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.

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.

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.

Hartree–Fock calculation for the electronic structure of H+3 using numerically optimized orbitals

2001 ◽  
Vol 79 (2-3) ◽  
pp. 673-679
Author(s):  
J D Talman
Keyword(s):  
Electronic Structure ◽  
Ground State ◽  
Equilateral Triangle ◽  
Wave Functions ◽  
Equilibrium Geometry ◽  
Molecular Ion ◽  
Interatomic Spacing ◽  
Hartree Fock ◽  
Gaussian Orbitals

The Hartree–Fock wave functions for the ground state of the H2 molecule and the H+3 molecular ion are computed using radial orbitals that are numerically optimized. It is shown that these orbitals yield results comparable in accuracy to those obtained using much larger bases of Gaussian orbitals. As in previous calculations, the equilibrium geometry for H+3 is found to be that of an equilateral triangle, with an interatomic spacing of 1.64a0. PACS No.: 13.15+q

Inelastic Scattering of High Energy Electrons by Helium

1973 ◽  
Vol 51 (3) ◽  
pp. 311-315 ◽  
Author(s):  
S. P. Ojha ◽  
P. Tiwari ◽  
D. K. Rai
Keyword(s):  
Ground State ◽  
High Energy ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Final States ◽  
Interaction Type ◽  
Hartree Fock ◽  
High Energy Electrons ◽  
Approximate Wave ◽  
Accurate Wave

Generalized oscillator strengths and the cross section for excitation of helium by electron impact have been calculated in the Born approximation. Transitions from the ground state to the n1P (n = 2 and 3) states have been considered. Highly accurate wave functions of the Hartree–Fock and "configuration–interaction" type have been used to represent the ground state. Approximate wave functions due to Messmer have been employed for the final states. The results are compared with other calculations and with experiment.

Analytical model of ground-state lasing phenomenon in broadband semiconductor quantum dot lasers

2013 ◽  
Author(s):  
Vladimir V. Korenev ◽  
Artem V. Savelyev ◽  
Alexey E. Zhukov ◽  
Alexander V. Omelchenko ◽  
Mikhail V. Maximov
Keyword(s):  
Quantum Dot ◽  
Analytical Model ◽  
Ground State ◽  
Quantum Dot Lasers ◽  
Semiconductor Quantum Dot

Coherent X-ray Scattering Factors for Various Configurations of Lanthanides and Their Positive Ions

1975 ◽  
Vol 53 (1) ◽  
pp. 93-96 ◽  
Author(s):  
Robert Benesch ◽  
K. M. S. Saxena
Keyword(s):  
Ground State ◽  
Wave Functions ◽  
X Ray ◽  
Hartree Fock ◽  
Positive Ions ◽  
X Ray Scattering ◽  
Scattering Factor ◽  
Ray Scattering

Coherent X-ray scattering factors have been computed from numerical Hartree–Fock wave functions for the neutral lanthanides and for their single-, double-, and triple-positive ions having the most commonly occurring 6sm4fn ground state configurations. For small scattering angles, the scattering factors for the ions vary among the various configurations. At large scattering angles all configurations for a given ion yield similar values for the scattering factor.

Simplified Non-Empirical Unrestricted Hartree-Fock Approximation (SUHF) for the Calculation of Electronic Ground State Properties of Molecules with Closed and Open Valence Shells. I. Method

1993 ◽  
Vol 48 (7) ◽  
pp. 829-833
Author(s):  
Wolfhard Koch
Keyword(s):  
Electron Correlation ◽  
Ground State ◽  
Atomic Orbital ◽  
Closed Shell ◽  
Open Shell ◽  
Polyatomic Molecules ◽  
Correlation Effects ◽  
Hartree Fock ◽  
Electron Correlation Effects ◽  
Electronic Ground

Abstract Focusing on relative stabilities of electronic states with different spin multiplicities of polyatomic molecules, a simplified unrestricted Hartree-Fock (SUHF) procedure is described. Using different orbitals for different spins (DODS), electron correlation effects of both closed-shell and open-shell systems are expected to be taken into account in the simplest way. While working within a symmetrically orthogonalized (Löwdin) basis we make use of the NDDO approximation (neglect of diatomic differential overlap) concerning the evaluation of electron repulsion and nuclear attraction integrals. Originally, a locally orthogonalized all-electron atomic orbital set of Slater type is considered. The approximation method is completely non-empirical. Rotational invariance is fully retained.

ON THE STABILITY OF PROJECTION AFTER VARIATION SOLUTIONS

2004 ◽  
Vol 13 (01) ◽  
pp. 165-168 ◽  
Author(s):  
T. R. RODRÍGUEZ ◽  
J. L. EGIDO ◽  
L. M. ROBLEDO ◽  
R. R. RODRÍGUEZ-GUZMÁN
Keyword(s):  
Angular Momentum ◽  
Ground State ◽  
Quadrupole Deformation ◽  
Wave Functions ◽  
Degree Of Freedom ◽  
Angular Momentum Projection ◽  
Hartree Fock ◽  
The Stability ◽  
Relevant Degree ◽  
Stability Of The Solution

We have performed angular momentum projection with double-constrained Hartree-Fock-Bogoliubov wave functions with the Gogny interaction for the 32 Mg . We show that the more relevant degree of freedom is the quadrupole deformation. Minima of the ground state obtained in single-constrained calculations with this operator are hardly modified in double-constrained calculations insuring thereby the stability of the solution.

Sign in / Sign up

Export Citation Format

Share Document