Quantum–classical mechanics: On the problem of a two-photon resonance band shape in polymethine dyes

The J-Band of J-Aggregates as the Egorov Nano-Resonance

“…In photochemistry and nanophotonics, where the spatial extension of a molecular transition can be large, that is, of the order of a nanometer or more, it becomes necessary to take into account the regular nature of the dynamics of the transient state, which occurs against the background of transient or dozy chaos [8]. One of the most striking results of quantum-classical mechanics is the Egorov nano-resonance between the electron motion and the nuclear reorganization motion [6][7][8][27][28][29], which currently explains the nature of the well-known narrow and intense J-band of J-aggregates of polymethine dyes that arises in aqueous solutions of their monomers (Figures 3 and 4), as well as a resonance-like transformation of the optical band shape of a dye monomer with the varying length of its polymethine chain (Figure 2). A brickwork-like structure of the J-chromophore of four molecules and the J-aggregate (bottom) [12,17,20,21].…”

Quantum–Classical Mechanics and the Franck–Condon Principle

“…Comparison of theory with experiment shows that γ >> ω (ω κ = constant ≡ ω; see below, Section 3) [25,26,[28][29][30][31][32][33][34]40]. The dozy-chaos energy γ is a measure of dynamic or dozy chaos in the transient state [28,29] (see Section 4).…”

“…are included in the Egorov nano-resonance (see Section 1) [25][26][27][28][29][30][31][32][33][34] as follows:…”

“…4)-( 24) (η = 1 [28][29][30][31][32][33][34]40] in Equations ( 21) and ( 22)). The following numerical values of the parameters are used: m = me, where me is the electron mass; nrefr = 1.33; ω = 5 × 10 13 s -1 ; J1 = 5 eV; J1 − J2 = 0.5 eV; E = 1 eV; γ = 0.34 eV; and T = 298 K [26,27]. In this figure, for simplicity, the energy gap J1 − J2 ≡ 0.…”

“…In photochemistry and nanophotonics, where, as a rule, we deal with large molecules, where chaos is not strong but weak, elements of dynamic self-organization often appear in the chaotic dynamics of the transient state. A striking example of this is the well-known narrow and intense J-band of J-aggregates of polymethine dyes [15][16][17][18][19][20][21][22][23][24], which can no longer be explained on the basis of quantum mechanics but can be explained in quantum-classical mechanics as Egorov nano-resonance [25][26][27][28][29][30][31][32][33][34]. Thus, in the case of small molecules, the Franck-Condon principle gives the correct result, although an erroneous theory and an erroneous physical picture are used.…”