The dependence of the hyperfine interaction on the cellular potential in Na and K. II

1969 ◽  
Vol 47 (13) ◽  
pp. 1331-1336 ◽  
Author(s):  
R. A. Moore ◽  
S. H. Vosko
Keyword(s):  
Fermi Surface ◽  
Electron Density ◽  
Wave Functions ◽  
Electron Wave ◽  
Surface Electron ◽  
Conduction Electrons ◽  
Hartree Fock ◽  
A Value ◽  
Dependent Potential ◽  
Conduction Electron Density

The dependence of the Fermi surface electron wave functions in Na and K on (i) an L-dependent effective local cellular potential constructed to simulate Hartree-Fock theory and (ii) the inclusion of the Hartree field due to the conduction electrons in the cellular potential is investigated. All calculations are performed using the Wigner–Seitz spherical cellular approximation and the Schrödinger equation is solved by the Kohn variational method. It is found that to ensure a value of the Fermi surface electron density at the nucleus accurate to ~5%, it is necessary to use the L-dependent potential along with the Hartree field due to a realistic conduction electron density.

The dependence of the hyperfine interaction on the cellular potential in Li, Na, and K

1968 ◽  
Vol 46 (12) ◽  
pp. 1425-1434 ◽  
Author(s):  
R. A. Moore ◽  
S. H. Vosko
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Fermi Surface ◽  
Hyperfine Interaction ◽  
Electron Density ◽  
Electron Wave Function ◽  
Electron Wave ◽  
Surface Electron ◽  
Conduction Electrons ◽  
Hartree Fock

The effect of including the Hartree field due to the conduction electrons in the cellular potential on the Fermi surface electron wave function is investigated. It is found that the Fermi surface electron density at the nucleus is reduced by 10% to 20% by including this term. Also, an L dependent effective local potential constructed to simulate Hartree–Fock theory is calculated and applied to Li. All calculations are performed using the Wigner–Seitz spherical cellular approximation, and the Schrödinger equation is solved by the Kohn (1954) variational method.

scholarly journals Fermi Radii of Lithium by Positron Annihilation

1971 ◽  
Vol 49 (24) ◽  
pp. 3227-3233 ◽  
Author(s):  
J. J. Paciga ◽  
D. Llewelyn Williams
Keyword(s):  
Fermi Surface ◽  
Positron Annihilation ◽  
Wave Functions ◽  
Scattering Data ◽  
Electron Wave ◽  
A Value ◽  
Band Structure Calculations ◽  
Detector Geometry ◽  
Point Detector ◽  
Structure Calculations

A collinear-point detector geometry has been used to study positron annihilation in single-crystal lithium. The results are interpreted in terms of the higher momentum components of the electron wave functions and the lithium Fermi surface. A consistent interpretation favors a value for the Fourier component V110 of the lattice potential of close to 0.10 Ry and a Fermi surface whose radius in the [110] direction is 2.9% greater than in the [100] direction. This latter result is consistent with Compton-scattering data and both results are in close agreement with the recent band-structure calculations of Rudge.

"VECTAL" REPRESENTATION OF THE WAVE FUNCTION AND ITS PHYSICAL MEANING

1967 ◽  
Vol 45 (11) ◽  
pp. 3667-3676
Author(s):  
C. S. Lin
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Electron Wave Function ◽  
Electron Wave ◽  
Expectation Values ◽  
Expectation Value ◽  
Hartree Fock ◽  
The One ◽  
The Relationship ◽  
Determinantal Form

A new form of one-electron wave function, "vectal," is introduced. It is shown that an arbitrary CI geminal and a certain class of many-electron wave functions can be represented in a single-determinantal form in terms of the vectal. Eigenvalue equations for the vectal, similar to that of the Hartree–Fock theory, are derived and the vectal representation is shown to enable a formal interpretation of the CI theory in the Hartree–Fock manner. The eigenvalue, vectal energy, is interpreted as the negative of an ionization potential, in Koop-man's sense, of the system described by the CI wave function. It is also shown that the expectation value of any one-electron operator, [Formula: see text], where Ψ is the CI wave function, is expressible in terms of the expectation values of the same operator with respect to the vectals. The vectals are interpreted as the one-electron wave function in the CI space.A possible application of the vectal representation is briefly described, and the relationship between the vectal representation and the "scalar representation" is discussed.

