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Approximations in density functional theory
Local-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT)
Local-density_approximation
Computational quantum mechanical modelling method to investigate electronic structure
becomes the difficulty within KS DFT. The simplest approximation is the local-density approximation (LDA), which is based upon exact exchange energy for
Density_functional_theory
Method to determine the electronic structure of strongly correlated materials
successfully applied to real materials, in combination with the local density approximation of density functional theory. The DMFT treatment of lattice quantum
Dynamical_mean-field_theory
Scientific theory
exchange energy in orbital-free density functional theory (OFDFT) is the Dirac exchange as a Local Density Approximation (LDA) (1930) It is related to the
Orbital-free density functional theory
Orbital-free_density_functional_theory
American physicist (1937–2021)
zinc oxide varistor. He is also developed the time-dependent local-density approximation (TDLDA) and its author of various books in quantum many-body
Gerald_Mahan
Chemical compound
theoretic approaches—including density functional theory (DFT, using functionals based on the local-density approximation) and Hartree–Fock theory—to account
Nickel(II)_oxide
Simplification for simulating fluids under natural convection
density differences except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is
Boussinesq approximation (buoyancy)
Boussinesq_approximation_(buoyancy)
Open source software
of density functional theory approximations can be used, including the local-density approximation (LDA), the generalized gradient approximation (GGA)
Qbox
Topics referred to by the same term
diisopropylamide, a chemical base Local delivery agent, in e-mail Local-density approximation, in quantum mechanics Low density amorphous ice, a solid phase
LDA
phase approximation), the TDLDA or ALDA (adiabatic local-density approximation) plus other non-local approximations, including or neglecting local-field
DP_code
Physical model of solid metals as electron gases
itself provides the basis for the local-density approximation to the exchange-correlation energy density functional. The term jellium was coined by Conyers
Jellium
Number of available physical states per energy unit
like a spectral density. Local variations, most often due to distortions of the original system, are often referred to as local densities of states (LDOSs)
Density_of_states
Band gap Bloch waves Kohn–Sham equations Kronig–Penney model Local-density approximation Duan, Feng; Guojun, Jin (2005). Introduction to Condensed Matter
Muffin-tin_approximation
Quantum mechanical operator interchanging particle states as arguments to a function
Leonard (1990). "Good semiconductor band gaps with a modified local-density approximation". Physical Review B. 41 (11): 7868–7871. Bibcode:1990PhRvB..41
Exchange_operator
with the dissertation The Structure of Finite Nuclei in the Local Density Approximation. He was a postdoc at the Niels Bohr Institute of the University
John_W._Negele
Analytical expression in statistics
Laplace's approximation or the quadratic approximation (QUAP) provides an analytical expression for a posterior probability distribution by fitting a Gaussian
Laplace's_approximation
Crystallographic defect of atoms within gaps in a lattice
of interesting self-interstitials - recently discovered using Local-density approximation-calculations is the "spiro-interestitial" in graphite, named
Interstitial_defect
Arun Rojanasakul (2007) The Chachiyo correlation functional for local-density approximation, by Teepanis Chachiyo (2016) A new reconstruction of the phonology
List of Thai inventions and discoveries
List_of_Thai_inventions_and_discoveries
American mathematical physicist
Elliott H.; Seiringer, Robert (January 1, 2020). "The local density approximation in density functional theory". Pure and Applied Analysis. 2 (1): 35–73
Elliott_H._Lieb
Concept in statistics
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method
Kernel_density_estimation
Subfield of materials science
The simplest model is the Local-density approximation (LDA), becoming more complex with the generalized-gradient approximation (GGA) and beyond. An additional
Computational materials science
Computational_materials_science
Solution method for linear differential equations
In mathematical physics, the WKB approximation or WKB method is a technique for finding approximate solutions to linear differential equations with spatially
WKB_approximation
Solid-state physics model
Evan O. Kane). According to quantum mechanics (in the single-electron approximation), the quasi-free electrons in any solid are characterized by wavefunctions
K·p_perturbation_theory
Materials with electrical properties that cannot be explained by non-interacting entities
manner) by simple one-electron theories such as the local-density approximation (LDA) of density-functional theory or Hartree–Fock theory. For instance
Strongly_correlated_material
materials, the coherent potential approximation is frequently combined with the Korringa–Kohn–Rostoker (KKR) formulation of density functional theory (DFT) to
Coherent potential approximation
Coherent_potential_approximation
contributes to the free energy density due to their presence, often characterized by a term known as the Rapini approximation: F s = − ∮ 1 2 W ( n ^ ⋅ ν ^
