Novel Tautomerisation Mechanisms of the Biologically Important Conformers of the Reverse Löwdin, Hoogsteen, and Reverse Hoogsteen G*·C* DNA Base Pairs via Proton Transfer: A Quantum-Mechanical Survey

For the first time, in this study with the use of QM/QTAIM methods we have exhaustively investigated the tautomerization of the biologically-important conformers of the G*·C* DNA base pair—reverse Löwdin G*·C*(rWC), Hoogsteen G*′·C*(H), and reverse Hoogsteen G*′·C*(rH) DNA base pairs—via the single (SPT) or double (DPT) proton transfer along the neighboring intermolecular H-bonds. These tautomeric reactions finally lead to the formation of the novel G·CO2*(rWC), GN2*·C(rWC), G*′N2·C(rWC), GN7*·C(H), and G*′N7·C(rH) DNA base mispairs. Gibbs free energies of activation for these reactions are within the range 3.64–31.65 kcal·mol−1 in vacuum under normal conditions. All TSs are planar structures (Cs symmetry) with a single exception—the essentially non-planar transition state TSG*·C*(rWC)↔G+·C−(rWC) (C1 symmetry). Analysis of the kinetic parameters of the considered tautomerization reactions indicates that in reality only the reverse Hoogsteen G*′·C*(rH) base pair undergoes tautomerization. However, the population of its tautomerised state G*′N7·C(rH) amounts to an insignificant value−2.3·10−17. So, the G*·C*(rWC), G*′·C*(H), and G*′·C*(rH) base pairs possess a permanent tautomeric status, which does not depend on proton mobility along the neighboring H-bonds. The investigated tautomerization processes were analyzed in details by applying the author's unique methodology—sweeps of the main physical and chemical parameters along the intrinsic reaction coordinate (IRC). In general, the obtained data demonstrate the tautomeric mobility and diversity of the G*·C* DNA base pair.


