DFT studies on one-electron oxidation and one-electron reduction for 2- and 4-aminopyridines

Quantum-chemical calculations {DFT(B3LYP)/6-311+G(d,p)} were performed for all possible tautomers (aromatic and nonaromatic) of neutral 2- and 4-aminopyridines and their oxidized and reduced forms. One-electron oxidation has no important effect on the tautomeric preference for 2-aminopyridine. The amine tautomer is favored. However, oxidation increases the stability of the imine NH tautomer, and its contribution in the tautomeric mixture cannot be neglected. In the case of 4-aminopyridine, one-electron oxidation increases the stability of both the amine and imine NH tautomers. Consequently, they possess very close energies. As major tautomers, they dictate the composition of the tautomeric mixture. The CH tautomers may be considered as very rare forms for both neutral and oxidized aminopyridines. A reverse situation takes place for the reduced forms of aminopyridines. One-electron reduction favors the C3 atom for the labile proton for both aminopyridines. This may partially explain the origin of the CH tautomers for the anionic states of nucleobases containing the exo NH2 group.


Introduction
Intramolecular proton transfer, called prototropic tautomerism or prototropy, is the simplest process that occurs for natural products (bioamines such as histamine, amino acids such as histidine and arginine, nucleobases such as cytosine, thymine, uracil, adenine, and guanine, porphyrins, etc.) [1][2][3][4][5]. This elementary conversion dictates their structure, acid-base properties, hydrogen bond formation, solvent interactions, and other physicochemical properties. It influences also the mechanism of many chemical reactions and biochemical transformations, including those involving specific interactions with proteins, enzymes, and receptors.
To understand prototropic tautomerism for nucleobases possessing the exo NH 2 group (cytosine and adenine given in Fig. 1), it is very important to understand first the tautomeric conversions for their model compounds. For our investigations, we chose the neutral and unpaired ionic forms of convenient modelssix membered rings with the exo NH 2 group and the endo N-aza atom(s). In our previous papers, we studied the enamine-imine conversions for the neutral and redox forms of aniline (AN) [6] and the amineimine and enamine-imine conversions for the neutral and redox forms of 4-aminopyrimidine (4APM) [7]. We found an interesting change of the tautomeric preference for the unpaired anions. To complete these studies for model aminoazines and to analyze effects of the N-aza group(s), we chose 2-(2APY) and 4-aminopyridines (4APY). We applied the same methods as previously described for AN and 4APM [6,7].
In the literature, one can find numerous papers for neutral aminopyridines. For example, tautomeric equilibria for their methyl derivatives have been theoretically studied using the DFT, PCM and SCI-PCM methods [8]. The amine form strongly dominates in the gas phase as well as in solution. The fixed imine form {2(1H)-pyridinimine} has been investigated for its 1-methyl derivative [9][10][11][12][13]. Alkorta and Elguero analyzed the dimerization of 2APY by the hydrogen bond formation and studied the dimerization effect on tautomeric equilibria using ab initio methods [14]. They also discussed the substituent effects on the tautomeric preferences. Interesting studies have been carried out by chemists from Japan and Taiwan. They studied the hydrogen bonding and the imine form formation for the 2APY/ acetic acid system in the ground and excited state using various spectroscopic and quantum-chemical methods [15][16][17][18][19][20]. Photoinduced reversible amine-imine tautomerism has also been detected for 2APY and for its derivatives by Ar-matrix-isolation infrared spectroscopy and DFT calculations [21][22][23]. To our knowledge, there is no report on prototropy for redox forms of 2APY and 4APY, which may be formed in the presence of various oxidizing and reducing agents.
In this paper, we studied the consequences of oneelectron oxidation and one-electron reduction on tautomeric equilibria and on composition of the tautomeric mixture for 2-(2APY) and 4-aminopyridine (4APY). We considered various oxidation states of aminopyridines, neutral (2APY and 4APY), oxidized (2APY +• and 4APY +• ), and reduced state (2APY -• and 4APY -• ). To investigate variations of πelectron delocalization for the ring and for the whole tautomeric system, we analyzed the geometrical parameters of all possible tautomers for the neutral and ionic forms of aminopyridines. We discussed also the spin populations for heavy atoms in the ionic forms. We estimated the tautomeric equilibrium constants and the oxidation and reduction energies.
