**7. The Egorov Resonance**

One of the main results of quantum-classical mechanics is a dynamic electron-nuclearreorganization resonance (the so-called transferon resonance) [5,6] (see also [2]) or, according to [10], the Egorov resonance [1,10]

$$(2\tau\_{\varepsilon})^{-1} = \tau^{-1} \tag{29}$$

where τ*<sup>e</sup>* is the characteristic time of motion of the electron in the donor–acceptor system and τ is the characteristic time of motion of the reorganization of nuclear vibrations in the environment. These times are given by the following equations

$$
\tau\_{\mathfrak{C}} = \frac{L}{\sqrt{2f\_1/m}}\tag{30}
$$

where *L* is the distance between the donor and the acceptor of an electron (see Section 2; *L* is equal to the length of the polymethine chain—the main optical chromophore of polymethine dyes, (see Section 7 in [1]) [3–9]; *J*<sup>1</sup> is the binding energy of the electron on the donor 1 (see Section 3; electronic energy of the ground state of the dye) [3–9], and

$$
\pi = \frac{\hbar}{E} \tag{31}
$$

where *E* is the energy of reorganization of the nuclear vibrations in the medium (see Section 2, Equation (2)). Equations (30) and (31) are a part of Equation (13) (see Section 4).
