Density Functional Theory and Materials Modeling at Atomistic Length Scales

Swapan K Ghosh

doi:10.3390/i3040260

Abstract

We discuss the basic concepts of density functional theory (DFT) as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy density functional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.

Highlights

Designing materials with tailored properties has always been a long cherised dream and even its partial realisation heavily depends on the research on modeling and simulation
The properties of materials are determined by the nature of the electron density reorganisation that takes place during their formation from the constituent atoms, and in principle are obtainable through a detailed quantum mechanical calculation
The properties obtained at the mesoscopic length scale can in turn serve as input for the investigation in the macroscopic length scales, where one considers matter as a continuous medium and the conventional approaches of continuum mechanics and hydrodynamics of classical physics are used as theoretical tools

Summary

Introduction

Designing materials with tailored properties has always been a long cherised dream and even its partial realisation heavily depends on the research on modeling and simulation. The properties obtained at the mesoscopic length scale can in turn serve as input for the investigation in the macroscopic length scales, where one considers matter as a continuous medium and the conventional approaches of continuum mechanics and hydrodynamics of classical physics are used as theoretical tools. The corresponding basic variable is the single-particle density of the atoms (or molecules) and the effective interaction potentials can be obtained either by a detailed DFT calculation using the electron density or by modeling the chemical binding in terms of the atomic parameters defined within the DFT framework. We discuss here the basic structure of DFT as applied to quantum and classical systems covering the microscopic and mesoscopic length scales, with the main concern being on the atomistic length scale of materials modeling

Density Functional Theory of Quantum and Classical Systems

Density Functional Theory of Soft Matter: A Mesoscopic Domain

Density Functional Theory of Dynamical Phenomena

Concluding Remarks