Finally, we compared our results with those reported previously for aniline [6] and 4-aminopyrimidine [7], and we discussed effects of the N-aza group(s).

Computational details
Geometries of all neutral and ionic tautomers of 2-and 4aminopyridines were fully optimized without symmetry constraints employing the DFT(B3LYP) method [24][25][26] and the 6-311+G** basis set [27]. For all neutral, oxidized, and reduced isomers, the DFT minima were found with all real frequencies and thermodynamic parameters such as the energy (E), enthalpy (H), entropy (S), and Gibbs energy (G for T0298.15 K) were calculated at the same level of theory. All calculations were performed using the Gaussian 03 program [28].

Results and discussion
Choice of methods For our investigations on prototropy for the neutral and redox forms of aminopyridines, we chose quantumchemical methods because experimental techniques are incapable of detecting less than 0.1 % of minor tautomer(s) [15][16][17][18][19][20][21][22][23]. Tautomeric conversions are very fast and reversible processes, and thus it is difficult to separate and to study individual tautomers. Applying spectroscopic techniques such as ultraviolet (UV), infrared (IR), Raman, nuclear magnetic resonance (NMR), microwave (MW), mass spectrometry (MS), etc. to tautomeric mixtures one may identify signals of significant intensities solely for major tautomers (NH forms). Minor tautomers (CH forms) cannot be detected, because their amounts are too small (< 0.1 %) and their signals are in the background.
We applied the DFT method [24] with the B3LYP functional [25,26] and the 6-311+G(d,p) basis set with the diffuse and polarization functions [27]. The DFT method has been applied for proton transfer reactions, including the tautomeric conversions in the gas phase that models a polar environment [29][30][31][32][33][34][35][36][37]. However, it should be mentioned here that the B3LYP method should be very carefully used for tautomeric systems. In some cases, e.g., for amide-iminol equilibrium in 2-hydroxypyridine/2-pyridone, where the relative energies for the major tautomers are close to zero, the B3LYP predictions overestimate the experimental data [38]. Errors are slightly larger than 1 kcal mol -1 . For this reason, we tested various levels of theory for aniline [6] the parent system of azaanilines: B3LYP/6-311+G(d,p), B3LYP/6-311++G(3df,3pd), B3LYP/aug-cc-pVDZ, and G2, and we found that (i) the B3LYP/6-311+G(d,p) level is sufficient for the tautomeric  Fig. 1 Nucleobases with the NH 2 group and their convenient models systems of amino aromatics, (ii) the use of different basis set for DFT calculations has no important effect on the values of geometric and energetic parameters, and (iii) the DFT relative Gibbs energies are close to those at the G2 level, recommended for the proton-transfer reactions in the gas phase [39,40]. Using the quantum-chemical methods, we can study all possible prototropic tautomers and all possible tautomeric conversions for various oxidation states of 2-and 4aminopyridines: the neutral state (APY), the unpaired cation (APY − e → APY +• ), and the unpaired anion (APY + e → APY -• ). Transferring an electron from or to the tautomeric molecule may change the stabilities of individual tautomers, and consequently, the composition of the tautomeric mixture.

Possible tautomeric equilibria
Aminopyridines 2APY and 4APY contain two functional groups, the exo NH 2 group and the endo N-aza group which are n-π and π-π conjugated with the endo >C0C< groups. They exhibit prototropic tautomerism. One labile proton can move from the exo NH 2 group to the endo N or C atom. Combination of two types of conversions: amine- leads to six tautomeric equilibria for four tautomers (Scheme 1 and 2), one amine form with the labile proton at the exo N atom, and three imine form with the labile proton at the endo N and C atoms for the NH and CH tautomers, respectively. For all tautomers, the intramolecular proton-transfer is accompanied by migration of πelectrons.
