Theoretical study of NH and CH acidities of toluidine isomers – dependence on their oxidation states

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Introduction
Thanks to the availability of a variety of modern analytic and physicochemical methods, such as the short-time spectroscopy [1], emission spectroscopy [2] and spectroelectrochemistry [3], it is possible to elucidate in the last time the mechanism of many organic chemical reactions and to indicate and characterize certain short-living species occurring thereby. The important role in this research play the highly-sophisticated quantum-chemical methods [4,5] which enable the theoretical description of molecular chemical and electronic structure, as well as the evaluation of thermodynamic properties.
The theoretical calculations can be performed for the gas-phase and the role of solvent environment is standardly covered using the implicit solvent models [6].
Such an example of interesting problems in organic chemistry is the formation of acidic and basic species in the different electronic excited states. For these species, the corresponding dissociation constants and thermodynamic quantities differ mostly from the ones in the electronic ground states [7]. In this context of experimental and theoretical research activities, only few information exists on the estimation of such values for species in their reduced or oxidised states [8]. Similar to the electronic excited species, in the most cases such species are, owing to their open-shell nature, are highly reactive and are able to elude, therefore, their direct indication also. This situation will be more complicated if the corresponding acids or bases possess more than one acidic or basic centre in their molecular framework. This is the case, e.g. for the toluidines, which bear both at their amino and methyl groups protons which can be abstract principally by bases so that these compounds can exhibit, besides of their usual basic properties, also acidic properties. As far as these acidic properties are related to the protons at the N-atoms, they are called NH-acidity, whereas the basic properties which are related to the methyl groups are called CH-acidity.
Although the number of synthetic studies were focused on unravelling the products from oxidation of toluidine molecules under different conditions, the potential reactivity of oxidised toluidine isomers were discussed minimally. It is a lack of published experimental and theoretical knowledges about the reactive positions in the N-centred or C-centred species leasing to the CN or CC coupling 4 toluidine products. With respect to these facts, we decided to present the systematic theoretical analysis of parent and deprotonated toluidine and its oxidized species. The partial aims of this study are: (1) to calculate the optimal geometries of studied compounds in the gas-phase and two model environments; (2) to evaluate the reaction Gibb's free energies for selected reaction steps and (3) to estimate the corresponding acidity pKa constants. The obtained theoretical trends and results will be confronted with the results published for various coupling reactions of toluidine isomers.

Thermodynamics of Toluidine Acid-Base Reaction
Aniline (ANH2) as the simplest representative aromatic amine has basic as well as acidic, i.e. amphoteric, properties which can be quantified by the pK constants (Scheme 1) [9]. Comparing with ammonia, aniline solvated in water is a relative weak base. The corresponding experimental basicity pKb constant of aniline is 9.4 [10] and ammonia in water is 9.2 [11]. On the other hand, the acidity constant of positive charged anilinium ion (pKa), as conjugated acid of the base aniline at 298.15 K, in water is 4.6 and in DMSO is 3.7 (measured in aniline hydrochloride) [12]. Aniline is also a weak acid which can be deprotonated only by very strong bases, e.g. by lithium organyl compounds [13]. The available experimental pKa for heterolytic dissociation of aniline to deprotonated anion (ANH -) in DMSO is 30.6 [14]. The ammonia molecule represents an extremely weak acid due to the high pKa value of 41.0 (in water) and of 38 (in DMSO) [15]. As it is depicted in Scheme 2, the proton abstraction from amino or methyl groups can be occurred in seven possible acid-base reactions.

Scheme 2
The mutual comparison of reaction G4 Gibb's energies for reactions 1, 2 and a, b indicates minimal energy differences. The effect of methyl group position toward the amine group is also negligible, the maximal energy differences in solvents are up to the 6 kJ mol -1 . The results for reactions 4 and 5 6 clearly show that the CH acidities of toluidines are, as expected, much weaker than their NH acidities and nearly independently from the substitution pattern. The energetically less preferred dissociation represents the proton abstraction from CH3TNHanion (reaction No 5). Interestingly, the CH acidities of zwitterion species CH2TNH +in solvents are maximal for ortho isomer (reaction No. 3) and it is comparable with the NH acidity of aniline (reaction No 2). Next, the deprotonation of ammonium group in zwitterion species is also associated with the endothermic process (reaction No 2). The comparable reaction Gibb's energies in solvents are indicated for ortho isomer. Finally, our calculations predict that the proton abstraction from CH2TNH2is also possible. The calculated reaction Gibb's free energies for are ranged from 220.2 kJ mol -1 to 234.5 kJ mol -1 for DMSO and 234.4 kJ mol -1 to 266.0 kJ mol -1 for water.
The acid-base reactions of arylamines connected with the chemical oxidation of molecules are very often used in the preparation of poly-arylamines as materials with a high electric conductivity [18] or as starting materials for certain important organic dyes, such as Mauveine or Fuchsine [19]. It is from some practical interest to know that the NH and CH acidities of toluidines depend not only from the substitution position of their methyl groups at the aromatic ring but also from the oxidation state of the corresponding compounds. In this context, four possible acid-base reactions (Nos. 8, 9, 10 and 11) initiated upon the electron abstractions were theoretically investigated for toluidines (see calculations follow that in both cases the -type species are more stabilised than the -type species (see Fig. 2S). This is in agreement with calculations performed by other authors for various nitrogencentred radicals [20].

