*10.2. Optical Spectra, Nature of the Small Stokes Shift, and Dynamic Asymmetry of Luminescence and Absorption*

A striking example of the considered molecular "quantum" transitions, with the dynamics of their transient states taken into account, are the "quantum" transitions in the basic optical chromophore of J-aggregates of polymethine dyes embedded in a solvent—in the system "J-aggregate+environment" [4– 8,10,11].

Figure 3 compares the results of the experiment [50] with the result of fitting them to the theoretical result (6)–(26) for optical absorption and the same theoretical result, in which the sign in the heat energy ω<sup>12</sup> is changed to negative (Section 10.1), for luminescence (fluorescence). In the experiment, a very small Stokes shift was obtained for the J-band [50]. Therefore, we are forced to assume that the energy gap between the ground and excited electron states for fluorescence is greater than this gap for optical absorption [3]. This fact means that at the very initial stage of spontaneous emission, the binding energy of the electron in the excited state of the molecule, before the electron creates a photon, decreases markedly. This effect can be associated with the spontaneous loosening of the excited electronic state immediately before the act of production of a photon by an electron during spontaneous emission [3]. (For polymethine dyes and J-aggregates, the universal effect of spontaneous dynamic loosening is abnormally strong due to the very long π-electron systems in which the quantum-classical transitions under consideration occur [3].) Apparently, nothing of the kind occurs with optical absorption. In other words, with respect to the loosening effect, the processes of optical absorption and luminescence are asymmetric.

**Figure 3.** Experimental [50] (**a**) and theoretical [3] (**b**) absorption and fluorescence spectra of J-aggregates. In the analytical result for the shape of the optical bands (Equations (6)–(26)), the transition from absorption spectrum to fluorescence spectrum is carried out by changing the sign before the heat energy ω12. See details in the Egorov, Vladimir (2018), Mendeley Data, V2, https://doi.org/10.17632/ h4g2yctmvg.2.

## *10.3. Luminescence and Absorption Spectra. Their Mirror Asymmetry*

It can be seen from Figure 3 that when the sign changes only in the heat energy ω12, the theoretical absorption and luminescence spectra turn out to be symmetric with respect to each other (see Section 10.1), while the experiment shows their mirror asymmetry. According to quantum-classical mechanics [3], when passing from optical absorption to luminescence, the sign should be changed not only in the heat energy ω<sup>12</sup> but also in the quantity *L* (the distance between the donor and acceptor in the elementary electron-charge transfers). The change in the sign of *L* corresponds physically to the reverse motion in space of the electron charge in the luminescence process relative to the absorption process. After that, the luminescence and absorption spectra cease to be mirror-symmetric with respect to the "pure electronic" transition line -Ω = *J*<sup>1</sup> − *J*<sup>2</sup> and, as we can see from Figure 4, the theory reproduces well the asymmetry of the absorption and luminescence spectra, which is observed in the experiment. This mirror asymmetry of the spectra is a consequence of taking the chaotic dynamics of the transient state of quantum-classical transitions into account, and it manifests itself under conditions of fairly weak dozy chaos, that is, under conditions of a sufficiently high degree of self-organization of quantum-classical transitions.

**Figure 4.** (**a**) The same as in Figure 3a. (**b**) Theoretical absorption and fluorescence spectra [3], fitted to the experimental data [50] (see (**a**)) in the J-aggregates. In the analytical result for the shape of the optical bands (Equations (6)–(26)), the transition from absorption spectrum to fluorescence spectrum is carried out by changing the sign before the heat energy ω<sup>12</sup> and before the length of the optical chromophore (electron-charge-transfer distance) *L* as well. See details in the Egorov, Vladimir (2018), Mendeley Data, V2, https://doi.org/10.17632/h4g2yctmvg.2.
