scholarly journals Application of Thomas-Fermi model to fullerene molecule and nanotube

2007 ◽  
Vol 5 (1) ◽  
pp. 11-18
Author(s):  
Yuri Kornyushin
Keyword(s):  
Good Description ◽  
Fullerene Molecule ◽  
Semiclassical Approach ◽  
Fermi Model ◽  
Electronic Shell ◽  
Thomas Fermi ◽  
External Radius ◽  
Internal Radius ◽  
Experimental Values

Semiclassical description, based on electrostatics and Thomas-Fermi model is applied here to calculate dimensions of the electronic shell of a fullerene molecule and a nanotube. The internal radius of the electronic shell of a fullerene molecule, calculated within the framework of the model is 0.2808 nm. The external radius is 0.4182 nm. The experimental values are 0.279 nm and 0.429 nm correspondingly. This shows that semiclassical approach provides rather good description of the dimensions of the electronic shell in a fullerene molecule. Two types of dipole oscillations in a fullerene molecule are considered and their frequencies are calculated. Similar calculations are performed for a nanotube also. For a nanotube with a radius of the cylinder of the ions, Rn = 0.7 nm, the internal radius of the electronic shell, calculated within the framework of the model is 0.577 nm. The external radius is 0.816 nm. Three types of dipole oscillations in nanotube are considered and their frequencies are calculated.

Bond equilibrium theory for Te-rich liquid Tl–Te alloys

1977 ◽  
Vol 55 (11) ◽  
pp. 1930-1936 ◽  
Author(s):  
Melvin Cutler
Keyword(s):  
Free Energy ◽  
Good Description ◽  
Hole Concentration ◽  
Enthalpy Of Mixing ◽  
Dangling Bond ◽  
Fermi Model ◽  
Bond Model ◽  
Independent Information ◽  
Molecular Bond ◽  
Rich Liquid

Recent work has provided independent information about the behavior of the hole concentration c in TlxTe1−x as a function of temperature T and composition x in the range 0.2 ≤ x ≤ 0.6. This makes possible a critical reexamination of a molecular bond model for the structure of the alloy, in which holes are generated by broken Te—Te bonds. The earlier theory is revised to formulate an unrestricted independent bond model (ibm), for which the equations are simple and have obvious physical interpretations. This provides a good description of c(T) but only a qualitatively correct c(x). Using a Thomas–Fermi model for the screening interaction between holes and the acceptor ions, it is shown that the equilibrium constant can be expected to increase rapidly with c at large enough values. A modification in which the free energy of a dangling bond is decreased by proximity to a Tl—Te bond is found to significantly improve the result for c(x). The thermochemical behavior is derived. The entropy of mixing is in fair agreement with experiment, but the enthalpy of mixing is grossly wrong. This reflects the neglect of intermolecular interactions in the theory, which, it seems, can easily account for the remaining discrepancies in the predicted behavior of c.

Comparison of Variational Solutions of the Thomas-Fermi Model in Terms of the Corrected Ionization Energy

1987 ◽  
Vol 42 (9) ◽  
pp. 943-947
Author(s):  
I. Agil ◽  
A. Alharkan ◽  
H . Alhendi ◽  
A. Alnaghmoosh
Keyword(s):  
Ionization Energy ◽  
Trial Function ◽  
Binding Energies ◽  
Initial Slope ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Variational Solutions ◽  
Comparison Of The Results

It is shown that leading corrections, to the ionization energy, of many-electrons atom, can be expressed as leading corrections of initial slope of trial variational solutions of the Thomas-Fermi equation. Some variational solutions with different initial slopes are compared. A comparison of the results shows, that as far as the binding energies are concerned a trial function with its slope not close to the (negative) Baker’s constant may not be suited.

On sodium clusters in C60 fullerides

1997 ◽  
Vol 75 (1) ◽  
pp. 77-82 ◽  
Author(s):  
M. Apostol ◽  
F. Rachdi ◽  
C. Goze ◽  
L. Hajji
Keyword(s):  
Electric Charge ◽  
The Body ◽  
Electron Charge ◽  
Body Centered Cubic ◽  
Fermi Theory ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Sodium Clusters ◽  
Alkali Fullerides

Sodium (Na) clusters in octahedral cages of Na-intercalated fullerides Na6C60 and Na11C60 are studied within a Thomas–Fermi model. It is shown that the tetrahedral Na4 cluster in Na6C60 has an electric charge ~ +2.7 (in electron charge units), while the body-centered cubic Na9 cluster in Na11C60 is almost electrically neutral. Keywords: sodium clusters, alkali fullerides, Thomas–Fermi theory, ionization charge.

The Thomas-Fermi model: momentum expectation values

1983 ◽  
Vol 44 (3) ◽  
pp. 333-342 ◽  
Author(s):  
I.K. Dmitrieva ◽  
G.I. Plindov
Keyword(s):  
Expectation Values ◽  
Fermi Model ◽  
Thomas Fermi

scholarly journals X ɑ Method with Pseudopotentials

1980 ◽  
Vol 35 (6) ◽  
pp. 628-636 ◽  
Author(s):  
Levente Szasz
Keyword(s):  
Shell Structure ◽  
Virial Theorem ◽  
Radial Density ◽  
Fermi Model ◽  
New Formalism ◽  
Density Dependent ◽  
Thomas Fermi

The l a method for an atom or molecule is transformed into an all-electron pseudopotential formalism. The equations of the X ɑ method are exactly transformed into pseudo-orbital equations and the resulting pseudopotentials are replaced by simple density-dependent potentials derived from Thomas-Fermi model. It is shown that the new formalism satisfies the virial theorem. As the first application it is shown that the model explains the shell-structure of atoms by the property that the pseudo-orbitals for the (ns), (np), (nd) etc. electrons are, in a very good approximation, the solutions of the same equation and have their maxima at the same point thereby creating the peaks in the radial density characterizing the shell structure

Sign in / Sign up

Export Citation Format

Share Document