Distortion free energy density
Distortion_free_energy_density
Mathematical theorem in the study of analysis
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly
Stone–Weierstrass_theorem
Approximations in density functional theory
Hybrid functionals are a class of approximations to the exchange–correlation energy functional in density functional theory (DFT) that incorporate a portion
Hybrid_functionals
Swedish physicist (1930–2002)
worked in X-ray absorption fine structure (XAFS), introducing the local density approximation for the GW self energy. Hedin was editor of Solid State Communications
Lars_Hedin
Describes the range of energies of an electron within the solid
complex quantity and usually approximations are needed to solve the problem. One such approximation is the GW approximation, so called from the mathematical
Electronic_band_structure
Research professor in theoretical physics
simultaneous relaxation of atomic positions and charge densities in self-consistent local-density approximation calculations (1983). In 1990, Zunger and colleagues
Alex_Zunger
an existing approximation (here called the effective lattice model) to the many-body state (for example in the mean-field approximation where correlations
Density matrix embedding theory
Density_matrix_embedding_theory
variety of functionals including local-density approximation (LDA), many different generalized gradient approximations (GGA), Hubbard models, on-site hybrids
WIEN2k
DMFT with material-specific approaches, such as the "Local Density Approximation" (LDA) to the density functional theory, led to a new computational scheme
Dieter_Vollhardt
ISSN 0031-899X. Zhao, G. L.; Bagayoko, D.; Williams, T. D. (1999-07-15). "Local-density-approximation prediction of electronic properties of GaN, Si, C, and RuO2"
Rayleigh theorem for eigenvalues
Rayleigh_theorem_for_eigenvalues
Ratio of two densities
Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density (mass divided by volume) of a substance
Relative_density
Amount of charge flowing through a unit cross-sectional area per unit time
charge of the individual particles with density n (SI unit: coulombs). A common approximation to the current density assumes the current simply is proportional
Current_density
Markovian master equation of a quantum system weakly coupled to its environment
before the interaction-picture density operator changes significantly. In this case, the so-called Markov approximation ρ I ( t ′ ) ≈ ρ I ( t ) {\displaystyle
Redfield_equation
Measure of positive and negative charges
charges to an approximation involving only a dipole moment density p(r) requires additional considerations. The simplest approximation is to replace the
Electric_dipole_moment
Energy transfer in the form of electromagnetic radiation
and the density profile of the medium is sufficient to calculate a solution to the equation of radiative transfer. The Eddington approximation is distinct
Radiative_transfer
Bethe–Salpeter equation or by using the adiabatic local density approximation within time-dependent density functional theory. Yambo uses a plane waves basis
YAMBO_code
French physicist (1941–2000)
on the development of a density matrix expansion (local density approximation, LDA) in nuclear structure studies. The density matrix expansion "linked
Dominique_Vautherin
Fundamental theorem in probability theory and statistics
version of this theorem, that the normal distribution may be used as an approximation to the binomial distribution, is the de Moivre–Laplace theorem. Let
Central_limit_theorem
functional different parametrizations for the local density approximation, several generalized-gradient approximations, Hybrid functionals, and partial support
FLEUR
Mathematical tool in quantum physics
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed
Density_matrix
Projection of data onto lower-dimensional manifolds
includes a quality of data approximation and some penalty terms for the bending of the manifold. The popular initial approximations are generated by linear
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Quantum-mechanical framework for simulating molecules and solids
functional of the density, its explicit dependence on the density is unknown (only known in the simple Local density approximation (LDA) case), only its
Optimized effective potential method
Optimized_effective_potential_method
Theoretical condensed matter physicist
Walle (1999) Density-functional calculations for III-V nitrides using the local-density approximation and the generalized gradient approximation Physical
Catherine_Stampfl
(aeronautics) Local-density approximation Local density of states Local hidden-variable theory Local Lorentz covariance Local oxidation nanolithography Local quantum
Index_of_physics_articles_(L)
kinetics (gas and solid phases) Calculation of bound states and local-density approximations Code-breaking, using the GA to search large solution spaces of
List of genetic algorithm applications
List_of_genetic_algorithm_applications
Highly connected subgraph
Uriel; Vijayaraghavan, Aravindan (2010), "Detecting high log-densities—an O(n1/4) approximation for densest k-subgraph", STOC'10—Proceedings of the 2010 ACM
Dense_subgraph
Schrödinger equation of a fictitious system of non-interacting particles
are the only unknowns in the Kohn–Sham approach to density functional theory. An approximation that does not vary the orbitals is Harris functional
