Der Einfluß der Überlappung in der Theorie der π-Elektronensysteme von HÜCKEL und HARTMANN

1961 ◽  
Vol 16 (12) ◽  
pp. 1328-1333 ◽  
Author(s):  
W. A. Bingel ◽  
H. Preuss ◽  
H.-H. Schmidtke
Keyword(s):  
Excitation Energy ◽  
Wave Functions ◽  
Electron Systems ◽  
Level Spacing ◽  
Ionisation Potential ◽  
Pairing Property ◽  
The Difference ◽  
Mo Theory

The simple MO—LCAO-method for alternant π-electron systems has been extended recently to include higher p π-orbitals. In this version of the MO-method- the pairing property between the energies and wave functions of the bonding and antibonding π-MO's is no longer correct, the level spacing of the antibonding MO's is now smaller than that of the bonding ones. This effect has been used to explain 1 the approximate constancy of the difference: 1st excitation energy—1st ionisation potential for a great number of molecules, which was observed by SCHEIBE 2. In the present work the influence of atomic overlap on the extended MO-theory is investigated.

A Cluster Expansion Formalism for Direct Calculation of Ionisation Potential and Excitation Energy of Many Electron Systems Using H-F Ground State as Vacuum

1978 ◽  
Vol 33 (12) ◽  
pp. 1549-1551
Author(s):  
D. Mukherjee ◽  
A. Mukhopadhyay ◽  
R. K. Moitra
Keyword(s):  
Excitation Energy ◽  
Cluster Expansion ◽  
Ground State ◽  
Shell Theory ◽  
State Energy ◽  
Direct Calculation ◽  
Electron System ◽  
Open Shell ◽  
Electron Systems ◽  
Ionisation Potential

Abstract In this note, the authors’ recently developed non-perturbative open-shell theory is adapted for direct calculation o f ionisation potential and excitation energy of m any-electron systems. The H -F ground state is used as the “vacuum ” or “ core” in order to achieve a transparent separation o f the ground state energy. An application to a simple 4 π-electron system is discussed as an illustration o f the workability of the theory.

scholarly journals Studying the x- ray atomic Scattering form Factor and Nuclear Magnetic Shielding Constant for Be atom in its Excited state (1s2 2s 3s) and the Be - like ions

2015 ◽  
Vol 12 (1) ◽  
pp. 204-209
Author(s):  
Baghdad Science Journal
Keyword(s):  
Form Factor ◽  
Excited State ◽  
Computer Software ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Electron Systems ◽  
X Ray ◽  
Hartree Fock ◽  
Atomic Scattering ◽  
Nuclear Magnetic

The division partitioning technique has been used to analyze the four electron systems into six-pairs electronic wave functions for ( for the Beryllium atom in its excited state (1s2 2s 3s ) and like ions ( B+1 ,C+2 ) using Hartree-Fock wave functions . The aim of this work is to study atomic scattering form factor f(s) for and nuclear magnetic shielding constant. The results are obtained numerically by using the computer software (Mathcad).

scholarly journals SPIN – A Schrödinger-Poisson Solver Including Nonparabolic Bands

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 489-493
Author(s):  
H. Kosina ◽  
C. Troger
Keyword(s):  
Dispersion Relation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Two Dimensional ◽  
Electron Systems ◽  
Dimensional Electron ◽  
One Dimensional ◽  
Poisson Solver ◽  
Two Dimensional Electron Systems

Nonparabolicity effects in two-dimensional electron systems are quantitatively analyzed. A formalism has been developed which allows to incorporate a nonparabolic bulk dispersion relation into the Schrödinger equation. As a consequence of nonparabolicity the wave functions depend on the in-plane momentum. Each subband is parametrized by its energy, effective mass and a subband nonparabolicity coefficient. The formalism is implemented in a one-dimensional Schrödinger-Poisson solver which is applicable both to silicon inversion layers and heterostructures.

scholarly journals Plasma processes to detect fluorine with ICPMS/MS as [M–F]+: an argument for building a negative mode ICPMS/MS

2018 ◽  
Vol 33 (8) ◽  
pp. 1304-1309 ◽  
Author(s):  
Nor Laili Azua Jamari ◽  
Arne Behrens ◽  
Andrea Raab ◽  
Eva M. Krupp ◽  
Jörg Feldmann
Keyword(s):  
Bond Energy ◽  
Fluoride Ion ◽  
Metal Fluoride ◽  
Ionisation Potential ◽  
Negative Mode ◽  
The Difference ◽  
Oxygen Bond

The paper describes that the 2nd ionisation potential and the difference in bond energy of a metal to fluorine bond and of a metal to oxygen bond are the most important parameters to form a metal fluoride ion for the detection of fluorine in ICPMS/MS.

scholarly journals Tunable fractional Fourier transform implementation of electronic wave functions in atomically thin materials

2018 ◽  
Vol 9 ◽  
pp. 1828-1833 ◽  
Author(s):  
Daniela Dragoman
Keyword(s):  
Wave Function ◽  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Berry Phase ◽  
Wave Functions ◽  
Electron Propagation ◽  
One Step ◽  
The Difference ◽  
Integrated Logic ◽  
The Fourier Transform

A tunable fractional Fourier transform of the quantum wave function of electrons satisfying either the Schrödinger or the Dirac equation can be implemented in an atomically thin material by a parabolic potential distribution applied on a direction transverse to that of electron propagation. The difference between the propagation lengths necessary to obtain a fractional Fourier transform of a given order in these two cases could be seen as a manifestation of the Berry phase. The Fourier transform of the electron wave function is a particular case of the fractional Fourier transform. If the input and output wave functions are discretized, this configuration implements in one step the discrete fractional Fourier transform, in particular the discrete Fourier transform, and thus can act as a coprocessor in integrated logic circuits.

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