The well-known optical absorption J-band arises as a result of the formation of J-aggregates of polymethine dyes in their aqueous solutions. Compared to dye monomers, this band is narrow and high intensity, and redshifted. The narrowness and high intensity of the J-band are used in many applications, in particular, in the development of modern dye lasers. The J-band was discovered experimentally by Jelley and independently by Scheibe in 1936 [1,2]. In 1938, Franck and Teller [3] gave a theoretical explanation of the J-band based on the Frenkel exciton model. In 1984, based on the same exciton model, Knapp explained the shape of the J-band [4]. Subsequently, within the framework of the Frenkel exciton model, the shape of the J-band was studied by a large number of theorists, including the author of this abstract [5]. The author's reviews [6,7] provide a detailed critique of the explanation of the nature of the J-band based on the Frenkel exciton model. In particular, a significant drawback of this model is its inability to explain in principle the nature and shape of the optical bands of polymethine dye monomers from which J-aggregates are formed [6–8]. The author gives an alternative explanation of the nature of the J-band in the framework of a new fundamental physical theory, namely, in the framework of quantum-classical mechanics of elementary electron transfers in condensed media, which includes an explanation of the nature and shape of the bands of polymethine monomers that form J-aggregates [8] . Quantum-classical mechanics is a significantly modified quantum mechanics, in which the initial and final states of the "electron + nuclear environment" system for its "quantum" transitions are quantum in the adiabatic approximation, and the transient chaotic electron-nuclear(-vibrational) state due to chaos is classical [8]. This chaos is called dozy chaos. The new explanation of the nature and shape of the J-band is based on the so-called Egorov nano-resonance discovered in quantum-classical mechanics [8]. Egorov nano-resonance is a resonance between the electron motion and the motion of the reorganization of the nuclei of the environment during quantum-classical transitions in the optical chromophore under the condition of weak dozy chaos in the electron-nuclear(-vibrational) transient state.

[1] Jelley, E.E. Spectral absorption and fluorescence of dyes in the molecular state. Nature 1936, 138, 1009–1010.

[2] Scheibe, G. Variability of the absorption spectra of some sensitizing dyes and its cause. Angew. Chem. 1936, 49, 563.

[3] Franck, J.; Teller, E. Migration and photochemical action of excitation energy in crystals. J. Chem. Phys. 1938, 6, 861–872.

[4] Knapp, E.W. Lineshapes of molecular aggregates, exchange narrowing and intersite correlation. Chem. Phys. 1984, 85, 73–82.

[5] Makhov, D.V.; Egorov, V.V.; Bagatur’yants, A.A.; Alfimov, M.V. Efficient approach to the numerical calculation of optical line shapes for molecular aggregates. J. Chem. Phys. 1999, 110, 3196–3199.

[6] Egorov, V.V.; Alfimov, M.V. Theory of the J-band: From the Frenkel exciton to charge transfer. Phys. Uspekhi 2007, 50, 985–1029.

[7] Egorov, V.V. Theory of the J-band: From the Frenkel exciton to charge transfer. Phys. Procedia 2009, 2, 223–326.

[8] Egorov, V.V. Quantum–classical mechanics: Nano-resonance in polymethine dyes. Mathematics 2022, 10(9), 1443-1–1443-25.