INTRODUCTION
The study of the tautomerization mechanisms of the hydrogen (H) bonded nucleotide base pair is an important topic of modern quantum biophysics, biochemistry, molecular, and structural biology (Sinden, 1994;Sponer and Lankas, 2006;Alkorta et al., 2018). For over 65 years, this area of research has been under the intense scrutiny of both theoretics and experimentators, since the establishment of the spatial organization of DNA and formulation of the so-called "tautomeric hypothesis of the origin of spontaneous point mutations (transitions and transversions)" (Watson and Crick, 1953a,b;Erdmann et al., 2014) for this biologically important macromolecule-carrier of the genetic information, which is transmitted from generation to generation.
Lately, this tautomeric hypothesis has been experiencing an era of renaissance (Brovarets' and Hovorun, 2018). Thus, for the first time, within the framework of this hypothesis the new structural mechanisms of the tautomerization of pairs of nucleotide bases have been discovered, in which the transition of bases within the base pair into the mutagenic tautomeric form is accompanied by a significant change in the geometry of the base pair itself (Brovarets' and Hovorun, 2009, 2015a,b,c,d,e, 2016. However, at the studying of the nature of the mutagenic tautomerization of DNA bases, the researchers limited themselves to the A·T and G·C Watson-Crick base pairs (Löwdin, 1963(Löwdin, , 1966Florian et al., 1994;Gorb et al., 2004;Bertran et al., 2006;Brovarets' and Hovorun, 2014a,b). Now this problem is considered more complex with the involvement of several biologically important conformers of these pairs (Hoogsteen, 1963;Pous et al., 2008;Alvey et al., 2014;Brovarets' and Hovorun, 2014a,b;Nikolova et al., 2014;Acosta-Reyes et al., 2015;Poltev et al., 2016;Zhou, 2016;Szabat and Kierzek, 2017;Ye et al., 2017).
These observations do not only allow to penetrate deeper into the essence of the phenomenon being studied, but also to answer, in particular, on a biologically important question-"Why Nature has exactly chosen the Watson-Crick DNA base pairs as elementary structural units for the construction of genetic material?" Nowadays, there is an explicit bias to the A·T DNA base pair at the investigations of this type. This is due to a large number of circumstances, which will be outlined and discussed below.
In this study, we aim to reapply the approach, which we launched in our previous works (Brovarets' et al., 2018a,b,c,d,e,f;Brovarets' and Tsiupa, 2019) in order to investigate in details the tautomerisation of the reverse Löwdin G * · C * (rWC), Hoogsteen G * ′ · C * (H), and reverse Hoogsteen G * ′ · C * (rH) base pairs via PT along the neighboring intermolecular H-bonds.
As a result of the previous investigations, it was established that proton mobility along the intermolecular H-bonds does not change the tautomeric status of the investigated base pairs. Along with this biologically important conclusion, for the first time we have obtained a number of important physical and chemical FIGURE 3 | Profiles of: (A) the relative electronic energy E, (B) the first derivative of the electronic energy with respect to the IRC (dE/dIRC), (C) the dipole moment µ, (D) the NBO charges q NBO , (E) the distance R(H 1 -H 9 ) between the H 1 and H 9 glycosidic hydrogens, (F) the α 1 ( N1H 1 (C)H 9 (G)) and α 2 ( N9H 9 (G)H 1 (C)) glycosidic angles, (G) the electron density ρ; (H) the Laplacian of the electron density ρ, (I) the ellipticity ε at the (3,−1) BCPs, (J) the distance d A···B between the electronegative A and B atoms; (K) the distance d AH/HB between the hydrogen and electronegative A or B atoms and (L) the angle AH···B of the covalent and hydrogen bonds along the IRC of the investigated I. G*·C*(rWC)↔G + ·C − (rWC)↔G·C* O2 (rWC) tautomerisation via the sequential SPT obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum.
characteristics. As such, it was documented that tautomerisation of the reverse Löwdin G * · C * (rWC) DNA base pair along the middle H-bond induces analogous SPT along its upper and lower H-bonds. Moreover, for the first time we have described the formation of a dynamically stable base pair with participation of the yilidic form of the purine base, formed through asynchronous DPT and participation of the CH group as proton donor.
Digging deeper into the mechanisms of tautomerisation of the reverse Löwdin G * · C * (rWC), Hoogsteen G * ′ · C * (H), and reverse Hoogsteen G * ′ · C * (rH) base pairs, we have carefully obtained sweeps of the physical and chemical parameters that characterize proton mobility along the IRC. Firstly, we have established a monotonic dependence of the base pair's dipole moment along the IRC. Second, it was shown that the SPT processes are characterized by the presence of 6 key points.

Density Functional Theory Geometry and Vibrational Frequencies Calculations
All calculations of the geometries and harmonic vibrational frequencies of the considered base mispairs and transition states Frontiers in Chemistry | www.frontiersin.org FIGURE 4 | Geometric structures of the 11 key points describing the evolution of the II. G*·C*(rWC)↔G + ·C − (rWC)↔G* N2 ·C(rWC) tautomerisation via the sequential SPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo (see Table 4). For more detailed designations see Figure 2.
of their conversion have been conducted using Gaussian'09 package (Frisch et al., 2010) at the DFT B3LYP/6-311++G(d,p) level of theory (Lee et al., 1988;Parr and Yang, 1989;Tirado-Rives and Jorgensen, 2008), that has been already applied for analogous systems and approved to give accurate geometrical structures, normal mode frequencies, barrier heights, and characteristics of intermolecular H-bonds (Matta, 2010;Arabi and Matta, 2018;Gatti et al., 2018). We have used a scaling factor equal to 0.9668 in order to correct harmonic frequencies for the investigated base pairs Hovorun, 2010, 2015f;Brovarets', 2013a,b;Palafox, 2014;El-Sayed et al., 2015;Brovarets' et al., 2018a,b,c,d,e,f;Brovarets' and Tsiupa, 2019). We have associated structures, which were localized on the potential energy landscape by means of Synchronous Transit-guided Quasi-Newton method (Peng et al., 1996), to the minima or transition state (TS) by the absence or presence of the imaginary frequency in the vibrational spectra of the complexes, respectively. We used standard TS theory (Atkins, 1998) in order to estimate the forward and reverse barriers of the investigated tautomerisation reaction.