Kohn–Sham_equations
Method in physics
DFT and the treatment of the full potential and charge density without any shape approximation. This is often referred to as the all-electron full-potential
Linearized augmented-plane-wave method
Linearized_augmented-plane-wave_method
DFT methods developed by Donald Truhlar's research group
functionals are based on the meta-GGA approximation, i.e. they include terms that depend on the kinetic energy density, and are all based on complicated functional
Minnesota_functionals
Star at the centre of the Solar System
space, forming what is called the interplanetary magnetic field. In an approximation known as ideal magnetohydrodynamics, plasma only moves along magnetic
Sun
Measure of a substance's ability to resist or conduct electric current
{\displaystyle \kappa } [clarification needed]. Because the linear approximation is only an approximation, α {\displaystyle \alpha } is different for different reference
Electrical resistivity and conductivity
Electrical_resistivity_and_conductivity
derivation based on the Kohn and Rostoker variational method, the muffin-tin approximation was used. Later calculations are done with full potentials having no
Korringa–Kohn–Rostoker_method
Emission of electrons induced by an electrostatic field
sharper emitters there is no general approximation for the current density. In order to obtain the current density, one has to calculate the electrostatic
Field_electron_emission
Method of approximating the properties of a composite material
In materials science, effective medium approximations (EMA) or effective medium theory (EMT) pertain to analytical or theoretical modeling that describes
Effective medium approximations
Effective_medium_approximations
Approximation method in statistics
refined iteratively, that is, the values are obtained by successive approximation: β j k + 1 = β j k + Δ β j , {\displaystyle {\beta _{j}}^{k+1}={\beta
Least_squares
Directional planes
nearby locations appear to be parallel. Such statements are nevertheless approximations; whether they are acceptable in any particular context or application
Vertical_and_horizontal
Astronomical trend of star formation
law can be a local law, defining regions less than 1 kiloparsec, or a global law, averaging SFR surface density and gas surface density over an entire
Kennicutt–Schmidt_law
Mathematical signal manipulation by computers
implementation and can give essentially any filter response, including excellent approximations to brickwall filters. There are some commonly used frequency domain
Digital_signal_processing
Manometric unit of pressure
the difference in height between two mercury levels by the density of mercury and the local gravitational acceleration. Because the specific weight of
Millimetre_of_mercury
Probability distribution to which random variables or distributions "converge"
main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution functions of statistical estimators.
Asymptotic_distribution
Size and shape used to model the Earth for geodesy
as a close approximation. However, a more accurate figure is needed for measuring distances and areas on the scale beyond the purely local. Better approximations
Figure_of_the_Earth
Concept in condensed matter physics
independent of the electron density at nearby points. Nevertheless, the Thomas–Fermi model is likely to be a reasonably accurate approximation as long as the potential
Thomas–Fermi_screening
Technique to solve partial differential equations
admissible solutions, increasing the generalizability of the function approximation. This way, embedding this prior information into a neural network results
Physics-informed neural networks
Physics-informed_neural_networks
Dimensionless quantity in fluid dynamics
surrounding gas. The Mach number is primarily used to determine the approximation with which a flow can be treated as an incompressible flow. The medium
Mach_number
Category of computational quantum chemistry technique
for example the density fitting MP2 is df-MP2 (many authors use lower-case to prevent confusion with DFT). In the local approximation, the molecular orbitals
Ab initio quantum chemistry methods
Ab_initio_quantum_chemistry_methods
Topics referred to by the same term
Seigneur des anneaux, French translation of The Lord of the Rings Local Spin-Density Approximation London School of Dramatic Art LSDA Northern Ireland This disambiguation
LSDA
Everything in space and time
considering one without the other. The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects
Universe
Concept in physics
In physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include
Pseudopotential
Speed of sound wave through elastic medium
values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities (for air, this includes
Speed_of_sound
symmetric dimers on a lattice: An analytical approximation with exact limits at low and high densities". The Journal of Chemical Physics. 127 (13). AIP
Lattice density functional theory
Lattice_density_functional_theory
Moving average and polynomial regression method for smoothing data
assigned to Y j {\displaystyle Y_{j}} . Henderson then uses a local polynomial approximation a + b j + c j 2 + d j 3 {\displaystyle a+bj+cj^{2}+dj^{3}}
Local_regression
In statistics and machine learning, Gaussian process approximation is a computational method that accelerates inference tasks in the context of a Gaussian
