A new theoretical approach is proposed to explain the nature of the well-known narrow and intense optical J-band of J-aggregates of polymethine dyes. The old approach proposed by Franck and Teller in 1938 and based on the Frenkel exciton theory does not take into account the specific properties of the main optical chromophore of polymethine dye monomers—the polymethine chain. In the new approach proposed by Egorov and based on a new fundamental physical theory—quantum‒classical mechanics, which takes into account the chaotic and regular dynamics of the transient state, the optical properties of the polymethine chain and monomers as a whole are considered as a key factor determining the unique optical properties of J-aggregates.
In theoretical physics, any physical theory has a limited area of applicability. This statement applies, among other things, to such a remarkable fundamental theory as quantum mechanics.
As is known, at the very beginning of the last century, in order to eliminate the singularity in the spectrum of blackbody radiation at high frequencies, Max Planck was forced to introduce into theoretical physics the concept of quanta by which the absorption and emission of light occurs. Although Planck's hypothesis contradicted the previous idea of the continuous nature of the processes of absorption and emission of light, it turned out to be extremely successful and later quantum mechanics was built on its basis as a kind of analogue of classical mechanics, which was well developed at that time. Quantum mechanics made it possible to successfully explain the discrete nature of the optical spectra of atoms, both at the qualitative and quantitative levels. The triumph of quantum mechanics in atomic spectroscopy provided a compelling basis for the dissemination of its ideas and mathematical apparatus to molecular physics, condensed matter physics and chemical physics. The first work in this direction was the famous article by Born and Oppenheimer on the theory of molecules based on the adiabatic approximation they proposed. The adiabatic approximation separates the fast motion of a very light electron from the slow motion of heavy nuclei by creating an electric potential with the electron in which the nuclei oscillate. Since in the adiabatic approximation the wave function of the entire electron‒nuclear system of a molecule can, roughly speaking, be represented as the product of the electron wave function, which depends only on the electron coordinates, and the wave function of the nuclei, which depends only on the nuclear coordinates, Franck and Condon proposed calculating the optical spectra of molecules by analogy with the calculation of atomic spectra. This hypothesis turned out to be successful and later it became known as the Franck‒Condon principle.
However, in the theory of quantum transitions in molecules, there is a fundamentally new physical effect that is not present in the theory of quantum transitions in atoms. In the process of quantum transitions in atoms, it can be considered that the electron does not interact or interacts very weakly with any physical substance, whereas in molecules, the electron interacts with nuclei that oscillate. In the process of an electron transition, the charge, and with it the mass, of the nuclei is forced to adapt to the new charge distribution that is formed in the quantum state to which the electron passes. This effect is called the effect of nuclear reorganization. The time of a quantum transition is equal to Planck's constant divided by the energy of nuclear reorganization, and it is of the order of magnitude femtoseconds. In such an extremely short time, a very light electron is physically incapable of reorganizing the enormous mass of nuclei surrounding it. Therefore, there must be some extremely effective physical mechanism by which the electron carries out such a reorganization of nuclei. Standard quantum mechanics does not contain such a physical mechanism, so the question immediately arises about the reason for the successful explanation of the optical spectra of molecules by quantum mechanics using the Born‒Oppenheimer adiabatic approximation and the Franck‒Condon principle.
Relatively recently, Vladimir Egorov found the answer to this question and the reason why a light electron manages to control the movement of heavy nuclei in a molecule during transitions between quantum states. The answer to this question is associated with the discovery of a new fundamental physical theory, quantum‒classical mechanics. According to Egorov's quantum‒classical mechanics, during transitions, an electron provokes chaos in the oscillatory motion of nuclei, as a result of which a component of motion appears in their motion associated with the translational movement of nuclei, which is consistent with the movement of the electron charge. In other words, the nuclei, under the control of the chaos created by the electron, shift themselves, creating a new structural configuration consistent with the new distribution of the electron charge. This chaos is called dozy chaos. In the case of strong dozy chaos, the rate of electron transitions ceases to depend on the chaotic dynamics of electrons and nuclei in the transient state, and we have a result that coincides with the result obtained in standard quantum mechanics using the Born‒Oppenheimer adiabatic approximation and the Franck‒Condon principle.