IRC Calculations
Reaction pathways have been monitored by following IRC in the forward and reverse directions from each TS using Hessian-based predictor-corrector algorithm for integration (Hratchian and Schlegel, 2005). In such a way we ensure that it was received proper reaction pathway from reactants to products. Further, we have obtained the sweeps of the energetic, polar, and geometric characteristics of the H-bonds and base pairs along the IRC by calculating them at each point of the IRC .

Single Point Energy Calculations
In order to take into account electronic correlation effects, we followed geometry optimizations with single point energy calculations using MP2 level of theory (Frisch et al., 1990) and 6-311++G(2df,pd) Pople's basis set of valence triple-ζ quality (Hariharan and Pople, 1973;Krishnan et al., 1980) and augcc-pVDZ Dunning's cc-type basis set (Kendall et al., 1992), augmented with polarization and/or diffuse function.
The Gibbs free energy G for all structures was calculated by the formula: where E el -electronic energy, while E corr -thermal correction.

Interaction Energies Calculations
We have obtained electronic interaction energies E int at the MP2/6-311++G(2df,pd) level of theory as the difference between the total electronic energy of the base mispair and the electronic energies of the separate monomers. Gibbs free energy of interaction has been obtained using similar approach. At this, we also corrected the interaction energy for the basis set superposition error (BSSE) (Boys and Bernardi, 1970;Gutowski et al., 1986) according to the counterpoise procedure (Sordo et al., 1988;Sordo, 2001).

Estimation of Kinetic Parameters
The time τ 99.9% spent for reaching the 99.9% of the equilibrium concentration between the initial and terminal base pairs in the system of reversible first-order forward (k f ) and reverse (k r ) reactions was estimated by formula (Atkins, 1998): The lifetime τ of the base pairs was calculated using the formula 1/k r , where the values of the reverse k r and forward k f rate FIGURE 6 | Geometric structures of the 9 key points describing the evolution of the III. G*·C*(rWC)↔G* ′ N2 ·C(rWC) tautomerisation via the DPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo (see Table 5). For more detailed designations see Figure 2.
constants for the tautomerisation reactions were calculated as (Atkins, 1998): where quantum tunneling effects are accounted by Wigner's tunneling correction (Wigner, 1932;, that has been successfully used for the DPT reactions ,b,c,d, 2014cBrovarets' et al., ,b, 2014aBrovarets' et al., ,b,c,d, 2015: where k B -Boltzmann's constant, h-Planck's constant, G f ,r -Gibbs free energy for the forward (f ) and reverse (r) tautomerisation reactions, ν i -value of the imaginary frequency at the TS of the tautomerisation reaction.

QTAIM Analysis
Bader's quantum theory of Atoms in Molecules (QTAIM) was used to analyse the electron density distribution (Bader, 1990). The topology of the electron density was analyzed using program package AIMAll (Keith, 2010) with all default options and wave functions obtained at the level of theory used 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 ( ρ >0) were considered altogether as criteria for the H-bond formation (Matta and Hernández-Trujillo, 2003;Matta et al., 2006a,b;Matta, 2014;Lecomte et al., 2015;Pérez-Sánchez, 2016, 2017;.

Energies of the Intermolecular H-Bonds
We calculated the energies of the intermolecular AH···B Hbonds in the base mispairs and TSs and of the sweeps of the Hbond energies by the empirical Espinosa-Molins-Lecomte (EML) formula (Espinosa et al., 1998;Matta et al., 2006b;Mata et al., 2011;Lecomte et al., 2015;Alkorta et al., 2016Alkorta et al., , 2017 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. EML fomula has been also used for the estimation of the energy of the non-standard H-bonds CH···O in the stationary points of the base pairs on the hypersurface of their electronic energy.
We evaluated the energies of the classical NH···N/O and OH···O/N intermolecular AH···B H-bonds by the empirical Iogansen's formula (Iogansen, 1999): where ν-magnitude of the frequency shift of the stretching mode of the AH H-bonded group involved in the AH···B H-bond relatively the unbound group. We applied partial deuteration in order to minimize the effect of vibrational resonances Hovorun, 2014d,e, 2015h,i;. The energies of the NH· · · N and OH· · · O H-bonds in the TSs containing loosened covalent bridges were calculated by the Nikolaienko-Bulavin-Hovorun formula (Nikolaienko et al., 2012): where ρ-the electron density at the (3,−1) BCP of the H-bond. The atom numbering scheme for the DNA bases is conventional (Saenger, 1984).

