Localized Orbital Description of Electronic Structure

We present a simple and general method for construction of localized orbitals to describe electronic structure of extended periodic metals and insulators as well as confined systems. Spatial decay of these orbitals is found to exhibit exponential behavior for insulators and power law for metals. While these orbitals provide a clear description of bonding, they can be also used to determine polarization of insulators. Within density functional theory, we illustrate applications of this method to crystalline Aluminium, Copper, Silicon, PbTiO$_3$ and molecules such as ethane and diborane.