Simplified LCAO Method for the Periodic Potential Problem Export

@article{citeulike:875548, abstract = {The LCAO; or Bloch; or tight binding; approximation for solids is discussed as an interpolation method; to be used in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods. It is proposed that the various integrals be obtained as disposable constants; so that the tight binding method will agree with accurate calculations at symmetry points in the Brillouin zone for which these calculations have been made; and that the LCAO method then be used for making calculations throughout the Brillouin zone. A general discussion of the method is given; including tables of matrix components of energy for simple cubic; face-centered and body-centered cubic; and diamond structures. Applications are given to the results of Fletcher and Wohlfarth on Ni; and Howarth on Cu; as illustrations of the fcc case. In discussing the bcc case; the splitting of the energy bands in chromium by an antiferromagnetic alternating potential is worked out; as well as a distribution of energy states for the case of no antiferromagnetism. For diamond; comparisons are made with the calculations of Herman; using the orthogonalized plane-wave method. The case of such crystals as InSb is discussed; and it is shown that their properties fit in with the energy band picture.}, author = {Slater, J. C. and Koster, G. F.}, citeulike-article-id = {875548}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRev.94.1498}, citeulike-linkout-1 = {http://link.aps.org/abstract/PR/v94/i6/p1498_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/PR/v94/i6/p1498_1}, day = {15}, doi = {10.1103/PhysRev.94.1498}, journal = {Physical Review}, keywords = {graphene, tightbinding}, month = {June}, number = {6}, pages = {1498+}, posted-at = {2008-08-21 14:33:33}, priority = {0}, publisher = {American Physical Society}, title = {Simplified LCAO Method for the Periodic Potential Problem}, url = {http://dx.doi.org/10.1103/PhysRev.94.1498}, volume = {94}, year = {1954} }

TY - JOUR ID - citeulike:875548 L3 - citeulike-article-id:875548 N2 - The LCAO; or Bloch; or tight binding; approximation for solids is discussed as an interpolation method; to be used in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods. It is proposed that the various integrals be obtained as disposable constants; so that the tight binding method will agree with accurate calculations at symmetry points in the Brillouin zone for which these calculations have been made; and that the LCAO method then be used for making calculations throughout the Brillouin zone. A general discussion of the method is given; including tables of matrix components of energy for simple cubic; face-centered and body-centered cubic; and diamond structures. Applications are given to the results of Fletcher and Wohlfarth on Ni; and Howarth on Cu; as illustrations of the fcc case. In discussing the bcc case; the splitting of the energy bands in chromium by an antiferromagnetic alternating potential is worked out; as well as a distribution of energy states for the case of no antiferromagnetism. For diamond; comparisons are made with the calculations of Herman; using the orthogonalized plane-wave method. The case of such crystals as InSb is discussed; and it is shown that their properties fit in with the energy band picture. IS - 6 JF - Physical Review TI - Simplified LCAO Method for the Periodic Potential Problem PB - American Physical Society VL - 94 SP - 1498 KW - graphene KW - tightbinding AU - Slater, JC AU - Koster, GF PY - 1954/06/15/ UR - http://dx.doi.org/10.1103/PhysRev.94.1498 ER -