Gaussian process approximations
Gaussian_process_approximations
Solid state physics calculation technique
pseudopotential and linear augmented-plane-wave methods, and allows for density functional theory calculations to be performed with greater computational
Projector augmented wave method
Projector_augmented_wave_method
of support points is mapped to q {\displaystyle q} subsets. Then the approximation model is built by removing subset i {\displaystyle i} from the support
OptiSLang
Type of artificial neural network
of stochastic data flow. Assume a stochastic kernel approximation for the joint probability density P ( x ∧ y ) = 1 N ∑ i = 1 N ρ ( ‖ x − c i ‖ ) σ ( |
Radial_basis_function_network
Relations between flows and forces, or gradients, in thermodynamic systems
diffusion. Since this is also a linear approximation and since the chemical potential is monotonically increasing with density at a fixed temperature, Fick's
Onsager_reciprocal_relations
Indian chemist (born 1942)
ISBN 978-1-4665-0531-5. Jens Peder Dahl; John Avery (11 November 2013). Local Density Approximations in Quantum Chemistry and Solid State Physics. Springer Science
Bidyendu_Mohan_Deb
Model of electrical conduction
theory of metals. This is because metals have essentially a better approximation to the free electron model, i.e. metals do not have complex band structures
Drude_model
Quantum mechanical system that interacts with a quantum-mechanical environment
weakly coupled systems that used the Born-Markov approximation. However, it does not always guarantee density matrix positivity. In 1970, H. Dieter Zeh formalized
Open_quantum_system
Interatomic potentials constructed by machine learning programs
interatomic potential is the Gaussian Approximation Potential (GAP), which combines compact descriptors of local atomic environments with Gaussian process
Machine-learned interatomic potential
Machine-learned_interatomic_potential
Algorithm for finding zeros of functions
Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version
Newton's_method
Concept in quantum mechanics
\right|^{2}.} This is sometimes referred to as the sudden approximation. The validity of the approximation for a given process can be characterized by the probability
Adiabatic_theorem
Quantities describing probability of absorption or emission of light
line occurs, including the local spectral radiance (or, in some presentations, the local spectral radiant energy density). When that state is either
Einstein_coefficients
Type of algorithm for data clustering
Fuzzy clustering by Local Approximation of MEmberships (FLAME) is a data clustering algorithm that defines clusters in the dense parts of a dataset and
FLAME_clustering
Apparent curve that separates earth from sky
applied as a fairly good approximation when atmospheric conditions are close to standard. When conditions are unusual, this approximation fails. Refraction is
Horizon
Description of particle density in statistical mechanics
{\displaystyle \rho =N/V} is the average number density of particles, then the local time-averaged density at a distance r {\displaystyle r} from O is ρ
Radial_distribution_function
Mathematical methods used in Bayesian inference and machine learning
shows the method by which the variational-Bayesian approximation to a posterior probability density in a given Bayesian network is derived: Describe the
Variational_Bayesian_methods
Concept in atmospheric science
\over f}{{\rm {d}}z \over {\rm {d}}y}} The validity of this approximation depends on the local Rossby number. It is invalid at the equator, because f is
Geostrophic_wind
Vast empty spaces between filaments with few or no galaxies
catalog as its target and then uses the Nearest Neighbor Approximation to calculate the cosmic density in the region contained in a spherical radius determined
Void_(astronomy)
Extension of scanning tunneling microscopy
the WKB approximation, is where ρ s {\displaystyle \rho _{s}} is the sample density of states, ρ t {\displaystyle \rho _{t}} is the tip density of states
Scanning tunneling spectroscopy
Scanning_tunneling_spectroscopy
Property of space that quantifies the magnetic influence at a given location
any point is parallel to the direction of nearby field lines, and the local density of field lines can be made proportional to its strength. Magnetic field
Magnetic_field
Extension of quantum field theory to curved spacetime
Standard Model, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in
Quantum field theory in curved spacetime
Quantum_field_theory_in_curved_spacetime
Distribution of distances between pairs of particles in a given volume
between the sparsely packed (HC approximation) and the densely packed (delta function) models, depending on the packing density f {\displaystyle f} . Of special
Pair_distribution_function
Optimization algorithm
differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient
Stochastic_gradient_descent
Failure of convergence in interpolation
is similar to the Gibbs phenomenon in Fourier series approximations. The Weierstrass approximation theorem states that for every continuous function f
Runge's_phenomenon
LOCAL DENSITY-APPROXIMATION
LOCAL DENSITY-APPROXIMATION
Surname or Lastname
English (Somerset)
English (Somerset) : apparently a habitational name from an unidentified place. It is probably a variant of Denslow or possibly Denley, neither of which are of identified origin.
