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GW Approximation
The ''GW'' approximation (GWA) is an approximation made in order to calculate the self-energy of a many-body system of electrons. The approximation is that the expansion of the self-energy ''Σ'' in terms of the single particle Green's function ''G'' and the screened Coulomb interaction ''W'' (in units of \hbar=1) : \Sigma = iGW - GWGWG + \cdots can be truncated after the first term: : \Sigma \approx iG W In other words, the self-energy is expanded in a formal Taylor series in powers of the screened interaction ''W'' and the lowest order term is kept in the expansion in GWA. Theory The above formulae are schematic in nature and show the overall idea of the approximation. More precisely, if we label an electron coordinate with its position, spin, and time and bundle all three into a composite index (the numbers 1, 2, etc.), we have : \Sigma(1,2) = iG(1,2)W(1^+,2) - \int d3 \int d4 \, G(1,3)G(3,4)G(4,2)W(1,4)W(3,2) + ... where the "+" superscript means the time index is shif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-energy
In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and its environment. In electrostatics, the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero. In a condensed matter context relevant to electrons moving in a material, the self-energy represents the potential felt by the electron due to the surrounding medium's interactions with it. Since electrons repel each other the moving electron polarizes, or causes to displace the electrons in its vicinity and then changes the potential of the moving electron fields. These are examples of self-energy. Characteristics Mathematically, this energy is equal to the so-called on mass shell value of the proper self- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CP2K
CP2K is a freely available (GPL) quantum chemistry and solid state physics program package, written in Fortran 2008, to perform atomistic simulations of solid state, liquid, molecular, periodic, material, crystal, and biological systems. It provides a general framework for different methods: density functional theory (DFT) using a mixed Gaussian and plane waves approach (GPW) via LDA, GGA, MP2, or RPA levels of theory, classical pair and many-body potentials, semi-empirical ( AM1, PM3, MNDO, MNDOd, PM6) and tight-binding Hamiltonians, as well as Quantum Mechanics/Molecular Mechanics (QM/MM) hybrid schemes relying on the Gaussian Expansion of the Electrostatic Potential (GEEP). The Gaussian and Augmented Plane Waves method (GAPW) as an extension of the GPW method allows for all-electron calculations. CP2K can do simulations of molecular dynamics, metadynamics, Monte Carlo, Ehrenfest dynamics, vibrational analysis, core level spectroscopy, energy minimization, and transition sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vienna Ab-initio Simulation Package
The Vienna Ab initio Simulation Package, better known as VASP, is a package for performing ab initio quantum mechanical calculations using either Vanderbilt pseudopotentials, or the projector augmented wave method, and a plane wave basis set. The basic methodology is density functional theory (DFT), but the code also allows use of post-DFT corrections such as hybrid functionals mixing DFT and Hartree–Fock exchange (e.g. HSE, PBE0 or B3LYP), many-body perturbation theory (the GW method) and dynamical electronic correlations within the random phase approximation (RPA) and MP2. Originally, VASP was based on code written by Mike Payne (then at MIT), which was also the basis of CASTEP. It was then brought to the University of Vienna, Austria, in July 1989 by Jürgen Hafner. The main program was written by Jürgen Furthmüller, who joined the group at the Institut für Materialphysik in January 1993, and Georg Kresse. VASP is currently being developed by Georg Kresse; recent addit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TURBOMOLE
TURBOMOLE is an ab initio computational chemistry program that implements various quantum chemistry methods. It was initially developed by the group of Prof. Reinhart Ahlrichs at the University of Karlsruhe. In 2007, TURBOMOLE GmbH, founded by R. Ahlrichs, F. Furche, C. Hättig, W. Klopper, M. Sierka, and F. Weigend, took over the responsibility for the coordination of the scientific development of TURBOMOLE program, for which the company holds all copy and intellectual property rights. In 2018 David P. Tew joined the TURBOMOLE GmbH. Since 1987, this program is one of the useful tools as it involves in many fields of research including heterogeneous and homogeneous catalysis, organic and inorganic chemistry, spectroscopy as well as biochemistry. This can be illustrated by citation records of Ahlrich's 1989 publication which is more than 6700 times as of 18 July 2020. In the year 2014, the second Turbomole article has been published. The number of citations from both papers indica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum ESPRESSO
Quantum ESPRESSO 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. It is based on density-functional theory, plane wave basis sets, and pseudopotentials (both norm-conserving and ultrasoft). ESPRESSO is an acronym for opEn-Source Package for Research in Electronic Structure, Simulation, and Optimization. The core plane wave DFT functions of QE are provided by the PWscf component (PWscf previously existed as an independent project). PWscf (Plane-Wave Self-Consistent Field) is a set of programs for electronic structure calculations within density functional theory and density functional perturbation theory, using plane wave basis sets and pseudopotentials. The software is released under the GNU General Public License. The latest version QE-7.1 was released on 16 June 2022. Quantum ESPRESSO Project Quantum ESPRESSO is an open initiative of the CNR-IOM DEMOCRITOS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PySCF