Due to geometric isomerism of the exo 0NH group in 2aminopyridine (Scheme 1), two isomers are possible for 2APY2-2APY4, one (a) with the imine H atom synperiplanar to the ring N1 atom and the other one (b) with the imine H atom antiperiplanar to the ring N1 atom. Similarly, two isomers are possible for the imine forms 4APY2 and 4APY4 of 4-aminopyridine (Scheme 2), one (a) with the imine H atom synperiplanar to the ring C3 (for 4APY2) and C5 (for 4APY4) atom, and the other one (b) with the imine H atom antiperiplanar. The structures 4APY2a and 4APY4a, and also 4APY2b and 4APY4b are identical for 4-aminopyridine, and thus the tautomeric equilibrium constants K T for the conversions 4APY2a → 4APY4a and 4APY2b → 4APY4b are equal to unity. However, to estimate well the composition of the tautomeric mixture, all isomers (4APY1-4APY4) should be considered for 4-aminopyridine. In the literature, four tautomers have been solely considered for the neutral forms of methyl derivatives of aminopyridines [8].
The DFT-calculated CC and CN bond lengths for the neutral and redox isomers of 2-and 4-aminopyridines are given in Figs. 2 and 3, respectively. For neutral 2APY1, 2APY2a, and 2APY2b, they are close to those calculated by Akai et al. [21] at the B3LYP/6-31++G(d,p) level. Differences in bond lengths are not larger than 0.01 Å. Variations of the CC and CN bond lengths for the neutral and charged isomers of aminopyridines are also similar to those previously observed for aniline [6] and 4-aminopyrimidine [7]. Generally, the CC bond lengths for 2APY and 4APY vary from 1. 34  When proceeding from the neutral isomers to their charged ions, the CC and CN bond lengths vary by 0.0-0.9 Å for the radical cations and by 0.0-0.7 Å for the radical anions. These variations influence π-electron delocalization in the ring (six atoms) and also in the whole tautomeric system (seven atoms including the exo N atom). In this paper, we quantitatively measured the changes of πelectron delocalization by means of the geometry based harmonic oscillator model of electron delocalization (HOMED) index [6,7,35,[45][46][47][48] which describes well any type of conjugation (π-π, n-π, and σ-π) possible in heteroatomic systems. This index was applied here to the DFT-calculated bond lengths.

HOMED indices
The HOMED procedure has been described in detail in ref [46] and applied to various cyclic and acyclic π-electron systems containing heteroatoms [6,7,35,[45][46][47][48]. The HOMED index is based on the original harmonic oscillator model of aromaticity (HOMA) index [49,50]. The HOMA index reformulated in 1993 [51] seems to be inappropriate for π-electron delocalized systems containing heteroatoms. The main reason is a use of different measures of π-electron delocalization for the reference CC and CX bonds [6,7,35,[45][46][47][48]. The reformulated HOMA index can be solely applied for homoaromatics. Its application to heteroaromatics leads to artificial positive or negative values for well delocalized π-electron systems [46].
The HOMED index can be estimated on the basis of the theoretically derived bond lengths using the following This equation is similar to that for the reformulated HOMA index [51], but the values of its parameters (α and R o ) are different. In this equation, α is a normalization constant, R o is the optimum bond length (assumed to be realized for fully delocalized system), R i are the running bond lengths in the system, and n is the number of bonds taken into account. The following R o values (in Å), calculated at the B3LYP/6-311+G(d,p) level [46], were taken here: 1.394 (benzene) and 1.334 (1,3,5triazine) for the CC and CN bonds, respectively. Similarly as in the case of aniline [6], 4-aminopyrimidine [7], and other heteroaromatic molecules [46], the normalization α constants equal to 88.09 (CC) and 91.60 (CN) were used for the ring (six bonds), and 80.90 (CC) and 84.52 (CN) for the whole tautomeric system (seven bonds including the exo N atom). The α constants differ from those employed for the reformulated HOMA index, because of use of simple only slightly delocalized reference CC (ethane and ethene [46] instead of 1,3butadiene [51]) and CN bonds (methylamine and methylimine [46,51]), and different procedures for the even and odd number of bonds in the system [6,7,45,46]. For estimation of the α constants, the reference CC and CN bond lengths were calculated at the B3LYP/6-311+G(d,p) level.
