Maximally localized Wannier functions constructed from projector-augmented waves or ultrasoft pseudopotentials

We report a theoretical scheme that enables the calculation of maximally localized Wannier functions within the formalism of projector-augmented waves (PAW), which also includes the ultrasoft pseudopotential (USPP) approach. We give a description of the basic underlying formalism and explicitly write out all the required matrix elements using the common ingredients of the PAW/USPP theory. We report an implementation of the method in a form suitable for accepting the input electronic structure from USPP plane-wave DFT simulations. We apply the method to the calculation of Wannier functions, dipole moments and spontaneous polarizations for a range of test cases. A comparison with norm-conserving pseudopotentials is reported as a benchmark.