# Dozy-Chaos Mechanics for a Broad Audience

## Abstract

**:**

**2019**, 5, e02579), is introduced to a wide general readership.

## 1. Introduction

## 2. Dozy-Chaos Mechanics on a Qualitative Level of Consideration

#### 2.1. Full-Fledged Electron-Nuclear Motion in the Transient State of Molecular Quantum Transitions, Singularity in Their Rates, and the Franck–Condon Principle as a Primitive Singularity Damper

#### 2.2. Potential Box with a Movable Wall and Dozy Chaos as a Damper of the Singularity

## 3. Dozy-Chaos Mechanics: Hamiltonian, Green’s Function, and Dozy Chaos

## 4. Dozy-Chaos Mechanics, Quantum Mechanics, and Classical Mechanics: Some Analogy

## 5. Dynamic Electron–Nuclear–Reorganization Resonance

## 6. Absorption and Luminescence Spectra

## 7. Optical Electron-Transfer-Polymethine-Chain Chromophore

## 8. Implementation of the Dynamic Electron–Nuclear–Reorganization Resonance in the Optical Band Shape

## 9. Dozy-Chaos Mechanics and the Franck–Condon Principle

## 10. Conclusions

## Funding

## Conflicts of Interest

## References

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**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 [37]. 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 [6], this results in the dozy-chaos dependent optical absorption band being displaced to the red spectral region and narrowed (

**b**). The position, the intensity and the width of the optical absorption band are determined by the ratio between the dozy-chaos energy $\gamma $ and the reorganization energy $E$ (see Section 3). The smaller the value of $\gamma $ is, the higher the degree of organization of the molecular “quantum” transition, and the more the intensity and less the width of the optical band (

**b**). The position of the wing maximum is determined by the energy $E$, whereas the position of the peak is determined by the energy $\gamma $ [37]. (Original citation)—reproduced by permission of The Royal Society of Chemistry.

**Figure 2.**Distribution function of black light $\varphi \left(\lambda ,T\right)$ (Equation (4)) and singularity in this function in the framework of classical mechanics (on the right). The wavelength $\lambda $, indicated on the x-axis, corresponds to the frequency $\mathsf{\Omega}$ by the standard formula $\lambda =2\pi c/\mathsf{\Omega}$ ($c$ is the speed of light in vacuum).

**Figure 3.**Ideal polymethine state (IPS) [50,51]. Charges reside on carbon atoms of the polymethine chain in the ground state; charges: 1, positive; 2, negative [37]. The polymethine chain length $L$ is defined as the distance between nitrogen atoms N. (Original citation)—Reproduced by permission of The Royal Society of Chemistry.

**Figure 4.**Experimental [52,53] (

**a**) and theoretical [4] (

**b**) monomer’s optical absorption spectra dependent on the length of the polymethine chain $L=2\left(n+2\right)d$, where $d$ are certain roughly equal bond lengths in the chain (thiapolymethinecyanine in methanol at room temperature; $\epsilon $ is the extinction coefficient) [37,39,54]. The optical absorption band with $n=3$ corresponds to the dynamic electron–nuclear–reorganization resonance (the Egorov resonance, see Section 5) or is close to it. (Original citation)—reproduced by permission of The Royal Society of Chemistry.

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Egorov, V.V. Dozy-Chaos Mechanics for a Broad Audience. *Challenges* **2020**, *11*, 16.
https://doi.org/10.3390/challe11020016

**AMA Style**

Egorov VV. Dozy-Chaos Mechanics for a Broad Audience. *Challenges*. 2020; 11(2):16.
https://doi.org/10.3390/challe11020016

**Chicago/Turabian Style**

Egorov, Vladimir V. 2020. "Dozy-Chaos Mechanics for a Broad Audience" *Challenges* 11, no. 2: 16.
https://doi.org/10.3390/challe11020016