Equivalent quantum approach to nuclei and electrons in molecules

AbstractThe equilibrium carbon-carbon (C-C) bond lengths in π-electron hydrocarbons are very sensitive to the electronic ground-state characteristic. In the recent two papers by Stolarczyk and Krygowski (J Phys Org Chem, 34:e4154,e4153, 2021) a simple quantum approach, the Augmented Hückel Molecular Orbital (AugHMO) model, is proposed for the qualitative, as well as quantitative, study of this phenomenon. The simplest realization of the AugHMO model is the Hückel-Su-Schrieffer-Heeger (HSSH) method, in which the resonance integral β of the HMO model is a linear function the bond length. In the present paper, the HSSH method is applied in a study of C-C bond lengths in a set of 34 selected polycyclic aromatic hydrocarbons (PAHs). This is exactly the set of molecules analyzed by Riegel and Müllen (J Phys Org Chem, 23:315, 2010) in the context of their electronic-excitation spectra. These PAHs have been obtained by chemical synthesis, but in most cases no diffraction data (by X-rays or neutrons) of sufficient quality is available to provide us with their geometry. On the other hand, these PAHs are rather big (up to 96 carbon atoms), and ab initio methods of quantum chemistry are too expensive for a reliable geometry optimization. That makes the HSSH method a very attractive alternative. Our HSSH calculations uncover a modular architecture of certain classes of PAHs. For the studied molecules (and their fragments – modules), we calculate the values of the aromaticity index HOMA.

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Quantum Decoherence and Quantum-Holographic Information Processes: From Biomolecules to Biosystems

Materials Science Forum ◽

10.4028/www.scientific.net/msf.518.485 ◽

2006 ◽

Vol 518 ◽

pp. 485-490 ◽

Cited By ~ 4

Author(s):

D. Raković ◽

M. Dugić ◽

M.B. Plavšić ◽

G. Keković ◽

Irena Ćosić ◽

...

Keyword(s):

Conformational Changes ◽

Energy State ◽

Quantum Decoherence ◽

Biomolecular Recognition ◽

Control Mechanisms ◽

Macroscopic Quantum ◽

Resonant Recognition Model ◽

Expression Of Genes ◽

Quantum Approach ◽

Quantum Ensemble

Our recently proposed quantum approach to biomolecular recognition processes is hereby additionally supported by biomolecular Resonant Recognition Model and by quantum-chemical theory of biomolecular non-radiative resonant transitions. Previously developed general quantumdecoherence framework for biopolymer conformational changes in very selective ligandproteins/ target-receptors key/lock biomolecular recognition processes (with electron-conformational coupling, giving rise to dynamical modification of many-electron energy-state hypersurface of the cellular quantum-ensemble ligand-proteins/target-receptors biomolecular macroscopic quantum system, with revealed possibility to consider cellular biomolecular recognition as a Hopfield-like quantum-holographic associative neural network) is further extended from nonlocal macroscopicquantum level of biological cell to nonlocal macroscopic-quantum level of biological organism, based on long-range coherent microwave excitations (as supported by macroscopic quantum-like microwave resonance therapy of the acupuncture system) - which might be of fundamental importance in understanding of underlying macroscopic quantum (quantum-holographic Hopfieldlike) control mechanisms of embryogenesis/ontogenesis and morphogenesis, and their backward influence on the expression of genes.

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Mössbauer studies of harmonically bound oscillators in Brownian motion: a quantum approach

Physics Letters A ◽

10.1016/0375-9601(91)90974-d ◽

1991 ◽

Vol 154 (9) ◽

pp. 461-464 ◽

Cited By ~ 2

Author(s):

Ashok Kumar

Keyword(s):

Brownian Motion ◽

Mössbauer Studies ◽

Quantum Approach

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Coarse, Medium or Fine? A Quantum Mechanics Approach to Single Species Population Dynamics

10.1101/2020.07.22.215061 ◽

2020 ◽

Author(s):

Olcay Akman ◽

Leon Arriola ◽

Aditi Ghosh ◽

Ryan Schroeder

Keyword(s):

Population Dynamics ◽

Quantum Mechanics ◽

Single Species ◽

Stable Equilibrium Point ◽

Ode Model ◽

Deterministic Models ◽

Species Population ◽

Quantum Approach ◽

Single Species Population ◽

Quantum Framework

AbstractStandard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the possibility of searching for “black–swan” events. In other words, using the more sophisticated quantum approach, we may be able to make quantitative statements about rare events that have significant ramifications to the dynamical system.

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