  Since the seminal work of Marzari and Vanderbilt, maximally localized Wannier
functions have become widely used as a real-space representation of the
electronic structure of periodic materials. In this paper we introduce
selectively localized Wannier functions which extend the method of Marzari and
Vanderbilt in two important ways. First, our method allows us to focus on
localizing a subset of orbitals of interest. Second, our method allows us to
fix centers of these orbitals, and ensure the preservation of the point-group
symmetry. These characteristics are important when Wannier functions are used
in methodologies that go beyond density functional theory by treating a local
subspace of the Hamiltonian more effectively. Application of our method to
GaAs, SrMnO$_3$, and Co demonstrates that selectively localized Wannier
functions can offer improvements over the maximally localized Wannier function
technique.
