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| Kohn–Sham method | |
|---|---|
| Name | Kohn–Sham method |
| Field | Computational chemistry, Condensed matter physics |
| Introduced | 1965 |
| Creators | Walter Kohn; Lu Jeu Sham |
| Institution | University of California, San Diego; University of Ottawa |
Kohn–Sham method is a computational framework in electronic structure theory that transforms the many-electron problem into an auxiliary system of noninteracting particles, enabling tractable calculations of ground-state properties for atoms, molecules, and solids. Developed to complement density-based approaches, the method underpins widely used techniques in computational materials science, quantum chemistry, and nanoscience. It provides a practical route from formal theorems to implementable algorithms used across academic, industrial, and national laboratory settings.
The method originated from theoretical work by Walter Kohn and Lu Jeu Sham and was published amid active research communities at University of California, San Diego, University of Ottawa, and associated institutions, influencing later developments at Bell Labs, IBM Research, and Los Alamos National Laboratory. It complemented foundational results such as the Hohenberg–Kohn theorems and interacted with computational programs developed at Argonne National Laboratory, Lawrence Livermore National Laboratory, and Oak Ridge National Laboratory. Early adopters included researchers affiliated with Harvard University, Massachusetts Institute of Technology, and Stanford University.
The Kohn–Sham method builds on the Hohenberg–Kohn framework, which establishes a mapping between ground-state electronic density and external potentials, a result that resonated in work by scientists at Princeton University, Columbia University, and University of Cambridge. The method constructs an auxiliary system of noninteracting particles whose density matches the interacting system studied in research groups at California Institute of Technology and University of Chicago, enabling use of single-particle orbitals. Conceptual links tie to variational principles employed by theorists at Max Planck Society institutes and to exchange and correlation ideas debated in conferences hosted by Royal Society and American Physical Society symposia.
The formalism yields a set of single-particle equations, often implemented using basis sets and pseudopotentials developed in collaborations involving University of Tokyo, École Polytechnique, and Imperial College London. The self-consistent field procedure used to solve the Kohn–Sham equations echoes numerical strategies refined at Los Alamos National Laboratory and Sandia National Laboratories. Computational realizations exploit matrix diagonalization, iterative diagonalizers, and preconditioning techniques advanced at Cornell University and Yale University, and leverage parallelization methods pioneered at National Center for Supercomputing Applications and Argonne National Laboratory.
A central unknown in the Kohn–Sham framework is the exchange–correlation functional, whose approximations include local density approximations influenced by work at Bell Labs and generalized gradient approximations refined by researchers at University of California, Berkeley and University of Pennsylvania. More advanced functionals, such as hybrid functionals combining Hartree–Fock exchange developed by proponents linked to ETH Zurich and University of Oxford, meta-GGAs, and range-separated forms, emerged from collaborations across Duke University, Princeton University, and University of Illinois Urbana–Champaign. Development of functionals has been a focus in meetings hosted by The Royal Society of Chemistry and workshops linked to American Chemical Society divisions.
The Kohn–Sham method has been implemented in numerous software packages originating from groups at MIT, University of Cambridge, Indiana University, and University of Vienna, and distributed by consortia involving European Commission projects and national supercomputing centers. Popular plane-wave and pseudopotential codes reflect design choices influenced by researchers at Paul Scherrer Institute, National Institute for Materials Science, and Forschungszentrum Jülich. Algorithms for linear-scaling Kohn–Sham solvers were developed in programs associated with Lawrence Berkeley National Laboratory and tested on architectures from Cray Inc., Intel Corporation, and NVIDIA Corporation.
Kohn–Sham calculations are used to study structural, electronic, and magnetic properties of materials investigated at Brookhaven National Laboratory, SLAC National Accelerator Laboratory, and Argonne National Laboratory, and to predict reaction energetics in catalysis research at Caltech and ETH Zurich. In chemistry, the method supports studies by research groups at Columbia University and University of Michigan on spectroscopy, conformational analysis, and excited-state modeling when coupled to many-body perturbation theory developed in collaborations with Bell Labs and Rutgers University. Kohn–Sham results inform experimental programs at facilities such as Diamond Light Source, European Synchrotron Radiation Facility, and Stanford Synchrotron Radiation Lightsource.
Limitations of the Kohn–Sham approach, debated in forums at American Physical Society meetings and workshops at Institute for Advanced Study, include difficulties with strongly correlated systems studied at Rutgers University and challenges in excited-state dynamics addressed by time-dependent extensions developed at University of Oxford and Princeton University. Extensions such as time-dependent formulations, DFT+U methods, and hybrid schemes have been advanced by teams at University of California, Berkeley, Los Alamos National Laboratory, and Tokyo Institute of Technology. Ongoing research driven by consortia including European Research Council and national funding agencies seeks to improve functionals and scaling for exascale platforms supported by Oak Ridge National Laboratory and Argonne National Laboratory.
Category:Electronic structure methods