scholarly journals A STUDY OF THE ALKYLPROPARGYL RADICAL ELECTRON STRUCTURES IN THE FRAMEWORK OF QTAIM

2020 ◽  
pp. 46-52
Author(s):  
Елена Михайловна Чернова ◽  
Андрей Анатольевич Репин ◽  
Владимир Владимирович Туровцев ◽  
Юрий Димитриевич Орлов
Keyword(s):  
Quantum Theory ◽  
Electron Density ◽  
Spin Density ◽  
Classical Theory ◽  
Propargyl Radical ◽  
Significant Volume

Методом DFT B3LYP/6-311++G(3df,3pd) найдено распределение электронной плотности соединений гомологического ряда пропаргильных радикалов. В рамках квантовой теории атомов в молекуле (QTAIM) проведено исследование их электронного строения, выделен радикальный центр и отмечена делокализация спиновой плотности по значительному объему радикалов, что можно объяснить в рамках классической теории как суперпозицию структур. The electron density of the homologues of the propargyl radical series were found by DFT B3LYP/6-311++G(3df, 3pd) method. Within the “quantum theory of atoms in a molecules” (QTAIM) their electron structures were studied, radical centres were specified and it was shown that the spin density was delocalized over a significant volume of radicals. This phenomenon can be explained in the framework of classical theory as a superposition of structures.

A new classical theory of electrons

1951 ◽  
Vol 209 (1098) ◽  
pp. 291-296 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Classical Theory ◽  
Physical Significance ◽  
Gauge Transformations

In the theory of the electromagnetic field without charges, the potentials are not fixed by the field, but are subject to gauge transformations. The theory thus involves more dynamical variables than are physically needed. It is possible by destroying the gauge transformations to make the superfluous variables acquire a physical significance and describe electric charges. One gets in this way a simplified classical theory of electrons, which appears to be more suitable than the usual one as a basis for a passage to the quantum theory.

scholarly journals Free paths and transport phenomena gases and the quantum theory of collisions. I.—The rigid sphere model

1933 ◽  
Vol 141 (844) ◽  
pp. 434-453 ◽  
Keyword(s):  
Quantum Theory ◽  
Classical Theory ◽  
Transport Phenomena ◽  
Wave Theory ◽  
Molecular Beams ◽  
Rigid Sphere ◽  
Sphere Model ◽  
Experimental Proof ◽  
Additional Advantage ◽  
Recent Developments

The necessity for the use of quantum mechanics in the theory of atomic phenomena is most clearly manifest in the study of collision processes. Diffrac­tion effects have been observed in the scattering of electrons from crystals and by atoms, while the recent developments of molecular ray technique have made it possible to establish the existence of cross-grating spectra in the reflection of molecular beams from crystal surfaces. In view of the importance of wave theory in these phenomena, it is clearly necessary to examine the conditions under which the classical theory of gases must be modified and to determine the nature of the modifications. Such an investigation receives added importance owing to the possibility of experimental test by molecular ray methods. Also, considerable interest is attached to the possibility of direct experimental proof of the Bose-Einstein statistics for neutral atoms and molecules from collision experiments as has already been possible for α-particles. In order to develop the quantum theory of collisions in a form suitable for this purpose, we first discuss the simplest model which bears sufficient re­semblance to the actual facts, and so we consider the rigid sphere model for gas atoms. This model has already proved valuable in the classical theory of transport phenomena and has the additional advantage of permitting an exact quantum mechanical solution. It will be seen that the results obtained by the use of this model are of great interest and suggest several new lines of investigation, both experimental and theoretical. Finally, a method for dealing with the general case of any law of force will be discussed.

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

On the transferability of electron density in binary vanadium borides VB, V3B4 and VB2

2015 ◽  
Vol 71 (6) ◽  
pp. 777-787 ◽  
Author(s):  
Bürgehan Terlan ◽  
Lev Akselrud ◽  
Alexey I. Baranov ◽  
Horst Borrmann ◽  
Yuri Grin
Keyword(s):  
Quantum Theory ◽  
Crystal Structures ◽  
Electron Density ◽  
Critical Points ◽  
Atoms In Molecules ◽  
Model Systems ◽  
Suitable Model ◽  
Interatomic Distances ◽  
Systematic Analysis ◽  
A Charge

Binary vanadium borides are suitable model systems for a systematic analysis of the transferability concept in intermetallic compounds due to chemical intergrowth in their crystal structures. In order to underline this structural relationship, topological properties of the electron density in VB, V3B4 and VB2 reconstructed from high-resolution single-crystal X-ray diffraction data as well as derived from quantum chemical calculations, are analysed in terms of Bader's Quantum Theory of Atoms in Molecules [Bader (1990). Atoms in Molecules: A Quantum Theory, 1st ed. Oxford: Clarendon Press]. The compounds VB, V3B4 and VB2 are characterized by a charge transfer from the metal to boron together with two predominant atomic interactions, the shared covalent B—B interactions and the polar covalent B—M interactions. The resembling features of the crystal structures are well reflected by the respective B—B interatomic distances as well as by ρ(r) values at the B—B bond critical points. The latter decrease with an increase in the corresponding interatomic distances. The B—B bonds show transferable electron density properties at bond critical points depending on the respective bond distances.

