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A Never-Ending Conformational Story of the Quercetin Molecule: Quantum-Mechanical Investigation of the O3′H and O4′H Hydroxyl Groups Rotations

A Never-Ending Conformational Story of the Quercetin Molecule: Quantum-Mechanical Investigation... applied sciences Article A Never-Ending Conformational Story of the Quercetin Molecule: Quantum-Mechanical 0 0 Investigation of the O3 H and O4 H Hydroxyl Groups Rotations 1 , 1 , 2 Ol’ha O. Brovarets’ * and Dmytro M. Hovorun Department of Molecular and Quantum Biophysics, Institute of Molecular Biology and Genetics, National Academy of Sciences of Ukraine, 150 Akademika Zabolotnoho Street, 03680 Kyiv, Ukraine; dhovorun@imbg.org.ua Department of Molecular Biotechnology and Bioinformatics, Institute of High Technologies, Taras Shevchenko National University of Kyiv, 2-h Akademika Hlushkova Avenue, 03022 Kyiv, Ukraine * Correspondence: o.o.brovarets@imbg.org.ua Received: 8 January 2020; Accepted: 2 February 2020; Published: 8 February 2020 Abstract: The quercetin molecule is known to be an e ective pharmaceutical compound of a plant origin. Its chemical structure represents two aromatic A and B rings linked through the C ring 0 0 containing oxygen and five OH hydroxyl groups attached to the 3, 3 , 4 , 5, and 7 positions. In this study, a novel conformational mobility of the quercetin molecule was explored due to the turnings of 0 0 the O3 H and O4 H hydroxyl groups, belonging to the B ring, around the exocyclic C-O bonds. It was established that the presence of only three degrees of freedom of the conformational mobility of the 0 0 O3 H and O4 H hydroxyl groups is connected with their concerted behavior, which is controlled by the non-planar (in the case of the interconverting planar conformers) or locally non-planar (in 0 0 O3 H/O4 H 0 0 other cases) TSs transition states, in which O3 H and O4 H hydroxyl groups are oriented by the hydrogen atoms towards each other. We also explored the number of the physico-chemical and electron-topological characteristics of all intramolecular-specific contacts—hydrogen bonds and attractive van der Waals contacts at the conformers and also at the transition states. Long-terms perspectives for the investigations of the structural bases of the biological activity of this legendary molecule have been shortly described. Keywords: Quercetin molecule; conformational mobility; hydroxyl group; transition state; concerted rotation of the hydroxyl groups; quantum-chemical calculations; quantum technology 1. Introduction 0 0 The quercetin molecule (3, 3 , 4 , 5, 7—pentahydroxyflavone, C H O ) is an important flavonoid 15 10 7 compound, which is found in many foods and plants, in particular in honey [1], and is known to act as a natural drug molecule with a wide range of treatment properties—antioxidant, anti-toxic, etc.—and is also involved in drug delivery from the site of administration to the therapeutic target [2–9]. The structure of the quercetin contains two aromatic A and B rings linked through the C ring containing 0 0 oxygen and five OH hydroxyl groups attached to the 3, 3 , 4 , 5 and 7 positions (see Scheme 1) [10–15]. In a previous study [16], by using the quantum-mechanical (QM) calculations at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory together with Bader ’s “Quantum Theory of Atoms in Molecules”, for the first time, all possible conformers were established, corresponding to local minima on the potential energy hypersurface of the isolated quercetin molecule. Appl. Sci. 2020, 10, 1147; doi:10.3390/app10031147 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 1147 2 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 24 Scheme 1. Chemical structure of the quercetin molecule and standard numeration of its atoms. Scheme 1. Chemical structure of the quercetin molecule and standard numeration of its atoms. Altogether, 48 stable conformers were established, which have been divided into four di erent In a previous study [16], by using the quantum-mechanical (QM) calculations at the conformational subfamilies by their structural properties: subfamily I—conformers 1–12; subfamily MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory together with Bader’s “Quantum II—conformers 13-18, 20, 23, 24, 26, 29, and 30; subfamily III—conformers 19, 21, 22, 25, 27, 28, Theory of Atoms in Molecules”, for the first time, all possible conformers were established, and 31–36; subfamily IV—conformers 37–48 [16]. It was shown that these 48 stable conformers corresponding to local minima on the potential energy hypersurface of the isolated quercetin (24 planar structures (C point symmetry) and 24 non-planar structures (C point symmetry)) represent s 1 molecule. a comprehensive set of the theoretically possible structures. Altogether, 48 stable conformers were established, which have been divided into four different Conformers of quercetin are polar structures with a dipole moment, which varies within the range conformational subfamilies by their structural properties: subfamily I—conformers 1–12; subfamily from 0.35 to 9.87 Debye for di erent conformers with di erent direction for each. II—conformers 13-18, 20, 23, 24, 26, 29, and 30; subfamily III—conformers 19, 21, 22, 25, 27, 28, and Their relative Gibbs free energies are arranged within the range from 0.00 to 25.30 kcalmol 31–36; subfamily IV—conformers 37–48 [16]. It was shown that these 48 stable conformers (24 planar under normal conditions in vacuum. structures (Cs point symmetry) and 24 non-planar structures (C1 point symmetry)) represent a One half of these structures (24 conformers) possesses planar structure (C point symmetry), comprehensive set of the theoretically possible structures. whereas the other half (24 conformers) does not have symmetry at all (C point symmetry) Conformers of quercetin are polar structures with a dipole moment, which varies within the 0 0 (C3C2C1 C2 = 40.9–44.3 degree; C2C3O3H = 9.4–16.3 degree). range from 0.35 to 9.87 Debye for different conformers with different direction for each. We also defined their physico-chemical characteristics, in particular, structural, energetic, and −1 Their relative Gibbs free energies are arranged within the range from 0.00 to 25.30 kcal∙mol polar, which are necessary for understanding of the biological mechanisms of action of this molecule. under normal conditions in vacuum. Intramolecular specific contacts have also been explored in detail. One half of these structures (24 conformers) possesses planar structure (Cs point symmetry), Bader ’s “Quantum Theory of Atoms in Molecules” analysis shows that conformers of the quercetin whereas the other half (24 conformers) does not have symmetry at all (C1 point symmetry) molecule di er from each other by the intramolecular specific contacts (two or three), stabilizing all (C3C2C1′C2′ = 40.9–44.3 degree; C2C3O3H = 9.4–16.3 degree). possible conformers of the molecule—H-bonds (both classical OH ::: O and so-called unusual CH We also defined their physico-chemical characteristics, in particular, structural, energetic, and ::: O and OH ::: C) and attractive van der Waals contacts O ::: O. Energies of these cooperative polar, which are necessary for understanding of the biological mechanisms of action of this intramolecular specific contacts have been estimated [16]. molecule. Intramolecular specific contacts have also been explored in detail. Also, it was theoretically modeled the conformational interconversions [17–21] in the 24 pairs of Bader’s “Quantum Theory of Atoms in Molecules” analysis shows that conformers of the the conformers of the quercetin molecule through the rotation of its almost non-deformable (A+C) and quercetin molecule differ from each other by the intramolecular specific contacts (two or three), B rings around the C2-C1 bond through the quasi-orthogonal transition state (TS) with low values stabilizing all possible conformers of the molecule—H-bonds (both classical OH…O and so-called of the imaginary frequencies (28-33/29-36 cm ) and Gibbs free energies of activation in the range of unusual CH…O and OH…C) and attractive van der Waals contacts O…O. Energies of these 2.17 to 5.68/1.86 to 4.90 kcalmol in the continuum with dielectric permittivity " = 1/" = 4 under cooperative intramolecular specific contacts have been estimated [16]. normal conditions. Also, we studied the changes of the number of physico-chemical characteristics of Also, it was theoretically modeled the conformational interconversions [17–21] in the 24 pairs of all intramolecular specific contacts—hydrogen bonds and attractive van der Waals contacts during the conformers of the quercetin molecule through the rotation of its almost non-deformable (A+C) these conformational rearrangements. and B rings around the C2-C1′ bond through the quasi-orthogonal transition state (TS) with low This study is a logical development of the previous investigations [16–18] and is devoted to the −1 values of the imaginary frequencies (28-33/29-36 cm ) and Gibbs free energies of activation in the novel interconversions between the conformers of the quercetin molecule due to the rotations of the −1 range of 2.17 to 5.68/1.86 to 4.90 kcal∙mol in the continuum with dielectric permittivity ε = 1/ε = 4 0 0 O3 H and O4 H hydroxyl groups around the exocyclic C-O bonds outside. under normal conditions. Also, we studied the changes of the number of physico-chemical As a result, it was found that di erent conformers of the quercetin molecule are tightly characteristics of all intramolecular specific contacts—hydrogen bonds and attractive van der Waals interconnected with each other through the set of the TSs. Moreover, these conformational contacts during these conformational rearrangements. transformations are assisted by the intramolecular H-bonds and van der Waals contacts. This study is a logical development of the previous investigations [16–18] and is devoted to the In reality, it is not as easy a task as it seems, as the question of “Why two neighboring hydroxyl novel interconversions between the conformers of the quercetin molecule due to the rotations of the groups in the aromatic ring have only three, but not four conformational degrees of freedom?” remains O3′H and O4′H hydroxyl groups around the exocyclic C-O bonds outside. without answer [22,23]. As a result, it was found that different conformers of the quercetin molecule are tightly The main idea of this investigation is summarized in the following statements. interconnected with each other through the set of the TSs. Moreover, these conformational We suggest that the conformational mobility of the C ring of the quercetin molecule, which transformations are assisted by the intramolecular H-bonds and van der Waals contacts. 