August 4, 2001 | Ivo Souza, Nicola Marzari, and David Vanderbilt
A method is presented for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The method extends the traditional maximally-localized WFs approach by allowing for energy bands that are not isolated, such as those in metals or near the Fermi level in insulators. The approach involves defining an energy window encompassing the bands of interest and filtering out an optimally connected N-dimensional subspace to disentangle these bands. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The method is applied to copper's s and d bands and silicon's valence and low-lying conduction bands. For copper's low-lying nearly-free-electron bands, the WFs are found to be centered at tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization. The method is a postprocessing step using outputs from electronic-structure codes and is robust, requiring minimal user intervention. It successfully handles attached bands by first minimizing the "spillage" or mismatch between subspaces at neighboring k-points, followed by minimizing the spread of the WFs. The results show that the method can produce well-localized WFs for complex band structures, with applications in tight-binding models and electronic structure calculations. The method is particularly effective for copper, where the WFs are centered at interstitial sites, and for silicon, where the WFs are localized within the energy window. The results demonstrate the method's ability to handle non-isolated bands and provide accurate, localized orbitals for electronic structure analysis.A method is presented for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The method extends the traditional maximally-localized WFs approach by allowing for energy bands that are not isolated, such as those in metals or near the Fermi level in insulators. The approach involves defining an energy window encompassing the bands of interest and filtering out an optimally connected N-dimensional subspace to disentangle these bands. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The method is applied to copper's s and d bands and silicon's valence and low-lying conduction bands. For copper's low-lying nearly-free-electron bands, the WFs are found to be centered at tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization. The method is a postprocessing step using outputs from electronic-structure codes and is robust, requiring minimal user intervention. It successfully handles attached bands by first minimizing the "spillage" or mismatch between subspaces at neighboring k-points, followed by minimizing the spread of the WFs. The results show that the method can produce well-localized WFs for complex band structures, with applications in tight-binding models and electronic structure calculations. The method is particularly effective for copper, where the WFs are centered at interstitial sites, and for silicon, where the WFs are localized within the energy window. The results demonstrate the method's ability to handle non-isolated bands and provide accurate, localized orbitals for electronic structure analysis.