Intramolecular tautomerization of the quercetin molecule due to the proton transfer: QM computational study

Quercetin molecule (3, 3′, 4′, 5, 7-pentahydroxyflavone, C15H10O7) is an important flavonoid compound of natural origin, consisting of two aromatic A and B rings linked through the C ring with endocyclic oxygen atom and five hydroxyl groups attached to the 3, 3′, 4′, 5 and 7 positions. This molecule is found in many foods and plants, and is known to have a wide range of therapeutic properties, like an anti-oxidant, anti-toxic, anti-inflammatory etc. In this study for the first time we have revealed and investigated the pathways of the tautomeric transformations for the most stable conformers of the isolated quercetin molecule (Brovarets’ & Hovorun, 2019) via the intramolecular proton transfer. Energetic, structural, dynamical and polar characteristics of these transitions, in particular relative Gibbs free and electronic energies, characteristics of the intramolecular specific interactions–H-bonds and attractive van der Waals contacts, have been analysed in details. It was demonstrated that the most probable process among all investigated is the proton transfer from the O3H hydroxyl group of the C ring to the C2′ carbon atom of the C2′H group of the B ring along the intramolecular O3H…C2′ H-bond with the further formation of the C2′H2 group. It was established that the proton transfer from the hydroxyl groups to the carbon atoms of the neighboring CH groups is assisted at the transition states by the strong intramolecular HCH…O H-bond (~28.5 kcal∙mol-1). The least probable path of the proton transfer–from the C8H group to the endocyclic O1 oxygen atom–causes the decyclization of the C ring in some cases. It is shortly discussed the biological importance of the obtained results.

Currently, there are only some studies in the literature, devoted to the prototropic tautomerism of the quercetin molecule, in particular keto-enol tautomerism [34][35][36][37][38]. Their importance is caused by the relevance of the quercetin tautomers to the hydrogen$deuterium (H$D) exchange processes of its CH-groups [36], irreversible structural changes of the quercetin molecule at the increasing of the temperature [34][35] and tautomerization of the quercetin molecule at the transition to an excited electronic state [38]. However, possible ways of the formation of the rare prototropic tautomers of the quercetin molecule have not been carefully considered.
So, the aim of this study is to reveal and investigate the possible pathways of the prototropic transformations of the isolated quercetin molecule [65].
As a result of this scrupulous investigation we have revealed possible ways of tautomerization of the quercetin molecule via the single proton transfer, which are entangled with the following phenomena (Fig 1): a. Proton transfer from the C8H group to the neighboring O1 oxygen atom.
b. Transition of the proton from the O7H/O3 0 H hydroxyl groups to the carbon atoms of the neighboring C6H/C2 0 H groups.
Number of the important physico-chemical parameters of these transformations, in particular relative Gibbs free and electronic energies, characteristics of the intramolecular H-bonds and attractive van der Waals interactions have been analysed in details. Especial attention has been focused on the processes of the intramolecular tautomerization by proton transfer, which are more or less likely to occur. Possible chemical and biological roles of the obtained results have been shortly outlined.
The Hessian-based predictor-corrector integration algorithm [84] has been applied for obtaining the IRC pathways in the forward and reverse directions from each TS.
The time τ 99.9% , which is necessary to reach 99.9% of the equilibrium concentration of the reactant and product, the lifetime τ (1/k r ) of the prototropic tautomers, the forward k f and reverse k r rate constants have been obtained by the well-known formulas of physico-chemical kinetics [85], respectively: where quantum tunneling effect has been accounted by Wigner's tunneling correction Γ [86-88]: where k B −Boltzmann's constant, h-Planck's constant, ΔΔG f,r −Gibbs free energy of activation for the conformational transition in the forward (f) and reverse (r) directions, ν i −magnitude of the imaginary frequency associated with the vibrational mode at the TSs. The distribution of the electron density has been analyzed by application of the program package AIM'2000 [89] with all default options and wave functions obtained at the B3LYP/6-311++G(d,p) level of theory for geometry optimisation. The presence of the (3,-1) bond critical point (BCP), bond path between hydrogen donor and acceptor and positive value of the Laplacian at this BCP (Δρ>0) have been considered as criteria for the formation of the H-bond and attractive van der Waals contact [62][63][90][91][92].
Energies of the unusual intramolecular CH� � �O and OH� � �C H-bonds and attractive O� � �O and C� � �O van der Waals contacts have been obtained using Bader's quantum theory of Atoms in Molecules [93] by the empirical Espinosa-Molins-Lecomte (EML) formula [94,95], based on the electron density distribution at the (3,-1) BCPs of the H-bonds: where V(r)-value of a local potential energy at the (3,-1) BCP.
It should be noted, that for the CH. . .O H-bonds, which are strong with energy that exceeds 10 kcal�mol -1 , their energy have been estimated by the Brovarets'-Yurenko-Hovorun formula [96,97], considered in the literature [98,99]: The energies of the classical intramolecular OH� � �O H-bonds have been calculated by the Nikolaienko-Bulavin-Hovorun formula [100]: where ρ-the electron density at the (3,-1) BCP of the H-bond. All calculations have been performed for the tautomeric transitions of the quercetin molecule as their intrinsic property, that is adequate for modeling of the processes occurring in real systems [101][102][103][104][105][106].
In this work standard numeration of atoms has been used [2]. At this, prototropic tautomers of the quercetin molecule have been designated by the asterisk; subscript corresponds to the localization of the mobile protons. Numeration of the conformers (highlighted in bold) is the same, as in the previous work [26].