Similarly as for aniline [6] and 4-aminopyrimidine [7], the HOMED indices, estimated for the neutral isomers, are close to unity for the amine tautomers 2APY1 (Fig. 4) and 4APY1 (Fig. 5). Due to cross π-π and n-π conjugations possible in the whole tautomeric system, i.e., conjugation of n-electrons of the exo NH 2 group with π-electrons of the ring, the HOMED indices decrease when going from the ring (six bonds) to the whole tautomeric system (seven bonds). Transfer of the proton to the endo N and C atom decreases the HOMED indices by 0.2-0.3 and 0.6-0.7 units, respectively. The imine NH isomers (2APY2a, 2APY2b, and 4APY3) are less delocalized than the amine tautomers (2APY1 and 4APY1), but more delocalized than the imine CH isomers (2APY3a, 2APY3b, 2APY4a, 2APY4b, 4APY2a/4a, and 4APY2b/4b). The N1 atom taking the labile proton retains its planarity in the neutral form due to n-π conjugation similar to that for the N1 atom in the five membered ring of pyrrole, pyrazole, imidazole, etc., whereas the C3 and C5 atoms (C-sp 3 ), taking the labile proton, lose their planarity. For the imine CH isomers, π-electrons of the π-π conjugated −C0N−C0N−C0NH fragment are  . Fig. 2 The DFT-calculated CC and CN bond lengths (in Å) for isomers of neutral 2APY and its unpaired ions 2APY +• and 2APY -• cross hyperconjugated with σ-electrons of the CH 2 group. Usually, σ-π hyperconjugation leads to smaller electron delocalization than π-π and n-π conjugations [46]. Thus, the imine NH tautomers are still aromatic but the imine CH tautomers already have nonaromatic character. One-electron oxidation and also one-electron reduction decrease aromaticity of the amine tautomers (2APY1 and 4APY1). The HOMED indices are reduced by less than 0.1 units. On the other hand, one-electron oxidation increases the HOMED indices for the imine NH tautomers (2APY2a, 2APY2b, and 4APY3) by 0.1-0.2 units increasing also their aromatic character. One-electron reduction has a slight effect. It changes the HOMED indices for the NH tautomers by less than ±0.1 units. Interestingly, for the imine CH tautomers (2APY3a, 2APY3b, 2APY4a, 2APY4b, 4APY2a/4a, and 4APY2b/4b), both one-electron oxidation and oneelectron reduction increase the HOMED indices, but by different degree (by 0.2-0.4 and 0.1-0.2 units, respectively). For some cationic CH isomers (e.g., 2APY3a +• , 2APY3b +• , 2APY4a +• , and 4APY2b/4b +• ), the HOMED indices for the whole tautomeric system (seven bonds) are even close to 0.8, indicating exceptional π-electron delocalization.

Spin densities
Some additional information on delocalization of one unpaired electron may be derived on the basis of the distribution of the unpaired spin density calculated for the charged radicals of aminopyridines. The total atomic spin densities calculated at the DFT/B3LYP/6-311+G(d,p) level for seven heavy atoms in 2APY +• and 2APY -• , also in 4APY +• and 4APY -• are given in Figs. 6 and 7, respectively. Unfortunately, there is no experimental data for the aminopyridine charged radicals and no comparison can be made. Our DFT calculations indicate that the spin density exists on all atoms of the charged radicals. In the case of the amine radical cations 2APY1 +• and 4APY1 +• , most of the density is carried by the N1 and N7 atoms, and also by the C3 and C5 atoms. On the C2, C4, and C6 atoms, a spin population is also present, but it is negative or close to zero. For the amine radical anions 2APY1 -• and 4APY1 -• , most of the density is localized on the C2, C4, and C6 atoms. On the other atoms, a spin population also exists, but it is considerably lower or negative.
