What question did this study set out to answer?

To establish the tight-binding linear combination of atomic orbitals (LCAO) approximation as a practical interpolation method for computing electronic band structures across the entire Brillouin zone.

June 15, 1954Physical Review

Simplified LCAO Method for the Periodic Potential Problem

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Authors

JSJ. C. SlaterUniversity of Florida GKG. F. KosterRTX (United States)

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Implication

Theoretical analysis demonstrates a simplified tight-binding interpolation method for crystal lattices, enabling efficient electronic band structure calculations throughout the Brillouin zone.

Key Points

To establish the tight-binding linear combination of atomic orbitals (LCAO) approximation as a practical interpolation method for computing electronic band structures across the entire Brillouin zone.
Parameterized LCAO Hamiltonian matrix elements by treating interatomic integrals as disposable fitting constants matched to accurate cellular or orthogonalized plane-wave calculations at high-symmetry points.
Derived analytical energy matrix components for simple cubic, face-centered cubic, body-centered cubic, and diamond crystal lattices.
Applied the interpolation framework to model electronic and magnetic band behaviors in face-centered cubic nickel and copper, body-centered cubic chromium, diamond, and indium antimonide.
Reproduced existing electronic band configurations for face-centered cubic metals (Ni, Cu) and diamond while substantially reducing calculation complexity compared to plane-wave methods.
Resolved energy band splitting in body-centered cubic chromium induced by an alternating antiferromagnetic potential alongside the unperturbed state distribution.
Demonstrated that the semi-empirical tight-binding formulation accurately accounts for the energy band structures and electronic properties of compound semiconductors such as InSb.

Cite This Study

Slater et al. (1954) studied this question.

synapsesocial.com/papers/69d9c7be2a25b240b7a3db2c https://doi.org/10.1103/physrev.94.1498

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Implication

Theoretical analysis demonstrates a simplified tight-binding interpolation method for crystal lattices, enabling efficient electronic band structure calculations throughout the Brillouin zone.

Simplified LCAO Method for the Periodic Potential Problem

Discussion

Member takes

Implication

Key Points

Cite This Study

Simplified LCAO Method for the Periodic Potential Problem

Discussion

Member takes

Implication

Key Points

Cite This Study

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