Theoretical pKa Values of Toluidine Oxidation States
The theoretical pKa values evaluated from quantum chemical results (see Eq. 1) can lead to the values different from experiment (see Tab. 2S). This error is connected with the insufficient description of solvent effects using the implicit model. Next, the PCM models is employed to calculate solvation energies in high accuracy, it requires parametrization of the shape and size of the dielectric cavity of a molecule [21]. Unfortunately, computational works reported to date rarely involved extensive parametrization for radical species or charged states. To improve the reliability of theoretical pKa values, the approach based on the isodesmic reaction is applied [22]. In this work, we have used the available experimental pKa data for aniline, anilinium ion and aniline cation radical in DMSO and water (see Tab

Oxidation States and Reactivity of Toluidine
The calculated acidities of toluidine in their different oxidation states (Tab. 2) show that the toluidine radical cations CH3TNH2 +. as primary species generated by the oxidation of toluidines, can be deprotonated both at their NH2 and CH3 moieties. This deprotonation leads to the transformation into N-centred radical CH3TNH . and C-centred radical CH2TNH2. On the other hand, the toluidine dications CH2TNH2 2+ as secondary species generated by the oxidation of toluidines can be deprotonated exclusively at their methyl moieties and transformed thereby into C-centred cationic species CH2TNH2 + . Owing to the highly negative pKa values of reaction 10, the cationic species CH2TNH2 + can be formed also directly from the radical cations CH3TNH2 +. in course of a so-called proton-coupled electron transfer (PCET) process [25]. We would like to note that under usual pHconditions (0 < pH < 9), which are applied in course of the oxidation of aniline and its derivatives, there is no change for the formation of the dicationic species CH3TNH2 2 , although certain authors argue for its existence [25,26,27].
From the data derived follow, that by starting with p-toluidine (Scheme 4), an oxidatively mediated coupling of the N-centred radicals p-CH3TNH • , e.g. with a further p-toluidine, is expected. Indeed, such a coupling occurs at the N-atom and gives rise to the formation of a coupling product of the general structure D1. This compound is able to react with a further p-toluidine molecule yielding the so-called BARSILOWSKY's base T1 [26]. In the second case, namely by reaction of the radical cation CH3TNH2 +. , an oxidatively mediated coupling with p-toluidine is expected to occur at the CH2 moiety and gives rise to the formation of a coupling product of the general structure D2 [27]. This compound can subsequently transformed by further oxidation into the azomethine compound D3, which is able to yield, e.g. by further reaction with aniline, Fuchsine [28]. which the quinone iminium salts D5 is formed [29]. The C-centred cation o-CH2TNH2 + is highly reactive [30] and can be transformed either by reaction with certain nucleophiles into the adducts X2 or by reaction with further o-toluidine or aniline (ANH2), via the dimer D6, into the acridines D7 [31] or the Chrysaniline D8 [32].

Scheme 5
Although the oxidation of m-toluidine is also studied rather intensively, in contrast to the oxidation of o-and p-toluidine, there is only less information on the structure of products and on the mechanism of their formation. Thus, it was stated that by the electrochemical oxidation of mtoluidine, performed in acidic solution, in course of a CN coupling reaction a polymer is formed its structure D10 is similar to the one which is formed by the oxidation of aniline (Scheme 6) [33].
Moreover, similar to the aniline oxidation certain intermediates, such as the 1,4-phenylenediamine derivative D9 and the quinoneimine D10 with n = 1 [34], and the corresponding benzidine derivatives D11 and D12 [35] have been identified. Moreover, similar to the aniline oxidation, a corresponding azobenzene derivative, which can be formed from the radical species m-CH3TNH . in course of a NN coupling, has been identified also. However, there is no information at yet on the formation of products which could be generated from the zwitterion product m-CH2TNH2 +formed by a deprotonation at the methyl group in meta-position.

Conclusion
In this theoretical study, we have suggested possible acid-base reaction steps occurring during the oxidation of toluidine isomers. The reaction Gibb's energies were calculated using G4 and M062x approaches for the gas-phase, water and dimethylsulfoxid environments. The theoretical pKa values were evaluated for mono-and bi-cationic states using the isodesmic reaction approach with respect to the reference experimental data available for the aniline molecule. The comparison of these values showed that the transformation of toluidines into oxidised states significantly increases the acidity of methyl group. This study indicates that the presence or absence of these deprotonated species in reaction mixture will determine the CN or CC coupling toluidine products. The qualitatively similar theoretical results were also obtained using the reference density functional theory and M062x functional.

Computational methods
The quantum chemical calculations based on the Density Functional Theory were performed using the Minnesota M062x hybrid functional [36] and 6-311++G** basis set of atomic orbitals [37]. First the optimal geometries of the studied species were found in gas-phase and these optimal geometries were used as the starting geometries for the calculations using Gaussian-4 theory [38]. This theory involves the introduction of an extrapolation scheme for obtaining basis set limit Hartree-Fock energies and it was developed for the calculations of thermochemical properties. The solvent effects contributions in dimethylsulfoxide (DMSO) and in water (WAT) were described using the integral equation formalism version of PCM (IEF-PCM) [39]. Frequency analysis showed no imaginary frequencies confirming the real geometry of the energy minima. All Gibb's free energies were estimated for temperature T = 298.15 K and pressure p = 101325 Pa. These thermodynamic energies are calculated from the combination of energy contributions from various B3LYP and ab initio energies. All calculations were carried out using the Gaussian 16 program package [40]. The molecules and spin densities were visualised using the Molekel progam package [41].