0 0 contains two neighboring O3 H and O4 H hydroxyl groups, that is, conversion of one stable In reality, it is not as easy a task as it seems, as the question of “Why two neighboring hydroxyl groups in the aromatic ring have only three, but not four conformational degrees of freedom?” remains without answer [22,23]. Appl. Sci. 2020, 10, 1147 3 of 22 0 0 0 0 0 0 0 0 O3 HO4 H/O4 HO3 H configuration into the other O4 HO3 H/O3 HO4 H and vice versa, is realized by two significantly di erent pathways from the topological and energetical point of view. First, (this pathway is more or less evident) it occurs by the restricted rotations of the hydroxyls by the angle of 180 degrees through the corresponding TSs and through the high-energetical dynamically 0 0 0 0 stable O3 HO4 H/O4 HO3 H configuration. The other pathway is quite unusual—it is realized through one conformational transition, which has concerted character and is controlled by the non-planar 0 0 0 0 O3 HHO4 /O4 HHO3 TSs with the high values of the imaginary frequency. A previously suggested idea has been completely confirmed by careful QM investigation—we have identified for the first time the aforementioned pathways of the conformational variability of the quercetin molecule and documented their structural properties, including symmetrical, polar, energetical, and kinetic characteristics, which are quite important for the understanding of the structural grounds of the biological activity of the quercetin molecule. 2. Computational Methods Calculations of the geometrical structures of the TSs of the conformational interconversions and their vibrational spectra, corresponding to the local minima on the potential (electronic) energy hyper surface, have been performed at the DFT B3LYP/6-311++G(d,p) level of QM theory [24–26] by Gaussian’09 program package [27], which was successfully approved in our previous studies for the calculations of the heterocyclic compounds [28,29]. A scaling factor of 0.9668 has been used to correct the harmonic frequencies for the investigated structures [30]. Intrinsic reaction coordinate (IRC) calculations in the forward and reverse directions from each TS, which have been confirmed by the presence of one and only one imaginary frequency in the vibrational spectra, have been performed using Hessian-based predictor–corrector integration algorithm [31]. All calculations were performed for the quercetin molecule as their intrinsic property, that is adequate for modeling of the processes occurring in real systems [16,17,32]. Electronic and Gibbs free energies under normal conditions have been calculated by single point calculations at the MP2/6-311++G(2df,pd) level of theory [33–35]. The time  necessary to reach 99.9% of the equilibrium concentration of the reactant and 99.9% product in the system of the reversible first-order forward (k ) and reverse (k ) reactions can be estimated by the formula [36] ln10 = (1) 99.9% k + k The lifetime, , of the conformers has been calculated using the formula 1/k , where the values of the forward k and reverse k rate constants for the tautomerization reactions were obtained as [36] f r DDG f ,r k T RT k = G e (2) f ,r where the quantum tunneling e ect has been accounted by Wigner ’s tunneling correction [37], successfully used for the double proton reactions in DNA base pairs [28]: 1 h G = 1 + (3) 24 k T where k —Boltzmann’s constant, h—Planck’s constant, DDG —Gibbs free energy of activation for B f,r the conformational transition in the forward (f ) and reverse (r) directions, and  —magnitude of the imaginary frequency associated with the vibrational mode at the TS. The topology of the electron density was analyzed using the program package AIM’2000 [38] with all default options and wave functions obtained at the level of theory used for geometry optimization. The presence of the (3,1) bond critical point (BCP), bond path between hydrogen donor and acceptor, Appl. Sci. 2020, 10, 1147 4 of 22 and positive value of the Laplacian at this BCP (D > 0) were considered altogether as criteria for the formation of the H-bond and attractive van der Waals contact [39]. In this work, standard numeration of atoms has been used [16,17]. Numeration of the conformers, which are highlighted in bold in the text, have been used as in the work [16]. 3. Obtained Results and Their Discussion In this study, we logically continued to investigate the conformational mobility [16–18] of the 0 0 quercetin molecule and extend this approach to the rotations of the hydroxyl groups in the 3 and 4 positions, which are carefully presented in Tables 1–3 and Figures 1–3. The most obvious methods of the conformational interconversions between the 48 conformers [16] of the quercetin molecule were 0 0 considered and investigated in detail through the rotations of the O3 H and O4 H hydroxyl groups around the exocyclic C-O covalent bonds. In this case, the TSs have been formed gradually, starting from the 48 conformers of the quercetin molecule [16] by the single or concerted rotations of the O3 H 0 0 0 0 0 O3 H O4 H O3 H/O4 H and O4 H hydroxyl groups—designated as TS , TS , and TS , respectively. Therefore, detailed analysis of the obtained results enabled us to obtain the following observations 0 0 and their discussion. As individual, the concerted rotational transitions of the O3 H and O4 H hydroxyl groups proceed through the mirror-symmetrical pathways, which are controlled by the mirror-symmetrical TSs. Totally, we have revealed 48 TSs—16 TSs in each case (Figures 1–3; Tables 1–3). 0 0 O3 H O4 H Individual conformational transitions are controlled by the non-planar TS and TS (C 0 0 0 0 0 0 point symmetry) with non-orthogonal structure (see HO3 C3 C2 (78.7–83.3 degree) and HO4 C4 C5 (80.2–82.1 degree) dihedral angles in Tables 1 and 2 and Figures 1 and 2). Their non-orthogonal structure, most probably, could be connected with the non-symmetrical surrounding of the free electronic pairs of the oxygen atoms of the hydroxyl groups. The TSs for the concerted conformational 0 0 O3 H/O4 H transformations—TSs —possess non-planar structure in the case of the planar conformers 1-12, 19, 21, 22, 25, 27, 28, and 31–36 and local non-planar structure for the non-planar conformers, 13-18, 20, 23, 24, 26, 29, 30, and 37–48, which mutually interconvert (Figure 3, Table 3). O4 H Gibbs free energies of activation for these processes form the following order; DDG (3.33–7.05) TS 0 0 0 O3 H O3 H/O4 H 1 < DDG (4.23–7.08) < DDG (4.41–7.56 kcalmol under normal conditions) (Tables 1–3). TS TS 0 0 O3 H O4 H The imaginary frequencies are in the following ranges: 366.7–391.5 (TS ), 328.8–363.5 (TS ), 0 0 O3 H/O4 H and 454.5–483.1 (TS ). Without exception, 48 conformers of the quercetin molecule have been established to be the dynamically stable structures, based on the investigated conformational transitions. During their lifetime ( = (1.05–2.53)10 s) (Tables 1–3), the lowest frequency intramolecular vibrations can occur [16]. It is a characteristic feature that investigated conformational transitions are dipole-active, as they cause the changing of the dipole moment by the absolute value, so by the spatial orientation, and practically do not disturb the structure of the quercetin molecule and physico-chemical characteristics 0 0 of its specific intramolecular interactions. Even the energy of the intramolecular C2 /C6 H ::: O3 and 0 0 O3H ::: C2 /C6 H H-bonds between the B and C rings (Figures 1–3) change at these conformational transitions by no more than on ~4.7%. Interestingly, concerted conformational transitions, which 0 0 O3 H/O4 H are controlled by the TSs , proceed without intermediates on the hyperspace of the Gibbs free energy. Moreover, we did not register any specific intramolecular interactions in the B ring of the quercetin 0 0 molecule at the conformational motions of the O3 H and O4 H hydroxyl groups. All investigated 10 11 conformational transitions are quite rapid processes, for which 1.0410 >  > 7.3010 s. 99.9% Therefore, provided investigation gives total assurance that the availability of the three 0 0 conformational degrees of freedom for the O3 H and O4 H hydroxyl groups is connected with their concerted, coordinated behavior (Figure 3, Table 3). Let us to make one important notion before going to the conclusions. It is known, that biological activity of the molecules, is caused by at least two interdependent reasons—their intramolecular structural variability and specific interaction with the targets of the di erent origin. Appl. Sci. 2020, 10, 1147 5 of 22 Table 1. Energetic, polar, structural, and kinetic characteristics of the conformational transitions in the isolated quercetin molecule via the mirror-symmetrical 0 0 0 0 rotations of the O3 H hydroxyl group around the C3 -O3 bond through the transition states (TSs) with a non-perpendicularly-oriented O3 H group, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions (see Figure 1). TS of the a b c d e f g h i j k l 0 0 0 m Conformational   DG DE DDG DDE DDG DDE k k   HO3 C3 C2 TS i TS TS f r 99.9% Transition O3 H 7 10 10 11 TS 1.78 340.2 3.98 3.80 6.90 6.75 2.91 2.95 6.0110 5.0110 1.3810 2.0010 80.1 2$9 O3 H 7 10 10 11 TS 4.02 333.4 4.15 4.07 7.08 6.73 2.93 2.66 4.3610 4.8210 1.4310 2.0710 79.1 4$11 O3 H 8 10 10 11 4.10 361.1 3.29 3.21 6.25 6.53 2.97 3.32 82.8 TS 1.8010 4.6210 1.4910 2.1710 7$10 O3 H 8 10 10 11 TS 5.93 362.0 3.32 3.23 6.25 6.51 2.93 3.28 1.8010 4.9110 1.4010 2.0410 82.9 8$12 O3 H 8 10 10 11 5.08 355.2 3.70 3.75 6.50 6.92 2.80 3.17 81.3 TS 1.1710 6.0910 1.1310 1.6410 14$24 O3 H 8 10 11 11 TS 6.24 340.9 3.79 3.97 6.47 6.86 2.68 2.89 1.2310 7.4410 9.2710 1.3410 79.3 15$26 O3 H 7 10 10 11 7.60 355.6 3.81 3.91 6.62 7.05 2.81 3.15 80.6 TS 9.7010 6.0310 1.1410 1.6610 17$29 O3 H 8 10 11 11 TS 8.65 343.3 3.79 3.94 6.50 6.87 2.71 2.93 1.1710 7.0410 9.7910 1.4210 79.5 18$30 O3 H 8 10 11 11 3.08 328.8 4.01 4.14 6.54 6.70 2.53 2.56 78.7 TS 1.0910 9.5110 7.2610 1.0510 21$34 O3 H 8 10 10 11 TS 6.23 363.5 3.25 3.03 6.27 6.29 3.02 3.27 1.7510 4.2510 1.6210 2.3510 83.3 27$33 O3 H 8 10 11 11 TS 3.35 336.2 3.85 3.86 6.39 6.63 2.54 2.77 1.4210 9.4410 7.3010 1.0610 79.8 31$36 O3 H 8 10 10 11 TS 5.97 362.6 3.23 3.05 6.29 6.38 3.06 3.33 1.6910 3.9610 1.7410 2.5310 83.2 32$35 O3 H 7 10 10 11 TS 6.15 354.7 3.83 3.92 6.60 7.01 2.77 3.09 9.9710 6.4310 1.0710 1.5610 80.5 39$45 O3 H 8 10 10 11 TS 7.86 344.1 3.70 3.82 6.45 6.80 2.75 2.98 1.2710 6.6010 1.0410 1.5210 80.5 40$46 O3 H 8 10 11 11 TS 6.37 341.6 3.70 3.85 6.41 6.79 2.71 2.94 1.3610 7.0510 9.7810 1.4210 79.6 42$48 O3 H 9 10 11 11 TS 4.47 353.8 1.46 1.51 4.23 4.62 2.77 3.12 5.4710 6.4610 9.8510 1.5510 81.1 44$47 a b 1 c The dipole