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| Vignale-Kohn functional | |
|---|---|
| Name | Vignale–Kohn functional |
| Field | Condensed matter physics; Theoretical chemistry |
| Developed | 1990s |
| Developers | Giovanni Vignale; Walter Kohn |
| Applications | Time-dependent density functional theory; Optical responses; Electron dynamics |
Vignale-Kohn functional The Vignale–Kohn functional is an exchange–correlation functional formulated for time-dependent density functional theory and current-density functional theory, providing a frequency-dependent, nonlocal response kernel for interacting electrons. It extends concepts from ground-state Walter Kohn-based formulations to dynamical regimes relevant to linear and nonlinear optical response, and it connects to semiclassical and hydrodynamic descriptions used in diverse contexts from Solid-state physics to Quantum chemistry.
The Vignale–Kohn functional was introduced to address shortcomings of adiabatic approximations in Walter Kohn-inspired time-dependent frameworks, offering a nonadiabatic correction grounded in current-density variables. It aimed to reconcile insights from Giovanni Vignale's work on viscoelastic electron liquid with the formal foundations laid by Walter Kohn and collaborators, and to provide practical kernels for applications studied at institutions such as Massachusetts Institute of Technology and University of California, Santa Barbara. The development influenced research threads at laboratories like Bell Labs and groups associated with the Max Planck Society.
The functional builds on formal results from time-dependent Walter Kohn-theory and the Runge–Gross theorem developed in Australian National University-linked research, integrating constraints from conservation laws and sum rules familiar from Noether's theorem contexts and responses analyzed in Kubo formalism. Its foundation draws upon many-body techniques from researchers at CERN, methods used in Landau Fermi-liquid theory developed by figures such as Lev Landau, and hydrodynamic analogies invoked by researchers at Harvard University and Princeton University. The approach explicitly uses current-density variables inspired by current-density functional theory developed by theorists at institutions like University of California, Berkeley and Imperial College London.
The central elements are a viscoelastic stress tensor and a frequency-dependent exchange–correlation kernel that couple to the paramagnetic current, formulated to satisfy continuity equations and Galilean invariance as emphasized by work at Columbia University and University of Chicago. The functional expresses the exchange–correlation vector potential and scalar potential through convolution integrals similar to kernels used in linear-response theory by groups at University of Cambridge and California Institute of Technology. Equations employ quantities analogous to those in linear-response treatments by Ryogo Kubo and dispersion relations studied in the context of Hans Bethe and J. Robert Oppenheimer-era many-body theory at Los Alamos National Laboratory.
The Vignale–Kohn functional has been applied to optical spectra problems explored at Stanford University and University of Oxford, plasmonics investigations in research centers like Sandia National Laboratories, and electron dynamics simulations pursued at Argonne National Laboratory. It has informed studies of charge-transfer excitations in systems investigated by groups at Columbia University and Yale University, and nonlinear response analyses carried out at University of Michigan and University of Illinois Urbana–Champaign. Comparisons with experimental spectroscopy from facilities such as Diamond Light Source and European Synchrotron Radiation Facility helped validate aspects of the kernel.
Implementations appear in software packages developed by collaborative teams at institutions like Lawrence Berkeley National Laboratory and Oak Ridge National Laboratory, and in codes influenced by projects at University of Vienna and ETH Zurich. Practical use requires approximations: local or semilocal simplifications, interpolation schemes used by developers at Cornell University and Duke University, and parametrizations motivated by quantum Monte Carlo data from groups at Princeton University and University of Maryland. Numerical strategies borrow eigensolver and matrix techniques common to electronic structure codes developed at Fritz Haber Institute and Rudolf Peierls Centre for Theoretical Physics.
The functional improves on adiabatic local-density approximations in predicting damping, linewidths, and memory effects highlighted by studies at University of Cambridge and Imperial College London, but it faces limitations for strongly correlated regimes explored at Institute for Advanced Study and systems with pronounced static correlation studied at ETH Zurich. Extensions combine Vignale–Kohn ideas with hybrid functionals influenced by John Perdew-related research and many-body perturbation techniques such as GW approaches developed at Humboldt University of Berlin and University of Tokyo. Further work connects to time-dependent current-density corrections integrated into multiscale methods used at Sandia National Laboratories and Lawrence Livermore National Laboratory.
The original formulation emerged in the 1990s through collaborations involving Giovanni Vignale and Walter Kohn, following earlier foundational work by theorists associated with Bell Labs, Massachusetts Institute of Technology, and University of California, Berkeley. Key contributors and follow-up researchers include groups at Max Planck Institute for the Physics of Complex Systems, École Normale Supérieure, University of Rome La Sapienza, and University of Barcelona, with influential contributions from postdoctoral and faculty researchers trained at Princeton University, Harvard University, and University of Cambridge. The functional's trajectory intersects with developments in time-dependent methods at major centers including Argonne National Laboratory and Lawrence Berkeley National Laboratory.