**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Local-density approximation

Summary

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 local approximations to the XC energy. However, overwhelmingly successful local approximations are those that have been derived from the homogeneous electron gas (HEG) model. In this regard, LDA is generally synonymous with functionals based on the HEG approximation, which are then applied to realistic systems (molecules and solids).
In general, for a spin-unpolarized system, a local-density approximation for the exchange-correlation energy is written as
where ρ is the electronic density and εxc is the exchange-correlation energy per particle of a homogeneous electron gas of charge density ρ. The exchange-correlation energy is decomposed into exchange and correlation terms linearly,
so that separate expressions for Ex and Ec are sought. The exchange term takes on a simple analytic form for the HEG. Only limiting expressions for the correlation density are known exactly, leading to numerous different approximations for εc.
Local-density approximations are important in the construction of more sophisticated approximations to the exchange-correlation energy, such as generalized gradient approximations (GGA) or hybrid functionals, as a desirable property of any approximate exchange-correlation functional is that it reproduce the exact results of the HEG for non-varying densities. As such, LDA's are often an explicit component of such functionals.
Local density approximations, as with GGAs are employed extensively by solid state physicists in ab-initio DFT studies to interpret electronic and magnetic interactions in semiconductor materials including semiconducting oxides and spintronics. The importance of these computational studies stems from the system complexities which bring about high sensitivity to synthesis parameters necessitating first-principles based analysis.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (5)

Related lectures (27)

Related publications (372)

Related people (58)

Related concepts (1)

Related units (13)

MSE-468: Atomistic and quantum simulations of materials

Theory and application of quantum simulations to model, understand, and predict the properties of real materials.

CH-353: Introduction to electronic structure methods

Repetition of the basic concepts of quantum mechanics and main numerical algorithms used for practical implementions. Basic principles of electronic structure methods:Hartree-Fock, many body perturbat

CH-431: Physical and computational organic chemistry

This course introduces modern computational electronic structure methods and their broad applications to organic chemistry. It also discusses physical organic concepts to illustrate the stability and

Density functional theory

Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.

, , , , , , , , ,

DFT: Kohn-Sham Formulation

Covers the precursors of Kohn-Sham Density Functional Theory (DFT) and the Kohn-Sham formulation, explaining types of Exc[p] approximations and the performance of LDA.

Density Functional Theory: Basics and Improvements

Covers the basics of Density Functional Theory, challenges in DFT, and improvements in functional approximations and corrections for accurate calculations.

Density Functional Theory

Covers the Density Functional Theory, including the Hartree-Fock method and the Kohn-Sham scheme.

Nicola Marzari, Iurii Timrov, Eric Macke

We present an orbital-resolved extension of the Hubbard U correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particula ...

Real-world samples of graphene often exhibit various types of out-of-plane disorder-ripples, wrinkles and folds-introduced at the stage of growth and transfer processes. These complex out-of-plane defects resulting from the interplay between self-adhesion ...

Alfredo Pasquarello, Stefano Falletta

Through the use of the piecewise-linearity condition of the total energy, we correct the self-interaction for the study of polarons by constructing nonempirical functionals at the semilocal level of theory. We consider two functionals, the gamma DFT and mu ...