΔG taken from Figures S1–S5 and S8 (Supplementary Materials). ^b All isomer abbreviations are in bold like in the text.

, the effects of δG(=NH) and δG(−OH), estimated in this way for isomers of mono-substituted imidazoles (2AIm, 2A1MIm, 4AIm, 2OIm, 4OIm, and 4O1MIm) and creatinine (Crea), are compared with those for the corresponding isomers of isocytosine (iC).

The comparison indicates that some absolute δG values referring to changes in the intramolecular interactions for the isomers a and b in the mono-substituted azoles (2AIm, 2A1MIm, 4AIm, 2OIm, 4OIm, and 4O1MIm) are considerably higher than the Me effects in 2A1MIm and 4O1MIm (Table 3). The strongest effects (3.8–5.1 kcal mol⁻¹) take place for the tautomers, for which favorable interactions in a change into unfavorable interactions in b and vice versa. When interactions in both isomers (a and b) are unfavorable or favorable, the absolute δG values vary from 0.6 to 1.6 kcal mol⁻¹. Analogous effects are observed for Crea- and iC-isomers, for which the absolute δG values vary from 0.4–1.1 to 3.5–6.3 and from 0.4–3.3 to 4.4–8.0 kcal mol⁻¹, respectively. Although favorable intramolecular interactions between the functional exo- and endo-groups influence the stability of particular isomers (a or b) and reduce the relative Gibbs energies, these interactions can be considered as secondary factors that only change isomer-orders. In the case of Crea-isomers, they have slight effects on the energetic-order of the favored imino-isomers 35a and 35b (−0.4 kcal mol⁻¹), because similar intramolecular interactions operate in the two isomers between the exo =NH and endo NCH₃ and NH groups. A different situation takes place for the aromatic amino-hydroxy iC-isomers (78a and 78b), for which the difference between the favorable interactions in 78a and the unfavorable interactions in 78b considerably reduces the Gibbs energy of 78a (by 4.4 kcal mol⁻¹) that it predominates in the iC-isomeric mixture [34].

Finally, in the last step, we analyzed the effects of the additional functional group on the amine-imine (amidine), enamine-imine, and keto-enol conversions when proceeding from a pair of X1MIm-isomers to the corresponding pair of Crea-isomers. The two heteroatomic groups (NH₂ and OH) belong to the family of electron-donating substituents. In the gas phase, they act by the sum of their polarizability, field-inductive, and resonance effects. Additionally, they can interact (favorable or unfavorable) with the endo neighboring groups. Hence, the total effects of the additionally introduced exo-group can strongly influence the proton-transfer for the group already present in the molecule. For the estimation of these effects, the relative Gibbs energies can be used for the corresponding proton-transfers, and the effects of 2-NH₂ and 4-OH can be calculated as differences between ΔGs of the corresponding pairs of Crea-isomers and X1MIm-isomers: δG(2-NH₂) or δG(4-OH) = ΔG(Crea) − ΔG(X1MIm). The calculated δG(2-NH₂) and δG(4-OH) values are given in

Table 5. Effects of exo-heterogroups (2-NH₂ and 4-OH) ^a on tautomeric equilibria for creatinine ^b.

Pair of Isomers for Proton Transfer		Proton Transfer	δG(4-OH)	δG(2-NH2)
Crea	2A1MIm
Crea-67a→Crea-37aa	2A1MIm-6→2A1MIm-3a	N6→N3	6.47 (a)
Crea-67a→Crea-37ba	2A1MIm-6→2A1MIm-3b	N6→N3	6.56 (a)
Crea-67b→Crea-37ab	2A1MIm-6→2A1MIm-3a	N6→N3	2.17 (b)
Crea-67b→Crea-37bb	2A1MIm-6→2A1MIm-3b	N6→N3	2.04 (b)
Crea-37a→Crea-57aa	2A1MIm-3a→2A1MIm-5a	N3→C5	−16.67 (a)
Crea-37a→Crea-57ba	2A1MIm-3b→2A1MIm-5b	N3→C5	−16.39 (a)
Crea-37b→Crea-57ab	2A1MIm-3a→2A1MIm-5a	N3→C5	−9.53 (b)
Crea-37b→Crea-57bb	2A1MIm-3b→2A1MIm-5b	N3→C5	−9.69 (b)
Crea-67a→Crea-57aa	2A1MIm-6→2A1MIm-5a	N6→C5	−10.20 (a)
Crea-67a→Crea-57ba	2A1MIm-6→2A1MIm-5b	N6→C5	−9.83 (a)
Crea-67b→Crea-57ab	2A1MIm-6→2A1MIm-5a	N6→C5	−7.36 (b)
Crea-67b→Crea-57bb	2A1MIm-6→2A1MIm-5b	N6→C5	−7.65 (b)
Crea-67a→Crea-56	4O1MIm-6a→4O1MIm-5	O6→C5		−8.69
Crea-67b→Crea-56	4O1MIm-6b→4O1MIm-5	O6→C5		−8.21

^a In kcal mol⁻¹, estimated as δG(2-NH₂) = ΔG(Crea) − ΔG(2A1MIm), δG(4-OH) = ΔG(Crea) – ΔG(4O1MIm). ΔG taken from Figures S1, S4, and S5 (Supplementary Materials). ^b All isomer abbreviations are in bold like in the text.

