Maximally-localized generalized Wannier functions for composite energy bands

Maximally-localized generalized Wannier functions for composite energy bands

(July 10, 1997) | Nicola Marzari and David Vanderbilt
The paper discusses a method for determining the optimally localized set of generalized Wannier functions associated with Bloch bands in a crystalline solid. The authors introduce a functional that represents the total spread of the Wannier functions in real space, which is minimized to find the optimal set of functions. The method is designed to work directly from the Bloch functions represented on a mesh of k-points and operates in a space of unitary matrices describing the rotation among the Bloch bands at each k-point. This approach is suitable for use with conventional electronic-structure codes and also returns the total electric polarization and the location of each Wannier center. The paper presents sample results for Si, GaAs, molecular C$_2$H$_4$, and LiCl, and discusses the significance of the work, emphasizing its potential applications in linear-scaling methods and the theory of electronic polarization.The paper discusses a method for determining the optimally localized set of generalized Wannier functions associated with Bloch bands in a crystalline solid. The authors introduce a functional that represents the total spread of the Wannier functions in real space, which is minimized to find the optimal set of functions. The method is designed to work directly from the Bloch functions represented on a mesh of k-points and operates in a space of unitary matrices describing the rotation among the Bloch bands at each k-point. This approach is suitable for use with conventional electronic-structure codes and also returns the total electric polarization and the location of each Wannier center. The paper presents sample results for Si, GaAs, molecular C$_2$H$_4$, and LiCl, and discusses the significance of the work, emphasizing its potential applications in linear-scaling methods and the theory of electronic polarization.
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