Results and discussion
In the process of this study we have suggested different ways of the formation of the prototropic tautomers of the most stable conformer 1 [26] of the quercetin molecule. Then, by using the method of "trials and errors" we have localized TSs for these tautomeric transformations, occurring via the intramolecular proton transfer. However, only some of the suggested tautomeric transformations have been confirmed, while others of them have been modified in the course of the investigation.
So, in this study we have considered the following mechanisms of the tautomerization of the quercetin molecule, in particular of the most stable conformer 1, that can proceed in the different ways through the intramolecular proton transfer (see Figs 1 and 2, Tables 1 and 2).
It was established that these transformations of the quercetin molecule are accompanied by the changes of their geometry, dipole moment rearrangement and breakage and formation of the intramolecular specific contacts (H-bonds and attractive van der Waals contacts).
Analysis of the investigated mechanisms and their discussion are provided further one-byone. a) Proton transfer from the C8H group to the O1 atom. First of the considered mechanisms consists in the intramolecular transition of the proton, localized at the C8 carbon atom, to the neighboring endocyclic oxygen atom O1, leading to the formation of the new tautomer with formed O1H hydroxyl group (Figs 1 and 2). We have analysed this tranformation for the case of the main stable conformer 1 of the quercetin molecule and also checked it for the others-conformers 4, 7 (ΔG = 0.90), 7 � O1H (ΔG = 9.03) and 10 � O1H (ΔG = 9.14 kcal�mol -1 ) ( Table 1). Notably, all of them, except the case of the conformer 4, which contains opened C-ring and new exotic strong attractive van der Waals contact C9 o. . .O1 (~6.5 kcal�mol -1 ( Table 2)) instead of the C9-O1 covalent bond in the C ring. In the case of the 4$4 � O1H tautomeric transition, the covalent bond C9-O1 survives during this transformation. Notably, three lower H-bonds, stabilizing conformers-O5H . . .O4, O3H . . .O4 and C2'H . . .O3,-remain the same, changing only their energies during tautomerisation ( Table 2).
The 1$1 � O1H tautomerisation reaction occurs via quite high activation barrier and TS 1$1 � O1H with high imaginary frequency (v i = 1150.3 cm -1 ). Notably, that we have checked and revealed that this transition is typical for all investigated conformers. Thus, the Gibbs free

