3 Density functional theory and multiscale materials modeling*

Abstract. One of the vital ingredients in the theoretical tools useful in materials modeling at all the length scales of interest is the concept of density. In the microscopic length scale, it is the electron density that has played a major role in providing a deeper understanding of chemical binding in atoms, molecules and solids. In the intermediate mesoscopic length scale, an appropriate picture of the equilibrium and dynamical pro-cesses has been obtained through the single particle number density of the constituent atoms or molecules. A wide class of problems involving nanomaterials, interfacial science and soft co ensed matter has been addressed using the density based theoretical formalism as well as atomistic simulation in this regime. In the macroscopic length scale, however, matter is usually treated as a continuous medium and a description using local mass density, energy density and other related density functions has been found to be quite appropriate. A unique single unified theoretical framework that emerges through the density concept at these diverse length scales and is applicable to both quantum d classical systems is the so called density functional theory (DFT) which essentially provides a vehicle to project the many-particle picture to a single particle one. Thus, the central equation for quantum DFT is a one-particle Schrödinger-like Kohn–Sham equation, while the same for classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninter-acting particles in the field of a density-dependent effective potential. Selected illustrative applications of quantum DFT to microscopic modeling of intermolecular interaction and that of classical DFT to a meso-scopic modeling of soft condensed matter systems are presented