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.

11 pages, 9 figures