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| Perdew–Burke–Ernzerhof | |
|---|---|
| Name | Perdew–Burke–Ernzerhof |
| Developer | John P. Perdew; Kieron Burke; Matthias Ernzerhof |
| Released | 1996 |
| Genre | Density functional approximation |
Perdew–Burke–Ernzerhof is a generalized gradient approximation developed for use in Kohn–Sham density functional theory by John P. Perdew, Kieron Burke, and Matthias Ernzerhof in 1996. It provides an exchange–correlation functional intended to improve upon the Local-density approximation for atoms, molecules, and solids and has become one of the most widely used functionals in computational studies by researchers affiliated with institutions such as Princeton University, University of California, San Diego, and University of Vienna. The approximation influenced later developments in electronic structure methods applied in studies at laboratories including Lawrence Berkeley National Laboratory, Argonne National Laboratory, and Max Planck Society centers.
Perdew–Burke–Ernzerhof was introduced to address systematic errors noted in earlier approximations tested against benchmark calculations by groups at Harvard University, Stanford University, and University of Cambridge and experimental results from facilities like Brookhaven National Laboratory, CERN, and National Institute of Standards and Technology. The proposal drew on theoretical constraints framed in the tradition of work by Walter Kohn, Lu Jeu Sham, and later developments connected to researchers at Cornell University and University of Illinois Urbana–Champaign. Its adoption spread through community codes developed at organizations including Quantum ESPRESSO Foundation, SIESTA Developers, NWChem Project, and GPAW collaborations.
The construction rests on the Hohenberg–Kohn theorem and the Kohn–Sham method and leverages exact conditions discussed in the literature by authors at Massachusetts Institute of Technology, University of California, Berkeley, and Columbia University. It enforces known sum rules and scaling properties that echo analyses performed in seminal papers by John C. Slater and Per-Olov Löwdin. The approach contrasts with hybrid functionals developed later by teams at Bell Labs, IBM Research, and Microsoft Research, which mix in portions of Hartree–Fock exchange formalized by Dirac and advanced by Pople and collaborators.
The functional uses an exchange enhancement factor and a correlation expression parameterized to satisfy exact constraints rather than empirical fitting to datasets used by groups at Argonne National Laboratory and Los Alamos National Laboratory. Perdew, Burke, and Ernzerhof specified gradient-dependent terms reminiscent of earlier proposals from researchers at University of Oxford and École Normale Supérieure. Parameters were chosen to honor uniform electron gas limits studied by teams at Los Alamos and University of Cambridge and to reproduce known asymptotic behavior examined by scholars at Imperial College London and University of Toronto.
Numerous variants and extensions emerged, including revised forms developed by researchers at National Renewable Energy Laboratory, Tokyo Institute of Technology, and ETH Zurich; notable variants include versions tailored for solids, for surfaces, and for van der Waals corrections worked on by scientists at University of California, Santa Barbara, Rutgers University, and University of Michigan. Hybrid extensions incorporating exact exchange were pursued in collaborations with groups at University of Chicago and University of California, Los Angeles, while range-separated adaptations were proposed in work linked to Bell Labs and EPFL researchers. Meta-GGA and double-hybrid developments by teams at University of Minnesota and Weizmann Institute of Science built on the conceptual framework.
Perdew–Burke–Ernzerhof has been employed in studies spanning condensed matter investigations at Oak Ridge National Laboratory and Argonne National Laboratory, surface science projects at SLAC National Accelerator Laboratory, and molecular spectroscopy work at Lawrence Livermore National Laboratory. It often delivers reliable geometries and reasonable energetics for systems explored by groups at Caltech, Yale University, and University of Oxford, yet its performance varies for reaction barriers and dispersion-dominated assemblies probed in collaborations with Max Planck Institute for Solid State Research and Scripps Research. Benchmarks against high-level quantum chemistry methods such as coupled cluster and configuration interaction calculations performed by teams at Rice University and University of Wisconsin–Madison illuminate strengths and weaknesses.
Implementations exist across major electronic structure packages maintained by communities at Quantum ESPRESSO Foundation, VASP developers, ABINIT developers, CP2K consortium, and Gaussian, Inc.; these distributions enable studies by users at University College London and University of Sydney. The functional is available in open-source libraries produced by projects like LibXC and integrated into platforms supported by US DOE computing facilities and national supercomputing centers including NERSC and PRACE partnerships. Documentation and code contributions have come from contributors associated with GitHub, Inc. repositories and collaborative initiatives with European Molecular Biology Laboratory groups.
Critics from institutions such as University of Tokyo, University of Basel, and University of Cambridge note limitations in treating long-range dispersion interactions and strong correlation effects encountered in studies of transition-metal oxides and van der Waals complexes investigated at Argonne National Laboratory and Brookhaven National Laboratory. Subsequent developments by teams at Stanford University and Harvard University sought to remedy deficiencies via empirical dispersion corrections and beyond-GGA frameworks, while comparisons with quantum Monte Carlo results achieved by groups at Trinity College Dublin and University of Copenhagen highlight remaining quantitative discrepancies. Despite these caveats, the approximation remains a standard choice in many computational workflows used at research centers including Max Planck Society and Lawrence Berkeley National Laboratory.