RESULTS AND THEIR DISCUSSION
In this paper we have investigated in details the tautomerisation processes via the single (SPT) or double (DPT) proton transfer of the G * · C * (rWC), G * ′ · C * (H), and G * ′ · C * (rH) base pairs along the neighboring intermolecular H-bonds as their intrinsically inherent property (Figure 1).
This paper is organized in the following way-firstly, we would discuss the tautomerisation process separately for each base pair and then we would present in details sweeps of the most important physico-chemical parameters along the IRC altogether for all investigated base pairs (Figures 1-12, Tables 1-8).  Table 6). For more detailed designations see Figure 2.
Tautomerisation of the Reverse Löwdin G * · C * (rWC) Base Pair via the SPT: For the first time we have discovered three local minima on the hypersurface of the electronic energy of the G * · C * (rWC) base pair corresponding to the high-energy tautomerised G·C * O2 (rWC), G + · C − (rWC), and G * N2 · C(rWC) base pairs (Figure 1, Table 1). All of them are stabilized by the participation of three intermolecular H-bonds, among which the upper O6H. . . O2/O2H. . . O6 H-bonds are the strongest ( Table 2).
In fact, the tautomerisation of the G * ·C * (rWC) base pair with relative Gibbs free energy G = 0.00 kcal·mol −1 starts from the single transfer of the proton localized at the N3 nitrogen atom of the C base to the N1 nitrogen atom of the G base along the intermolecular H-bond (C)N3H. . . N1(G). This G * ·C * (rWC)↔G + ·C − (rWC) tautomerization process occurs via the TS G * ·C * (rWC)↔G + ·C − (rWC) (C s symmetry) ( G = 4.38 kcal·mol −1 ) containing N1-H-N3 covalent bridge and further proceeds through the intermediate-tight ion pair G + ·C − (rWC) ( G = 4.44 kcal·mol −1 ) (C s symmetry), which is the point of bifurcation. By the way, it should be noted that this is the first case of the reliable fixation of the ionic pair of bases, formed as a result of the SPT along the intermediate molecular H-bond, which is involved in its stabilization. Similar attempts to localize such structures for the A·T(WC) and G·C(WC) DNA base pairs didn't lead to result.
So, in fact the Löwdin G * ·C * (rWC) base pair does not tautomerise to the novel G·C * O2 (rWC) and G * N2 ·C(rWC) base mispairs via the SPT along the intermolecular H-bonds. However, despite this verdict, obtained data can be useful as an analogy or even as a heuristic push at the investigation of the tautomerisation mechanisms of the H-bonded complexes of any nature.
Tautomerisation of the Reverse Löwdin G * ·C * (rWC) Base Pair via the DPT: III. G * ·C * (rWC)↔G * ′ N2 ·C(rWC) We have also detected the unusual tautomerisation of the reverse Lowdin's G * ·C * (rWC) DNA base mispair via the asynchronous [with a level of asynchrony 3.49 Bohr (Brovarets' and Hovorun, 2019b)] concerted DPT to the G * ′ N2 ·C(rWC) DNA base mispair with trans-oriented N2H imino group of the G DNA base, in which participates the protons at the N3(C) and N2(G) nitrogen atoms moving in opposite directions. Unusual nature of this process consists in the fact that the transitions of the protons from N3(C) to N1(G) and from N2(G) to N4(C) along the intermolecular H-bonds provokes the rotation of the NH 2 amino group of the G base into the trans-position relatively the neighboring double C2N3(G) bond. As a results, this G * ·C * (rWC)↔G * ′ N2 ·C(rWC) tautomerisation FIGURE 10 | Geometric structures of the 9 key points describing the evolution of the V. G* ′ ·C*(rH)↔G* ′ N7 ·C(rH) tautomerisation via the DPT along the IRC obtained at the B3LYP/6-311++G(d,p) level of theory in vacuo (see Table 7). For more detailed designations see Figure 2.

