Abstract
The method of "symmetric orthonormalization" is shown to have a least-squares property: it constructs those unique orthonormal functions which minimize the sum of squared distances (in Hilbert space) between each initial function and a corresponding function of the orthonormal set. The localization of Wannier functions is a consequence of this property, since they can be obtained from localized atomic orbitals by symmetric orthonormalization. The theorem further implies an optimal resemblance of Wannier functions to atomic orbitals.
Keywords
Orthonormal basisOrthonormalityWannier functionOrthogonalizationHilbert spaceAtomic orbitalFunction (biology)PhysicsMathematicsOrthogonalitySpace (punctuation)Quantum mechanicsPure mathematicsMathematical analysisComputer scienceGeometry
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Publication Info
- Year
- 1957
- Type
- article
- Volume
- 105
- Issue
- 1
- Pages
- 102-103
- Citations
- 256
- Access
- Closed
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Cite This
B. C. Carlson,
Joseph M. Keller
(1957).
Orthogonalization Procedures and the Localization of Wannier Functions.
Physical Review
, 105
(1)
, 102-103.
https://doi.org/10.1103/physrev.105.102
Identifiers
- DOI
- 10.1103/physrev.105.102