From a formal point of view, in quantum mechanics applied in molecular and chemical physics, there is a singularity in the rates of transitions. The situation here is analogous to the situation with the singularity of the spectrum of blackbody radiation at high frequencies, which Planck eliminated by introducing quanta. This singularity and the method for eliminating it can be easily demonstrated by the example of electron transitions in a potential box with a movable wall, where the motion of the wall simulates the motion of the reorganization of the nuclei of the medium. In quantum mechanics, the singularity is eliminated by replacing the infinitesimal imaginary additive in the energy denominator of the full Green's function of the electron‒nuclear system with a finite value.
The same dozy chaos can be weak in large molecules and strong in small molecules, where it can be ignored, and standard quantum mechanics can be used in molecular spectroscopy. This explains the reason why the application of standard quantum mechanics is successful in molecular optical spectroscopy of small-atom molecules.
In the case of large molecules, in which the size of the optical chromophore can be a nanometer or more, standard quantum mechanics becomes inapplicable and quantum‒classical mechanics must be used for the theoretical interpretation of optical spectra. The term "quantum‒classical mechanics" is related to the fact that, as in quantum mechanics, the transition occurs between quantum states taken in the adiabatic approximation, however, due to chaotic dynamics, the transient state has a continuous energy spectrum that corresponds to the classical nature of the joint motion of the electron and nuclei.
The simplest problem in quantum‒classical mechanics is the theory of elementary electron transfers in condensed matter. The simplicity of elementary electron transfers is associated with the possibility of using the Green's function of a free electron as the electron part of the full Green's function of an electron‒nuclear system, as well as with the possibility of neglecting local phonons and taking into account only non-local phonons of the environment.
A striking result of the theory of elementary electron transfers is the so-called Egorov nano-resonance, where the characteristic frequency of the electron motion between the donor and acceptor of the electron is equal to the characteristic frequency of the motion of the reorganization of nuclei of the environment under conditions of weak chaos (dozy chaos) in the transient state. Egorov nano-resonance explains the narrow and intense optical J-absorption band of J-aggregates of polymethine dyes, discovered independently by Jelley and Scheibe in 1936. In Egorov nano-resonance, the regular component of the joint chaotic and regular motion of the reorganization of nuclei of the environment turns out to be coherent to the regular component of the motion of the electron charge in the quasi-linear structure of the optical chromophore of the J-aggregate. Egorov resonance is also observed in monomers of polymethine dyes, where it is not expressed as strongly as in J-aggregates.
Unlike previous theories of the shape of optical bands of molecular aggregates, based on quantum mechanics and Frenkel's exciton theory, Egorov's theory, based on quantum‒classical mechanics and Egorov's nano-resonance, makes it possible to explain, as aforementioned, not only the nature and shape of the J-band of J-aggregates, but also the nature and shape of the polymethine dye monomer bands from which these J-aggregates are formed. This fact made it possible for the first time to theoretically explain all the existing experimental shapes of optical bands of monomers and J-aggregates in well-known concentration equilibria in aqueous solutions of polymethine dyes, as well as to determine the number of molecules that make up the optical J-chromophore, which is four.
Based on quantum‒classical mechanics, the experimentally observed asymmetry of the shape of the luminescence bands of J-aggregates relative to their optical absorption is also explained, which is associated with a higher degree of organization of the elementary luminescence process compared to the absorption process. The well-known anomalously small Stokes shift of the J-band is explained by the anomalously large regular component in the chaotic dynamics of the quantum‒classical J-transition and the anomalously high degree of loosening of the excited -electron state of J-aggregates.
The shape of the optical bands of dimers, H- and H*-aggregates is explained by both the presence of charge transfer dynamics and the Frenkel exciton effect.
The detuning of the nano-resonance upon the transition from one-photon to two-photon absorption is explained by a shift of the main absorption region to the high-frequency region of optical absorption. The conditions for restoring nano-resonance in two-photon absorption are predicted, which consist of replacing the solvent with a less polar one and/or choosing a dye with a shorter polymethine chain length.
One of the main motivations for the further development of quantum‒classical mechanics is the fact that this new physical theory contains the source of dynamic and structural self-organization of molecular matter, up to the emergence of living matter.
This paper " Polymethine dyes and J-aggregates: quantum‒classical theory of the shape of optical bands" was published in Asymmetry .
Egorov VV. Polymethine dyes and J-aggregates: quantum‒classical theory of the shape of optical bands. Asymmetry 2025(1):0001, https://doi.org/10.55092/asymmetry20250001.
