Gradient expansion of the exchange energy density functional: A complementary expansion of the atomic energy functional

1980 ◽  
Vol 73 (3) ◽  
pp. 1340-1343 ◽  
Author(s):  
Chia C. Shih ◽  
Danny R. Murphy ◽  
Wen‐Ping Wang
Keyword(s):  
Energy Density ◽  
Density Functional ◽  
Energy Functional ◽  
Exchange Energy ◽  
Atomic Energy ◽  
Energy Density Functional ◽  
Gradient Expansion

CONSTRAINING SYMMETRY RESTORATION WITHIN THE NUCLEAR ENERGY DENSITY FUNCTIONAL METHOD

2010 ◽  
Vol 25 (21n23) ◽  
pp. 2016-2017
Author(s):  
J. SADOUDI ◽  
T. DUGUET
Keyword(s):  
Wave Function ◽  
Energy Density ◽  
Density Functional ◽  
Nuclear Energy ◽  
Density Functional Method ◽  
Energy Functional ◽  
Functional Method ◽  
Energy Density Functional ◽  
Density Functional Methods ◽  
Functional Methods

We review the notion of symmetry breaking and restoration within the frame of nuclear energy density functional methods. We focus on key differences between wave-function- and energy-functional-based methods. In particular, we point to difficulties to formulate the restoration of symmetries within the energy functional framework.

scholarly journals SYMMETRY RESTORATION FOR ODD-MASS NUCLEI WITH A SKYRME ENERGY DENSITY FUNCTIONAL

2012 ◽  
Vol 21 (05) ◽  
pp. 1250026 ◽  
Author(s):  
B. BALLY ◽  
B. AVEZ ◽  
M. BENDER ◽  
P.-H. HEENEN
Keyword(s):  
Energy Density ◽  
Density Functional ◽  
Particle Number ◽  
Model Space ◽  
Energy Functional ◽  
Density Functionals ◽  
Pairing Interaction ◽  
Energy Density Functional ◽  
Angular Momentum Projection ◽  
First Results

In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parametrization of the Skyrme energy functional and a volume-type pairing interaction are used.

On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems

1989 ◽  
Vol 67 (3) ◽  
pp. 460-472 ◽  
Author(s):  
Vincenzo Tschinke ◽  
Tom Ziegler
Keyword(s):  
Density Functional Theory ◽  
Correlation Function ◽  
Energy Density ◽  
Density Functional ◽  
Exchange Energy ◽  
Energy Density Functional ◽  
Functional Theory ◽  
Atomic Systems ◽  
Hartree Fock ◽  
Fermi Hole

We have compared, for atomic systems, the spherically averaged Fermi-hole correlation function [Formula: see text] in the Hartree–Fock theory with the corresponding function [Formula: see text] employed in local density functional theory. It is shown that, in contrast to [Formula: see text], the function [Formula: see text] behaves qualitatively incorrectly at positions r1 of the reference electron far from the nucleus. Furthermore, we have shown that the qualitatively incorrect behaviour of [Formula: see text] can be remedied by an approximate expansion of [Formula: see text] in powers of s, where s is the inter-electronic distance. However, such an expansion must be conducted in two regions due to the discontinuity of [Formula: see text] as a function of s at the atomic nucleus. Based on the two-region expansion of [Formula: see text] we have developed an alternative approximate density functional expansion [Formula: see text] for the spherically averaged Fermi-hole correlation function. The corresponding exchange energy density functional yields values for the exchange energies of atoms in good agreement with Hartree–Fock results. Keywords: atomic exchange energy, density functional theory, Fermi hole.

scholarly journals CONFIGURATION MIXING WITHIN THE ENERGY DENSITY FUNCTIONAL FORMALISM: PATHOLOGIES AND CURES

2009 ◽  
Vol 18 (10) ◽  
pp. 2108-2113 ◽  
Author(s):  
DENIS LACROIX ◽  
MICHAEL BENDER ◽  
THOMAS DUGUET
Keyword(s):  
Energy Density ◽  
Density Functional ◽  
Particle Number ◽  
Energy Functional ◽  
Fractional Powers ◽  
Functional Formalism ◽  
Energy Density Functional ◽  
Configuration Mixing ◽  
Wick Theorem ◽  
Do So

Configuration mixing calculations performed in terms of the Skyrme/Gogny Energy Density Functional (EDF) rely on extending the Single-Reference energy functional into non-diagonal EDF kernels. The standard way to do so, based on an analogy with the pure Hamiltonian case and the use of the generalized Wick theorem, is responsible for the recently observed divergences and steps in Multi-Reference calculations. We summarize here the minimal solution to this problem recently proposed1 and applied with success to particle number restoration2. Such a regularization method provides suitable corrections of pathologies for EDF depending on integer powers of the density. The specific case of fractional powers of the density3 is also discussed.

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