For the imine tautomers, the distribution of the spin density depends on the position of the labile proton and

Tautomeric preferences
As expected [6][7][8][14][15][16][17][18][19][20][21][22][23], the amine tautomers 2APY1 and 4APY1 with the labile proton at the exo N atom has the lowest energy for neutral aminopyridines. Similar to aniline [6] and 4-aminopyrimidine [7], aromaticity of the six membered ring seems to be one of the most important factors that dictates the high stability of the neutral amine tautomers and their tautomeric preference (100 %) in the tautomeric mixture. Tables 1 and 2  The neutral imine NH tautomers 2APY2 and 4APY3 possessing the labile proton at the endo N atom have larger energies than 2APY1 and 4APY1 by 14-17 kcal mol -1 at the B3LYP/6-311+G(d,p) level. Energetically favorable and energetically unfavorable interactions possible for the structures a and b of the 2APY2 tautomer differentiate their energies by only 3 kcal mol -1 . Slightly larger energy differences (4-5 kcal mol -1 ) occur for the structures a and b of the imine CH tautomers 2APY3 and 2APY4. In the case of the imine CH tautomers 4APY2/4, this energy difference is not larger than 1 kcal mol -1 . However, transfer of the labile proton to the endo C atom exceptionally decreases the stability of both isomers (a and b) of 2APY3, 2APY4, and 4APY2/4. Their energies are larger than that of 2APY1 and 4APY1 by 29-35 kcal mol -1 . The contributions of all imine NH and CH isomers in the tautomeric mixture of 2APY and 4APY are very low (< 1⋅10 -8 %).
According to the DFT results, one-electron oxidation has no important effect on the tautomeric preference in the gas phase for 2-aminopyridine ( Table 1). The amine tautomer 2APY1 +• has the lowest energy. However, oxidation changes the relative energies for the imine tautomers, and consequently, it changes also the composition of the tautomeric mixture. For the imine NH tautomer, the relative Gibbs energy decreases to 4 kcal mol -1 for 2APY2b +• with energetically favorable configurations and to 8 kcal mol -1 for 2APY2a +• with energetically unfavorable configurations. The reduction of the relative Gibbs energies for the NH isomers augments their contributions in the tautomeric mixture of 2APY +• . The percentage contents of 2APY2b +• and 2APY2a +• are considerably larger (0.1 and 3⋅10 -4 %, respectively) than those in neutral 2APY (< 1⋅10 -8 %). They cannot be neglected in the tautomeric mixture of 2APY +• . Quite a different situation takes place for the imine CH tautomers. The relative Gibbs energies increase to more than 50 kcal mol -1 for both isomers (a and b) of 2APY3 +• and 2APY4 +• . Change of the configuration for the exo 0NH group has a small effect on the relative Gibbs energies (< 3 kcal mol -1 ). The percentage contents of the imine CH isomers are very low (< 1·10 -29 %). As very rare isomers, they may be neglected in the tautomeric mixture of 2APY +• .
In the case of 4-aminopyridine, one-electron oxidation also changes the DFT-stabilities of the amine 4APY1 +• and imine 4APY3 +• tautomers ( Table 2) but in higher degree than for 2-aminopyridine (Table 1). Consequently, 4APY3 +• , instead of 4APY1 +• , seems to be the favored tautomer for the radical cation. Since the relative Gibbs energy between the two tautomers is not very large (ca. 2 kcal mol -1 ), they may dictate the composition of the tautomeric mixture (95.7 and 4.3 %, respectively). The relative Gibbs energies of the imine CH isomers 4APY2a/ 4a +• and 4APY2b/4b +• are larger than 40 kcal mol -1 and they seem to not depend on the configuration of the exo 0NH group. The two CH isomers may be neglected in the tautomeric mixture of 4APY +• . Their percentage contents are exceptionally low (< 1·10 -28 %).
