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In physics and quantum chemistry, specifically density functional theory, the Kohn–Sham equation is the non-interacting Schrödinger equation (more clearly, Schrödinger-like equation) of a fictitious system (the "Kohn–Sham system") of non-interacting particles (typically electrons) that generate the same density as any given system of interacting particles.
Since the Hartree term and V XC depend on n(r), which depends on the φ i, which in turn depend on V s, the problem of solving the Kohn–Sham equation has to be done in a self-consistent (i.e., iterative) way. Usually one starts with an initial guess for n(r), then calculates the corresponding V s and solves the Kohn–Sham equations for the ...
The formal foundation of TDDFT is the Runge–Gross (RG) theorem (1984) [1] – the time-dependent analogue of the Hohenberg–Kohn (HK) theorem (1964). [2] The RG theorem shows that, for a given initial wavefunction, there is a unique mapping between the time-dependent external potential of a system and its time-dependent density.
Local-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT) that depend solely upon the value of the electronic density at each point in space (and not, for example, derivatives of the density or the Kohn–Sham orbitals). Many approaches can yield ...
The linearized augmented-plane-wave method (LAPW) is an implementation of Kohn-Sham density functional theory (DFT) adapted to periodic materials. [1] [2] [3] It typically goes along with the treatment of both valence and core electrons on the same footing in the context of DFT and the treatment of the full potential and charge density without any shape approximation.
The Kohn–Sham method is widely used in materials science. [5] Kohn received a Nobel Prize in Chemistry in 1998 for the Kohn–Sham equations and other work related to DFT. Sham's other research interests include condensed matter physics and optical control of electron spins in semiconductor nanostructures for quantum information processing.
It uses the full-potential (linearized) augmented plane-wave and local-orbitals [FP-(L)APW+lo] basis set to solve the Kohn–Sham equations of density functional theory. WIEN2k was originally developed by Peter Blaha and Karlheinz Schwarz from the Institute of Materials Chemistry of the Vienna University of Technology.
A banner on a lightpole at the University of California, Santa Barbara, commemorating Walter Kohn being awarded the Nobel Prize in Chemistry in 1998.. Walter Kohn (German pronunciation: [ˈvaltɐ ˈkoːn]; March 9, 1923 – April 19, 2016) [3] was an Austrian-American theoretical physicist and theoretical chemist.