Density Functional Theory (B3LYP/6-311+G(d, p)) Study of Stability, Tautomerism and Acidity of 2-Thioxanthine in Gas and Aqueous Phases

This work is a contribution of theoretical chemistry to the knowledge of 2-thioxanthine's properties. Its aim first consists in checking the chemistry's results related to the exploitation of semi-empirical methods; it provides theoretical data on the acidity of 2-thioxanthine tautomers. To do this, the DFT method with the B3LYP functional, associated with the 6-311+G(d, p) basis set was used. The aqueous phase was modelled with the Polarizable Continuum Model (PCM). The results show that in gas and aqueous phases 2-thioxanthine can exist as a mixture of four tautomers 2TX(1,3,7), 2TXX(1,3,9), 2TX(1,7,10) and 2TX(1,9,10). The relative stability decreases in the order 2TX(1,3,7)> 2TX(1,3,9)> 2TX(1,9,10)> 2TX(1,7,10). This work establishes that the tautomer 2TX(1,9,10) comes from the 2TX(1,3,7) via the 2TX(1,3,9) one. It demonstrates that the acidity of the most stable tautomer’s nitrogen 2TX(1,3,7), decreases in the order 7> 3> 1 in gas phase and in the order 3> 7>1 in aqueous phase. It provides data to elucidate the mechanisms to understand biological activities of 2-thioxanthine.

Recently, 2-thioxanthine was the subject of an experimental study that allowed its determination from electrochemical sensor modified using poly-melamine and polyglutamic [16].
Most of the activities of thiopurines is expected to depend on the tautomeric équilibrium of the molécule [17,18]. Several experimental studies are reported on the tautomerism of 2-thioxanthine in literature. Indeed 2-thioxanthine has 14 shapes and three types of equilibria can be observed: keto enol, thione thiol and N7(H) N9(H). The UV spectra of 2-thioxanthine shows that the predominant tautomer exists in an oxothione form with the imidazole proton on N9-H [19]. Additionaly, 1 HNMR measurements establish that the predominant tautomer exists in an oxothione form with the imidazole proton on N(7) [20]. Although this molecule has been the subject of several researches, the theoretical ones of Pervin Unal Civcir have given a renewed interest. It has been studied by the semiempirical calculation methods AM1 and PM3, 2-thioxanthine [21], 6-thioxanthine [22], 2,6-dithioxanthine [23] and other molecules [24,25]. The research establishes that for 2-thioxanthine, the oxothione N7(H) form is more stable than the oxothione N9(H) form in the gas phase while the oxothione N9(H) form is predominant in aqueous phase [21]. Li [26] did the same investigations with B3LYP/6-311G(d, p) method, he also show that oxothione N7(H) form is the most stable tautomer while N9(H) form is the next.
The verification of semi-empirical methods' chemistry results remains at the centre of our team's concern. Furthermore, to our knowledge, there are no theoretical data on the acidity of 2-thioxanthine. To do this, we use DFT method with the B3LYP functional. This process yields convincing results for 6-thioxanthine, dithioxanthine and xanthine [27][28][29]. In this impetus, the present research aims to question those deducted from semi-empirical methods relating to 2-thioxanthine. Specifically, it focused on the stability, tautomerism and acidity of its tautomers.

Methods of Calculation
All calculations were carried out with DFT (B3LYP functional) using 6-311+G(d, p) basis set [30], as incorporated in the GAUSSIAN-03 program [31]. In aqueous phase, the solvation model Polarizable Continuum Model (PCM) was used [32,33]. The geometries of tautomers, transition states and intermediates have been fully optimized. The Gibbs free energies are obtained from the calculation of the frequencies. Frequency analyses were proceeded to confirm the structure being a minimum or a transition state (i.e without or with solely an imaginary frequency). To name the 14 tautomeric forms we have used the following notations: 2TX(i, j, k) where i, j, and k stand for the amount of the nitrogen, oxygen or sulfur atoms to which the hydrogen is attached ( Figure 1).
Moreover, to establish the presence of a tautomerism, this work determines, first of all, the possible equilibriums. Then, it highlights those that are likely to exist. It calculates their constants and their activation energies. The following section presents the results obtained.

Results and Discussions
The results concern the stability, the tautomerism of 2-thioxanthine and the acidity of its heteroatoms.

