**9. The Egorov Resonance and Its "Antisymmetric Twin"**

The five principal parameters of the problem, viz. electron mass *m*, electron-donor binding energy *J*<sup>1</sup> ≡ *J*, distance between the donor and the acceptor *L*, environmental reorganization energy *E*, and dozy-chaos energy γ, may be combined into three quantities:

$$
\tau\_{\varepsilon} = \frac{L}{\sqrt{2f/m}'}, \tau = \frac{\hbar}{E}, \text{ and } \tau\_0 = \frac{\hbar}{\gamma} \tag{32}
$$

having a time dimension (cf. Equations (13)) and representing two physically meaningful resonances [6]:

$$(2\tau\_{\varepsilon})^{-1} = \tau^{-1} \text{ and } (2\tau\_{\varepsilon})^{-1} = \tau\_0^{-1} \tag{33}$$

The former resonance is between the extended electron motion and the ordered constituent of the environmental nuclear reorganization motion, i.e., it is the Egorov resonance (cf. Equations (29)–(31)). The latter is between the electron motion and, conversely, the chaotic constituent of nuclear reorganization. Since the dozy-chaos energy γ can be considered, in a sense, as the imaginary part of a complex reorganization energy in which the reorganization energy *E* is its real part [9], then this second resonance can be considered as some antisymmetric twin with respect to the Egorov resonance. Both of these resonances can be regarded as the simplest dynamic invariants for the transient state. The dynamic resonance-invariants are alternatives to the Born–Oppenheimer adiabatic invariants (potential energy surfaces). In other words, these two resonances are the simplest manifestation of the relationship between electron and nuclear movements in the transient state.

Details of the transient-state-dynamics interpretation based on the Heisenberg uncertainty relation can be found in [6–8]. In particular, according to this interpretation, in the simplest cases, elementary electron transfers can be considered as a motion of a free electron–phonon quasiparticle, the so-called transferon, corresponding to the Egorov resonance, or, alternatively, as a motion of a free electron–phonon antiquasiparticle, the so-called dissipon, corresponding to the antisymmetric twin of the Egorov resonance.
