  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
centres and their bonding nature. 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 localised basis by projecting
the wave functions from a plane-wave density functional theory calculation on
to 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.
