It was established for the first time by DFT and MP2 quantum-mechanical (QM) methods either in vacuum, so in the continuum with a low dielectric constant (epsilon=4), typical for hydrophobic interfaces of specific protein-nucleic acid interactions, that the repertoire for the tautomerisation of the biologically important adenine center dot cytosine* (A center dot C*) mismatched DNA base pair, formed by the amino tautomer of the A and the imino mutagenic tautomer of the C, into the A*center dot C base mispair ( increment G=2.72kcal mol(-1) obtained at the MP2 level of QM theory in the continuum with epsilon=4), formed by the imino mutagenic tautomer of the A and the amino tautomer of the C, proceeds via the asynchronous concerted double proton transfer along two antiparallel H-bonds through the transition state (TSA center dot C*<-> A*center dot C). The limiting stage of the A center dot C*-> A*center dot C tautomerisation is the final proton transfer along the intermolecular N6H center dot center dot center dot N4 H-bond. It was found that the A center dot C*/A*center dot C DNA base mispairs with Watson-Crick geometry are associated by the N6HMIDLINE HORIZONTAL ELLIPSISN4/N4HMIDLINE HORIZONTAL ELLIPSISN6, N3HMIDLINE HORIZONTAL ELLIPSISN1/N1HMIDLINE HORIZONTAL ELLIPSISN3 and C2HMIDLINE HORIZONTAL ELLIPSISO2 H-bonds, respectively, while the TSA center dot C*<-> A*center dot C is joined by the N6-H-N4 covalent bridge and the N1HMIDLINE HORIZONTAL ELLIPSISN3 and C2HMIDLINE HORIZONTAL ELLIPSISO2 H-bonds. It was revealed that the A center dot C*<-> A*center dot C tautomerisation is assisted by the true C2HMIDLINE HORIZONTAL ELLIPSISO2 H-bond, that in contrast to the two others conventional H-bonds exists along the entire intrinsic reaction coordinate (IRC) range herewith becoming stronger at the transition from vacuum to the continuum with epsilon=4. To better understand the behavior of the intermolecular H-bonds and base mispairs along the IRC of the A center dot C*<-> A*center dot C tautomerisation, the profiles of their electron-topological, energetical, geometrical, polar and charge characteristics are reported in this study. It was established based on the profiles of the H-bond energies that all three H-bonds are cooperative, mutually strengthening each other. The nine key points, providing a detailed physicochemical picture of the A center dot C*<-> A*center dot C tautomerisation, were revealed and thoroughly examined along the IRC. It was shown that the A*center dot C base mispair with the population ~1 % obtained at the MP2 level of QM theory in the continuum with epsilon=4 is thermodynamically and dynamically stable structure. Its lifetime was calculated to be 5.76 center dot 10(-10) s at the MP2 level of QM theory in the continuum with epsilon=4. This lifetime, from the one side, enables all six low-frequency intermolecular vibrations to develop, but, from the other side, it is by order less than the time (several ns) required for the replication machinery to forcibly dissociate a base pair into the monomers during DNA replication. This means that the A*center dot C base mispair "slips away from the hands" of the replication machinery into the A center dot C* mismatched base pair. Consequently, the authors came to the conclusion that exactly the A center dot C* base mispair is an active player of the point mutational events and is effectively dissociated by the replication machinery into the A and C* monomers in contrast to the A*center dot C base mispair, playing the mediated role of a provider of the A center dot C* base mispair in DNA that is synthesised.