Tautomerisation of the
Notably, electronic ( E int = −35.66) and Gibbs free ( G int = −22.05 kcal·mol −1 ) energies of the interaction for the terminal G * N7 ·C(H) base mispair exceed the values for the initial base mispair ( E int = −21.24/ G int = −8.91 kcal·mol −1 ). At this, total energies of the H-bonds make a great contribution to the electronic interaction energy−78.1% for the G * ′ ·C * (H) DNA base mispair and 51.7% for the G * N7 ·C(H) DNA base mispair.
All low-frequency intermolecular vibrations of the G * N7 ·C(H) base mispair, which periods are in the range 8.06·10 −13 -1.16·10 −12 s, can't develop during its lifetime. This situation is typical for the structures, which are deprived of dynamic stability (Brovarets' and Hovorun, 2019b).
So, in this case in fact the G * ′ ·C * (H) base pair does not tautomerise via the DPT similarly to the previous G * ·C * (rWC) base pair. The G * ′ ·C * (rH) base pair differs from two previous ones, since it tautomerises via the asynchronous DPT (with the value of asynchronity 1.69 Bohr) along the intermolecular antiparallel (C)N3H. . . N7(G) and (G)C8H. . . N4(C) H-bonds with further formation of the yilidic form G * ′ N7 of the G DNA base (Govorun et al., 1995a,b;Kondratyuk et al., 2000), which is characterized by the transferred proton of the C8H group to the neighboring N7 nitrogen atom. The G * ′ ·C * (rH)↔G * ′ N7 ·C(rH) tautomerisation proceeds via the initial transfer of the proton localized at the N3 nitrogen atom of C base to the N7 nitrogen atom of G base through the formation of the G +′ N7 ·C − ion pair followed by further proton transfer localized at the C8 carbon atom of G * ′ base to the N4 nitrogen atom of C * base. Notably, that TS of this process-TS G * ′ ·C * (rH)↔G * ′ N7·C(rH) -has planar structure (C s symmetry) and contains C8-H-N4 covalent bridge, which angle is 158.8 • .
This process is become possible due to the fact that G base, from one side, is CH-acid (Kondratyuk et al., 2000) and from the FIGURE 12 | Profiles of the energy of the intermolecular H-bonds E HB estimated by the EML formula at the (3,−1) BCPs along the IRC of the investigated tautomerisations via the SPT or DPT obtained at the B3LYP/6-311++G(d,p) level of theory (see Table 3).
TABLE 1 | Energetic (in kcal·mol −1 ) and kinetic (in s) characteristics of the tautomerisation of the G * ·C * (rWC), G * ′ ·C * (H), and G * ′ ·C * (rH) DNA base pairs via the SPT or DPT obtained at the MP2/aug-cc-pVDZ//B3LYP/6-311++G(d,p) level of QM theory in the continuum with ε = 1 under normal conditions (see Figure 1). The imaginary frequency at the TS of the tautomeric transition, cm −1 . b The Gibbs free energy of the initial relatively the terminal base pair of the tautomerisation reaction (T = 298.15 K). c The electronic energy of the initial relatively the terminal base pair of the tautomerisation reaction. d The Gibbs free energy barrier for the forward tautomerisation reaction. e The electronic energy barrier for the forward tautomerisation reaction. f The Gibbs free energy barrier for the reverse tautomerisation reaction. g The electronic energy barrier for the reverse tautomerisation reaction. h The time necessary to reach 99.9% of the equilibrium concentration between the reactant and the product of the tautomerisation reaction. i The lifetime of the product of the tautomerisation reaction.
other-it is able to transfer into the zwitterionic tautomer-socalled yilidic form (Govorun et al., 1995a,b;Kondratyuk et al., 2000). Analysis of the obtained data (Table 1) evidences that G * ′ N7 ·C(rH) tautomer is dynamically stable structure with quite long lifetime (τ = 5.15·10 −12 s). Characteristically, that all 6 low-frequency intermolecular vibrations of the G * ′ N7 ·C(rH) base mispair, which period are in the range 6.83·10 −13 -1.51·10 −12 s, can develop during this lifetime. This is the first case (Brovarets' et al., 2018f), when the product of the tautomerization of the H-bonded base pair by the participation of the yilidic purine base is dynamically stable structure. However, formed G * ′ N7 ·C(rH) base pair has low population−2.3·10 −17 under normal conditions, which complicates the understanding of its biological role.