Fig 2. Reaction pathways for the intramolecular proton transfer in the isolated quercetin molecule; initial and terminal states with TSs between them have been obtained at the MP2/6-311++G(2df,pd) // B3LYP/6-311++G(d,p) level of QM theory (low index near formed tautomers denotes the site of the localization of the transferred proton).
Gibbs free ΔG and electronic ΔE energies (kcal�mol -1 ), imaginary frequencies v i at the TS and dipole moments μ (Debay) are provided below reaction paths. Dotted lines indicate intramolecular specific interactions. Red arrows denote the intramolecular transition of the proton, while yellow arrowsrotations of the hydroxyl groups. See also Tables 1 and 2. https://doi.org/10.1371/journal.pone.0224762.g002 Table 1  The electronic energy barrier for the forward tautomerisation reaction, kcal�mol -1 . f The Gibbs free energy barrier for the reverse tautomerisation reaction, kcal�mol -1 . g The electronic energy barrier for the reverse tautomerisation reaction, kcal�mol -1 . h The rate constant for the forward tautomerisation reaction, s -1 . i The rate constant for the reverse tautomerisation reaction, s -1 . j The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the tautomerisation reaction, s. Fig 1).   The energy of the AH� � �B / A� � �B specific contact, calculated by Espinose-Molins-Lecomte [94,95] (marked with an asterisk), Brovarets-Yurenko-Hovorun [96] (marked with a double asterisk) or Nikolaienko-Bulavin-Hovorun [100] formulas, kcal�mol -1 b The electron density at the (3,-1) BCP of the specific contact, a.u.  Table 1.
We have also tried to localize the tautomer with the proton, transferred to the O1 oxygen atom from the other neighboring C6H group for others conformers of the quercetin molecule [26] in the case, when these groups are closely located. However, since the stable structure could not be localized, that means that in fact this reaction would not occur.
So, intramolecular proton transfer from the C8H group to O1 oxygen atom causes decyclization (opening) of the C ring of the quercetin molecule. We consider this result quite important, taking into account how much attention attracts prototropic, in particular ring-chain tautomerism [107,108], in the modern computer-aided drug design [42,43]. b) Transition of the proton from the O7H/O3 0 H hydroxyl groups to the carbon atoms of the neighboring C6H/C2 0 H groups. Firstly, we have considered all possible sites for the proton transfer from the hydroxyl groups to the carbon atoms of the neighboring CH groups with the formation of the CH 2 group. It was revealed only two tautomerization reactions, which occur in this case-O7H!C6H and O3 0 H!C2 0 H. Investigated tautomeric transformations-1$1 � C6H2 (ΔΔG TS = 65.30) and 1$1 � C2'H2 (ΔΔG TS = 68.15 kcal�mol -1 )-occur via the intramolecular proton transfer, which are preceded by the rotations of the hydroxyl groups to the CH groups, with Gibbs free energy barriers of activation-65.30 and 68.15 kcal�mol -1 , respectively. As a result of these tautomerisations, the planar tautomers 1 � C6H2 and 1 �

C2'H2'
with relative Gibbs free energies 44.50 and 50.38 kcal�mol -1 , containing the C6H 2 and C2 0 H 2 groups have been formed, respectively (Fig 1, Tables 1 and 2). These processes of tautomerisation are assisted by the strong intramolecular HC6H . . .O7  Table 2). c) Transitions of the proton from the O7H/O5H/O3H/O4 0 H hydroxyl groups to the C8/ C6/C2 0 /C5 0 carbon atoms of the C8H/C6H/C2 0 H/C5 0 H groups, which are preceded by the rotations of the hydroxyl groups around the C7O7/C5O5/C3O3/C4 0 O4 0 bonds by 180 degree. We have also surveyed other sites of the proton attachment for the possibility of the proton transfer to them. However, analysed sites require rotation of the OH hydroxyl groups around the C-O bond by 180 degree, leading to the prototropic transformations-O7H!C8H, O5H!C6H, O3H!C2 0 H and O4 0 H!C5 0 H. Only in this way of the initial rotation of the OH hydroxyl group of the basic tautomer 1 of the quercetin molecule [26], it is possible to form new prototropic tautomers through the intramolecular transfer of single proton. However, precise investigation of the transformations via the rotations of the OH hydroxyl groups would be the subject of the next study [27], since in this paper we are focusing exactly on the mechanisms of the intramolecular proton transfer.
Thus, it was revealed the following chains of the SPT reactions (Fig 1, Table 1 (Table 2)) between the CH 2 group and neighboring oxygen atom. At this, all other H-bonds remain practically unchanged at the initial and terminal states (Fig 1, Table 2). Prototropic tautomers, which are formed in this case, are planar structures (Table 2).