Resonating UHF Study on Electron Correlation in a Ground State of Two Electrons Confined in 2D Quantum Dot

2012 ◽  
Vol 1423 ◽  
Author(s):  
Takuma Okunishi ◽  
Kyozaburo Takeda
Keyword(s):  
Quantum Dot ◽  
Electron Correlation ◽  
Ground State ◽  
Electron State ◽  
Wave Functions ◽  
Electron Wave ◽  
Temporal Fluctuation ◽  
Semiconductor Quantum Dot ◽  
Hartree Fock ◽  
Reference Description

ABSTRACTWe theoretically study the spatial and temporal fluctuation of two electrons confined in a semiconductor quantum dot (QD). Eigenstates are determined by the resonating unrestricted Hartree-Fock (res-UHF) approach in order to take into account the electron correlation via the configuration interaction (CI). The time-dependent (TD) wave function is, then, expanded by the UHF solutions, and the CI treatment is combined with the TD Schrödinger equation (TD-CI). The present TD-CI approach has an advantage to study how the electron correlation fluctuates the multi-electron state spatially and/or temporally through the multi-reference description of many-electron wave functions.

3D WAVELET TREATMENT OF SOLVATED BIPOLARON AND POLARON

2005 ◽  
Vol 04 (03) ◽  
pp. 751-767 ◽  
Author(s):  
G. N. CHUEV ◽  
M. V. FEDOROV ◽  
H. J. LUO ◽  
D. KOLB ◽  
E. G. TIMOSHENKO
Keyword(s):  
Free Energy ◽  
Three Dimensional ◽  
Energy Functional ◽  
Wave Functions ◽  
Basis Set ◽  
Electron Wave ◽  
Solvated Electron ◽  
Hartree Fock ◽  
Free Energy Functional ◽  
Excess Electrons

Three-dimensional discrete tensor wavelets are applied to calculate wave functions of excess electrons solvated in polar liquids. Starting from the Hartree–Fock approximation for the electron wave functions and from the linear response to the solute charge for the solvent, we have derived the approximate free energy functional for the excess electrons. The orthogonal Coifman basis set is used to minimize the free energy functional and to approximate the electron wave functions. The scheme is applied to the calculation of the properties of the solvated electron and the singlet bipolaron formation. The obtained results indicate that the proposed algorithm is fast and rather efficient for calculating the electronic structure of the solvated molecular solutes.

Low-temperature transport properties of the alkali metals. I. The electron-phonon interaction

1961 ◽  
Vol 263 (1315) ◽  
pp. 531-544 ◽  
Keyword(s):  
Fermi Surface ◽  
Alkali Metals ◽  
Plane Waves ◽  
Wave Functions ◽  
Electron Wave ◽  
Thermo Electric ◽  
Fermi Surfaces ◽  
Electron Phonon Interaction ◽  
Symmetry Properties ◽  
Umklapp Scattering

The form of the electron-phonon matrix element is calculated for metals with non-spherical Fermi surfaces by using electron wave functions, which are linear combinations of two plane waves, as in the model of nearly free electrons. Numerical calculations are made with the use of the ‘twelve cone’ approximation to the Brillouin zone. It is shown that, if the Fermi surface bulges towards the zone faces, there is a significant increase in the probability of Umklapp scattering of electrons, the increase depending on the amount of distortion of the Fermi surface, and on the symmetry properties of the electron wave functions. The increase in Umklapp scattering has important consequences for calculations of the resistivities of metals, and particularly for calculations of the ‘phonon drag’ contribution to the thermo-electric power.

Über die Berechnung der Korrelationsenergie der Atomelektronen

1960 ◽  
Vol 15 (10) ◽  
pp. 909-926 ◽  
Author(s):  
Levente Szász
Keyword(s):  
Wave Function ◽  
Numerical Calculation ◽  
Ground State ◽  
Correlation Functions ◽  
Correlation Energy ◽  
Wave Functions ◽  
Electron Wave ◽  
Hartree Fock ◽  
Experimental Values ◽  
The One

To calculate the correlation energy of an atom with N electrons we suggest the wave functionwhere à is the antisymmetrizer operator, φ1, φ2, ..., φN are one electron wave functions, and Wjk are correlation functions of the following form:where the constants c j km, n, l are variational parameters. The function (a) is a generalization of thewave function of Hylleraas for He. After a discussion of the properties of our function, an energy expression is derived. Numerical calculation is made for the ground state of the Be atom with the functionwhere φ1 and φ2 are ls wave functions, φ3 and φ4 are 2s wave functions, r1, r2, r3 and r4 are the radial coordinates of the four electrons, r12 and r34 are the distances between the corresponding electrons, and C1 and c2 are variational parameters. Using the one electron wave functions calculated by Roothaan and coll. with the Roothaan procedure, we got the energy value E= -14.624 a. u. while the Hartree-Fock and experimental values are EH,F= -14.570 a. u. and Eexp= -14.668 a. u. respectively. Thus the function (c) gives about one-half of the correlation energy of the Be atom.

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