Profiles of the Physico-Chemical Parameters of the Investigated SPT and DPT Tautomerisations
We have investigated in details the mechanisms of the abovementioned processes of the tautomerisation of the reverse Lowdin's G * ·C * (rWC), Hoogsteen G * ′ ·C * (H), and reverse Hoogsteen G * ′ ·C * (rH) base pairs via the PT along the intermolecular H-bonds. Tautomerisations proceed in a synchronous concerted manner via the stepwise SPT in the case of the I. G * ·C * (rWC)↔G + ·C − (rWC)↔G·C * O2 (rWC) and II. G * ·C * (rWC)↔G + ·C − (rWC)↔G * N2 ·C(rWC) reactions, while in an asynchronous concerted manner via the DPT in the case of the 4 | Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 11 key points and the polarity of the latters along the IRC of the II. G*·C*(rWC)↔G + ·C − (rWC)↔G* N2 ·C(rWC) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 4). For footnote definitions see Table 3.
We have established following regularities of the general character for the obtained sweeps of the most important physicochemical parameters along the IRC.
According to the authors' conception ,b,c,d, 2014cBrovarets' et al., ,b, 2014aBrovarets' et al., ,b,c, 2015, it was introduced key points, namely 11 key points were obtained in the cases of the I. G * ·C * (rWC)↔G·C * O2 (rWC) and II. G * ·C * (rWC)↔G * N2 ·C(rWC) SPT along the IRC in contrast to the processes of the III. G * ·C * (rWC)↔G * ′ N2 ·C(rWC), IV. G * ′ ·C * (H)↔G * N7 ·C(H) and V. G * ′ ·C * (rH)↔G * ′ N7 ·C(rH) DPT, for which 9 key points have been localized. At this, it was obtained typical crossings of the profiles for the electron density ρ, the Laplacian of the electron density ρ and the distance d AH/HB between the hydrogen and electronegative A or B atoms for the H-bonds involved in the tautomerisation, notifying the equalization of these parameters. They occur at the 3rd and 9th key points in the case of the reaction I, 3rd and 8th-for the reaction II, 3rd and 7th-for the reactions III and IV and 3rd and 6th-for the reaction V (Figures 3G,H,K, 5G,H,K, 7G,H,K,  9G,H,K, 11G,H,K).
One and the same regularity is observed for the dE/dIRC function in all cases of tautomerisations-with two local maxima and two local minima achieved at the TS zone (Figures 3B, 5B,  7B, 9B, 11B).
Also it was observed five patterns for the energy E HB of the intermolecular H-bonds, estimated by the EML method (Espinosa et al., 1998;Matta et al., 2006b;  6 | Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 9 key points and the polarity of the latters along the IRC of the IV. G* ′ ·C*(H)↔G* N7 ·C(H) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 8). For footnote definitions see Table 3. Lecomte et al., 2015;Alkorta et al., 2016Alkorta et al., , 2017, along the IRC for the I, II, IV and V reactions and four patterns-for the III reaction (Figure 12, Table 8). These sweeps allow to estimate numerically the cooperativity of the neighboring H-bonds according to the methodology, proposed by us earlier (Brovarets' and Hovorun, 2019b). It was established the general pattern-the anti-parallel H-bonds amplify each other and parallel-weaken each other (Turaeva and Brown-Kennerly, 2015). Moreover, some of the dependencies of the energy E HB of the intermolecular H-bonds exist during entire IRC, such as (G)N2H. . . N4(C) for the I. G * ·C * (rWC)↔G·C * O2 (rWC) reaction, (G)O6H. . . O2(C) for the II. G * ·C * (rWC)↔G * N2 ·C(rWC) reaction, (G)O6H. . . O2(C) for the III. G * ·C * (rWC)↔G * ′ N2 ·C(rw WC ) reaction, (G)C8H. . . O2(C) (its energy remains almost unchangeable during the IRC) for the G * ′ ·C * (H)↔G * N7 ·C(H) reaction and (G)O6H. . . O2(C) for the G * ′ ·C * (rH)↔G * ′ N7 ·C(rH) reaction.
Finally, we would like to note some general regularities, which are characteristic for all without exclusion processes of tautomerisation.
Thus, in the vast majority of cases base pairs are plane symmetric structures during the entire PT and DPT tautomerization processes along the IRC, despite the ability of the DNA bases for the out-of-plane bending (Govorun et al., 1992;Hovorun et al., 1999;Nikolaienko et al., 2011), excluding two mentioned above cases, when there are deviation from the planarity-III. G * ·C * (rWC)↔G * ′ N2 ·C(rWC) (Figure 1). 7 | Electron-topological and structural characteristics of the specific intermolecular bonds revealed in the 9 key points and the polarity of the latters along the IRC of the V. G* ′ ·C*(rH)↔G* ′ N7 ·C(rH) tautomerisation obtained at the B3LYP/6-311++G(d,p) level of theory in vacuum (see Figure 10). For footnote definitions see Table 3.