From Classical to Quantum Mechanics

2021 ◽  
pp. 207-219
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Classical Theory ◽  
Constrained Systems ◽  
Experimental Results ◽  
Basic Assumptions ◽  
Original Approach

In Chapter 2 we presented the method of canonical quantisation which yields a quantum theory if we know the corresponding classical theory. In this chapter we argue that this method is not unique and, furthermore, it has several drawbacks. In particular, its application to constrained systems is often problematic. We present Feynman’s path integral quantisation method and derive from it Schroödinger’s equation. We follow Feynman’s original approach and we present, in addition, more recent experimental results which support the basic assumptions. We establish the equivalence between canonical and path integral quantisation of the harmonic oscillator.

Canonical quantization of free fields

2021 ◽  
pp. 70-98
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Electromagnetic Fields ◽  
Classical Theory ◽  
Canonical Quantization ◽  
Classical Mechanics ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Spinor Fields ◽  
Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

scholarly journals ANYONS AS SPINNING PARTICLES

1996 ◽  
Vol 11 (18) ◽  
pp. 3331-3362 ◽  
Author(s):  
JOSÉ L. CORTÉS ◽  
MIKHAIL S. PLYUSHCHAY
Keyword(s):  
Quantum Theory ◽  
Classical Theory ◽  
Spinning Particles ◽  
General Properties ◽  
Fractional Spin ◽  
Model Independent ◽  
The Relationship

A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are investigated. The relationship between all the known approaches to anyons as spinning particles is established. Some widespread misleading notions on the general properties of (2+1)-dimensional anyons are removed.

scholarly journals The active site of hen egg-white lysozyme: flexibility and chemical bonding

2014 ◽  
Vol 70 (4) ◽  
pp. 1136-1146 ◽  
Author(s):  
Jeanette Held ◽  
Sander van Smaalen
Keyword(s):  
Quantum Theory ◽  
Electron Density ◽  
Active Site ◽  
Egg White ◽  
Hen Egg White Lysozyme ◽  
Acta Cryst ◽  
Covalent Bonds ◽  
Egg White Lysozyme ◽  
Hen Egg White ◽  
Hen Egg

Chemical bonding at the active site of hen egg-white lysozyme (HEWL) is analyzed on the basis of Bader's quantum theory of atoms in molecules [QTAIM; Bader (1994),Atoms in Molecules: A Quantum Theory.Oxford University Press] applied to electron-density maps derived from a multipole model. The observation is made that the atomic displacement parameters (ADPs) of HEWL at a temperature of 100 K are larger than ADPs in crystals of small biological molecules at 298 K. This feature shows that the ADPs in the cold crystals of HEWL reflect frozen-in disorder rather than thermal vibrations of the atoms. Directly generalizing the results of multipole studies on small-molecule crystals, the important consequence for electron-density analysis of protein crystals is that multipole parameters cannot be independently varied in a meaningful way in structure refinements. Instead, a multipole model for HEWL has been developed by refinement of atomic coordinates and ADPs against the X-ray diffraction data of Wang and coworkers [Wanget al.(2007),Acta Cryst.D63, 1254–1268], while multipole parameters were fixed to the values for transferable multipole parameters from the ELMAM2 database [Domagalaet al.(2012),Acta Cryst.A68, 337–351] . Static and dynamic electron densities based on this multipole model are presented. Analysis of their topological properties according to the QTAIM shows that the covalent bonds possess similar properties to the covalent bonds of small molecules. Hydrogen bonds of intermediate strength are identified for the Glu35 and Asp52 residues, which are considered to be essential parts of the active site of HEWL. Furthermore, a series of weak C—H...O hydrogen bonds are identified by means of the existence of bond critical points (BCPs) in the multipole electron density. It is proposed that these weak interactions might be important for defining the tertiary structure and activity of HEWL. The deprotonated state of Glu35 prevents a distinction between the Phillips and Koshland mechanisms.

scholarly journals Modelling the experimental electron density: only the synergy of various approaches can tackle the new challenges

IUCrJ ◽  
2015 ◽  
Vol 2 (4) ◽  
pp. 441-451 ◽  
Author(s):  
Piero Macchi ◽  
Jean-Michel Gillet ◽  
Francis Taulelle ◽  
Javier Campo ◽  
Nicolas Claiser ◽  
...  
Keyword(s):  
Electron Density ◽  
Spin Density ◽  
Physical Property ◽  
General Meeting ◽  
Short Review ◽  
Experimental Techniques ◽  
X Rays ◽  
Position Space ◽  
Accuracy Of Measurements ◽  
A Charge

Electron density is a fundamental quantity that enables understanding of the chemical bonding in a molecule or in a solid and the chemical/physical property of a material. Because electrons have a charge and a spin, two kinds of electron densities are available. Moreover, because electron distribution can be described in momentum or in position space, charge and spin density have two definitions and they can be observed through Bragg (for the position space) or Compton (for the momentum space) diffraction experiments, using X-rays (charge density) or polarized neutrons (spin density). In recent years, we have witnessed many advances in this field, stimulated by the increased power of experimental techniques. However, an accurate modelling is still necessary to determine the desired functions from the acquired data. The improved accuracy of measurements and the possibility to combine information from different experimental techniques require even more flexibility of the models. In this short review, we analyse some of the most important topics that have emerged in the recent literature, especially the most thought-provoking at the recent IUCr general meeting in Montreal.

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