moment of the TS, Debye. The imaginary frequency at the TS of the conformational transition, cm . The Gibbs free energy of the initial relative to the terminal conformer 1 d 1 e of the quercetin molecule (T = 298.15 K), kcalmol . The electronic energy of the initial relative to the terminal conformer of the quercetin molecule, kcalmol . The Gibbs free 1 f energy barrier for the forward conformational transformation of the quercetin molecule, kcalmol . The electronic energy barrier for the forward conformational transformation of the 1 g 1 h quercetin molecule, kcalmol . The Gibbs free energy barrier for the reverse conformational transformation of the quercetin molecule, kcalmol . The electronic energy barrier for the 1 i 1 j reverse conformational transformation of the quercetin molecule, kcalmol . The rate constant for the forward conformational transformation, s . The rate constant for the reverse 1 k conformational transformation, s . The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the reaction of the conformational l m 0 transformation, s. The lifetime of the product of the conformational transition, s. The dihedral angle, which describes at the TS the orientation of the O3 H hydroxyl group relatively the B ring of the quercetin molecule, degree; sings “” correspond to enantiomers. Appl. Sci. 2020, 10, 1147 6 of 22 Table 2. Energetic, polar, structural, and kinetic characteristics of the conformational transitions in the isolated quercetin molecule via the mirror-symmetrical 0 0 0 0 rotations of the O4 H hydroxyl group around the C4 -O4 bond through the transition states (TSs) with a non-perpendicularly-oriented O4 H group, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions (see Figure 2). TS of the 0 0 0 Conformational   DG DE DDG DDE DDG DDE k k   HO4 C4 C5 TS i TS TS f r 99.9% Transition O4 H 7 10 10 11 TS 2.41 381.6 4.20 4.30 7.05 7.38 2.84 3.08 4.7510 5.7710 1.2010 1.7310 81.1 1$10 O4 H 7 10 10 11 TS 2.82 391.5 3.92 4.03 6.86 7.23 2.94 3.21 6.6010 4.9510 1.3910 2.0210 81.9 3$9 O4 H 7 10 11 3.63 379.7 4.24 4.37 6.93 7.35 2.69 2.98 9.32E-11 80.8 TS 5.8010 7.4110 1.3510 5$12 O4 H 7 10 10 11 TS 3.99 389.2 3.86 4.00 6.92 7.14 3.07 3.14 5.9010 3.9810 1.7310 2.5110 82.1 6$11 O4 H 7 10 10 11 4.78 375.8 4.07 4.13 6.81 7.22 2.74 3.09 80.4 TS 7.1210 6.8910 1.0010 1.4510 13$24 O3 H 7 10 10 11 TS 6.83 374.4 4.01 4.11 6.78 7.16 2.77 3.04 7.4210 6.5210 1.0610 1.5310 80.7 16$30 O4 H 7 10 11 11 4.64 371.6 4.12 4.49 6.74 7.25 2.62 2.76 80.2 TS 7.9810 8.4010 8.2210 1.1910 19$33 O4 H 7 8 8 9 TS 4.64 371.6 0.63 0.72 6.71 7.51 6.08 6.79 8.3610 2.4210 2.1210 4.1310 80.2 20$26 O4 H 7 10 11 11 5.05 380.8 4.04 3.97 6.71 7.00 2.67 3.03 81.8 TS 8.4310 7.7410 8.9110 1.2910 22$34 O4 H 10 10 11 11 TS 7.10 375.3 0.55 0.60 3.33 3.73 2.78 3.13 2.5210 6.4110 7.7310 1.5610 80.7 23$29 O4 H 7 10 11 11 TS 5.37 373.7 4.12 4.35 6.84 7.22 2.71 2.88 6.7710 7.1710 9.6210 1.3910 80.5 25$35 O4 H 7 10 11 11 TS 5.70 382.7 4.07 4.06 6.74 7.08 2.67 3.02 7.9910 7.7110 8.9510 1.3010 81.6 28$36 O4 H 7 10 11 11 TS 6.56 369.1 4.03 4.05 6.75 7.11 2.72 3.06 7.8010 7.0910 9.7410 1.4110 80.4 37$45 O4 H 7 10 11 11 TS 6.19 367.5 4.03 4.16 6.72 7.10 2.69 2.95 8.1410 7.4010 9.3210 1.3510 80.2 38$46 O4 H 7 10 11 11 TS 5.09 366.7 4.00 4.10 6.69 7.05 2.69 2.94 8.6410 7.4210 9.3010 1.3510 80.4 41$48 O4 H 9 10 10 11 TS 5.49 369.4 1.83 1.88 4.73 5.10 2.90 3.22 2.3710 5.2110 1.2710 1.9210 80.2 43$47 For designations see Table 1. Appl. Sci. 2020, 10, 1147 7 of 22 Table 3. Energetic, polar, structural, and kinetic characteristics of the conformational transitions in the isolated quercetin molecule via the mirror-symmetrical 0 0 0 0 0 0 concerted rotations of the O3 H and O4 H hydroxyl groups around the C3 -O3 and C4 -O4 bonds through the non-planar or locally non-planar transition states (TSs), obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions (see Figure 3). TS of the 0 0 0 0 0 0 Conformational   DG DE DDG DDE DDG DDE k k   HO3 C3 C4 /HO4 C4 C3 TS i TS TS r 99.9% Transition 0 0 O3 H/O4 H 7 8 8 9 TS 2.97 457.1 0.92 1.09 7.50 7.99 6.59 6.90 2.3110 1.0910 5.2310 9.1710 12.5/14.4 1$7 0 0 O3 H/O4 H 7 7 8 8 TS 3.73 470.5 0.07 -0.23 7.03 7.19 6.96 7.42 5.1610 5.8010 6.3010 1.7210 12.3/14.1 2$3 0 0 O3 H/O4 H 7 7 8 8 TS 6.15 467.7 0.27 0.07 7.18 7.19 6.91 7.12 4.0410 6.3810 6.6310 1.5710 12.5/14.3 4$6 0 0 O3 H/O4 H 7 8 8 9 TS 5.56 459.1 0.92 1.14 7.40 7.96 6.48 6.82 2.7410 1.2910 4.4110 7.7310 12.4/14.3 5$8 0 0 O3 H/O4 H 8 8 8 9 TS 6.37 483.1 0.37 0.37 6.56 7.55 6.19 7.18 1.1610 2.1710 2.0710 4.6110 8.3/9.3 13$14 0 0 O3 H/O4 H 8 10 10 11 TS 6.09 466.9 3.13 3.25 6.30 7.13 3.17 3.88 1.7910 3.5310 1.9510 2.8310 10.0/12.3 15$20 0 0 O3 H/O4 H 8 8 8 9 TS 8.76 469.1 0.22 0.17 6.49 7.26 6.27 7.09 1.2910 1.8810 2.1810 5.3110 9.1/11.3 16$18 0 0 O3 H/O4 H 8 10 10 11 TS 8.97 473.2 3.25 3.31 6.32 7.21 3.07 3.90 1.7310 4.1910 1.6410 2.3910 10.3/11.2 17$23 0 0 O3 H/O4 H 7 8 8 9 4.38 455.1 0.87 1.46 7.46 8.11 6.59 6.64 13.9/15.6 TS 2.5010 1.0910 5.1710 9.2010 19$27 0 0 O3 H/O4 H 7 7 8 8 TS 5.41 461.5 0.03 0.17 6.75 7.21 6.72 7.04 8.3010 8.7310 4.0610 1.1510 14.1/15.6 21$22 0 0 O3 H/O4 H 7 7 8 8 3.43 454.5 0.86 1.29 7.56 8.08 6.70 6.78 14.0/15.8 TS 2.1110 9.0210 6.2110 1.1110 25$32 0 0 O3 H/O4 H 7 7 8 8 TS 4.51 465.7 0.22 0.20 6.89 7.34 6.67 7.14 6.5610 9.5010 4.3010 1.0510 13.8/15.3 28$31 0 0 O3 H/O4 H 8 8 8 9 7.18 468.7 6.58 7.32 6.58 7.32 6.38 7.19 12.3/13.0 TS 1.1110 1.5510 2.6010 6.4610 37$39 0 0 O3 H/O4 H 8 8 8 9 TS 6.91 470.9 0.33 0.33 6.56 7.36 6.23 7.03 1.1410 2.0110 2.1910 4.9810 9.6/11.7 38$40 0 0 O3 H/O4 H 8 8 8 9 4.74 467.2 0.30 0.25 6.56 7.33 6.26 7.07 10.7/12.9 TS 1.1510 1.9010 2.2710 5.2610 41$42 0 0 O3 H/O4 H 9 9 10 10 TS 5.12 476.2 0.37 0.37 4.41 5.29 4.04 4.92 4.3710 8.1310 5.5310 1.2310 10.6/11.3 43$44 For designations see Table 1. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 25 Appl. Sci. 2020, 10, 1147 8 of 22 2↔9 21↔34 O3′H O3′H 2 TS 2↔9 9 21 TS 21↔34 34 -1 -1 (ΔG=0.18 / ΔE=0.78/µ=2.71) (νi=340.2 cm ) (ΔG=4.17 / ΔE=4.58/µ=1.41) (ΔG=11.52 / ΔE=12.53/µ=3.09) (νi=328.8 cm ) (ΔG=15.53 / ΔE=16.67/µ=3.71) (ΔG=7.08 / ΔE=7.53/ µ=1.78) (ΔG=18.06 / ΔE=19.23/ µ=3.08) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.98 / ΔETS=3.80) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.01 / ΔETS=4.14) (ΔGTS=6.90 / ΔETS=6.75) (ΔGTS=6.54 / ΔETS=6.70) 4↔11 27↔33 O3′H O3′H 4 TS 4↔11 11 27 TS 27↔33 33 -1 -1 (ΔG=0.26 / ΔE=1.01/µ=5.33) (νi=333.4 cm ) (ΔG=4.39 / ΔE=5.08/µ=3.66) (ΔG=11.95 / ΔE=13.12/µ=6.97) (νi=363.5 cm ) (ΔG=15.20 / ΔE=16.15/µ=5.37) (ΔG=7.32 / ΔE=7.75/ µ=4.02) (ΔG=18.22 / ΔE=19.42 / µ=6.23) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.15 / ΔETS=4.07) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.25 / ΔETS=3.03) (ΔGTS=7.08 / ΔETS=6.73) (ΔGTS=6.27 / ΔETS=6.29) Figure 1. Cont. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 25 Appl. Sci. 2020, 10, 1147 9 of 22 7↔10 31↔36 O3′H O3′H 7 TS 7 10 10 31 TS 31 36 36 ↔ ↔ -1 -1 (ΔG=0.92 / ΔE=1.09/µ=5.05) (νi=361.1 cm ) (ΔG=4.20 / ΔE=4.30/µ=2.99) (ΔG=12.26 / ΔE=13.41/µ=1.73) (νi=336.2 cm ) (ΔG=16.11 / ΔE=17.27/µ=4.16) (ΔG=7.17 / ΔE=7.62/ µ=4.10) (ΔG=18.64 / ΔE=20.04/ µ=3.35) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.29 / ΔETS=3.21) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.85 / ΔETS=3.86) (ΔGTS=6.25 / ΔETS=6.53) (ΔGTS=6.39 / ΔETS=6.63) 8↔12 32↔35 O3′H O3′H 8 TS 8 12 12 32 TS 32 35 35 ↔ ↔ -1 -1 (ΔG=1.26 / ΔE=1.46/µ=7.26) (νi=362.0 cm ) (ΔG=4.58 / ΔE=4.69/µ=4.76) (ΔG=12.54 / ΔE=13.74 / 6.03) (νi=362.6 cm ) (ΔG=15.77 / ΔE=16.79/5.49) (ΔG=7.51 / ΔE=7.96 / µ=5.93) (ΔG=18.83 / ΔE=20.12 / µ=5.97) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.32 / ΔETS=3.23) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.23 / ΔETS=3.05) (ΔGTS=6.25 / ΔETS=6.51) (ΔGTS=6.29 / ΔETS=6.38) Figure 1. Cont. Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 25 Appl. Sci. 2020, 10, 1147 10 of 22 14↔24 39↔45 O3′H O3′H 14 TS 14↔24 24 39 TS 39↔45 45 -1 -1 (ΔG=7.96 / ΔE=8.03 / 5.96) (νi=355.2 cm ) (ΔG=11.66 / ΔE=11.79/4.07) (ΔG=20.98 / ΔE=22.05/µ=6.28) (νi=354.7 cm ) (ΔG=24.81 / ΔE=25.97/µ=5.30) (ΔG=14.47 / ΔE=14.96/ µ=5.08) (ΔG=27.58 / ΔE=29.06/ µ=6.15) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.70 / ΔETS=3.75) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.83 / ΔETS=3.92) (ΔGTS=6.50 / ΔETS=6.92) (ΔGTS=6.60 / ΔETS=7.01) 15↔26 40↔46 O3′H O3′H 15 TS 15 26 26 40 TS 40 46 46 ↔ ↔ -1 -1 (ΔG=7.98 / ΔE=8.15/µ=7.35) (νi=340.9 cm ) (ΔG=11.74 / ΔE=12.12/µ=4.79) (ΔG=21.17/ΔE=22.36/µ=8.50) (νi=344.1 cm ) (ΔG=24.87/ΔE=26.18/µ=6.29) (ΔG=14.42 / ΔE=15.01 / µ=6.24) (ΔG=27.62 / ΔE=29.16/ µ=7.86) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.79 / ΔETS=3.97) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.70 / ΔETS=3.82) (ΔGTS=6.47 / ΔETS=6.86) (ΔGTS=6.45 / ΔETS=6.80) Figure 1. Cont. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 25 Appl. Sci. 2020, 10, 1147 11 of 22 Figure 1. Geometrical structures of the quercetin molecule conformers and TSs with non-perpendicularly-oriented hydroxyl groups of their mutual interconversions via the 17↔29 42↔48 O3′H O3′H 17 TS 17↔29 29 42 TS 42↔48 48 -1 -1 (ΔG=8.31 / ΔE=8.39/µ=8.60) (νi=355.6 cm ) (ΔG=12.12 / ΔE=12.30/µ=6.70) (ΔG=21.60 / ΔE=22.94/µ=6.59) (νi=341.6 cm ) (ΔG=25.30 / ΔE=26.79/µ=4.90) (ΔG=14.93 / ΔE=15.44/ µ=7.60) (ΔG=28.01 / ΔE=29.73/ µ=6.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.81 / ΔETS=3.91) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.70 / ΔETS=3.85) (ΔGTS=6.62 / ΔETS=7.05) (ΔGTS=6.41 / ΔETS=6.79) 18↔30 44↔47 O3′H O3′H 18 TS 18↔30 30 44 TS 44↔47 47 -1 -1 (ΔG=8.40 / ΔE=8.62/µ=9.87) (νi=343.3 cm ) (ΔG=12.19 / ΔE=12.56/µ=7.28) (ΔG=23.77 / ΔE=25.00/µ=3.89) (νi=353.8 cm ) (ΔG=25.23 / ΔE=26.51/3.77) (ΔGTS=0.00 / ΔETS=0.00) (ΔG=14.90 / ΔE=15.49 / µ=8.65) (ΔGTS=3.79 / ΔETS=3.94) (ΔGTS=0.00 / ΔETS=0.00) (ΔG=28.00 / ΔE=29.62/ µ=4.47) (ΔGTS=6.50 / ΔETS=6.87) (ΔGTS=4.23 / ΔETS=4.62) (ΔGTS=1.46 / ΔETS=1.51) mirror-symmetrical rotation of the O3'H hydroxyl group around the C3'-O3' bonds, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under Figure 1. Geometrical structures of the quercetin molecule conformers and TSs with non-perpendicularly-oriented hydroxyl groups of their mutual interconversions via the mirror-symmetrical rotation of the O3’H hydroxyl group around the C3’-O3’ bonds, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions. Relative Gibbs free DG and electronic DE energies (in kcalmol ) (upper row represents energies relatively the conformer 1, whereas the lower row presents the initial conformer for each transformation), dipole moments  (Debye), and imaginary frequencies at TSs are provided at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory). Dotted lines indicate specific intramolecular contacts; their lengths are presented in Angstrom. Appl. Sci. 2020, 10, 1147 12 of 22 1↔10 23↔29 Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 24 O4′H O4′H 1 10 22 34 TS 1↔10 TS 22↔34 -1 -1 (ΔG=0.00 / ΔE=0.00 / µ=0.35) (νi=381.6 cm ) (ΔG=4.20 / ΔE=4.30/µ=2.99) (ΔG=11.55 / ΔE=12.70/µ=6.50) (νi=380.8 cm ) (ΔG=15.53 / ΔE=16.67/µ=3.71) (ΔG=7.05 / ΔE=7.38/ µ=2.41) (ΔG=18.20 / ΔE=19.70 / µ=5.05) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.20 / ΔETS=4.30) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.04 / ΔETS=3.97) (ΔGTS=7.05 / ΔETS=7.38) (ΔGTS=6.71 / ΔETS=7.00) 3↔9 23↔29 O4′H O4′H 3 TS 3↔9 9 23 TS 23↔29 29 -1 -1 (ΔG=0.25 / ΔE=0.55/µ=4.13) (νi=391.5 cm ) (ΔG=4.17 / ΔE=4.58/µ=1.41) (ΔG=11.56 / ΔE=11.70/µ=7.89) (νi=375.3 cm ) (ΔG=12.12 / ΔE=12.30/µ=6.70 (ΔG=7.11 / ΔE=7.79/ µ=2.82) (ΔG=14.90 / ΔE=15.43 / µ=7.10) ) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.92 / ΔETS=4.03) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.55 / ΔETS=0.60) (ΔGTS=6.86 / ΔETS=7.23) (ΔGTS=3.33 / ΔETS=3.73) Figure 2. Cont. Appl. Sci. 2020, 10, 1147 13 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 25 5↔12 25↔35 O4′H O4′H 5 TS 5↔12 12 25 TS 25↔35 35 -1 -1 (ΔG=0.34 / ΔE=0.32/ µ=3.01) (νi=379.7 cm ) (ΔG=4.58 / ΔE=4.69/µ=4.76) (ΔG=11.68 / ΔE=12.45/µ=3.55) (νi=373.7 cm ) (ΔG=15.77 / ΔE=16.79/5.49) (ΔG=7.27 / ΔE=7.67 / µ=3.63) (ΔG=18.48 / ΔE=19.67/ µ=5.