Geometric phases, localized orbitals and distribution of electron charge centres

Abstract

In this thesis, we have developed formaUsms to obtain an insightful partitioning of electron charge density of materials in terms of the localized orbital description of electrons and implemented them in a plane wave density functional theory code. Based on parallel transport and resulting geometric phases of Bloch functions, we have presented simple and formally analytic schemes to construct highly localized Wannier orbitals as Fourier transforms of Bloch functions which are smooth and periodic in the reciprocal space. Subsequently, we have proposed a new analytic function, "distribution of electron charge centers" or DECC, which gives information about the sites at which the electrons are centered and their population, without explicit construction of the orbitals. DECC provides an accurate characterization of bonding in periodic as well as confined systems, irrespective of their metallic or insulating nature. We have applied our methods to explore chemical bonding and their energetics in a wide variety of systems like molecules, clusters (0-D), one dimensional chains, monolayers (2-D), bulk insulators and metals (3-D). These applications lead to microscopic understanding of macroscopic phenomena such as ferroelectricity in transition metal oxides and anomalous mechanical behavior of bulk Al relative to that of Cu. To link the localized Wannier orbital based description to the different chemical bonding mechanisms, we have introduced "Bond Orbital Overlap Population" (BOOP) and "Bond Orbital Position Population" (BOPP). We have used these ideas to decompose the anomalous Born effective (dynamical) in insulators into contributions from mechanisms such as charge transfer, local polarizability, covalency and rigid shift of orbitals. BOOP also provides a precise quantification of charge population associated with an atom.