.

Interestingly, the total internal effects of the exo-heterogroups are very strong and can be responsible for the change of the tautomeric preferences in Crea. Although the additional exo –OH group, structurally linked to C4 in 2A1MIm, increases ΔGs for proton transfer from N6 to N3 in Crea by ca. 2 kcal mol⁻¹ for conformation b and by 6–7 kcal mol⁻¹ for conformation a, the successive proton-transfer from N3 to C5 is so favorable in Crea in comparison to 2A1MIm that ΔGs are strongly reduced by 9–10 kcal mol⁻¹ for conformation b, and even by 16–17 kcal mol⁻¹ for conformation a. Consequently, direct proton transfer from N6 to C5 is also strongly favored in Crea. The ΔG values decrease by 7–8 kcal mol⁻¹ for conformation b and by ca. 10 kcal mol⁻¹ for conformation a. The additional exo NH₂ group, structurally introduced in 4O1MIm at 2-position, also reduces ΔGs for proton transfer from O6 to C5 in Crea when compared to those in 4O1MIm by 8–9 kcal mol⁻¹. The high ΔGs-reduction effects of the additional exo-groups indicate that they can be the main factors that influence tautomeric preferences in Crea.

4. Conclusions

The application of the same level of theory for investigation of the complete tautomeric, conformational, and configurational transformations in creatinine and model azoles gave us the possibility to find some origins for exceptional tautomeric preferences in creatinine, and also to explain why the non-aromatic amino-oxo (Crea-56) and imino-oxo tautomers (Crea-35) are more stable in the gas phase than the aromatic amino-hydroxy form (Crea-67). On the basis of our DFT data for creatinine and model azoles, compared to those previously reported for the complete isomeric conversions in pyrimidine nucleic acid bases and their model azines [33,52], we can derive the following conclusions.

Aromaticity is not the main factor that influences the tautomeric preference in creatinine containing the five-membered ring, contrary to isocytosine possessing the six-membered ring [34,35]. Nevertheless, variations of electron delocalization in isomers of the two molecules, having the tautomeric sites at analogous positions, are parallel. The aromatic isomers with the labile protons at the exo-groups are well delocalized and their HOMED indices (measure of electron delocalization) are larger than 0.8. The imino-oxo isomers without endo-C-sp³ are moderately delocalized and their HOMED indices are between 0.7 and 0.8, and those with C-sp³ in the ring are weakly delocalized and their HOMED indices are lower than 0.5. Good linear relationships exist between the HOMED indices for isomers of creatinine and isocytosine (Figure 7). However, variations of electron delocalization (HOMEDs) are not parallel to those of isomeric stability (measured by ΔGs), because of the lack of linear trends between energetic parameters (ΔGs) of their isomers (Figure 8).

Only detailed analyses of various internal effects in investigated derivatives such as the electronic effects of the exo-groups (Me, NH₂, and OH) and the intramolecular interactions between the exo- and endo-heterogroups made it possible to select the most important factors that decide about the tautomeric preferences in creatinine. We found that the Me group at N1 has a small effect on the tautomeric conversion {δG(Me) not higher than 1 kcal mol⁻¹, see in Table 3}. The effects of favorable intramolecular interactions between exo- and endo-heterogroups are slightly stronger, and in some cases, the relative Gibbs energies change even by 5–6 kcal mol⁻¹ (Table 4). The intramolecular interactions affect mainly relative stabilities of the isomers a and b. They only slightly influence tautomeric preferences in creatinine {δG(=NH) < 1 kcal mol⁻¹ for pair of the favored imino-oxo isomers Crea-35a and Crea-35b}.

The most important internal effects that strongly change the relative Gibbs energies result from the presence of additional exo-group in creatinine when compared with model mono-substituted 1-methyl imidazoles 2A1MIm and 4O1MIm (Table 5). Figure 10 summarizes the selected effects of the additional exo-heterogroup. The NH₂ group introduced at 2-position in Crea strongly favors the proton-transfer from O7 to C5 when compared to the analogous one in 4O1MIm, and its total effect can explain significant participation of the amino-oxo tautomer (56) in the tautomeric mixture of creatinine. On the other hand, the introduction of the more stable keto form in 2A1MIm favors proton transfer from N6 to N3 and can explain the high stability of the imino-oxo isomers (35a and 35b). These energetic effects in derivatives with the five-membered ring are completely different from those in isocytosine with the six-membered ring, for which isomers with endo-C-sp³ are exceptionally rare forms and the aromatic amino-hydroxy form iC-78a is favored [34,35].