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.24 / ΔETS=4.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.12 / ΔETS=4.35) (ΔGTS=6.93 / ΔETS=7.35) (ΔGTS=6.84 / ΔETS=7.22) 6↔11 28↔36 O4′H O4′H 6 TS 6 11 11 28 TS 28 36 36 ↔ ↔ -1 -1 (ΔG=0.53 / ΔE=1.08 / µ=5.65) (νi=389.2 cm ) (ΔG=4.39 / ΔE=5.08/µ=3.66) (ΔG=12.04 / ΔE=13.21/µ=6.54) (νi=382.7 cm ) (ΔG=16.11 / ΔE=17.27/µ=4.16) (ΔG=7.45 / ΔE=8.22/ µ=3.99) (ΔG=18.78 / ΔE=20.29 / µ=5.70) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.86 / ΔETS=4.00) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.07 / ΔETS=4.06) (ΔGTS=6.92 / ΔETS=7.14) (ΔGTS=6.74 / ΔETS=7.08) Figure 2. Cont. Appl. Sci. 2020, 10, 1147 14 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 25 13↔24 37↔45 O4′H O4′H 13 TS 13 24 24 37 TS 37 45 45 ↔ ↔ -1 -1 (ΔG=7.59 / ΔE=7.66/µ=5.64) (νi=375.8 cm ) (ΔG=11.66 / ΔE=11.79/4.07) (ΔG=20.78 / ΔE=21.92/µ=7.22) (νi=369.1 cm ) (ΔG=24.81 / ΔE=25.97/µ=5.30) (ΔG=14.40 / ΔE=14.88 / µ=4.78) (ΔG=27.53 / ΔE=29.03/ µ=6.56) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.07 / ΔETS=4.13) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.03 / ΔETS=4.05) (ΔGTS=6.81 / ΔETS=7.22) (ΔGTS=6.75 / ΔETS=7.11) 16↔30 38↔46 O3′H O4′H 16 TS 16↔30 30 38 TS 38↔46 46 -1 -1 (ΔG=8.18/ΔE=8.45/µ=6.24) (νi=374.4 cm ) (ΔG=12.19 / ΔE=12.56/µ=7.28) (ΔG=20.84 / ΔE=22.03 / µ=4.53) (νi=367.5 cm ) (ΔG=24.87/ΔE=26.18/µ=6.29) (ΔG=14.96 / ΔE=15.60/ µ=6.83) (ΔG=27.56 / ΔE=29.13/ µ=6.19) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.01 / ΔETS=4.11) (ΔGTS=6.78 / ΔETS=7.16) (ΔGTS=6.72 / ΔETS=7.10) Figure 2. Cont. Appl. Sci. 2020, 10, 1147 15 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 25 19↔33 41↔48 O4′H O4′H 19 TS 19↔33 33 41 TS 41↔48 48 -1 -1 (ΔG=11.08 / ΔE=11.66 / µ=2.63) (νi=371.6 cm ) (ΔG=15.20 / ΔE=16.15/µ=5.37) (ΔG=21.30 / ΔE=22.69/µ=2.99) (νi=366.7 cm ) (ΔG=25.30 / ΔE=26.79/µ=4.90) (ΔG=17.82 / ΔE=18.91/ µ=4.64) (ΔG=27.99 / ΔE=29.74/ µ=5.09) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.12 / ΔETS=4.49) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.00 / ΔETS=4.10) (ΔGTS=6.74 / ΔETS=7.25) (ΔGTS=6.69 / ΔETS=7.05) 20↔26 43↔47 O4′H O4′H 20 26 43 47 TS 20↔26 TS 43↔47 -1 -1 (ΔG=11.11 / ΔE=11.40/µ=3.62) (νi=371.6 cm ) (ΔG=11.74 / ΔE=12.12/µ=4.79) (ΔG=23.40 / ΔE=24.63/µ=6.05) (νi=369.4 cm ) (ΔG=25.23 / ΔE=26.51/3.77) (ΔGTS=0.00 / ΔETS=0.00) (ΔG=17.82 / ΔE=18.91/ µ=4.64) (ΔG=28.13 / ΔE=29.73/ µ=5.49) (ΔGTS=0.63 / ΔETS=0.72) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=1.83 / ΔETS=1.88) (ΔGTS=6.71 / ΔETS=7.51) (ΔGTS=4.72/ ΔETS=5.10) Figure 2. Geometrical structures of the quercetin molecule conformers and TSs with a non-perpendicularly-oriented hydroxyl groups of their mutual interconversions via the mirror-symmetrical rotation of the O4’H hydroxyl group around the C4’-O4’ bond, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions. For designations see Figure 1. Appl. Sci. 2020, 10, 1147 16 of 22 1↔7 19↔27 O3′H/O4′H 19 TS 19↔27 27 O3′H/O4′H TS 1 7 7 -1 1 (ΔG=11.08 / ΔE=11.66 / µ=2.63) (νi=455.1 cm ) (ΔG=11.95 / ΔE=13.12/µ=6.97) -1 (νi=457.1 cm ) (ΔG=0.92 / ΔE=1.09/µ=5.05) (ΔG=0.00 / ΔE=0.00 / µ=0.35) (ΔG=18.54 / ΔE=19.77 / µ=4.38) (ΔG=7.50 / ΔE=7.99/ µ=2.97) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=7.46 / ΔETS=8.11) (ΔGTS=0.87 / ΔETS=1.46) 2↔3 21↔22 O3′H/O4′H TS 2 3 -1 (νi=470.5 cm ) O3′H/O4′H 2 3 21 TS 21↔22 22 (ΔG=7.22 / ΔE=7.7.97/ µ=3.73) -1 (ΔG=0.18 / ΔE=0.78/µ=2.71) (ΔG=0.25 / ΔE=0.55/µ=4.13) (ΔG=11.52 / ΔE=12.53/µ=3.09) (νi=461.5 cm ) (ΔG=11.55 / ΔE=12.70/µ=6.50) (ΔG=18.27 / ΔE=19.74 / µ=5.41) (ΔGTS=7.03 / ΔETS=7.19) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.07 / ΔETS=-0.23) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=6.75 / ΔETS=7.21) (ΔGTS=0.03 / ΔETS=0.17) Figure 3. Cont. Appl. Sci. 2020, 10, 1147 17 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 25 4↔6 25↔32 O3′H/O4′H TS 4↔6 O3′H/O4′H 4 6 25 TS 25 32 32 -1 (νi=467.7 cm ) -1 (ΔG=0.26 / ΔE=1.01/µ=5.33) (ΔG=0.53 / ΔE=1.08 / µ=5.65) (ΔG=11.68 / ΔE=12.45/µ=3.55) (νi=454.5 cm ) (ΔG=12.54 / ΔE=13.74 / 6.03) (ΔG=7.42 / ΔE=8.21/ µ=6.15) (ΔG=19.20 / ΔE=20.52 / µ=3.43) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.27 / ΔETS=0.07) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=7.56 / ΔETS=8.08) (ΔGTS=0.86 / ΔETS=1.29) (ΔGTS=7.18 / ΔETS=7.19) 5↔8 28↔31 O3′H/O4′H TS 5 8 O3′H/O4′H TS 28↔31 -1 5 (νi=459.1 cm ) 8 28 31 -1 (νi=465.7 cm ) (ΔG=0.34 / ΔE=0.32/ µ=3.01) (ΔG=7.75 / ΔE=8.28 / µ=5.56) (ΔG=1.26 / ΔE=1.46/µ=7.26) (ΔG=12.04 / ΔE=13.21/µ=6.54) (ΔG=12.26 / ΔE=13.41/µ=1.73) (ΔG=18.93 / ΔE=20.55 / µ=4.51) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=7.40 / ΔETS=7.96) (ΔGTS=0.92 / ΔETS=1.14) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.22 / ΔETS=0.20) (ΔGTS=6.89 / ΔETS=7.34) Figure 3. Cont. Appl. Sci. 2020, 10, 1147 18 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 20 of 25 13↔14 37↔39 O3′H/O4′H O3′H/O4′H TS 13↔14 TS 37↔39 13 14 37 39 -1 -1 (νi=483.1 cm ) (νi=468.7 cm ) (ΔG=7.59 / ΔE=7.66/µ=5.64) (ΔG=7.96 / ΔE=8.03 / 5.96) (ΔG=20.78 / ΔE=21.92/µ=7.22) (ΔG=20.98 / ΔE=22.05/µ=6.28) (ΔG=14.15 / ΔE=15.21 / µ=6.37) (ΔG=27.36 / ΔE=29.24/ µ=7.18) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.37 / ΔETS=0.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.20 / ΔETS=0.13) (ΔGTS=9.82 / ΔETS=10.19) (ΔGTS=6.58 / ΔETS=7.32) 15↔20 38↔40 O3′H/O4′H O3′H/O4′H TS 15 20 TS 38 40 ↔ ↔ 15 20 38 40 -1 -1 (νi=466.9 cm ) (νi=470.9 cm ) (ΔG=7.98 / ΔE=8.15/µ=7.35) (ΔG=11.11 / ΔE=11.40/µ=3.62) (ΔG=20.84 / ΔE=22.03 / µ=4.53) (ΔG=21.17/ΔE=22.36/µ=8.50) (ΔG=14.24 / ΔE=15.27 / µ=6.09) (ΔG=27.40 / ΔE=29.39/ µ=6.91) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.13 / ΔETS=3.25) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.33 / ΔETS=0.33) (ΔGTS=6.30 / ΔETS=7.13) (ΔGTS=6.56 / ΔETS=7.36) Figure 3. Cont. Appl. Sci. 2020, 10, 1147 19 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 21 of 25 16↔18 41↔42 O3′H/O4′H O3′H/O4′H TS 16 18 TS 41 42 ↔ ↔ 16 18 41 42 -1 -1 (νi=469.1 cm ) (νi=467.2 cm ) (ΔG=8.18/ΔE=8.45/µ=6.24) (ΔG=8.40 / ΔE=8.62/µ=9.87) (ΔG=21.30 / ΔE=22.69/µ=2.99) (ΔG=21.60 / ΔE=22.94/µ=6.59) (ΔG=14.67 / ΔE=15.70 / µ=8.76) (ΔG=27.86 / ΔE=30.02/ µ=4.74) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.22 / ΔETS=0.17) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.30 / ΔETS=0.25) (ΔGTS=6.49 / ΔETS=7.26) (ΔGTS=6.56 / ΔETS=7.33) 17↔23 43↔44 O3′H/O4′H O3′H/O4′H TS 17↔23 TS 43↔44 17 23 43 44 -1 -1 (νi=473.2 cm ) (νi=476.2 cm ) (ΔG=8.31 / ΔE=8.39/µ=8.60) (ΔG=11.56 / ΔE=11.70/µ=7.89) (ΔG=23.40 / ΔE=24.63/µ=6.05) (ΔG=23.77 / ΔE=25.00/µ=3.89) (ΔG=14.63 / ΔE=15.60 / µ=8.97) (ΔG=27.81 / ΔE=29.92/ µ=5.12) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.25 / ΔETS=3.31) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.37 / ΔETS=0.37) (ΔGTS=6.32 / ΔETS=7.21) (ΔGTS=4.41 / ΔETS=5.29) Figure 3. Geometrical structures of the quercetin molecule conformers and non-planar or locally non-planar TSs of their mutual concerted 0 0 0 0 0 0 interconversions via the mirror-symmetrical rotation of the O3 H and O4 H hydroxyl groups around the C3 -O3 and C4 -O4 bonds, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions. For detailed designations see Figure 1. Appl. Sci. 2020, 10, 1147 20 of 22 In the case of the quercetin molecule, both of these tasks are overcomplicated. The reason is that the conformational mobility of this molecule is closely connected with its prototropic tautomerism [40,41]. It is known that the quercetin molecule has 202 molecular prototropic tautomers [40]. By contrast, now it is not known for sure all possible targets and their structure, despite all reasons to think that the range of this information would continuously grow together with the growing of the progress in bioinformatics and structural analysis. If also consider the conformationally-tautomeric variability of the targets, it would become clear that clarification of the structural grounds for the biological activity of the quercetin molecule is quite dicult task. We aimed to highlight this obstacle by the title of this paper. 4. Conclusions and Perspective for the Future Research In this study, which is a logical continuation of our previous works on this topic [16–21], new pathways of the transformations of the conformers of the quercetin molecule into each other were 0 0 found, which occurred due to the torsional mobility of the O3 H and O4 H hydroxyl groups. It was established that the presence of only three degrees of freedom of the conformational mobility 0 0 of the O3 H and O4 H hydroxyl groups is connected with their concerted behavior, which is controlled by the non-planar (in the case of the interconverting planar conformers) or locally non-planar (in other 0 0 O3 H/O4 H 0 0 cases) TSs , in which O3 H and O4 H hydroxyl groups are oriented by the hydrogen atoms towards each other. All these results assert that quercetin is a rather dynamical molecule, which is able to transform through the pathways into di erent conformers, forming complex networking. We also shortly described the long-term perspectives for the investigation of the structural basis of the biological activity of quercetin. Author Contributions: Setting of an idea of investigation, data preparation, analysis of the received results, writing and proofreading of the text of manuscript, references, Tables and Figures have been performed jointly by O.O.B. and D.M.H. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Sciences Multidisciplinary Digital Publishing Institute

