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Projector Augmented Wave Method
The projector augmented wave method (PAW) is a technique used in ab initio electronic structure calculations. It is a generalization of the pseudopotential and linear augmented-plane-wave methods, and allows for density functional theory calculations to be performed with greater computational efficiency. Valence wavefunctions tend to have rapid oscillations near ion cores due to the requirement that they be orthogonal to core states; this situation is problematic because it requires many Fourier components (or in the case of grid-based methods, a very fine mesh) to describe the wavefunctions accurately. The PAW approach addresses this issue by transforming these rapidly oscillating wavefunctions into smooth wavefunctions which are more computationally convenient, and provides a way to calculate all-electron properties from these smooth wavefunctions. This approach is somewhat reminiscent of a change from the Schrödinger picture to the Heisenberg picture. Transforming the wavef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ab Initio Quantum Chemistry Methods
''Ab initio'' quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. The background is described by Parr. ''Ab initio'' means "from first principles" or "from the beginning", implying that the only inputs into an ''ab initio'' calculation are physical constants. ''Ab initio'' quantum chemistry methods attempt to solve the electronic Schrödinger equation given the positions of the nuclei and the number of electrons in order to yield useful information such as electron densities, energies and other properties of the system. The ability to run these calculations has enabled theoretical chemists to solve a range of problems and their importance is highlighted by the awarding of the Nobel prize to John Pople and Walter Kohn. Accuracy and scaling ''Ab initio'' electronic structure method ... [...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] |
Computational Chemistry
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new drugs and materials. Examples of such properties are structure (i.e., the expected positions of the constituent atoms), absolute and relative (interaction) energies, electronic charge density distributions, dipoles and higher multipole moments, vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Structure Methods
Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor * ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic device *Electronic commerce or e-commerce, the trading in products or services using computer networks, such as the Internet *Electronic publishing or e-publishing, the digital publication of books and magazines using computer networks, such as the Internet *Electronic engineering, an electrical engineering discipline Entertainment *Electronic (band), an English alternative dance band ** ''Electronic'' (album), the self-titled debut album by British band Electronic *Electronic music, a music genre *Electronic musical instrument *Electronic game, a game that employs electronics See also *Electronica, an electronic music genre *Consumer electronics Consumer electronics or home electronics are electronic (analog or digital) equipment intended for everyday ... [...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] |
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] |
Pwpaw
PWPAW A Projector Augmented Wave (PAW) code for electronic structure calculation. It is a free software package, distributed under the copyleft GNU General Public License. It is a plane wave implementation of the projector augmented wave (PAW) method developed by Peter E. Blöchl for electronic structure calculations within the framework of density functional theory. In addition to the self-consistent calculation of the electronic structure of a periodic solid, the program has a number of other capabilities, including structural geometry optimization and molecular dynamics simulations within the Born–Oppenheimer approximation. www.wfu.edu, undated (accessed 21 January 2007) See also * Atompaw Software package for ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ONETEP
ONETEP (Order-N Electronic Total Energy Package) is a linear-scaling density functional theory software package able to run on parallel computers. It uses a basis of non-orthogonal generalized Wannier functions (NGWFs) expressed in terms of periodic cardinal sine (psinc) functions, which are in turn equivalent to a basis of plane-waves. ONETEP therefore combines the advantages of the plane-wave approach (controllable accuracy and variational convergence of the total energy with respect to the size of the basis) with computational effort that scales linearly with the size of the system. The ONETEP approach involves simultaneous optimization of the density kernel (a generalization of occupation numbers to non-orthogonal basis, which represents the density matrix in the basis of NGWFs) and the NGWFs themselves. The optimized NGWFs then provide a minimal localized basis set, which can be considerably smaller in size, but of equal or higher accuracy, than the unoptimized basis sets used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CASTEP
CASTEP is a shared-source academic and commercial software package which uses density functional theory with a plane wave basis set to calculate the electronic properties of crystalline solids, surfaces, molecules, liquids and amorphous materials from first principles. CASTEP permits geometry optimisation and finite temperature molecular dynamics with implicit symmetry and geometry constraints, as well as calculation of a wide variety of derived properties of the electronic configuration. Although CASTEP was originally a serial, Fortran 77-based program, it was completely redesigned and rewritten from 1999 to 2001 using Fortran 95 and MPI for use on parallel computers by researchers at the Universities of York, Durham, St. Andrews, Cambridge and Rutherford Labs. History CASTEP was created in the late 1980s and early 1990s in the TCM Group of the Cavendish Laboratory in Cambridge. It was then an academic code written in Fortran77, and the name was originally derived from CAmbr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudopotential
In physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include atomic physics and neutron scattering. The pseudopotential approximation was first introduced by Hans Hellmann in 1934. Atomic physics The pseudopotential is an attempt to replace the complicated effects of the motion of the core (i.e. non- valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of the Coulombic potential term for core electrons normally found in the Schrödinger equation. The pseudopotential is an effective potential constructed to replace the atomic all-electron potential (full-potential) such that core states are eliminated ''and'' the valence electrons are described by pseudo-wavefunctions with significantly fewer nodes. This allows the pseudo-wavefunctions to be described with far ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Functions
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when the Helmholtz equation is solved in spherical coordinates. Applications of Bessel functions The Bessel function is a generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