One-electron reduction changes the tautomeric preference for both 2-and 4-aminopyridines. For reduced aminopyridines, the imine CH isomers 2APY4a -• and 4APY2b/ 4b -• with the labile proton at the endo C3/C5 atom and with the imine H atom antiperiplanar to the C3/C5 atom have the lowest energies at the B3LYP/6-311+G(d,p) level (Tables 1  and 2 larger Gibbs energies than 2APY4a -• and 4APY2b/4b -• by ca. 5 and 1 kcal mol -1 , respectively. The other reduced tautomers have larger Gibbs energies than those of 2APY4a -• and 4APY2b/4b -• by 4-16 kcal mol -1 . The tautomeric mixture of 2APY -• seems to consist mainly of 2APY4a -• (99.9 %) and that of 4APY -• contains 4APY2b/ 4b -• and 4APY2a/4a -• (86.8 and 13.2 %, respectively). The percentage contents of the other isomers are lower than 0.1 %. If we consider solely the DFT-favored neutral and redox forms of 2-and 4-aminopyridines, the following scheme of the redox reactions can be drawn (Scheme 3). The percentage contents of the major amine and imine tautomers are also given in this scheme. Generally, the tautomeric preferences for aminopyridines are the same for the neutral and reduced forms. The neutral tautomeric mixtures of 2APY and 4APY contain mainly the amine tautomers (100 %), and those of 2APY -• and 4APY -• consists of the major imine CH tautomers (99.9-100 %) and of the minor amine tautomers (≤ 0.1 %). Solely, the tautomeric preferences for the oxidized forms seem to be dependent on the positions of the exo and endo N atoms. The amine tautomer (99.9 %) is favored for 2APY +• whereas the imine NH tautomer (95.7 %) dominates for 4APY +• .
Since the relative energies between the major tautomers of the ionic forms of 4APY are only slightly larger than the error of the B3LYP method estimated for 2-hydroxypyridine/2hydroxypyridone (ca. 1 kcal mol -1 ) [38], the DFT results should be very carefully used for interpretation of oxidation and reduction reactions. A slight change of environment may change the relative energy values, and consequently, it may change the composition of the tautomeric mixture.
The relative entropy terms (TΔS T ) for the neutral and redox forms of 2-and 4-aminopyridines are not larger than ±1 kcal mol -1 . This may suggest that all tautomeric conversions are isoentropic in the gas phase and do not depend on the oxidation or reduction state of the molecule. Generally, there are not large structural changes during tautomerization. Some exceptions are those resulting from loss of the molecule planarity. The relative thermal corrections (from zero to 298.15 K) are close to zero, and thus, ΔE T ≈ ΔH T ≈ ΔG T . All these observations suggest that the relative thermodynamic parameters do not depend very much on temperature (thermal corrections and entropy terms cancel out), and thus the percentage contents of the same order of magnitude may be expected for individual tautomers in a jet- cooled experiments. Very low thermal corrections and entropy terms have been also observed for aniline [6] and 4-aminopyrimidine [7].

