Closest Wannier functions to a given set of localized orbitals

A noniterative method is presented to calculate the closest Wannier functions (CWFs) to a given set of localized guiding functions, such as atomic orbitals, hybrid atomic orbitals, and molecular orbitals, based on minimization of a distance measure function. It is shown that the minimization is directly achieved by a polar decomposition of a projection matrix via singular value decomposition, making iterative calculations and complications arising from the choice of the gauge irrelevant. The disentanglement of bands is inherently addressed by introducing a smoothly varying window function and a greater number of Bloch functions, even for isolated bands. In addition to atomic and hybrid atomic orbitals, we introduce embedded molecular orbitals in molecules and bulks as the guiding functions, and demonstrate that the Wannier interpolated bands accurately reproduce the targeted conventional bands of a wide variety of systems including Si, Cu, the TTF-TCNQ molecular crystal, and a topological insulator of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. We further show the usefulness of the proposed method for calculating effective atomic charges. These numerical results not only establish our proposed method as an efficient alternative for calculating WFs, but also suggest that the concept of CWF can serve as a foundation for developing novel methods to analyze electronic structures and calculate physical properties.