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Local-density approximation

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 :E_{\rm xc}^{\mathrm{LDA}}[\rho] = \int \rho(\mathbf{r})\epsilon_{\rm xc}(\rho(\mathbf{r}))\ \mathrm{d}\mathbf{r}\ , where ρ is the electronic density and εxc is the exchange-correl

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Théorie de la fonctionnelle de la densité

La théorie de la fonctionnelle de la densité (DFT, sigle pour Density Functional Theory) est une méthode de calcul quantique permettant l'étude de la structure électronique, en principe de manière ex

Strongly correlated material

Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such

Implications of the DFT plus U method on polaron properties in energy materials

Amina Matt

To model polaronic behavior in strongly correlated transition-metal oxideswith ab initio methods, one typically requires a level of theory beyond that of local density or general gradient density functional theory (DFT) approximations to account for the strongly correlated d-shell interactions of transition-metal oxides. In the present work, we utilize density functional theory with additional on-site Hubbard corrections (DFT+ U) to calculate polaronic properties in two lithium ion battery cathode materials, Li x FePO4 and Li x Mn2O4, and two photocatalytic materials, TiO2 and Fe2O3. We investigate the effects of the + U on-site projection on polaronic properties. Through systematic comparison with hybrid functional calculations, it is shown that + U projection in these model materials can impact upon the band gap, polaronic hopping barrier, and polaronic eigenstate offset from the band edges in a nontrivial manner. These properties are shown to have varying degrees of coupling and dependence on the + U projection in each example material studied, which has important implications for arriving at systematic material predictions of polaronic properties in transition-metal oxides.

Amer Physical Soc2017

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Defect Formation in Ga-Catalyzed Silicon Nanowires

Sonia Conesa Boj, Anna Fontcuberta i Morral, Père Roca i Cabarrocas, Li Wei

The synthesis of silicon nanowires by Ga-assisted plasma enhanced chemical vapor deposition (PECVD) has been recently demonstrated. In the present work, we study in detail the structural characteristics of the synthesized nanowires. High resolution transmission electron microscopy (HRTEM) analysis reveals the existence of various types of structural defects, which can be classified mainly according to the orientation into axial twins, lateral twins, and transverse twins. We compare our results with previous studies of Si nanowires synthesized with other catalyst metals. Understanding, both the origin and the effects of the observed defects is important for technological applications. The presence of twinned domains changes locally the structure of the material. As a consequence, one should find a different local density of states and band gap, which should result in a variation of the carrier transport and optical properties of the nanowires.

American Chemical Society2010

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Jahn-Teller distortion and electronic structure of LiMn2O4

LiMn2O4 is one of the important cathode material for rechargeable lithium batteries. Standard ab initio studies within local density approximation (LDA) and generalized gradient approximation (GGA) are not able to reproduce the intrinsic insulating electronic structure and Jahn-Teller-type local atomic distortion of LiMn2O4. In the present work, GGA+U method is shown to be able to localize electrons to Mn 3d(z2) orbits in the majority spin channel, and open a gap of about 0.5 eV between the Mn 3d(z2) and Mn 3d(x2-y2). Results from GGA+U calculation showed that Mn ions are in the mixed valence state of Mn3+ and Mn4+. This is in good agreements with experimental observations and different to Mn3.5+ obtained from standard GGA calculations. While Jahn-Teller distortion is not observed in Mn4+O6 octahedra, it is clearly seen in Mn3+O6 octahedra, in which Mn-O bond lengths along the z-axis direction are obviously elongated. (C) 2008 Elsevier B.V. All rights reserved.

2009

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FIN-472: Computational finance

Participants of this course will master computational techniques frequently used in mathematical finance applications. Emphasis will be put on the implementation and practical aspects.

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 reactivity of organic molecules.

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 perturbation theory, configuration interaction, coupled-cluster theory, density functional theory.