C5'H2
tautomerisations are quite high (~62-71 kcal�mol -1 ), except the cases 5$5 � C8H2 (ΔG = 20.46) and 20$1 �� C2'H2 (ΔG = 34.71 kcal�mol -1 ). This relatively small value of the barrier can be explained by the formation of the six-membered ring at the TS 20$1 � � C2'H2 and by moving of the proton along the O3H. . .C2 0 H-bond [26]. In those cases, when TS 25$25 � C6H2 , TS 5$5 � C8H2 and TS 10$1 � C5'H2 contains four-membered rings and proton does not move along the intramolecular H-bond-the values of the activation barriers are much higher. At this, 1 �� C2'H2 tautomer is the only one structure, which has the C2 = C1 0 double bond. d) Transition of the proton from the O3H hydroxyl group to the O4 atom. Further we investigated structural mechanisms of the single proton transfer, occurring between the O5H and O3H hydroxyl groups. Thus, it was found that proton can transfer from the O3H hydroxyl group to the O4 oxygen atom through the 1$1 � O5H/O4H tautomerization reaction with the barrier ΔΔG TS = 13.10 kcal�mol -1 . However, terminal localized complex is dynamically unstable-reverse Gibbs free energy barrier has negative value (ΔΔG = -1.20 kcal�mol -1 ) (exactly in this case it is observed at TSs the lowest value of the imaginary frequency ν i = 892.1 cm -1 ) ( Table 1).
It is logically to think by analogy that the same intramolecular proton transfer should occur from the O5H hydroxyl group to the O4 oxygen atom. But in this case the TSs and tautomers could not be localized at all. e) Proton migration from the O7H/O5H hydroxyl groups to the C6 atom of the C6H group.
We also considered tautomeric transformation of the 1 � O5H/O4H/O3H tautomer by the transition of the protons from the O7H/O5H hydroxyl groups to the neighboring C6 atom of the C6H group.
It can be expected the reduction of the values of the activation barriers at the consideration of these transitions in the polar solutions or assisted by various ligands.

Conclusions and perspectives
Presented QM/QTAIM computational modeling of the tautomers formation through the intramolecular proton transfer shows that the quercetin molecule is able to tautomerise via the different routes within the framework of the classical valency rules: a. Proton transfer from the C8H group to the O1 atom, leading in three cases to the breakage of the C ring: 1$1 � O1H , 7$7 � O1H and 10$10 � O1H , except the case of 4$4 � O1H reaction (ΔΔG TS~9 3-96 kcal�mol -1 ). (ΔΔG TS = 70.59 kcal�mol -1 ).
These prototropic transformations of the quercetin molecule are accompanied by the geometrical changes, dipole moment rearrangement and breakage or formation of the intramolecular specific contacts (H-bonds and attractive van der Waals contacts).
It was demonstrated that the most probable process among all investigated is the proton transfer from the O3H hydroxyl group to the C2 0 carbon atom of the C2 0 H of the B ring along the intramolecular O3H. . .C2 0 H-bond with the further formation of the C2 0 H 2 group, while the least probable proton transfer occurs from the C8H group to the O1 oxygen atom-causes the decyclization of the C ring.
Obtained results can be useful for the planning of targeted chemical experiments, aimed at the acceleration of the reaction of intramolecular tautomerization of a quercetin molecule by the ligands of different structure and origin, as well as for the better understanding of the mechanisms of the course of reactions, related to the metabolism of the quercetin molecule.