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The Kohn–Sham equation is defined by a local effective (fictitious) external potential in which the non-interacting particles move, typically denoted as v s (r) or v eff (r), called the Kohn–Sham potential. If the particles in the Kohn–Sham system are non-interacting fermions (non-fermion Density Functional Theory has been researched [3 ...
Octopus is a software package for performing Kohn–Sham density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations. [1]Octopus employs pseudopotentials and real-space numerical grids to propagate the Kohn–Sham orbitals in real time under the influence of time-varying electromagnetic fields.
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 WIEN2k package is a computer program written in Fortran that performs quantum mechanical calculations on periodic solids.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.
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.
Quantum ESPRESSO (Quantum Open-Source Package for Research in Electronic Structure, Simulation, and Optimization; QE) [2] [3] is a suite for first-principles electronic-structure calculations and materials modeling, distributed for free and as free software under the GNU General Public License.
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.