A Never-Ending Conformational Story of the Quercetin Molecule: Quantum-Mechanical Investigation of the O3′H and O4′H Hydroxyl Groups Rotations

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applied sciences Article A Never-Ending Conformational Story of the Quercetin Molecule: Quantum-Mechanical 0 0 Investigation of the O3 H and O4 H Hydroxyl Groups Rotations 1 , 1 , 2 Ol’ha O. Brovarets’ * and Dmytro M. Hovorun Department of Molecular and Quantum Biophysics, Institute of Molecular Biology and Genetics, National Academy of Sciences of Ukraine, 150 Akademika Zabolotnoho Street, 03680 Kyiv, Ukraine; dhovorun@imbg.org.ua Department of Molecular Biotechnology and Bioinformatics, Institute of High Technologies, Taras Shevchenko National University of Kyiv, 2-h Akademika Hlushkova Avenue, 03022 Kyiv, Ukraine * Correspondence: o.o.brovarets@imbg.org.ua Received: 8 January 2020; Accepted: 2 February 2020; Published: 8 February 2020 Abstract: The quercetin molecule is known to be an e ective pharmaceutical compound of a plant origin. Its chemical structure represents two aromatic A and B rings linked through the C ring 0 0 containing oxygen and five OH hydroxyl groups attached to the 3, 3 , 4 , 5, and 7 positions. In this study, a novel conformational mobility of the quercetin molecule was explored due to the turnings of 0 0 the O3 H and O4 H hydroxyl groups, belonging to the B ring, around the exocyclic C-O bonds. It was established that the presence of only three degrees of freedom of the conformational mobility of the 0 0 O3 H and O4 H hydroxyl groups is connected with their concerted behavior, which is controlled by the non-planar (in the case of the interconverting planar conformers) or locally non-planar (in 0 0 O3 H/O4 H 0 0 other cases) TSs transition states, in which O3 H and O4 H hydroxyl groups are oriented by the hydrogen atoms towards each other. We also explored the number of the physico-chemical and electron-topological characteristics of all intramolecular-specific contacts—hydrogen bonds and attractive van der Waals contacts at the conformers and also at the transition states. Long-terms perspectives for the investigations of the structural bases of the biological activity of this legendary molecule have been shortly described. Keywords: Quercetin molecule; conformational mobility; hydroxyl group; transition state; concerted rotation of the hydroxyl groups; quantum-chemical calculations; quantum technology 1. Introduction 0 0 The quercetin molecule (3, 3 , 4 , 5, 7—pentahydroxyflavone, C H O ) is an important flavonoid 15 10 7 compound, which is found in many foods and plants, in particular in honey [1], and is known to act as a natural drug molecule with a wide range of treatment properties—antioxidant, anti-toxic, etc.—and is also involved in drug delivery from the site of administration to the therapeutic target [2–9]. The structure of the quercetin contains two aromatic A and B rings linked through the C ring containing 0 0 oxygen and five OH hydroxyl groups attached to the 3, 3 , 4 , 5 and 7 positions (see Scheme 1) [10–15]. In a previous study [16], by using the quantum-mechanical (QM) calculations at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory together with Bader ’s “Quantum Theory of Atoms in Molecules”, for the first time, all possible conformers were established, corresponding to local minima on the potential energy hypersurface of the isolated quercetin molecule. Appl. Sci. 2020, 10, 1147; doi:10.3390/app10031147 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 1147 2 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 24 Scheme 1. Chemical structure of the quercetin molecule and standard numeration of its atoms. Scheme 1. Chemical structure of the quercetin molecule and standard numeration of its atoms. Altogether, 48 stable conformers were established, which have been divided into four di erent In a previous study [16], by using the quantum-mechanical (QM) calculations at the conformational subfamilies by their structural properties: subfamily I—conformers 1–12; subfamily MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory together with Bader’s “Quantum II—conformers 13-18, 20, 23, 24, 26, 29, and 30; subfamily III—conformers 19, 21, 22, 25, 27, 28, Theory of Atoms in Molecules”, for the first time, all possible conformers were established, and 31–36; subfamily IV—conformers 37–48 [16]. It was shown that these 48 stable conformers corresponding to local minima on the potential energy hypersurface of the isolated quercetin (24 planar structures (C point symmetry) and 24 non-planar structures (C point symmetry)) represent s 1 molecule. a comprehensive set of the theoretically possible structures. Altogether, 48 stable conformers were established, which have been divided into four different Conformers of quercetin are polar structures with a dipole moment, which varies within the range conformational subfamilies by their structural properties: subfamily I—conformers 1–12; subfamily from 0.35 to 9.87 Debye for di erent conformers with di erent direction for each. II—conformers 13-18, 20, 23, 24, 26, 29, and 30; subfamily III—conformers 19, 21, 22, 25, 27, 28, and Their relative Gibbs free energies are arranged within the range from 0.00 to 25.30 kcalmol 31–36; subfamily IV—conformers 37–48 [16]. It was shown that these 48 stable conformers (24 planar under normal conditions in vacuum. structures (Cs point symmetry) and 24 non-planar structures (C1 point symmetry)) represent a One half of these structures (24 conformers) possesses planar structure (C point symmetry), comprehensive set of the theoretically possible structures. whereas the other half (24 conformers) does not have symmetry at all (C point symmetry) Conformers of quercetin are polar structures with a dipole moment, which varies within the 0 0 (C3C2C1 C2 = 40.9–44.3 degree; C2C3O3H = 9.4–16.3 degree). range from 0.35 to 9.87 Debye for different conformers with different direction for each. We also defined their physico-chemical characteristics, in particular, structural, energetic, and −1 Their relative Gibbs free energies are arranged within the range from 0.00 to 25.30 kcal∙mol polar, which are necessary for understanding of the biological mechanisms of action of this molecule. under normal conditions in vacuum. Intramolecular specific contacts have also been explored in detail. One half of these structures (24 conformers) possesses planar structure (Cs point symmetry), Bader ’s “Quantum Theory of Atoms in Molecules” analysis shows that conformers of the quercetin whereas the other half (24 conformers) does not have symmetry at all (C1 point symmetry) molecule di er from each other by the intramolecular specific contacts (two or three), stabilizing all (C3C2C1′C2′ = 40.9–44.3 degree; C2C3O3H = 9.4–16.3 degree). possible conformers of the molecule—H-bonds (both classical OH ::: O and so-called unusual CH We also defined their physico-chemical characteristics, in particular, structural, energetic, and ::: O and OH ::: C) and attractive van der Waals contacts O ::: O. Energies of these cooperative polar, which are necessary for understanding of the biological mechanisms of action of this intramolecular specific contacts have been estimated [16]. molecule. Intramolecular specific contacts have also been explored in detail. Also, it was theoretically modeled the conformational interconversions [17–21] in the 24 pairs of Bader’s “Quantum Theory of Atoms in Molecules” analysis shows that conformers of the the conformers of the quercetin molecule through the rotation of its almost non-deformable (A+C) and quercetin molecule differ from each other by the intramolecular specific contacts (two or three), B rings around the C2-C1 bond through the quasi-orthogonal transition state (TS) with low values stabilizing all possible conformers of the molecule—H-bonds (both classical OH…O and so-called of the imaginary frequencies (28-33/29-36 cm ) and Gibbs free energies of activation in the range of unusual CH…O and OH…C) and attractive van der Waals contacts O…O. Energies of these 2.17 to 5.68/1.86 to 4.90 kcalmol in the continuum with dielectric permittivity " = 1/" = 4 under cooperative intramolecular specific contacts have been estimated [16]. normal conditions. Also, we studied the changes of the number of physico-chemical characteristics of Also, it was theoretically modeled the conformational interconversions [17–21] in the 24 pairs of all intramolecular specific contacts—hydrogen bonds and attractive van der Waals contacts during the conformers of the quercetin molecule through the rotation of its almost non-deformable (A+C) these conformational rearrangements. and B rings around the C2-C1′ bond through the quasi-orthogonal transition state (TS) with low This study is a logical development of the previous investigations [16–18] and is devoted to the −1 values of the imaginary frequencies (28-33/29-36 cm ) and Gibbs free energies of activation in the novel interconversions between the conformers of the quercetin molecule due to the rotations of the −1 range of 2.17 to 5.68/1.86 to 4.90 kcal∙mol in the continuum with dielectric permittivity ε = 1/ε = 4 0 0 O3 H and O4 H hydroxyl groups around the exocyclic C-O bonds outside. under normal conditions. Also, we studied the changes of the number of physico-chemical As a result, it was found that di erent conformers of the quercetin molecule are tightly characteristics of all intramolecular specific contacts—hydrogen bonds and attractive van der Waals interconnected with each other through the set of the TSs. Moreover, these conformational contacts during these conformational rearrangements. transformations are assisted by the intramolecular H-bonds and van der Waals contacts. This study is a logical development of the previous investigations [16–18] and is devoted to the In reality, it is not as easy a task as it seems, as the question of “Why two neighboring hydroxyl novel interconversions between the conformers of the quercetin molecule due to the rotations of the groups in the aromatic ring have only three, but not four conformational degrees of freedom?” remains O3′H and O4′H hydroxyl groups around the exocyclic C-O bonds outside. without answer [22,23]. As a result, it was found that different conformers of the quercetin molecule are tightly The main idea of this investigation is summarized in the following statements. interconnected with each other through the set of the TSs. Moreover, these conformational We suggest that the conformational mobility of the C ring of the quercetin molecule, which transformations are assisted by the intramolecular H-bonds and van der Waals contacts. 