An exactly solvable quantum-mechanical model of DNA bases is presented. The proposed model is based on the harmonic approximation of the potential energy of the canonical and tautomeric forms for the bases in question. The transition rate of single-proton transfer in the base pairs adenine-thymine and guanine-cytosine is determined within this model using the Fermi Golden Rule. The transition rates derived from the application of the 'bare' Fermi Golden Rule can be approximated by the Fano line curves. In turn, the application of the thermally averaged Fermi Golden Rule leads to an exponential increase in transition rates across the biologically relevant temperature range for the base pairs under consideration. The kinetic isotope effect for the base pairs at room temperature is also estimated. All calculations are consistently carried out in a phase-space representation using the Wigner distribution function.
Wleklińska et al. (Thu,) studied this question.