Python-based Simulations of Chemistry Framework (PySCF) is an ab initio computational chemistry program natively implemented in Python program language. The package aims to provide a simple, light-weight and efficient platform for quantum chemistry code developing and calculation. It provides various functions to do the Hartree–Fock, MP2, density functional theory, MCSCF, coupled cluster Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in ... theory at non-relativistic level and 4-component relativistic Hartree–Fock theory. Although most functions are written in Python, the computation critical modules are intensively optimized in C. As a result, the package works as efficient as other C/ Fortran-based quantum chemistry program. PySCF is developed by Qiming Sun. PySCF2.0 is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WIEN2k
The WIEN2k package is a computer program written in Fortran which performs Computational chemical methods in solid state physics, quantum mechanical calculations on periodic solids. It uses the full-potential Linearized augmented-plane-wave method, (linearized) augmented plane-wave and local-orbitals [FP-(L)APW+lo] basis set (chemistry), 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. The first public release of the code was done in 1990. Then, the next releases were WIEN93, WIEN97, and WIEN2k. The latest version WIEN2k_23.2 was released in February 2023. It has been licensed by more than 3400 user groups and has about 16000 citations on Google scholar (Blaha WIEN2k). WIEN2k uses density functional theory to calculate the electronic structure of a solid. It is based on the most accurate scheme for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FHI-aims
FHI-aims (Fritz Haber Institute ab initio materials simulations) is a software package for computational molecular and materials science written in Fortran. It uses density functional theory and many-body perturbation theory to simulate chemical and physical properties of atoms, molecules, nanostructures, solids, and surfaces. Originally developed at the Fritz Haber Institute in Berlin, the ongoing development of the FHI-aims source code is now driven by a worldwide community of collaborating research institutions. Overview The FHI-aims software package is an all-electron, full-potential electronic structure code utilizing numeric atom-centered basis functions for its electronic structure calculations. The localized basis set enables the accurate treatment of all electrons on the same footing in periodic and non-periodic systems without relying on the approximation for the core states, such as pseudopotentials. Importantly, the basis sets enable high numerical accuracy on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ABINIT
ABINIT is an open-source suite of programs for materials science, distributed under the GNU General Public License. ABINIT implements density functional theory, using a plane wave basis set and pseudopotentials, to compute the electronic density and derived properties of materials ranging from molecules to surfaces to solids. It is developed collaboratively by researchers throughout the world. A web-based easy-to-use graphical version, which includes access to a limited set of ABINIT's full functionality, is available for free use through the nanohub. The latest version 9.6.1 was released on October 04, 2021. Overview ABINIT implements density functional theory by solving the Kohn–Sham equations describing the electrons in a material, expanded in a plane wave basis set and using a self-consistent conjugate gradient method to determine the energy minimum. Computational efficiency is achieved through the use of fast Fourier transforms, and pseudopotentials to describe core electr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many Body Problem
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of many interacting particles. ''Microscopic'' here implies that quantum mechanics has to be used to provide an accurate description of the system. ''Many'' can be anywhere from three to infinity (in the case of a practically infinite, Homogeneity (physics), homogeneous or periodic system, such as a crystal), although three- and four-body systems can be treated by specific means (respectively the Faddeev equations, Faddeev and Faddeev–Yakubovsky equations) and are thus sometimes separately classified as few-body systems. In general terms, while the underlying physical laws that govern the motion of each individual particle may (or may not) be simple, the study of the collection of particles can be extremely complex. In such a quantum system, the repeated interactions between particles create quantum correlations, or entanglement. As a consequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas–Fermi Screening
Thomas–Fermi screening is a theoretical approach to calculate the effects of electric field screening by electrons in a solid.N. W. Ashcroft and N. D. Mermin, ''Solid State Physics'' (Thomson Learning, Toronto, 1976) It is a special case of the more general Lindhard theory; in particular, Thomas–Fermi screening is the limit of the Lindhard formula when the wavevector (the reciprocal of the length-scale of interest) is much smaller than the Fermi wavevector, i.e. the long-distance limit. It is named after Llewellyn Thomas and Enrico Fermi. The Thomas–Fermi wavevector (in Gaussian-cgs units) is k_0^2 = 4\pi e^2 \frac, where ''μ'' is the chemical potential ( Fermi level), ''n'' is the electron concentration and ''e'' is the elementary charge. Under many circumstances, including semiconductors that are not too heavily doped, , where ''k''B is Boltzmann constant and ''T'' is temperature. In this case, k_0^2 = \frac, i.e. is given by the familiar formula for Debye length. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dielectric Function
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor. In the simplest case, the electric displacement field D resulting from an applied electric field E is :\mathbf = \varepsilon \mathbf. More generally, the permittivity is a thermodynamic function of state. It can depend on the frequency, magnitude, and direction of the applied field. The SI unit for permittivity is farad per meter (F/m). The permittivity is often represented by the relative permittivity ''ε''r which is the ratio of the absolute permittivity ''ε'' and the vacuum permittivity ''ε''0 :\kappa = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