Complex AH· · · B H-bond/ A-H/H-B covalent bond
Interestingly, the total energy of the intermolecular H-bonds only partially contributes to the electron energy of the monomers interactions among all without any exceptions H-bonded structures investigated in this work (see Figures 1, 12). This result is in a good accordance with generalized literature data Hovorun, 2014e, 2019b).
Obtained data evidence that among the G * ·C * (rWC), G ′ ·C * (H) and G * ′ · C * (rH) base pairs only the tautomerisation of the latest of them lead to the formation of the dynamically stable G * ′ N7 ·C(rH) base pair with lifetime 5.15 ps with a miserable population 2.3·10 −17 .
Moreover, it was revealed that the I. G * ·C * (rWC)↔G + ·C − (rWC)↔G·C * O2 (rWC) and II. G * ·C * (rWC)↔G + ·C − (rWC)↔G * N2 ·C(rWC) tautomerization reactions proceed in a synchronous concerted manner via the stepwise SPT, while the III. G * ·C * (rWC)↔G * ′ N2 ·C(rWC), IV. G * ′ ·C * (H)↔G * N7 ·C(H), and V. G * ′ ·C * (rH)↔G * ′ N7 ·C(rH) reactions occur in an asynchronous concerted manner via the DPT. 8 | Patterns of the specific intermolecular interactions including AH···B H-bonds and loosened A-H-B covalent bridges that sequentially replace each other along the IRC of the investigated tautomerisations via the SPT or DPT obtained at the B3LYP/6-311++G(d,p) level of theory (see Figure 12). We have also established dependencies of the most important physico-chemical parameters along the IRC enabling to understand more precisely the inherent nature of the investigated processes.

DATA AVAILABILITY
The datasets generated for this study are available on request to the corresponding author.

AUTHOR CONTRIBUTIONS
OB analysis and preparation of the current literature survey, discussion of the strategy of the current investigation, study conception and design, acquisition of data, drafting of manuscript analysis and interpretation of data, performance of calculations, discussion of the obtained data, preparation of the numerical data for Tables 1-8, graphical materials for Figures 1-12, and text of the manuscript. TO preparation of the numerical data for Tables 1-8 and graphical materials for Figures 1-12. DH study conception, critical revision of manuscript, proposition of the task of the investigation, discussion of the obtained data, and preparation of the text of the manuscript. All authors were involved in the proofreading of the final version of the manuscript.