Quantum-classical mechanics as an alternative to quantum mechanics in molecular and chemical physics

Abstract

In quantum mechanics, the theory of quantum transitions is grounded on the convergence of a series of time-dependent perturbation theory. In nuclear and atomic physics, this series converges because the dynamics of quantum transitions (quantum jumps) are absent by definition. In molecular and chemical physics, on the contrary, the dynamics of “quantum” transitions, being determined by the joint motion of a light electron (or electrons) and very heavy nuclei, are present by definition, and the series of time-dependent perturbation theory becomes singular. An exception is the dynamic problem for stationary states in the Born-Oppenheimer adiabatic approximation, when the electronic subsystem turns out to be “off” from the general dynamic process and therefore is not dynamically full-fledged: it only forms an electric potential in which the nuclei oscillate. Removing the aforementioned singularity can be accomplished in two ways. The first method was consisted of introducing an additional postulate in the form of the Franck-Condon principle into molecular quantum mechanics, in which the adiabatic approximation is used. The second method was proposed by the author and consisted of damping the singular dynamics of the joint motion of an electron and nuclei in the intermediate (transient) state of molecular “quantum” transitions by introducing chaos. This chaos arises only during molecular quantum transitions and is called dozy chaos. Formally, the damping is carried out by replacing an infinitely small imaginary addition in the spectral representation of the complete Green's function of the system with its finite quantity. The damping chaos (dozy chaos) leads to the continuity of the energy spectrum in the molecular transient state, which is a sign of classical mechanics. Meanwhile, the initial and final states of the molecule obey quantum mechanics in the adiabatic approximation. Molecular quantum mechanics, which takes into account the chaotic dynamics of the transient state of molecular “quantum” transitions, can be called quantum-classical (dozy-chaos) mechanics. The efficacy of the damping for the aforementioned singularity was previously shown by dozy-chaos mechanics of elementary electron transfers in condensed matter, which is the simplest case of dozy-chaos mechanics, and its applications to a whole number of problems, especially to the optical spectra in polymethine dyes and their aggregates. This paper provides a regular exposition of this dozy-chaos (quantum-classical) mechanics of the elementary electron transfers. The main results of its applications presented in the introduction are also described.

Quantum-Classical Electron as an Organizing Principle in Nature

“…This singularity can be easily demonstrated by the example of a one-dimensional potential box with a movable wall (see Figure 1) moving without friction, in which such a wall simulates a nuclear reorganization [1,8,9]. This example can serve as the simplest model of a molecule [1]. The simplest model of an atom in this example is a potential box with a rigid, fixed wall.…”

“…When going beyond the adiabatic approximation, the electronic subsystem of the molecule becomes dynamically full-fledged along with its nuclear subsystem, and therefore, due to the enormous difference in the masses of light electrons and heavy nuclei, the aforementioned singularity in the transition rates arises. This singularity can be easily demonstrated by the example of a one-dimensional potential box with a movable wall (see Figure 1) moving without friction, in which such a wall simulates a nuclear reorganization [1,8,9]. This example can serve as the simplest model of a molecule [1].…”

“…Figure 1. Singularity in the rate of molecular quantum transitions: a potential box with a movable wall (a) and the optical absorption band shape dependent on the dozy chaos available to a given quantum transition (b); the band shape with the strongly pronounced peak (J-band) corresponds to the least dozy chaos [1,8,9]. The wall is fastened to the abscissa axis by a freely movable hinge and can move with a certain friction or without friction against the axis.…”

“…Such a wall simulates the environmental nuclear reorganization in the molecular "quantum" transitions, where dozy chaos plays the role of friction. In the theory [1,10,11], this results in the dozy-chaos dependent optical absorption band being displaced to the red spectral region and narrowed (b)…”

“…In Ref. 1, a critical revision of modern physical concepts about the dynamics of molecular quantum transitions based on quantum mechanics is carried out, and a fundamentally new physical theory having universal naturequantum-classical mechanics -is proposed. It is shown that the existing and widespread physical ideas about the dynamics of molecular quantum transitions, based on the Born-Oppenheimer adiabatic approximation [2] and the Franck-Condon principle [3][4][5][6] (see also Refs.…”