scholarly journals Imaging Electron Wave Functions of Quantized Energy Levels in Carbon Nanotubes

Science ◽  
1999 ◽  
Vol 283 (5398) ◽  
pp. 52-55 ◽  
Author(s):  
L. C. Venema
Keyword(s):  
Carbon Nanotubes ◽  
Energy Levels ◽  
Wave Functions ◽  
Electron Wave

scholarly journals Calculation of One-Electron Wave Functions and Energy Levels of N-Butane Molecule on the Basis of Slater Atomic Orbitals

2021 ◽  
Vol 75 (3) ◽  
pp. 229-233
Author(s):  
Faig Pashaev ◽  
Arzuman Gasanov ◽  
Musaver Musaev ◽  
Ibrahim Abbasov
Keyword(s):  
Group Theory ◽  
Energy Levels ◽  
Wave Functions ◽  
Electron Wave ◽  
Hamilton Operator ◽  
Atomic Orbitals ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Space Symmetry ◽  
Polyatomic Systems

Abstract It is known that the application of the group theory greatly simplifies the problems of polyatomic systems possessing to any space symmetry. The symmetry properties of such systems are their most important characteristics. In such systems, the Hamilton operator is invariant under unitary symmetry transformations and rearrangements of identical particles in the coordinate system. This allows to obtain information about the character of one-electron wave functions — molecular orbitals — the considered system, i.e. to symmetrise the original wave functions without solving the Schrödinger equation.

Magnetotunneling spectroscopy imaging of electron wave functions in self-assembled InAs quantum dots

2001 ◽  
Vol 171 (12) ◽  
pp. 1365
Author(s):  
E.E. Vdovin ◽  
Yu.N. Khanin ◽  
Yu.V. Dubrovskii ◽  
A. Veretennikov ◽  
A. Levin ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Wave Functions ◽  
Electron Wave ◽  
Inas Quantum Dots ◽  
Self Assembled

Quantum Mechanical Investigation of Geometrical Structure and Dynamic Behavior of h-BNNT (9,9-5) and h-AlNNT (9,9-5)Single-Walled Nanotubes: NBO Analysis

2019 ◽  
Vol 16 (9) ◽  
pp. 705-717
Author(s):  
Mehrnoosh Khaleghian ◽  
Fatemeh Azarakhshi
Keyword(s):  
Carbon Nanotubes ◽  
Density Functional ◽  
Structural Parameters ◽  
Energy Levels ◽  
Nbo Analysis ◽  
Electronic Energy ◽  
Boron Nitride Nanotubes ◽  
Basis Set ◽  
B3lyp Method ◽  
Mechanical Investigation

In the present research, B45H36N45 Born Nitride (9,9) nanotube (BNNT) and Al45H36N45 Aluminum nitride (9,9) nanotube (AlNNT) have been studied, both having the same length of 5 angstroms. The main reason for choosing boron nitride nanotubes is their interesting properties compared with carbon nanotubes. For example, resistance to oxidation at high temperatures, chemical and thermal stability higher rather than carbon nanotubes and conductivity in these nanotubes, unlike carbon nanotubes, does not depend on the type of nanotube chirality. The method used in this study is the density functional theory (DFT) at Becke3, Lee-Yang-Parr (B3LYP) method and 6-31G* basis set for all the calculations. At first, the samples were simulated and then the optimized structure was obtained using Gaussian 09 software. The structural parameters of each nanotube were determined in 5 layers. Frequency calculations in order to extract the thermodynamic parameters and natural bond orbital (NBO) calculations have been performed to evaluate the electron density and electrostatic environment of different layers, energy levels and related parameters, such as ionization energy and electronic energy, bond gap energy and the share of hybrid orbitals of different layers.

A free-electron theory of conjugated molecules

1953 ◽  
Vol 49 (4) ◽  
pp. 650-658 ◽  
Author(s):  
J. Stanley Griffith
Keyword(s):  
Free Electron ◽  
Wave Functions ◽  
Electron Charge ◽  
Algebraic Equations ◽  
Electron Wave ◽  
Electron Theory ◽  
Conjugated Molecules ◽  
Electron Charge Density ◽  
Linear Polyenes ◽  
Alternant Hydrocarbons

ABSTRACTThe values of a free-electron eigenfunotion at the carbon nuclei of a conjugated hydrocarbon are found to satisfy a system of algebraic equations. These equations are similar in form to those obtained in the method known as the linear combination of atomic orbitale but only coincide with them for linear polyenes and benzene. The symmetry, degeneracy and energy of the eigenvectors of these free-electron equations correspond exactly to those of the free-electron wave functions found by the usual methods. From this correspondence, a theorem is deduced about the free-electron charge density in alternant hydrocarbons.

Electron wave functions at the nuclear surface

1974 ◽  
Vol 48 (2) ◽  
pp. 91-94 ◽  
Author(s):  
H. Ogata ◽  
J. Asai
Keyword(s):  
Wave Functions ◽  
Nuclear Surface ◽  
Electron Wave

scholarly journals Intercombination Transitions between Levels X1Σg+ and A 3Πu in C2

1987 ◽  
Vol 120 ◽  
pp. 103-105
Author(s):  
J. Le Bourlot ◽  
E. Roueff
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Energy Matrix ◽  
First Order ◽  
Emission Transition ◽  
Intercombination Transition ◽  
The One ◽  
Potential Curves

We present a new calculation of intercombination transition probabilities between levels X1Σg+ and a 3Πu of the C2 molecule. Starting from experimental energy levels, we calculate RKR potential curves using Leroy's Near Dissociation Expansion (NDE) method; these curves give us wave functions for all levels of interest. We then compute the energy matrix for the four lowest states of C2, taking into account Spin-Orbit coupling between a 3Πu and A 1Πu on the one hand and X 1Σ+g and b 3Σg− on the other. First order wave functions are then derived by diagonalization. Einstein emission transition probabilities of the Intercombination lines are finally obtained.

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