A CRITIQUE OF PAULI REPULSIONS AND MOLECULAR GEOMETRY

1966 ◽  
Vol 44 (10) ◽  
pp. 1131-1145 ◽  
Author(s):  
R. F. W. Bader ◽  
H. J. T. Preston
Keyword(s):  
Polyatomic Molecule ◽  
Electron Density Distribution ◽  
Electron Pair ◽  
Three Dimensional ◽  
Molecular Geometry ◽  
Theoretical Method ◽  
Pauli Exclusion Principle ◽  
Pauli Principle ◽  
Exclusion Principle ◽  
Binding Region

A theoretical method, which allows one to determine the effect of the Pauli exclusion principle on the electron density distribution, is used to test the concepts underlying the electron pair repulsion theory of molecular geometry. It is shown that pictures of overlapping orbitals frequently do not correspond to the actual effect which the Pauli principle has on the three-dimensional charge density. An alternative electrostatic approach, involving the concept of a binding region for a polyatomic molecule, is proposed to account for the observed molecular geometries.

scholarly journals COVALENT MOLECULAR BINDING IN A SUSY BACKGROUND

2009 ◽  
Vol 24 (23) ◽  
pp. 4245-4259 ◽  
Author(s):  
L. CLAVELLI ◽  
SANJOY K. SARKER
Keyword(s):  
Bound States ◽  
Vacuum Energy ◽  
Diatomic Molecules ◽  
Covalent Binding ◽  
Pauli Exclusion Principle ◽  
Pauli Principle ◽  
Exclusion Principle ◽  
Vacuum Decay ◽  
Molecular Binding ◽  
Homonuclear Diatomic Molecules

The Pauli exclusion principle plays an essential role in the structure of the current universe. However, in an exactly supersymmetric (susy) universe, the degeneracy of bosons and fermions plus the ability of fermions to convert in pairs to bosons implies that the effects of the Pauli principle would be largely absent. Such a universe may eventually occur through vacuum decay from our current positive vacuum energy universe to the zero vacuum energy universe of exact susy. It has been shown that in such a susy universe ionic molecular binding does exist but homonuclear diatomic molecules are left unbound. In this paper we provide a first look at covalent binding in a susy background and compare the properties of the homonuclear bound states with those of the corresponding molecules in our universe. We find that covalent binding of diatomic molecules is very strong in an exact susy universe and the interatomic distances are in general much smaller than in the broken susy universe.

Heisenberg’s Derivation of the Pauli Exclusion Principle

2020 ◽  
pp. 157-178
Author(s):  
Jim Baggott
Keyword(s):  
Magnetic Field ◽  
Quantum Number ◽  
Electron Spin ◽  
Pauli Exclusion Principle ◽  
Pauli Principle ◽  
Exclusion Principle ◽  
Electron Atom

Despite the success of Schrödinger’s description of the H-atom, it became apparent that the spectrum of the simplest multi-electron atom—helium—could not be so readily explained. And the spectra of other atoms showed ‘anomalous’ splitting in a magnetic field. In 1920 Sommerfeld introduced a fourth quantum number. A few years later Pauli was led to the inspired conclusion that the electron must have a curious ‘two-valuedness’ characterized by a quantum number of ½, and went on to discover the exclusion principle. Perhaps this is because the electron possesses a self-rotation, leading to the notion of electron spin, potentially explaining why each orbital can accommodate only two electrons. Heisenberg traced this behaviour back to the symmetry properties of the wavefunctions. By observing which transitions in the spectrum of helium are allowed and which are forbidden, we can deduce the generalized Pauli principle, from which the exclusion principle follows.

scholarly journals THE PAULI EXCLUSION PRINCIPLE AND SU(2) VERSUS SO(3) IN LOOP QUANTUM GRAVITY

2003 ◽  
Vol 12 (09) ◽  
pp. 1729-1736 ◽  
Author(s):  
JOHN SWAIN
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Gauge Group ◽  
Loop Quantum Gravity ◽  
Pauli Exclusion Principle ◽  
Pauli Principle ◽  
Exclusion Principle ◽  
Spin Networks

Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that j=1 edges of spin-networks dominate in their contribution to black hole areas as opposed to j=1/2 which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from j=1 punctures rather than j=1/2 punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.

scholarly journals Pauli Crystals–Interplay of Symmetries

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1886
Author(s):  
Mariusz Gajda ◽  
Jan Mostowski ◽  
Maciej Pylak ◽  
Tomasz Sowiński ◽  
Magdalena Załuska-Kotur
Keyword(s):  
Three Dimensional ◽  
Pauli Exclusion Principle ◽  
Harmonic Trap ◽  
Exclusion Principle ◽  
Repulsive Interaction ◽  
Two Dimensional ◽  
Quantum Mechanism ◽  
Coulomb Crystals ◽  
Square Well ◽  
Electrically Charged

