Comparison of Local-Density and Quantal hypernetted-Chain Approximations in the Calculation of Electron Density Distribution

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概要

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• Density distributions n(γ|υ) around a fixed electron in jellim are calculated with the use of two types of approximations for the exchange-correlation potential υ_<XC>(γ): One is the local-density approximation (LDA) and the other the quantal hypernetted chain (QHNC) equation which leads to a nonlocal-density approximation for υ_<XC>(γ). In the range γ_S = 1~6, the density distributions n(γ|ν) calculated with the LDA exhibit excellent agreement with those of the QHNC equation. The Fourier transform of the displaced density n(γ|ν) -n_0 can afford to give the exchange-correlation factor G(Q) on the basis of a certain Ansatz. There are however great discrepancies in G(Q) 's cluculated from the LDA and QHNC n(γ|ν) . The LDA G(Q) does not reveal the correct behavior [G(Q)~Q^2] in the small wave-number region in contrast to the QHNC results. Also, a similar behavior of G(Q) is shown to be explicit in the classical electron system. The defect of the LDA is found in that the phase-shifts in the calculation of n(γ|ν) do not satisfy the Friedel sum (US) rule. for example, at γ_S=6 the US value of the LDA is -0.90, while the Hartree one is -0.30 in contrast with the QHNC value -0.999.

• 理論物理学刊行会の論文
• 1983-08-25

著者

• CHIHARA Junzo

  Japan Atomic Energy Research Institute

• Chihara Junzo

  Japan Atomic Eneryg Research Institute

• CHIHARA Junzo

  Department of Physics, Japan Atomic Energy Research Institute

関連論文

• Equivalence of Three Kinetic Methods for Calculating the Space- Time Correlation Function
• Thermodynamics in Density-Functional Theory and Force Theorems
• Integral Equations for Neutral and Charged Quantum Fluids Including Extension of the Percus-Yevick Equation
• Space-Time Correlation Functions in Quantal and Classical Binary Mixtures.II : Liquid Metals as Coupled Electron-Ion Systems
• Integral Equations for Fluids with Long-Range and Short-Range Potentials : Application to a Charged Particle System
• Pair Correlation Functions in Liquid Metallic Hydrogen : Condensed Matter and Statistical Physics
• Comparison of Local-Density and Quantal hypernetted-Chain Approximations in the Calculation of Electron Density Distribution
• Calculation of Pair Correlations in a Degenerate Electron Liquid
• Static Density Response Function of a Degenerate Electron Gas Calculated by Quantal Hyper-Netted Chain Equation
• Nonlocal Exchange-Correlation Potential for Inhomogeneous Electron Gas and Quantum Fluids
• A Series of Integral Equations for Liquids Varying from the PY to HNC Equation
• Derivation of Quantal Hyper-Netted Chain Equation from the Kohn-Sham Theory
• Kinetic Theory of Collective Modes in Classical Liquids
• Space-Time Correlation Functions in Quantal and Classical Binary Mixtures. I : General Formalism and Its Application to Classical Hard-Sphere Mixtures
• Pair Correlation Functions in Classical and Quantal Electron Gases
• A Generalization of the Hartree Approximation and the Quantal Space-Time Correlation Function
• Radial Distribution Functions and Bound Electronic Energy Levels in Hydrogen Plasmas
• Radial Distribution Function for Hard-Sphere Fermions at Zero and Finite Temperatures

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