0 0 contains two neighboring O3 H and O4 H hydroxyl groups, that is, conversion of one stable In reality, it is not as easy a task as it seems, as the question of “Why two neighboring hydroxyl groups in the aromatic ring have only three, but not four conformational degrees of freedom?” remains without answer [22,23]. Appl. Sci. 2020, 10, 1147 3 of 22 0 0 0 0 0 0 0 0 O3 HO4 H/O4 HO3 H configuration into the other O4 HO3 H/O3 HO4 H and vice versa, is realized by two significantly di erent pathways from the topological and energetical point of view. First, (this pathway is more or less evident) it occurs by the restricted rotations of the hydroxyls by the angle of 180 degrees through the corresponding TSs and through the high-energetical dynamically 0 0 0 0 stable O3 HO4 H/O4 HO3 H configuration. The other pathway is quite unusual—it is realized through one conformational transition, which has concerted character and is controlled by the non-planar 0 0 0 0 O3 HHO4 /O4 HHO3 TSs with the high values of the imaginary frequency. A previously suggested idea has been completely confirmed by careful QM investigation—we have identified for the first time the aforementioned pathways of the conformational variability of the quercetin molecule and documented their structural properties, including symmetrical, polar, energetical, and kinetic characteristics, which are quite important for the understanding of the structural grounds of the biological activity of the quercetin molecule. 2. Computational Methods Calculations of the geometrical structures of the TSs of the conformational interconversions and their vibrational spectra, corresponding to the local minima on the potential (electronic) energy hyper surface, have been performed at the DFT B3LYP/6-311++G(d,p) level of QM theory [24–26] by Gaussian’09 program package [27], which was successfully approved in our previous studies for the calculations of the heterocyclic compounds [28,29]. A scaling factor of 0.9668 has been used to correct the harmonic frequencies for the investigated structures [30]. Intrinsic reaction coordinate (IRC) calculations in the forward and reverse directions from each TS, which have been confirmed by the presence of one and only one imaginary frequency in the vibrational spectra, have been performed using Hessian-based predictor–corrector integration algorithm [31]. All calculations were performed for the quercetin molecule as their intrinsic property, that is adequate for modeling of the processes occurring in real systems [16,17,32]. Electronic and Gibbs free energies under normal conditions have been calculated by single point calculations at the MP2/6-311++G(2df,pd) level of theory [33–35]. The time  necessary to reach 99.9% of the equilibrium concentration of the reactant and 99.9% product in the system of the reversible first-order forward (k ) and reverse (k ) reactions can be estimated by the formula [36] ln10 = (1) 99.9% k + k The lifetime, , of the conformers has been calculated using the formula 1/k , where the values of the forward k and reverse k rate constants for the tautomerization reactions were obtained as [36] f r DDG f ,r k T RT k = G e (2) f ,r where the quantum tunneling e ect has been accounted by Wigner ’s tunneling correction [37], successfully used for the double proton reactions in DNA base pairs [28]: 1 h G = 1 + (3) 24 k T where k —Boltzmann’s constant, h—Planck’s constant, DDG —Gibbs free energy of activation for B f,r the conformational transition in the forward (f ) and reverse (r) directions, and  —magnitude of the imaginary frequency associated with the vibrational mode at the TS. The topology of the electron density was analyzed using the program package AIM’2000 [38] with all default options and wave functions obtained at the level of theory used for geometry optimization. The presence of the (3,1) bond critical point (BCP), bond path between hydrogen donor and acceptor, Appl. Sci. 2020, 10, 1147 4 of 22 and positive value of the Laplacian at this BCP (D > 0) were considered altogether as criteria for the formation of the H-bond and attractive van der Waals contact [39]. In this work, standard numeration of atoms has been used [16,17]. Numeration of the conformers, which are highlighted in bold in the text, have been used as in the work [16]. 3. Obtained Results and Their Discussion In this study, we logically continued to investigate the conformational mobility [16–18] of the 0 0 quercetin molecule and extend this approach to the rotations of the hydroxyl groups in the 3 and 4 positions, which are carefully presented in Tables 1–3 and Figures 1–3. The most obvious methods of the conformational interconversions between the 48 conformers [16] of the quercetin molecule were 0 0 considered and investigated in detail through the rotations of the O3 H and O4 H hydroxyl groups around the exocyclic C-O covalent bonds. In this case, the TSs have been formed gradually, starting from the 48 conformers of the quercetin molecule [16] by the single or concerted rotations of the O3 H 0 0 0 0 0 O3 H O4 H O3 H/O4 H and O4 H hydroxyl groups—designated as TS , TS , and TS , respectively. Therefore, detailed analysis of the obtained results enabled us to obtain the following observations 0 0 and their discussion. As individual, the concerted rotational transitions of the O3 H and O4 H hydroxyl groups proceed through the mirror-symmetrical pathways, which are controlled by the mirror-symmetrical TSs. Totally, we have revealed 48 TSs—16 TSs in each case (Figures 1–3; Tables 1–3). 0 0 O3 H O4 H Individual conformational transitions are controlled by the non-planar TS and TS (C 0 0 0 0 0 0 point symmetry) with non-orthogonal structure (see HO3 C3 C2 (78.7–83.3 degree) and HO4 C4 C5 (80.2–82.1 degree) dihedral angles in Tables 1 and 2 and Figures 1 and 2). Their non-orthogonal structure, most probably, could be connected with the non-symmetrical surrounding of the free electronic pairs of the oxygen atoms of the hydroxyl groups. The TSs for the concerted conformational 0 0 O3 H/O4 H transformations—TSs —possess non-planar structure in the case of the planar conformers 1-12, 19, 21, 22, 25, 27, 28, and 31–36 and local non-planar structure for the non-planar conformers, 13-18, 20, 23, 24, 26, 29, 30, and 37–48, which mutually interconvert (Figure 3, Table 3). O4 H Gibbs free energies of activation for these processes form the following order; DDG (3.33–7.05) TS 0 0 0 O3 H O3 H/O4 H 1 < DDG (4.23–7.08) < DDG (4.41–7.56 kcalmol under normal conditions) (Tables 1–3). TS TS 0 0 O3 H O4 H The imaginary frequencies are in the following ranges: 366.7–391.5 (TS ), 328.8–363.5 (TS ), 0 0 O3 H/O4 H and 454.5–483.1 (TS ). Without exception, 48 conformers of the quercetin molecule have been established to be the dynamically stable structures, based on the investigated conformational transitions. During their lifetime ( = (1.05–2.53)10 s) (Tables 1–3), the lowest frequency intramolecular vibrations can occur [16]. It is a characteristic feature that investigated conformational transitions are dipole-active, as they cause the changing of the dipole moment by the absolute value, so by the spatial orientation, and practically do not disturb the structure of the quercetin molecule and physico-chemical characteristics 0 0 of its specific intramolecular interactions. Even the energy of the intramolecular C2 /C6 H ::: O3 and 0 0 O3H ::: C2 /C6 H H-bonds between the B and C rings (Figures 1–3) change at these conformational transitions by no more than on ~4.7%. Interestingly, concerted conformational transitions, which 0 0 O3 H/O4 H are controlled by the TSs , proceed without intermediates on the hyperspace of the Gibbs free energy. Moreover, we did not register any specific intramolecular interactions in the B ring of the quercetin 0 0 molecule at the conformational motions of the O3 H and O4 H hydroxyl groups. All investigated 10 11 conformational transitions are quite rapid processes, for which 1.0410 >  > 7.3010 s. 99.9% Therefore, provided investigation gives total assurance that the availability of the three 0 0 conformational degrees of freedom for the O3 H and O4 H hydroxyl groups is connected with their concerted, coordinated behavior (Figure 3, Table 3). Let us to make one important notion before going to the conclusions. It is known, that biological activity of the molecules, is caused by at least two interdependent reasons—their intramolecular structural variability and specific interaction with the targets of the di erent origin. Appl. Sci. 2020, 10, 1147 5 of 22 Table 1. Energetic, polar, structural, and kinetic characteristics of the conformational transitions in the isolated quercetin molecule via the mirror-symmetrical 0 0 0 0 rotations of the O3 H hydroxyl group around the C3 -O3 bond through the transition states (TSs) with a non-perpendicularly-oriented O3 H group, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions (see Figure 1). TS of the a b c d e f g h i j k l 0 0 0 m Conformational   DG DE DDG DDE DDG DDE k k   HO3 C3 C2 TS i TS TS f r 99.9% Transition O3 H 7 10 10 11 TS 1.78 340.2 3.98 3.80 6.90 6.75 2.91 2.95 6.0110 5.0110 1.3810 2.0010 80.1 2$9 O3 H 7 10 10 11 TS 4.02 333.4 4.15 4.07 7.08 6.73 2.93 2.66 4.3610 4.8210 1.4310 2.0710 79.1 4$11 O3 H 8 10 10 11 4.10 361.1 3.29 3.21 6.25 6.53 2.97 3.32 82.8 TS 1.8010 4.6210 1.4910 2.1710 7$10 O3 H 8 10 10 11 TS 5.93 362.0 3.32 3.23 6.25 6.51 2.93 3.28 1.8010 4.9110 1.4010 2.0410 82.9 8$12 O3 H 8 10 10 11 5.08 355.2 3.70 3.75 6.50 6.92 2.80 3.17 81.3 TS 1.1710 6.0910 1.1310 1.6410 14$24 O3 H 8 10 11 11 TS 6.24 340.9 3.79 3.97 6.47 6.86 2.68 2.89 1.2310 7.4410 9.2710 1.3410 79.3 15$26 O3 H 7 10 10 11 7.60 355.6 3.81 3.91 6.62 7.05 2.81 3.15 80.6 TS 9.7010 6.0310 1.1410 1.6610 17$29 O3 H 8 10 11 11 TS 8.65 343.3 3.79 3.94 6.50 6.87 2.71 2.93 1.1710 7.0410 9.7910 1.4210 79.5 18$30 O3 H 8 10 11 11 3.08 328.8 4.01 4.14 6.54 6.70 2.53 2.56 78.7 TS 1.0910 9.5110 7.2610 1.0510 21$34 O3 H 8 10 10 11 TS 6.23 363.5 3.25 3.03 6.27 6.29 3.02 3.27 1.7510 4.2510 1.6210 2.3510 83.3 27$33 O3 H 8 10 11 11 TS 3.35 336.2 3.85 3.86 6.39 6.63 2.54 2.77 1.4210 9.4410 7.3010 1.0610 79.8 31$36 O3 H 8 10 10 11 TS 5.97 362.6 3.23 3.05 6.29 6.38 3.06 3.33 1.6910 3.9610 1.7410 2.5310 83.2 32$35 O3 H 7 10 10 11 TS 6.15 354.7 3.83 3.92 6.60 7.01 2.77 3.09 9.9710 6.4310 1.0710 1.5610 80.5 39$45 O3 H 8 10 10 11 TS 7.86 344.1 3.70 3.82 6.45 6.80 2.75 2.98 1.2710 6.6010 1.0410 1.5210 80.5 40$46 O3 H 8 10 11 11 TS 6.37 341.6 3.70 3.85 6.41 6.79 2.71 2.94 1.3610 7.0510 9.7810 1.4210 79.6 42$48 O3 H 9 10 11 11 TS 4.47 353.8 1.46 1.51 4.23 4.62 2.77 3.12 5.4710 6.4610 9.8510 1.5510 81.1 44$47 a b 1 c The dipole moment of the TS, Debye. The imaginary frequency at the TS of the conformational