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The Vienna Ab initio Simulation Package, better known as VASP, is a package written primarily in Fortran for performing ab initio quantum mechanical calculations using either Vanderbilt pseudopotentials, or the projector augmented wave method, and a plane wave basis set. [2]
The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave: a travelling plane wave whose profile () is a sinusoidal function. That is, (,) = (() +) The parameter , which may be a scalar or a vector, is called the amplitude of the wave; the scalar coefficient is its "spatial frequency"; and the scalar is its "phase shift".
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 DFT and density functional perturbation theory, using plane wave basis sets and pseudopotentials .
A plane wave is an important mathematical idealization where the disturbance is identical along any (infinite) plane normal to a specific direction of travel. Mathematically, the simplest wave is a sinusoidal plane wave in which at any point the field experiences simple harmonic motion at one frequency.
Top: plane wave. Bottom: wave packet. When I conceived the first basic ideas of wave mechanics in 1923–1924, I was guided by the aim to perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.
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.
The atomic orbitals used are typically those of hydrogen-like atoms since these are known analytically i.e. Slater-type orbitals but other choices are possible such as the Gaussian functions from standard basis sets or the pseudo-atomic orbitals from plane-wave pseudopotentials. Example of a molecular orbital diagram.
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.