Topic

# Local-density approximation

About: Local-density approximation is a research topic. Over the lifetime, 6901 publications have been published within this topic receiving 451187 citations.

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TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.

Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

117,932 citations

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TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.

Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.

42,177 citations

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TL;DR: A way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects as well as significant interconfigurational and interterm errors remain.

Abstract: Generalized gradient approximations (GGA's) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3--4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.

16,870 citations

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TL;DR: In this paper, the self-interaction correction (SIC) of any density functional for the ground-state energy is discussed. But the exact density functional is strictly selfinteraction-free (i.e., orbitals demonstrably do not selfinteract), but many approximations to it, including the local spin-density (LSD) approximation for exchange and correlation, are not.

Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

14,881 citations

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TL;DR: In this paper, it was shown that quantum-mechanical molecular-dynamics simulations in a finite-temperature local density approximation based on the calculation of the electronic ground state and of the Hellmann-Feynman forces after each time step are feasible for liquid noble and transition metals.

Abstract: We show that quantum-mechanical molecular-dynamics simulations in a finite-temperature local-density approximation based on the calculation of the electronic ground state and of the Hellmann-Feynman forces after each time step are feasible for liquid noble and transition metals. This is possible with the use of Vanderbilt-type ``ultrasoft'' pseudopotentials and efficient conjugate-gradient techniques for the determination of the electronic ground state. Results for liquid copper and vanadium are presented.

5,077 citations