ORALS

SESSION: SolidStateChemistryThuAM-R4	Poeppelmeier International Symposium(3rd Intl Symp on Solid State Chemistry for Applications & Sustainable Development)
Thu. 30 Nov. 2023 / Room: Dreams 4
Session Chairs: Steven De Feyter; Session Monitor: TBA

12:50: [SolidStateChemistryThuAM04] OS Invited
QUANTUM-CLASSICAL MECHANICS AND NATURE OF THE FRANCK-CONDON PRINCIPLE
Vladimir Egorov¹ ; ¹FSRS "Crystallography and Photonics" Rus Acad Sci, Photochemistry Center, Moscow, Russian Federation;
Paper Id: 269 [Abstract]

As is known, quantum mechanics is inextricably linked with classical mechanics. Its justification is connected with the need to consider the interaction of a microparticle with a macroscopic classical measuring device [1]. The basic dynamical equation, the Schrödinger equation, was postulated by Schrödinger but actually derived from the Hamilton-Jacobi equation for action in classical mechanics by introducing the wave function in some form, which is now called the semiclassical approximation. The width of the levels, "inside which" the energy spectrum is continuous, is a sign of the partially classical nature of the dynamics in quantum systems. Quantum-classical mechanics is not a "mixture" of quantum mechanics and classical mechanics, but is a substantially modified quantum mechanics, in which the initial and final states are quantum in the adiabatic approximation, and the chaotic transient state due to chaos is classical. The Franck-Condon principle in molecular physics avoids the consideration of transient state dynamics, which is unreasonably assumed to be unimportant. Classicality, which is immanently inherent in quantum mechanics itself, in molecular physics, is supplemented by classicism, which is associated with the Franck-Condon principle. It is assumed that the fast quantum transition of an electron from the ground to the excited electronic state of the molecule occurs between the turning points of classically moving nuclei, where the nuclei are at rest. In fact, the classical nature of motion in molecular physics is not associated with the Franck-Condon principle, but with the chaotic dynamics of the motion of an electron and nuclei in a transient state. As is known, the theory of quantum transitions in quantum mechanics is based on the convergence of a series of time-dependent perturbation theory. This series converges in atomic and nuclear physics, as well as in molecular physics, provided that the Born-Oppenheimer adiabatic approximation and the Franck-Condon principle are strictly observed. If this condition is not met, the series of time-dependent perturbation theory diverges. Obviously, in real molecules, the adiabatic approximation is not strictly observed, which makes the application of Franck-Condon principle unfounded in theory, and with it the whole physical picture of molecular transitions based on it. The only physical way to eliminate the singularity of the series of time-dependent perturbation theory in molecular physics is the postulate of the presence of dynamics in the transient electron-nuclear(-vibrational) state, which the Franck-Condon principle ignores, and that this dynamics is chaotic. In this case, in the case of strong chaos, as in the case of the Franck-Condon picture of molecular transitions, the transition rates do not depend on the specific dynamics of the transient state, but depend only on the initial and final states, taken in the adiabatic approximation. In the case of weak chaos, against the background of chaos, the regular nature of the dynamics of the transient state manifests itself. Chaos, which is weak in the case of large molecules, may be strong in the case of small molecules. Therefore, the Franck-Condon picture of transitions often gives good agreement with experimental data on optical spectra in conventional molecular spectroscopy of small molecules. In photochemistry, 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 [2]. 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. In the case of large molecules, this erroneous theory and the erroneous physical picture no longer lead to the correct result. The analogue of this situation is the collision between two pictures of the world, namely, geocentric and heliocentric. As is well known, the correct picture is the heliocentric picture of the world, in which the Earth rotates around its own axis. However, being on the surface of the Earth, this rotation is perceived by the observer as the movement of the Sun across the sky, which is well simulated by an erroneous geocentric picture. The exit from the surface of the Earth to a sufficiently large distance into space directly shows the fallacy of the geocentric picture of the world. This is analogous to the transition from the transient state dynamics in standard optical spectroscopy, which is strongly chaotic in small molecules and therefore insignificant, to the transient state dynamics in photochemistry, where elements of regular motion appear for large molecules against the background of transient chaos (dozy chaos [3]).

References:
[1] Landau, L.D.; Lifshitz, E.M. Quantum Mechanics, Non-Relativistic Theory, 3rd ed.; Elsevier: Amsterdam, The Netherlands, 1977. [2] Egorov, V.V. The J-Band of J-Aggregates as the Egorov Nano-Resonance. Comput. Sci. Math. Forum 2023, 7, 31. [3] Egorov, V.V. Quantum–classical mechanics: Nano-resonance in polymethine dyes. Mathematics 2022, 10(9), 1443.

SESSION: SolidStateChemistryFriAM1-R4	Poeppelmeier International Symposium(3rd Intl Symp on Solid State Chemistry for Applications & Sustainable Development)
Fri. 1 Dec. 2023 / Room: Dreams 4
Session Chairs: Richard Dronskowski; Session Monitor: TBA

08:40: [SolidStateChemistryFriAM102] OS
THE J-BAND OF J-AGGREGATES AS THE EGOROV NANO-RESONANCE
Vladimir Egorov¹ ; ¹FSRS "Crystallography and Photonics" Rus Acad Sci, Photochemistry Center, Moscow, Russian Federation;
Paper Id: 268 [Abstract]

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 [9].

References:
[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. [9] Egorov, V.V. The J-Band of J-Aggregates as the Egorov Nano-Resonance. Comput. Sci. Math. Forum 2023, 7, 31.