We propose a microscopic analytical approach to the description of the low-temperature dissipative intracluster electron transfer dynamics in centrosymmetric one-electron mixed-valence (MV) dimers. The dissipative system (bath) is supposed to consist of the acoustic phonons of the crystal surrounding that are coupled to the delocalized electron(s) of a MV dimer. Although the concept of the bath is the spin-boson model is more generic, the present consideration is relevant, for example, to a MV bi-center impurity in an ionic crystal. The model allows us to develop an approximate microscopic approach within which the relaxation processes are explicitly taken into account without additional assumption regarding spectral function of the bath. It is assumed that initially the extra electron is localized on a certain center and then the time-dependent localization probability (averaged value of the electron dipole moment) is evaluated with the emphasis on the damping of the amplitude of the Rabi oscillations. The approach assumes the following conditions: (i) the vibrational spectrum of the crystal does not show the presence of local modes; (ii) the itinerant electron is weakly coupled to the long-waves acoustic phonons which is peculiar to fully delocalized Robin and Day class III MV systems; (iii) the Debye energy ℏωD exceeds the electronic resonance energy gap 2β (β is the electron transfer parameter). We have demonstrated that the dissipation in this case is super-ohmic with the low-frequency spectral function J(ω) ∝ ω(5). The time dependences of the localization probabilities show nearly picosecond damped oscillations. The longitudinal relaxation time T1 has been shown to be two times shorter than the decoherence time T2 thus giving the upper bound for T2, T2 ≤ 2T1.