# Maximally-localized Wannier functions

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Wannier functions (WFs) are obtained from a unitary transformation of the extended Bloch orbitals of a periodic system. This transformation has a large degree of arbitrariness; a unique set of maximally-localized WFs (MLWFs) can be obtained by minimizing the sum of the second central moments of the orbitals in the set.

MLWFs can be used in a variety of contexts, e.g., to obtain a chemically intuitive representation of the electronic structure, as an optimal localized basis set for performing fine Brillouin zone interpolation, or for the study of the dielectric properties of materials within the modern theory of polarization.

A detailed discussion of the theory of MLWFs and their application is given here^{[1]}.

## References

- ↑ N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt,
*Maximally localized Wannier functions: Theory and applications*, Rev. Mod. Phys.**84**, 1419 (2012). DOI: 10.1103/RevModPhys.84.1419