TY - JOUR

T1 - An optimized LCAO method for crystals

AU - Halpern, V.

PY - 1970

Y1 - 1970

N2 - A modification is proposed to the linear combination of atomic orbitals (LCAO) method for calculating electronic wave functions in crystals. Instead of using fixed atomic orbitals, atomic orbitals characterized by an internal parameter, such as scaling factor are used. This is optimized by applying a variational principle for Wannier functions, using as a trial function a localized orbital constructed from the atomic orbitals by a symmetric orthogonalization procedure. In this way, both the accuracy and range of applicability of the LCAO method for crystals are greatly increased. As shown for the example of the one-dimensional Mathieu problem, the optimum atomic orbital tends to expand as the interatomic distance decreases, and the optimized LCAO orbital tends to expand as the interatomic distance decreases, and the optimized LCAO method describes accurately the change in the energy bands and wave functions as the lattice parameter decreases and the electron states change from tight-binding to free-electron like. The application of the method to crystals containing defects and to amorphous materials is discussed.

AB - A modification is proposed to the linear combination of atomic orbitals (LCAO) method for calculating electronic wave functions in crystals. Instead of using fixed atomic orbitals, atomic orbitals characterized by an internal parameter, such as scaling factor are used. This is optimized by applying a variational principle for Wannier functions, using as a trial function a localized orbital constructed from the atomic orbitals by a symmetric orthogonalization procedure. In this way, both the accuracy and range of applicability of the LCAO method for crystals are greatly increased. As shown for the example of the one-dimensional Mathieu problem, the optimum atomic orbital tends to expand as the interatomic distance decreases, and the optimized LCAO orbital tends to expand as the interatomic distance decreases, and the optimized LCAO method describes accurately the change in the energy bands and wave functions as the lattice parameter decreases and the electron states change from tight-binding to free-electron like. The application of the method to crystals containing defects and to amorphous materials is discussed.

UR - http://www.scopus.com/inward/record.url?scp=36149067527&partnerID=8YFLogxK

U2 - 10.1088/0022-3719/3/9/009

DO - 10.1088/0022-3719/3/9/009

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AN - SCOPUS:36149067527

SN - 0022-3719

VL - 3

SP - 1900

EP - 1911

JO - Journal of Physics C: Solid State Physics

JF - Journal of Physics C: Solid State Physics

IS - 9

M1 - 009

ER -