Computational Materials Science by Kaoru Ohno Keivan Esfarjani & Yoshiyuki Kawazoe

Author:Kaoru Ohno, Keivan Esfarjani & Yoshiyuki Kawazoe
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

3.2.2 Calculation of the Matrix Elements

In the usual TB parametrizations, the distance dependence of the overlap and hopping matrix elements (Slater–Koster parameters) between orbitals at different sites is given as previously shown in (3.3). The index of each of these functions contains the two orbital types involved and their hybridization. For example, is the hopping matrix element between an s orbital on the first atom and a p orbital on the second atom forming a bond. The Hamiltonian matrix, however, is composed of matrix elements such as representing the hopping element between the s orbital of atom i and the orbital of atom j. This must then be expressed in terms of the standard Slater–Koster (SK) parameters, which are hybridizations either along a bond ( type) or perpendicular to the bond ( type). For example, if one considers atom j at the origin, and an atom i at making an angle of with the x direction, the matrix element can be expressed as

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