Quantum–Classical Mechanics: Nano-Resonance in Polymethine Dyes

It is well known in quantum mechanics that the theory of quantum transitions is based on the convergence of the series of time-dependent perturbation theory. This series converges in atomic and nuclear physics. However, in molecular and chemical physics, this series converges only in the Born–Oppenheimer adiabatic approximation and due to the application of the Franck–Condon principle, and it diverges as a result of going beyond the adiabatic approximation and the Franck–Condon principle. This divergence (singularity) is associated with the incommensurability of the masses of light electrons and heavy nuclei which jointly participate in the full-fledged movement in the transient state of molecular “quantum” transitions. In a new physical theory—quantum–classical mechanics (Egorov, V.V. Heliyon Physics 2019, 5, e02579)—this singularity is damped by introducing chaos into the transient state. This transient chaos is introduced by replacing the infinitely small imaginary additive in the energy denominator of the spectral representation of the total Green’s function of the system with a finite value and is called dozy chaos. In this article, resonance at the nanoscale (nano-resonance) between electron and nuclear reorganization motions in the quantum–classical (dozy-chaos) mechanics of elementary electron transfers in condensed media and their applications to polymethine dyes and J-aggregates in solutions are reviewed. Nano-resonance explains the resonant character of the transformation of the shape of the optical absorption band in a series of polymethine dyes in which the length of the polymethine chain changes, as well as the nature of the red-shifted absorption band of the J-aggregates of polymethine dyes (J-band), which is narrow and intense. The process of dye aggregation in an aqueous solution with an increase in its concentration by the formation of J-aggregates is considered a structural tuning of the “polymethine dye + environment” system into resonance with light absorption. For J-aggregates in Langmuir films, the asymmetry of the luminescence and absorption bands, as well as the small value of their Stokes shifts, are explained. The parasitic transformation of the resonant shape of the optical absorption band of a polymethine dye in solution during the transition from one-photon to two-photon absorption is also explained, and the conditions for the restoration of this nano-resonance shape are predicted.