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Local Density Approximation

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Local Density Approximation
NameLocal Density Approximation
FieldDensity functional theory
Introduced1960s
ContributorsWalter Kohn, John Pople, Pierre Hohenberg, Lu Jeu Sham

Local Density Approximation The Local Density Approximation is an approach within density functional theory used to approximate exchange–correlation energy by assuming it depends only on the local electron density; it underpins many implementations in computational materials science and quantum chemistry and connects to methods employed at institutions such as Bell Labs, Los Alamos National Laboratory, IBM Research, Argonne National Laboratory and Oak Ridge National Laboratory. In practice LDA informs calculations performed with software packages developed by groups at MIT, Caltech, Stanford University, University of Cambridge, and ETH Zurich, and it has been influential in studies associated with awards such as the Nobel Prize in Chemistry and the Buckminster Fuller Challenge.

Introduction

The Local Density Approximation was formulated as a practical approximation for use in density functional theory alongside foundational work by Pierre Hohenberg and Walter Kohn and practical schemes by Lu Jeu Sham and others; it approximates the exchange–correlation functional using results drawn from the homogeneous electron gas, linking to concepts studied at Cavendish Laboratory, Bell Laboratories, Princeton University, University of California, Berkeley, and University of Chicago. LDA enabled early numerical studies of condensed matter systems in collaborations involving researchers from Harvard University, University of Oxford, Max Planck Society, National Institute of Standards and Technology, and European Molecular Biology Laboratory.

Theoretical Foundation

LDA is grounded in the Hohenberg–Kohn theorems established by Pierre Hohenberg and the Kohn–Sham equations by Walter Kohn and Lu Jeu Sham; it substitutes the exact exchange–correlation functional with a local function derived from the homogeneous electron gas, a model extensively analyzed in work connected to J. Robert Schrieffer, Lev Landau, Richard Feynman, John Bardeen, and David Pines. The approximation relies on many-body results and quantum statistical mechanics from traditions at Landau Institute for Theoretical Physics, Institute for Advanced Study, Cambridge Philosophical Society, Royal Society, and American Physical Society.

Exchange–Correlation Functionals

Common LDA exchange–correlation functionals include parameterizations based on quantum Monte Carlo data and analytic forms developed by groups led by John Perdew, Angelos Michaelides, Luiz N. Oliveira, Richard M. Martin, and researchers at Argonne National Laboratory and Oak Ridge National Laboratory; notable parametrizations reference quantum Monte Carlo studies by David Ceperley and Bernard Alder. These functionals are implemented alongside gradient-corrected schemes promoted by John P. Perdew, Yves Savin, Axel Becke, Jochen Köhler, and developer teams at Gaussian Inc. and Quantum ESPRESSO.

Applications in Solid-State Physics and Chemistry

LDA has been applied to band-structure calculations for materials studied at Bell Labs and IBM, to cohesive-energy estimates for compounds examined by groups at Los Alamos National Laboratory and Argonne National Laboratory, and to surface science problems investigated at Lawrence Berkeley National Laboratory and SLAC National Accelerator Laboratory; it underpins simulations related to superconductivity research influenced by John Bardeen and Brian Josephson, and to catalysis studies originating from collaborations at École Polytechnique, Max Planck Institute for Solid State Research, and Salk Institute. Practitioners have used LDA in investigations connected with Semiconductor Research Corporation projects, NATO-funded collaborations, and multinational consortia including European Research Council initiatives.

Limitations and Corrections

LDA systematically overbinds in molecular dissociation and underestimates band gaps, deficiencies explored in comparative studies involving methods developed by Walter Kohn, John Pople, Martin Karplus, Aage N. Bohr, and remedied in part by gradient-corrected functionals (GGA) advanced by John Perdew and Kieron Burke, hybrid functionals introduced by Alexandre D. Becke and John Pople, and many-body perturbation theory techniques like the GW approximation from work by Lars Hedin; corrections also relate to approaches from Dmitri Mendeleev-inspired materials databases and high-throughput projects at Materials Project and NOMAD.

Computational Implementation

LDA is implemented in plane-wave pseudopotential codes and all-electron methods developed by teams at University of Cambridge, Trinity College Dublin, Princeton University, University of California, Los Angeles, Barcelona Supercomputing Center, and commercial packages by Schrödinger, Inc. and ACCLAB; implementations rely on numerical techniques associated with fast Fourier transforms popularized at Los Alamos National Laboratory and linear algebra libraries from Lawrence Livermore National Laboratory and National Center for Supercomputing Applications. Computational projects using LDA are often carried out on hardware provided by National Science Foundation supercomputing centers, U.S. Department of Energy facilities, European Grid Infrastructure, and national infrastructures in Japan and China.

Historical Development and Key Contributors

Key contributors include Pierre Hohenberg and Walter Kohn for the theoretical basis, Lu Jeu Sham for the Kohn–Sham formalism, and David Ceperley and Bernard Alder for quantum Monte Carlo data informing LDA parameterizations; subsequent influential figures span John Perdew, Alexandre D. Becke, Richard M. Martin, Lars Hedin, and research groups at Bell Labs, IBM Research, Los Alamos National Laboratory, Max Planck Society, and Argonne National Laboratory. The development trajectory links to major scientific milestones like the awarding of the Nobel Prize in Chemistry to Walter Kohn and collaborations fostered by organizations such as the Royal Society and American Physical Society.

Category:Density functional theory