Population analysis with Wannier orbitals.

We formulate Wannier orbital overlap population and Wannier orbital Hamilton population to describe the contribution of different orbitals to electron distribution and their interactions. These methods, which are analogous to the well-known crystal orbital overlap population and crystal orbital Hamilton population, provide insight into the distribution of electrons at various atom centers and their contributions to bonding. We apply this formalism in the context of a plane-wave density functional theory calculation. This method provides a means to connect the non-local plane-wave basis to a localized basis by projecting the wave functions from a plane-wave density functional theory calculation to a localized Wannier orbital basis. The main advantage of this formulation is that the spilling factor is strictly zero for insulators and can systematically be made small for metals. We use our proposed method to study and obtain bonding and electron localization insights in five different materials.