Tautomerism of 2-Thioxanthine
To evaluate the tautomerism of 2-thioxanthine, we first consider the possible equilibriums between the potential tautomers and then we calculate the equilibrium constants and activation energies.

Probable Tautomeric Equilibriums in 2-Thioxanthine
Most therapeutic activities of thiopurines depend on potential equilibriums between their tautomeric forms [17,18]. Here, it is accepted that the exchange of hydrogen atoms remains possible only between neighbouring heteroatoms or separated by at most two atoms. Moreover, this research prohibits simultaneous transfers of more than two hydrogen atoms. Under these conditions, there are four potential equilibriums between the most stable tautomers of 2-thioxanthine. The Figure 2 shows that the most stable tautomer 2TX (1,3,7) can be in equilibrium with 2TX(1,7,10) or 2TX (1,3,9). The tautomer 2TX (1,7,10) can also be in equilibrium with 2TX (1,9,10), which is itself with 2TX(1, 3,9). Their actual existence suggests calculating their constants and activation energies.

Tautomeric Equilibrium Constants
A chemical equilibrium between two tautomers A and B (A B) is characterized by its constant K T . The calculation of K T makes it possible to highlight the real 2-thioxanthine's tautomeric equilibrium. K T 's values are obtained with the relation: The Table 2 collects the K T values in gas or aqueous phase at B3LYP/6-311+G(d, p). When K T <10 -4 , the form A exists alone. If K T > 10 4 , compound B predominates. The equilibrium becomes effective if K T ranging from 10 -4 to 10 4 .

Activation Energies of Possible Tautomeric Equilibriums
The Figure 3 illustrates two access pathway to the most stable tautomer 2TX(1,3,7) starting from 2TX (1,9,10) . The  table 3 show the Gibbs free energies of all the species involved in tautomerism as well as the imaginary frequencies of the different transition states; these last quantities characterize them. The table 4 contains activation energies. This article also explains the energy profile of 2-thioxanthine's tautomerism (Figure 4) In the first pathway (Figure 4), The hydrogen atom bonded to the sulfur atom S10 of the tautomer 2TX (1,9,10) transfers onto the nitrogen atom N3. This result carried out through the transition state TS1 with an energy barrier of 27.44 Kcal/mol to give 2TX (1,3,9). Then, in 2TX (1,3,9), the hydrogen atom bonded to the nitrogen atom N9 firstly transfers onto the carbon atom C8 via the transition state TS2, with an energy barrier of 47.63 Kcal/mol to give intermediate IM1.
In the second step, the same hydrogen atom passes from this latter one onto tautomer 2TX (1,3,7) via the transition state TS3; this process corresponds an energy barrier of 28.43 Kcal/mol. In the other pathway, in 2TX (1,9,10), the hydrogen atom bonded to the nitrogen atom N9 firstly transfers onto the carbon atom C8. This displacement is realized through the transition state TS4, with an energy barrier of 54.17 Kcal/mol to give intermediate IM2, then it passes from IM2 onto tautomer 2TX(1,7,10) via the transition state TS5, with a barrier energy of 25.75 Kcal/mol. Finally, the hydrogen atom bonded to the sulfur atom S10 in 2TX(1,7,10) transfers onto the nitrogen atom N3 via the transition state TS6, with an energy barrier of 23.15 Kcal/mol to give 2TX (1,3,7).
The highest activation energy in both pathways is obtained at the breaking of the bond N9-H (47.63 and 54.17 Kcal/mol respectively). That of the second is 6.54 Kcal/mol higher than that of the first. This latter remains thus the most favourable for the reaction between 2-Thioxanthine's tautomers which may exist. In other words, the tautomerism is preferentially realized by the first pathway.
The preceding results make it possible to discuss the 2-thioxanthine's heteroatom acidity. This article also explains the energy profile of 2-Thioxanthine's tautomerism (Figure 4).

Acidity of the Potential Tautomers
The tautomers of 2-thioxanthine have hydrogenated sites that may be deprotonated. The choice of these depends on the acid's strength [36]. The relative Gibbs free energy (∆G) of the associated general reaction (AH → A -+ H + ) helps evaluate the 2-thioxanthine's heteroatom acidity.

Conclusion
The study concerns the stability, tautomerism and acidity of 2-thioxanthine from literature results. In particular, it relies on elaborate methods of theoretical chemistry to take stock of its tautomeric forms and the acidity of its heteroatoms.