Recently observed Pauli crystals are structures formed by trapped ultracold atoms with the Fermi statistics. Interactions between these atoms are switched off, so their relative positions are determined by joined action of the trapping potential and the Pauli exclusion principle. Numerical modeling is used in this paper to find the Pauli crystals in a two-dimensional isotropic harmonic trap, three-dimensional harmonic trap, and a two-dimensional square well trap. The Pauli crystals do not have the symmetry of the trap—the symmetry is broken by the measurement of positions and, in many cases, by the quantum state of atoms in the trap. Furthermore, the Pauli crystals are compared with the Coulomb crystals formed by electrically charged trapped particles. The structure of the Pauli crystals differs from that of the Coulomb crystals, this provides evidence that the exclusion principle cannot be replaced by a two-body repulsive interaction but rather has to be considered to be a specifically quantum mechanism leading to many-particle correlations.

The relation between zero-energy scattering phase-shifts, the Pauli exclusion principle and the number of composite bound states

1955 ◽  
Vol 228 (1172) ◽  
pp. 10-33 ◽  
Keyword(s):  
Phase Shift ◽  
Bound States ◽  
Pauli Exclusion Principle ◽  
Pauli Principle ◽  
Bound State ◽  
Exclusion Principle ◽  
Zero Energy ◽  
Energy Scattering ◽  
Quantum Numbers ◽  
Scattering Phase

It is shown that for the interaction of systems described by integro-differential equations, such as the scattering of electrons by atoms or of nucleons by deuterons, tritons and other nuclei, that the zero-energy scattering phase-shift is ( n + m ) π, where n is the number of composite bound states of the impacted and incident particles, and m is the number of states from which the incident particle is excluded by the Pauli principle. Each of these excluded states corresponds to a solution of the integro-differential equation asymptotic to e~7 r for which the complete wave function vanishes identically, and which therefore does not represent a bound state. It is possible to predict the zero-energy phase-shift without calculation by a knowledge of the composite bound states and of the distribution and quantum numbers of the elementary particles contained in the impacted and incident systems.

Hardness and HOMO-LUMO Gap Probed by the Helium Atom Pushing the Molecular Surface of the First-Row Hydride Molecules

2003 ◽  
Vol 68 (12) ◽  
pp. 2344-2354 ◽  
Author(s):  
Edyta Małolepsza ◽  
Lucjan Piela
Keyword(s):  
Helium Atom ◽  
Pauli Exclusion Principle ◽  
Structure Change ◽  
Molecular Surface ◽  
Exclusion Principle ◽  
Probe Position ◽  
Repulsion Energy ◽  
Ionic Dissociation ◽  
Probe Site ◽  
Homo Lumo

A molecular surface defined as an isosurface of the valence repulsion energy may be hard or soft with respect to probe penetration. As a probe, the helium atom has been chosen. In addition, the Pauli exclusion principle makes the electronic structure change when the probe pushes the molecule (at a fixed positions of its nuclei). This results in a HOMO-LUMO gap dependence on the probe site on the isosurface. A smaller gap at a given probe position reflects a larger reactivity of the site with respect to the ionic dissociation.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

scholarly journals The role of visuospatial thinking in students’ predictions of molecular geometry

2021 ◽  
Author(s):  
Nicola A. Kiernan ◽  
Andrew Manches ◽  
Michael K. Seery
Keyword(s):  
High School Students ◽  
Cognitive Processing ◽  
Three Dimensional ◽  
Molecular Geometry ◽  
School Level ◽  
School Students ◽  
Reasoning Strategies ◽  
Analytical Reasoning ◽  
Diagrammatic Representations ◽  
Method Of Instruction

Visuospatial thinking is considered crucial for understanding of three-dimensional spatial concepts in STEM disciplines. Despite their importance, little is known about the underlying cognitive processing required to spatially reason and the varied strategies students may employ to solve visuospatial problems. This study seeks to identify and describe how and when students use imagistic or analytical reasoning when making pen-on-paper predictions about molecular geometry and if particular reasoning strategies are linked to greater accuracy of responses. Student reasoning was evidenced through pen-on-paper responses generated by high attaining, high school students (N = 10) studying Valence Shell Electron Pair Repulsion (VSEPR) Theory in their final year of chemistry. Through analysis and coding of students’ open-ended paper-based responses to an introductory task, results revealed that students employed multiple reasoning strategies, including analytical heuristics and the spontaneous construction of external diagrammatic representations to predict molecular geometry. Importantly, it was observed that despite being instructed on the use of VSEPR theory to find analytical solutions, some students exhibited preference for alternative reasoning strategies drawing on prior knowledge and imagistic reasoning; showing greater accuracy with 3D diagrammatic representations than students who used the algorithmic method of instruction. This has implications for both research and practice as use of specific reasoning strategies are not readily promoted as a pedagogical approach nor are they given credit for in national examinations at school level.

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