transition, cm . The Gibbs free energy of the initial relative to the terminal conformer 1 d 1 e of the quercetin molecule (T = 298.15 K), kcalmol . The electronic energy of the initial relative to the terminal conformer of the quercetin molecule, kcalmol . The Gibbs free 1 f energy barrier for the forward conformational transformation of the quercetin molecule, kcalmol . The electronic energy barrier for the forward conformational transformation of the 1 g 1 h quercetin molecule, kcalmol . The Gibbs free energy barrier for the reverse conformational transformation of the quercetin molecule, kcalmol . The electronic energy barrier for the 1 i 1 j reverse conformational transformation of the quercetin molecule, kcalmol . The rate constant for the forward conformational transformation, s . The rate constant for the reverse 1 k conformational transformation, s . The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the reaction of the conformational l m 0 transformation, s. The lifetime of the product of the conformational transition, s. The dihedral angle, which describes at the TS the orientation of the O3 H hydroxyl group relatively the B ring of the quercetin molecule, degree; sings “” correspond to enantiomers. Appl. Sci. 2020, 10, 1147 6 of 22 Table 2. Energetic, polar, structural, and kinetic characteristics of the conformational transitions in the isolated quercetin molecule via the mirror-symmetrical 0 0 0 0 rotations of the O4 H hydroxyl group around the C4 -O4 bond through the transition states (TSs) with a non-perpendicularly-oriented O4 H group, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions (see Figure 2). TS of the 0 0 0 Conformational   DG DE DDG DDE DDG DDE k k   HO4 C4 C5 TS i TS TS f r 99.9% Transition O4 H 7 10 10 11 TS 2.41 381.6 4.20 4.30 7.05 7.38 2.84 3.08 4.7510 5.7710 1.2010 1.7310 81.1 1$10 O4 H 7 10 10 11 TS 2.82 391.5 3.92 4.03 6.86 7.23 2.94 3.21 6.6010 4.9510 1.3910 2.0210 81.9 3$9 O4 H 7 10 11 3.63 379.7 4.24 4.37 6.93 7.35 2.69 2.98 9.32E-11 80.8 TS 5.8010 7.4110 1.3510 5$12 O4 H 7 10 10 11 TS 3.99 389.2 3.86 4.00 6.92 7.14 3.07 3.14 5.9010 3.9810 1.7310 2.5110 82.1 6$11 O4 H 7 10 10 11 4.78 375.8 4.07 4.13 6.81 7.22 2.74 3.09 80.4 TS 7.1210 6.8910 1.0010 1.4510 13$24 O3 H 7 10 10 11 TS 6.83 374.4 4.01 4.11 6.78 7.16 2.77 3.04 7.4210 6.5210 1.0610 1.5310 80.7 16$30 O4 H 7 10 11 11 4.64 371.6 4.12 4.49 6.74 7.25 2.62 2.76 80.2 TS 7.9810 8.4010 8.2210 1.1910 19$33 O4 H 7 8 8 9 TS 4.64 371.6 0.63 0.72 6.71 7.51 6.08 6.79 8.3610 2.4210 2.1210 4.1310 80.2 20$26 O4 H 7 10 11 11 5.05 380.8 4.04 3.97 6.71 7.00 2.67 3.03 81.8 TS 8.4310 7.7410 8.9110 1.2910 22$34 O4 H 10 10 11 11 TS 7.10 375.3 0.55 0.60 3.33 3.73 2.78 3.13 2.5210 6.4110 7.7310 1.5610 80.7 23$29 O4 H 7 10 11 11 TS 5.37 373.7 4.12 4.35 6.84 7.22 2.71 2.88 6.7710 7.1710 9.6210 1.3910 80.5 25$35 O4 H 7 10 11 11 TS 5.70 382.7 4.07 4.06 6.74 7.08 2.67 3.02 7.9910 7.7110 8.9510 1.3010 81.6 28$36 O4 H 7 10 11 11 TS 6.56 369.1 4.03 4.05 6.75 7.11 2.72 3.06 7.8010 7.0910 9.7410 1.4110 80.4 37$45 O4 H 7 10 11 11 TS 6.19 367.5 4.03 4.16 6.72 7.10 2.69 2.95 8.1410 7.4010 9.3210 1.3510 80.2 38$46 O4 H 7 10 11 11 TS 5.09 366.7 4.00 4.10 6.69 7.05 2.69 2.94 8.6410 7.4210 9.3010 1.3510 80.4 41$48 O4 H 9 10 10 11 TS 5.49 369.4 1.83 1.88 4.73 5.10 2.90 3.22 2.3710 5.2110 1.2710 1.9210 80.2 43$47 For designations see Table 1. Appl. Sci. 2020, 10, 1147 7 of 22 Table 3. Energetic, polar, structural, and kinetic characteristics of the conformational transitions in the isolated quercetin molecule via the mirror-symmetrical 0 0 0 0 0 0 concerted rotations of the O3 H and O4 H hydroxyl groups around the C3 -O3 and C4 -O4 bonds through the non-planar or locally non-planar transition states (TSs), obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions (see Figure 3). TS of the 0 0 0 0 0 0 Conformational   DG DE DDG DDE DDG DDE k k   HO3 C3 C4 /HO4 C4 C3 TS i TS TS r 99.9% Transition 0 0 O3 H/O4 H 7 8 8 9 TS 2.97 457.1 0.92 1.09 7.50 7.99 6.59 6.90 2.3110 1.0910 5.2310 9.1710 12.5/14.4 1$7 0 0 O3 H/O4 H 7 7 8 8 TS 3.73 470.5 0.07 -0.23 7.03 7.19 6.96 7.42 5.1610 5.8010 6.3010 1.7210 12.3/14.1 2$3 0 0 O3 H/O4 H 7 7 8 8 TS 6.15 467.7 0.27 0.07 7.18 7.19 6.91 7.12 4.0410 6.3810 6.6310 1.5710 12.5/14.3 4$6 0 0 O3 H/O4 H 7 8 8 9 TS 5.56 459.1 0.92 1.14 7.40 7.96 6.48 6.82 2.7410 1.2910 4.4110 7.7310 12.4/14.3 5$8 0 0 O3 H/O4 H 8 8 8 9 TS 6.37 483.1 0.37 0.37 6.56 7.55 6.19 7.18 1.1610 2.1710 2.0710 4.6110 8.3/9.3 13$14 0 0 O3 H/O4 H 8 10 10 11 TS 6.09 466.9 3.13 3.25 6.30 7.13 3.17 3.88 1.7910 3.5310 1.9510 2.8310 10.0/12.3 15$20 0 0 O3 H/O4 H 8 8 8 9 TS 8.76 469.1 0.22 0.17 6.49 7.26 6.27 7.09 1.2910 1.8810 2.1810 5.3110 9.1/11.3 16$18 0 0 O3 H/O4 H 8 10 10 11 TS 8.97 473.2 3.25 3.31 6.32 7.21 3.07 3.90 1.7310 4.1910 1.6410 2.3910 10.3/11.2 17$23 0 0 O3 H/O4 H 7 8 8 9 4.38 455.1 0.87 1.46 7.46 8.11 6.59 6.64 13.9/15.6 TS 2.5010 1.0910 5.1710 9.2010 19$27 0 0 O3 H/O4 H 7 7 8 8 TS 5.41 461.5 0.03 0.17 6.75 7.21 6.72 7.04 8.3010 8.7310 4.0610 1.1510 14.1/15.6 21$22 0 0 O3 H/O4 H 7 7 8 8 3.43 454.5 0.86 1.29 7.56 8.08 6.70 6.78 14.0/15.8 TS 2.1110 9.0210 6.2110 1.1110 25$32 0 0 O3 H/O4 H 7 7 8 8 TS 4.51 465.7 0.22 0.20 6.89 7.34 6.67 7.14 6.5610 9.5010 4.3010 1.0510 13.8/15.3 28$31 0 0 O3 H/O4 H 8 8 8 9 7.18 468.7 6.58 7.32 6.58 7.32 6.38 7.19 12.3/13.0 TS 1.1110 1.5510 2.6010 6.4610 37$39 0 0 O3 H/O4 H 8 8 8 9 TS 6.91 470.9 0.33 0.33 6.56 7.36 6.23 7.03 1.1410 2.0110 2.1910 4.9810 9.6/11.7 38$40 0 0 O3 H/O4 H 8 8 8 9 4.74 467.2 0.30 0.25 6.56 7.33 6.26 7.07 10.7/12.9 TS 1.1510 1.9010 2.2710 5.2610 41$42 0 0 O3 H/O4 H 9 9 10 10 TS 5.12 476.2 0.37 0.37 4.41 5.29 4.04 4.92 4.3710 8.1310 5.5310 1.2310 10.6/11.3 43$44 For designations see Table 1. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 25 Appl. Sci. 2020, 10, 1147 8 of 22 2↔9 21↔34 O3′H O3′H 2 TS 2↔9 9 21 TS 21↔34 34 -1 -1 (ΔG=0.18 / ΔE=0.78/µ=2.71) (νi=340.2 cm ) (ΔG=4.17 / ΔE=4.58/µ=1.41) (ΔG=11.52 / ΔE=12.53/µ=3.09) (νi=328.8 cm ) (ΔG=15.53 / ΔE=16.67/µ=3.71) (ΔG=7.08 / ΔE=7.53/ µ=1.78) (ΔG=18.06 / ΔE=19.23/ µ=3.08) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.98 / ΔETS=3.80) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.01 / ΔETS=4.14) (ΔGTS=6.90 / ΔETS=6.75) (ΔGTS=6.54 / ΔETS=6.70) 4↔11 27↔33 O3′H O3′H 4 TS 4↔11 11 27 TS 27↔33 33 -1 -1 (ΔG=0.26 / ΔE=1.01/µ=5.33) (νi=333.4 cm ) (ΔG=4.39 / ΔE=5.08/µ=3.66) (ΔG=11.95 / ΔE=13.12/µ=6.97) (νi=363.5 cm ) (ΔG=15.20 / ΔE=16.15/µ=5.37) (ΔG=7.32 / ΔE=7.75/ µ=4.02) (ΔG=18.22 / ΔE=19.42 / µ=6.23) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.15 / ΔETS=4.07) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.25 / ΔETS=3.03) (ΔGTS=7.08 / ΔETS=6.73) (ΔGTS=6.27 / ΔETS=6.29) Figure 1. Cont. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 25 Appl. Sci. 2020, 10, 1147 9 of 22 7↔10 31↔36 O3′H O3′H 7 TS 7 10 10 31 TS 31 36 36 ↔ ↔ -1 -1 (ΔG=0.92 / ΔE=1.09/µ=5.05) (νi=361.1 cm ) (ΔG=4.20 / ΔE=4.30/µ=2.99) (ΔG=12.26 / ΔE=13.41/µ=1.73) (νi=336.2 cm ) (ΔG=16.11 / ΔE=17.27/µ=4.16) (ΔG=7.17 / ΔE=7.62/ µ=4.10) (ΔG=18.64 / ΔE=20.04/ µ=3.35) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.29 / ΔETS=3.21) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.85 / ΔETS=3.86) (ΔGTS=6.25 / ΔETS=6.53) (ΔGTS=6.39 / ΔETS=6.63) 8↔12 32↔35 O3′H O3′H 8 TS 8 12 12 32 TS 32 35 35 ↔ ↔ -1 -1 (ΔG=1.26 / ΔE=1.46/µ=7.26) (νi=362.0 cm ) (ΔG=4.58 / ΔE=4.69/µ=4.76) (ΔG=12.54 / ΔE=13.74 / 6.03) (νi=362.6 cm ) (ΔG=15.77 / ΔE=16.79/5.49) (ΔG=7.51 / ΔE=7.96 / µ=5.93) (ΔG=18.83 / ΔE=20.12 / µ=5.97) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.32 / ΔETS=3.23) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.23 / ΔETS=3.05) (ΔGTS=6.25 / ΔETS=6.51) (ΔGTS=6.29 / ΔETS=6.38) Figure 1. Cont. Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 25 Appl. Sci. 2020, 10, 1147 10 of 22 14↔24 39↔45 O3′H O3′H 14 TS 14↔24 24 39 TS 39↔45 45 -1 -1 (ΔG=7.96 / ΔE=8.03 / 5.96) (νi=355.2 cm ) (ΔG=11.66 / ΔE=11.79/4.07) (ΔG=20.98 / ΔE=22.05/µ=6.28) (νi=354.7 cm ) (ΔG=24.81 / ΔE=25.97/µ=5.30) (ΔG=14.47 / ΔE=14.96/ µ=5.08) (ΔG=27.58 / ΔE=29.06/ µ=6.15) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.70 / ΔETS=3.75) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.83 / ΔETS=3.92) (ΔGTS=6.50 / ΔETS=6.92) (ΔGTS=6.60 / ΔETS=7.01) 15↔26 40↔46 O3′H O3′H 15 TS 15 26 26 40 TS 40 46 46 ↔ ↔ -1 -1 (ΔG=7.98 / ΔE=8.15/µ=7.35) (νi=340.9 cm ) (ΔG=11.74 / ΔE=12.12/µ=4.79) (ΔG=21.17/ΔE=22.36/µ=8.50) (νi=344.1 cm ) (ΔG=24.87/ΔE=26.18/µ=6.29) (ΔG=14.42 / ΔE=15.01 / µ=6.24) (ΔG=27.62 / ΔE=29.16/ µ=7.86) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.79 / ΔETS=3.97) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.70 / ΔETS=3.82) (ΔGTS=6.47 / ΔETS=6.86) (ΔGTS=6.45 / ΔETS=6.80) Figure 1. Cont. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 25 Appl. Sci. 2020, 10, 1147 11 of 22 Figure 1. Geometrical structures of the quercetin molecule conformers and TSs with non-perpendicularly-oriented hydroxyl groups of their mutual interconversions via the 17↔29 42↔48 O3′H O3′H 17 TS 17↔29 29 42 TS 42↔48 48 -1 -1 (ΔG=8.31 / ΔE=8.39/µ=8.60) (νi=355.6 cm ) (ΔG=12.12 / ΔE=12.30/µ=6.70) (ΔG=21.60 / ΔE=22.94/µ=6.59) (νi=341.6 cm ) (ΔG=25.30 / ΔE=26.79/µ=4.90) (ΔG=14.93 / ΔE=15.44/ µ=7.60) (ΔG=28.01 / ΔE=29.73/ µ=6.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.81 / ΔETS=3.91) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.70 / ΔETS=3.85) (ΔGTS=6.62 / ΔETS=7.05) (ΔGTS=6.41 / ΔETS=6.79) 18↔30 44↔47 O3′H O3′H 18 TS 18↔30 30 44 TS 44↔47 47 -1 -1 (ΔG=8.40 / ΔE=8.62/µ=9.87) (νi=343.3 cm ) (ΔG=12.19 / ΔE=12.56/µ=7.28) (ΔG=23.77 / ΔE=25.00/µ=3.89) (νi=353.8 cm ) (ΔG=25.23 / ΔE=26.51/3.77) (ΔGTS=0.00 / ΔETS=0.00) (ΔG=14.90 / ΔE=15.49 / µ=8.65) (ΔGTS=3.79 / ΔETS=3.94) (ΔGTS=0.00 / ΔETS=0.00) (ΔG=28.00 / ΔE=29.62/ µ=4.47) (ΔGTS=6.50 / ΔETS=6.87) (ΔGTS=4.23 / ΔETS=4.62) (ΔGTS=1.46 / ΔETS=1.51) mirror-symmetrical rotation of the O3'H hydroxyl group around the C3'-O3' bonds, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under Figure 1. Geometrical structures of the quercetin molecule conformers and TSs with non-perpendicularly-oriented hydroxyl groups of their mutual interconversions via the mirror-symmetrical rotation of the O3’H hydroxyl group around the C3’-O3’ bonds, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions. Relative Gibbs free DG and electronic DE energies (in kcalmol ) (upper row represents energies relatively the conformer 1, whereas the lower row presents the initial conformer for each transformation), dipole moments  (Debye), and imaginary frequencies at TSs are provided at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory). Dotted lines indicate specific intramolecular contacts; their lengths are presented in Angstrom. Appl. Sci. 2020, 10, 1147 12 of 22 1↔10 23↔29 Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 24 O4′H O4′H 1 10 22 34 TS 1↔10 TS 22↔34 -1 -1 (ΔG=0.00 / ΔE=0.00 / µ=0.35) (νi=381.6 cm ) (ΔG=4.20 / ΔE=4.30/µ=2.99) (ΔG=11.55 / ΔE=12.70/µ=6.50) (νi=380.8 cm ) (ΔG=15.53 / ΔE=16.67/µ=3.71) (ΔG=7.05 / ΔE=7.38/ µ=2.41) (ΔG=18.20 / ΔE=19.70 / µ=5.05) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.20 / ΔETS=4.30) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.04 / ΔETS=3.97) (ΔGTS=7.05 / ΔETS=7.38) (ΔGTS=6.71 / ΔETS=7.00) 3↔9 23↔29 O4′H O4′H 3 TS 3↔9 9 23 TS 23↔29 29 -1 -1 (ΔG=0.25 / ΔE=0.55/µ=4.13) (νi=391.5 cm ) (ΔG=4.17 / ΔE=4.58/µ=1.41) (ΔG=11.56 / ΔE=11.70/µ=7.89) (νi=375.3 cm ) (ΔG=12.12 / ΔE=12.30/µ=6.70 (ΔG=7.11 / ΔE=7.79/ µ=2.82) (ΔG=14.90 / ΔE=15.43 / µ=7.10) ) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.92 / ΔETS=4.03) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.55 / ΔETS=0.60) (ΔGTS=6.86 / ΔETS=7.23) (ΔGTS=3.33 / ΔETS=3.73) Figure 2. Cont. Appl. Sci. 2020, 10, 1147 13 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 25 5↔12 25↔35 O4′H O4′H 5 TS 5↔12 12 25 TS 25↔35 35 -1 -1 (ΔG=0.34 / ΔE=0.32/ µ=3.01) (νi=379.7 cm ) (ΔG=4.58 / ΔE=4.69/µ=4.76) (ΔG=11.68 / ΔE=12.45/µ=3.55) (νi=373.7 cm ) (ΔG=15.77 / ΔE=16.79/5.49) (ΔG=7.27 / ΔE=7.67 / µ=3.63) (ΔG=18.48 / ΔE=19.67/ µ=5.