**5. Potential Box with a Movable Wall. Optical Absorption Band Shapes as Dependent on the Dozy-Chaos Energy** γ**: From Symmetry to Asymmetry**

The reason for the appearance of a singularity in the rates of molecular "quantum" transitions can be seen already from the example of a one-dimensional potential box with a movable wall [1]. The movable wall corresponds to the reorganization of the nuclear subsystem of the molecular system. As indicated above (Section 1), within the framework of quantum mechanics, due to the incommensurability of the masses of electrons and nuclei, the dynamics of nuclear reorganization is singular. Accordingly, if the movable wall of the potential box moves without friction, then this corresponds to an infinitely fast expansion of the potential box during the transition of an electron from the ground state to the first excited state, which leads to a singular "collapse" of their energy levels.

The singularity can be eliminated by assuming that the wall moves with friction [1]. In the exact theory, this assumption corresponds to the introduction of transient chaos into the dynamics of reorganization of the electron-nuclear motion, that is, the introduction of dozy chaos.

In Figure 1, optical absorption band shapes (for *k*B*T* > ωκ/2), as dependent on the dozy-chaos energy γ, are computed from Equations (6)–(26). At high energies γ, the band shape is close to symmetric and is Gaussian-like (see Section 6). With a decrease in the value of γ, in the red region of the spectrum, a peak appears against the background of a Gaussian-like band, which, with decreasing γ, shifts more and more to the red region of the spectrum and becomes more and more pronounced. Thus, with a decrease in the value of the dozy-chaos energy γ, the band shape transforms from symmetric to asymmetric.

**Figure 1.** Singularity in the rate of molecular quantum transitions: the optical absorption band shape dependent on the dozy chaos available to a given quantum transition; the band shape with the strongly pronounced peak (J-band) corresponds to the least dozy chaos [9]. The dozy-chaos-dependent optical absorption band is displaced to the red spectral region and narrowed. The position, the intensity, and the width of the optical absorption band are determined by the ratio between the dozy-chaos energy γ and the reorganization energy *E* (see Section 4). The smaller the value of γ is, the higher the degree of organization of the molecular "quantum" transition and the higher the intensity and lower the width of the optical band. The position of the wing maximum is determined by the energy *E*, whereas the position of the peak is determined by the energy γ [9].