Oxidation and reduction energies
For each isomer of 2APY and 4APY, thermodynamic parameters of oxidation (ΔE ox , ΔH ox , TΔS ox , and ΔG ox ) and reduction (ΔE red , ΔH red , TΔS red , and ΔG red ) were estimated at the DFT(B3LYP)/6-311+G(d,p) level. They were calculated as differences between the corresponding parameters for the charged and neutral forms. First perusal of these parameters indicates that one-electron oxidation is a very endothermic process ( Table 3). The lowest energies (173-174 kcal mol -1 ) are needed for the imine NH tautomers, and the largest energies (201-205 kcal mol -1 ) for the imine CH tautomers. For the amine tautomers, the oxidation Gibbs energies (ΔG ox 183-192 kcal mol -1 ) are between those for the imine NH and CH tautomers. Change of the configuration of the imine H atom in structures a and b has small effect on the ΔG ox values (< 3 kcal mol -1 ). Interestingly, the literature ionization energies for 2aminopyridine (8.5 eV [52], 1 eV 023.06037 kcal mol -1 ) and for 4-aminopyridine (8.8 eV [52]) are of the same order of magnitude as the DFT estimated energies of oxidation. One-electron reduction is a more favorable process than one-electron oxidation. Comparison of the DFT calculated thermodynamic parameters for the reduced and neutral tautomers of 2APY and 4APY shows that one-electron reduction requires less than 20 kcal mol -1 (Table 4). For the imine CH isomers, the reduction Gibbs energies (ΔG red ) are even negative, indicating that aminopyridines may take spontaneously one electron from a reducing agent. They may be more easily transformed to the reduced forms than the imine NH and amine tautomers for which the ΔG red values are positive. This trend confirms preference of the imine CH tautomers in the tautomeric mixtures of 2APY -• and 4APY -• . Change of the Table 2 The DFT-calculated relative thermodynamic parameters (ΔE T , ΔH T , TΔS T , ΔG T , and pK T ) and the percentage contents (x in %) for the neutral isomers of 4APY and for its unpaired ions 4APY +• and 4APY -• a ΔZPE included b In kcal mol -1 c At 298.15 K d Thermodynamic parameters relative to those for 4APY1 e Thermodynamic parameters relative to those for 4APY3 +• f Thermodynamic parameters relative to those for 4APY2b/4b -•

Isomer
Charge  [53] for the electron affinity of 2APY and 4APY and no comparison can be made. Similar to the proton-transfer interconversions, the entropy terms for both one-electron oxidation (TΔS ox ) and one-electron reduction (TΔS red ) are not very large (≤ 1.3 kcal mol -1 ). This suggests that the electron-transfer processes (electron-loss and electron-gain) are isoentropic in the gas phase for aminopyridines. The relative thermal corrections are also close to zero, and thus, ΔE ox ≈ ΔH ox ≈ ΔG ox and ΔE red ≈ ΔH red ≈ ΔG red . If we consider solely the most favored neutral and redox forms of aminopyridines and the favored oxidation and reduction processes (Scheme 3), the following DFT Gibbs energies are found: 183 kcal mol -1 for 2APY − e → 2APY +• , 190 kcal mol -1 for 4APY − e → 4APY +• , 11 kcal mol -1 for 2APY − e → 2APY -• , and 12 kcal mol -1 for 4APY − e → 4APY -• . The oxidation and reduction reactions for 4APY requires more energy (by 7 and 1 kcal mol -1 , respectively) than those for 2APY. Larger difference for the oxidation reaction results from the difference in the tautomeric preferences, 2APY1 +• and 4APY3 +• . Interestingly, the literature ionization energy difference for 2APY and 4APY is also equal to 7 kcal mol -1 (0.3 eV [52]).

N-aza-effects
The amino derivatives of azines studied here (2APY and 4APY) and previously (4APM) can be considered as N-aza derivatives of aniline (AN). All of them exhibit prototropic tautomerism (Scheme 4). Such kind of treatment of azaanilines gives the possibility to estimate effects of the N-aza group in different position of aniline, 2-N, 4-N and 2,4-N 2 . In this paper, we analyzed the N-aza effects on π-electron delocalization, intramolecular proton-transfer processes (prototropy) and redox reactions for azaanilines. We compared the corresponding parameters (HOMED, pK T , ΔG ox , and ΔG red ) calculated at the same level of theory, DFT (B3LYP)/6-311+G(d,p), i.e., those reported in refs [6] and [7] and also those given here in Figs. 4 and 5 and Tables 1,  2, 3, and 4. Table 5 summarizes the N-aza effects on the HOMED indices estimated for the ring (six bonds) when going from similar isomers of aniline (AN) without the N-aza group to those of 2-aminopyridine (2APY) and 4-aminopyridine (4APY) with one N-aza group in 2-and 4-position, respectively, vis-à-vis the amine group, and to those of 4aminopyrimidine (4APM) with two N-aza groups in 2-and 4-position. The comparison shows that for the amine tautomer 1, each N-aza group decreases the HOMED indices in higher degree for the anionic than neutral forms (by 0.09 and 0.01 units, respectively), while it increases them for the cationic forms (by ca. 0.02 units). The N-aza effects seem to be additive when going from AN1 to 2APY1, 4APY1, and 4APM1.