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.24 / ΔETS=4.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.12 / ΔETS=4.35) (ΔGTS=6.93 / ΔETS=7.35) (ΔGTS=6.84 / ΔETS=7.22) 6↔11 28↔36 O4′H O4′H 6 TS 6 11 11 28 TS 28 36 36 ↔ ↔ -1 -1 (ΔG=0.53 / ΔE=1.08 / µ=5.65) (νi=389.2 cm ) (ΔG=4.39 / ΔE=5.08/µ=3.66) (ΔG=12.04 / ΔE=13.21/µ=6.54) (νi=382.7 cm ) (ΔG=16.11 / ΔE=17.27/µ=4.16) (ΔG=7.45 / ΔE=8.22/ µ=3.99) (ΔG=18.78 / ΔE=20.29 / µ=5.70) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.86 / ΔETS=4.00) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.07 / ΔETS=4.06) (ΔGTS=6.92 / ΔETS=7.14) (ΔGTS=6.74 / ΔETS=7.08) Figure 2. Cont. Appl. Sci. 2020, 10, 1147 14 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 25 13↔24 37↔45 O4′H O4′H 13 TS 13 24 24 37 TS 37 45 45 ↔ ↔ -1 -1 (ΔG=7.59 / ΔE=7.66/µ=5.64) (νi=375.8 cm ) (ΔG=11.66 / ΔE=11.79/4.07) (ΔG=20.78 / ΔE=21.92/µ=7.22) (νi=369.1 cm ) (ΔG=24.81 / ΔE=25.97/µ=5.30) (ΔG=14.40 / ΔE=14.88 / µ=4.78) (ΔG=27.53 / ΔE=29.03/ µ=6.56) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.07 / ΔETS=4.13) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.03 / ΔETS=4.05) (ΔGTS=6.81 / ΔETS=7.22) (ΔGTS=6.75 / ΔETS=7.11) 16↔30 38↔46 O3′H O4′H 16 TS 16↔30 30 38 TS 38↔46 46 -1 -1 (ΔG=8.18/ΔE=8.45/µ=6.24) (νi=374.4 cm ) (ΔG=12.19 / ΔE=12.56/µ=7.28) (ΔG=20.84 / ΔE=22.03 / µ=4.53) (νi=367.5 cm ) (ΔG=24.87/ΔE=26.18/µ=6.29) (ΔG=14.96 / ΔE=15.60/ µ=6.83) (ΔG=27.56 / ΔE=29.13/ µ=6.19) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.01 / ΔETS=4.11) (ΔGTS=6.78 / ΔETS=7.16) (ΔGTS=6.72 / ΔETS=7.10) Figure 2. Cont. Appl. Sci. 2020, 10, 1147 15 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 25 19↔33 41↔48 O4′H O4′H 19 TS 19↔33 33 41 TS 41↔48 48 -1 -1 (ΔG=11.08 / ΔE=11.66 / µ=2.63) (νi=371.6 cm ) (ΔG=15.20 / ΔE=16.15/µ=5.37) (ΔG=21.30 / ΔE=22.69/µ=2.99) (νi=366.7 cm ) (ΔG=25.30 / ΔE=26.79/µ=4.90) (ΔG=17.82 / ΔE=18.91/ µ=4.64) (ΔG=27.99 / ΔE=29.74/ µ=5.09) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.12 / ΔETS=4.49) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=4.00 / ΔETS=4.10) (ΔGTS=6.74 / ΔETS=7.25) (ΔGTS=6.69 / ΔETS=7.05) 20↔26 43↔47 O4′H O4′H 20 26 43 47 TS 20↔26 TS 43↔47 -1 -1 (ΔG=11.11 / ΔE=11.40/µ=3.62) (νi=371.6 cm ) (ΔG=11.74 / ΔE=12.12/µ=4.79) (ΔG=23.40 / ΔE=24.63/µ=6.05) (νi=369.4 cm ) (ΔG=25.23 / ΔE=26.51/3.77) (ΔGTS=0.00 / ΔETS=0.00) (ΔG=17.82 / ΔE=18.91/ µ=4.64) (ΔG=28.13 / ΔE=29.73/ µ=5.49) (ΔGTS=0.63 / ΔETS=0.72) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=1.83 / ΔETS=1.88) (ΔGTS=6.71 / ΔETS=7.51) (ΔGTS=4.72/ ΔETS=5.10) Figure 2. Geometrical structures of the quercetin molecule conformers and TSs with a non-perpendicularly-oriented hydroxyl groups of their mutual interconversions via the mirror-symmetrical rotation of the O4’H hydroxyl group around the C4’-O4’ bond, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions. For designations see Figure 1. Appl. Sci. 2020, 10, 1147 16 of 22 1↔7 19↔27 O3′H/O4′H 19 TS 19↔27 27 O3′H/O4′H TS 1 7 7 -1 1 (ΔG=11.08 / ΔE=11.66 / µ=2.63) (νi=455.1 cm ) (ΔG=11.95 / ΔE=13.12/µ=6.97) -1 (νi=457.1 cm ) (ΔG=0.92 / ΔE=1.09/µ=5.05) (ΔG=0.00 / ΔE=0.00 / µ=0.35) (ΔG=18.54 / ΔE=19.77 / µ=4.38) (ΔG=7.50 / ΔE=7.99/ µ=2.97) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=7.46 / ΔETS=8.11) (ΔGTS=0.87 / ΔETS=1.46) 2↔3 21↔22 O3′H/O4′H TS 2 3 -1 (νi=470.5 cm ) O3′H/O4′H 2 3 21 TS 21↔22 22 (ΔG=7.22 / ΔE=7.7.97/ µ=3.73) -1 (ΔG=0.18 / ΔE=0.78/µ=2.71) (ΔG=0.25 / ΔE=0.55/µ=4.13) (ΔG=11.52 / ΔE=12.53/µ=3.09) (νi=461.5 cm ) (ΔG=11.55 / ΔE=12.70/µ=6.50) (ΔG=18.27 / ΔE=19.74 / µ=5.41) (ΔGTS=7.03 / ΔETS=7.19) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.07 / ΔETS=-0.23) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=6.75 / ΔETS=7.21) (ΔGTS=0.03 / ΔETS=0.17) Figure 3. Cont. Appl. Sci. 2020, 10, 1147 17 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 25 4↔6 25↔32 O3′H/O4′H TS 4↔6 O3′H/O4′H 4 6 25 TS 25 32 32 -1 (νi=467.7 cm ) -1 (ΔG=0.26 / ΔE=1.01/µ=5.33) (ΔG=0.53 / ΔE=1.08 / µ=5.65) (ΔG=11.68 / ΔE=12.45/µ=3.55) (νi=454.5 cm ) (ΔG=12.54 / ΔE=13.74 / 6.03) (ΔG=7.42 / ΔE=8.21/ µ=6.15) (ΔG=19.20 / ΔE=20.52 / µ=3.43) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.27 / ΔETS=0.07) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=7.56 / ΔETS=8.08) (ΔGTS=0.86 / ΔETS=1.29) (ΔGTS=7.18 / ΔETS=7.19) 5↔8 28↔31 O3′H/O4′H TS 5 8 O3′H/O4′H TS 28↔31 -1 5 (νi=459.1 cm ) 8 28 31 -1 (νi=465.7 cm ) (ΔG=0.34 / ΔE=0.32/ µ=3.01) (ΔG=7.75 / ΔE=8.28 / µ=5.56) (ΔG=1.26 / ΔE=1.46/µ=7.26) (ΔG=12.04 / ΔE=13.21/µ=6.54) (ΔG=12.26 / ΔE=13.41/µ=1.73) (ΔG=18.93 / ΔE=20.55 / µ=4.51) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=7.40 / ΔETS=7.96) (ΔGTS=0.92 / ΔETS=1.14) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.22 / ΔETS=0.20) (ΔGTS=6.89 / ΔETS=7.34) Figure 3. Cont. Appl. Sci. 2020, 10, 1147 18 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 20 of 25 13↔14 37↔39 O3′H/O4′H O3′H/O4′H TS 13↔14 TS 37↔39 13 14 37 39 -1 -1 (νi=483.1 cm ) (νi=468.7 cm ) (ΔG=7.59 / ΔE=7.66/µ=5.64) (ΔG=7.96 / ΔE=8.03 / 5.96) (ΔG=20.78 / ΔE=21.92/µ=7.22) (ΔG=20.98 / ΔE=22.05/µ=6.28) (ΔG=14.15 / ΔE=15.21 / µ=6.37) (ΔG=27.36 / ΔE=29.24/ µ=7.18) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.37 / ΔETS=0.37) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.20 / ΔETS=0.13) (ΔGTS=9.82 / ΔETS=10.19) (ΔGTS=6.58 / ΔETS=7.32) 15↔20 38↔40 O3′H/O4′H O3′H/O4′H TS 15 20 TS 38 40 ↔ ↔ 15 20 38 40 -1 -1 (νi=466.9 cm ) (νi=470.9 cm ) (ΔG=7.98 / ΔE=8.15/µ=7.35) (ΔG=11.11 / ΔE=11.40/µ=3.62) (ΔG=20.84 / ΔE=22.03 / µ=4.53) (ΔG=21.17/ΔE=22.36/µ=8.50) (ΔG=14.24 / ΔE=15.27 / µ=6.09) (ΔG=27.40 / ΔE=29.39/ µ=6.91) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.13 / ΔETS=3.25) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.33 / ΔETS=0.33) (ΔGTS=6.30 / ΔETS=7.13) (ΔGTS=6.56 / ΔETS=7.36) Figure 3. Cont. Appl. Sci. 2020, 10, 1147 19 of 22 Appl. Sci. 2020, 10, x FOR PEER REVIEW 21 of 25 16↔18 41↔42 O3′H/O4′H O3′H/O4′H TS 16 18 TS 41 42 ↔ ↔ 16 18 41 42 -1 -1 (νi=469.1 cm ) (νi=467.2 cm ) (ΔG=8.18/ΔE=8.45/µ=6.24) (ΔG=8.40 / ΔE=8.62/µ=9.87) (ΔG=21.30 / ΔE=22.69/µ=2.99) (ΔG=21.60 / ΔE=22.94/µ=6.59) (ΔG=14.67 / ΔE=15.70 / µ=8.76) (ΔG=27.86 / ΔE=30.02/ µ=4.74) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.22 / ΔETS=0.17) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.30 / ΔETS=0.25) (ΔGTS=6.49 / ΔETS=7.26) (ΔGTS=6.56 / ΔETS=7.33) 17↔23 43↔44 O3′H/O4′H O3′H/O4′H TS 17↔23 TS 43↔44 17 23 43 44 -1 -1 (νi=473.2 cm ) (νi=476.2 cm ) (ΔG=8.31 / ΔE=8.39/µ=8.60) (ΔG=11.56 / ΔE=11.70/µ=7.89) (ΔG=23.40 / ΔE=24.63/µ=6.05) (ΔG=23.77 / ΔE=25.00/µ=3.89) (ΔG=14.63 / ΔE=15.60 / µ=8.97) (ΔG=27.81 / ΔE=29.92/ µ=5.12) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=3.25 / ΔETS=3.31) (ΔGTS=0.00 / ΔETS=0.00) (ΔGTS=0.37 / ΔETS=0.37) (ΔGTS=6.32 / ΔETS=7.21) (ΔGTS=4.41 / ΔETS=5.29) Figure 3. Geometrical structures of the quercetin molecule conformers and non-planar or locally non-planar TSs of their mutual concerted 0 0 0 0 0 0 interconversions via the mirror-symmetrical rotation of the O3 H and O4 H hydroxyl groups around the C3 -O3 and C4 -O4 bonds, obtained at the MP2/6-311++G(2df,pd)//B3LYP/6-311++G(d,p) level of QM theory under normal conditions. For detailed designations see Figure 1. Appl. Sci. 2020, 10, 1147 20 of 22 In the case of the quercetin molecule, both of these tasks are overcomplicated. The reason is that the conformational mobility of this molecule is closely connected with its prototropic tautomerism [40,41]. It is known that the quercetin molecule has 202 molecular prototropic tautomers [40]. By contrast, now it is not known for sure all possible targets and their structure, despite all reasons to think that the range of this information would continuously grow together with the growing of the progress in bioinformatics and structural analysis. If also consider the conformationally-tautomeric variability of the targets, it would become clear that clarification of the structural grounds for the biological activity of the quercetin molecule is quite dicult task. We aimed to highlight this obstacle by the title of this paper. 4. Conclusions and Perspective for the Future Research In this study, which is a logical continuation of our previous works on this topic [16–21], new pathways of the transformations of the conformers of the quercetin molecule into each other were 0 0 found, which occurred due to the torsional mobility of the O3 H and O4 H hydroxyl groups. It was established that the presence of only three degrees of freedom of the conformational mobility 0 0 of the O3 H and O4 H hydroxyl groups is connected with their concerted behavior, which is controlled by the non-planar (in the case of the interconverting planar conformers) or locally non-planar (in other 0 0 O3 H/O4 H 0 0 cases) TSs , in which O3 H and O4 H hydroxyl groups are oriented by the hydrogen atoms towards each other. All these results assert that quercetin is a rather dynamical molecule, which is able to transform through the pathways into di erent conformers, forming complex networking. We also shortly described the long-term perspectives for the investigation of the structural basis of the biological activity of quercetin. Author Contributions: Setting of an idea of investigation, data preparation, analysis of the received results, writing and proofreading of the text of manuscript, references, Tables and Figures have been performed jointly by O.O.B. and D.M.H. 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Published: Feb 8, 2020

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