Towards A New Exchange-Correlation Density Functional for More Accurate Band Gap Predictions

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Abstract

Density-Functional Theory (DFT) offers a simplification to electronic structure prob- lems by using the electron density instead of the wave-function.

Unlike the wave- function which is a function of 3N variables (excluding spin) for an N -electron system, the density depends only on three variables, irrespective of the number of electrons in the system.

While DFT, in principle, gives an accurate description of ground-state properties, practical applications of DFT are based on approximations to the so-called exchange-correlation (xc) potential.

The exchange-correlation po- tential describes the effects of the Pauli exclusion principle and the electron-electron Coulomb repulsion beyond a purely electrostatic interaction of the electrons.

A common description of exchange-correlation functional is the so-called local den- sity approximation (LDA) which locally substitutes the exchange-correlation energy density of an inhomogeneous system by that of an electron gas evaluated at that local density.

Introduction

Density-Functional Theory (DFT) is one of the most popular and successful Quan- tum Mechanics (QM) approach for large systems.

It is a widely used methods for “ab initio” calculations of the structure of atoms, molecules, crystals, surfaces and their interactions.

It is nowadays routinely applied for calculating e.g., the binding energy of molecules in chemistry and the band structure of solids in physics.

First application relevant for fields traditionally considered more distant from quantum mechanics, such as biology and mineralogy are beginning to appear.

Superconduc- tivity, atoms in the focus of strong laser pulses, relativistic effects in heavy elements and in atomic nuclei, classical liquids, and magnetic properties of alloys have been studied with DFT.

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