For the neutral and ionic imine NH tautomers 2 and 3 in 4APM, the additional N-aza group diminishes the HOMED indices in comparison to 2APY and 4APY (by less than 0.1 units). Some exceptions are the cationic isomers 2a and 2b, for which the HOMED indices slightly augment (by 0.01 units). The HOMED indices also decease for the neutral and cationic imine CH tautomer 4. Larger effects take place for the cationic forms (> 0.5 units) than for the neutral forms (< 0.2 units). Some exceptions are the anionic forms, the HOMED indices slightly increase for 4b (by 0.07 units), however, for 4a the total effect of the two N-aza groups is equal to zero because one N-aza group decreases and the other N-aza group increases the HOMED index in almost similar degree. In the case of the imine CH tautomer 3, the N-aza group in 2-position (when going from AN to 2APY) changes the HOMED indices by less than ±0.06 units. However, all these variations of the HOMED indices for tautomers of azaanilines do not change the general trend of π-electron delocalization: the amine and imine NH tautomers are more delocalized than the imine CH ones.
Comparison of the pK T values estimated for AN, 2APY, 4APY, and 4APM gives some information on the effects of the N-aza group(s) in 2-, 4-and 2,4-positions (Table 6). Generally, the 2-N-aza group increases the pK T values for both the NH 2 → CH and NH 2 → NH conversions (δ 0-7 pK T units) in the neutral and ionic forms of azaanilines. The 4-N-aza group has considerably smaller effect (δ 0−±2 pK T units). It slightly increases the pK T values for the neutral and reduced NH 2 → CH conversions, and it decreases them for the NH 2 → NH conversions. The effect of the two N-aza groups seems to be additive only for the neutral forms.
Independent on the position in the ring, the N-aza group increases the oxidation Gibbs energies (Table 7) and it decreases the reduction Gibbs energies (Table 8). For example, when going from aniline to aminopyridines and 4aminopyrimidine, the oxidation reaction for the amine tautomer 2APY1, 4APY1 and 4APM1 requires more energy than that for AN1 (by 10, 18, and 28 kcal mol -1 , respectively), whereas lower energy (by 7, 6, and 12 kcal mol -1 , respectively) is sufficient for the reduction reaction. The effects of the two N-aza groups included in the ring of 4APM1 seem to be additive.

Conclusions
DFT studies performed for all possible amine and imine tautomers of neutral aminopyridines and its unpaired ions show interesting changes of the tautomeric preferences. Solely for 2-aminopyridine, aromaticity seems to dictate the tautomeric preferences for the neutral and oxidized forms. The amine tautomer 2APY1 +• predominates for the oxidized tautomeric mixture of 2-aminopyridine, similarly Table 5 The N-aza effects (δ) on the HOMED indices estimated for the ring (six bonds) in individual tautomers of azaanilines as 2APY1 for the neutral molecule. However, one-electron oxidation changes the composition of the tautomeric mixture. The neutral tautomeric mixture consists mainly of 2APY1 (100 %), whereas the oxidized tautomeric mixture contains at least two tautomers: 2APY1 +• (99.9 %) and 2APY2 +• (0.1 %). For comparison, lack of the N-aza group in aniline totally favors AN1 (100 %) and AN1 +• (100 %) for the neutral and oxidized tautomeric mixture [6].
The importance of the CH tautomers in the tautomeric mixtures of APY -• may partially explain the origin of the CH isomers for the anionic states of nucleobases (cytosine and adenine) [54,55]. On the other hand, the change of the compositions of the tautomeric mixtures for neutral and charged forms of aminoazines should also be taken into account for all processes in which the charged radicals can be formed, e.g., in electrochemical or photochemical processes and during positive or negative ionization in various types of mass spectrometers when the molecule loses or gains one electron [56][57][58].
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