Boy/Male
Irish Welsh
Loyal.
Girl/Female
Indian
Another Name of Happness
Boy/Male
British, English
Loyal
Girl/Female
Muslim
Loyal
Boy/Male
Italian Greek
Loyal.
Girl/Female
American, Australian
God is My Judge
Girl/Female
Indian
Loyal
Boy/Male
American, Australian, British, English, French
Faithful; True
Boy/Male
American, British, English
Loyal
Boy/Male
Indian
Royal Boy
Boy/Male
English American French
Faithful; unswerving.
Boy/Male
British, English
Loyal
Girl/Female
French
Loyal.
Boy/Male
Irish American Welsh
Loyal.
Boy/Male
English American
Loyal.
Boy/Male
Irish
Loyal.
Boy/Male
Indian
Loyal
Boy/Male
Irish
Loyal.
Boy/Male
Irish Welsh
Loyal.
LOCAL DENSITY-APPROXIMATION
LOCAL DENSITY-APPROXIMATION
Boy/Male
Hebrew Polish
God's healer.
Boy/Male
Indian, Sanskrit
Universal Father
Girl/Female
Arabic, Muslim
Harmony; Agreement
Boy/Male
Hindu
Boy/Male
Tamil
Great one
Boy/Male
Hebrew
Of God's flock.
Girl/Female
Australian, British, Christian, English
God is Gracious
Boy/Male
Arabic Muslim
Winner; to win.
Girl/Female
Hindu, Indian, Marathi
Silken
Female
Hungarian
Hungarian form of Roman Latin Victoria, VIKTÓRIA means "conqueror" or "victory."
LOCAL DENSITY-APPROXIMATION
LOCAL DENSITY-APPROXIMATION
LOCAL DENSITY-APPROXIMATION
LOCAL DENSITY-APPROXIMATION
LOCAL DENSITY-APPROXIMATION
n.
Depth of shade.
n.
The quality of being dense, close, or thick; compactness; -- opposed to rarity.
n.
The condition of being the same with something described or asserted, or of possessing a character claimed; as, to establish the identity of stolen goods.
a.
Of or pertaining to a particular place, or to a definite region or portion of space; restricted to one place or region; as, a local custom.
n.
A train which receives and deposits passengers or freight along the line of the road; a train for the accommodation of a certain district.
n.
The quality of being dense; density.
n.
The quality or state of being tenuous; thinness, applied to a broad substance; slenderness, applied to anything that is long; as, the tenuity of a leaf; the tenuity of a hair.
n.
Grossness; coarseness; thickness; density.
n.
Thickness; density; compactness.
a.
Loyal.
a.
Uttered or modulated by the voice; oral; as, vocal melody; vocal prayer.
a.
Faithful; loyal.
n.
The ratio of mass, or quantity of matter, to bulk or volume, esp. as compared with the mass and volume of a portion of some substance used as a standard.
n.
A vocal sound; specifically, a purely vocal element of speech, unmodified except by resonance; a vowel or a diphthong; a tonic element; a tonic; -- distinguished from a subvocal, and a nonvocal.
n.
Rarily; rareness; thinness, as of a fluid; as, the tenuity of the air; the tenuity of the blood.
a.
Belonging to,or concerning, a focus; as, a focal point.
n.
A local name of the burbot.
n.
A principle, practice, form of speech, or other thing of local use, or limited to a locality.
n.
The collection of attributes which make up the nature of a god; divinity; godhead; as, the deity of the Supreme Being is seen in his works.
n.
On newspaper cant, an item of news relating to the place where the paper is published.