Automatic Generation of Matrix Element Derivatives for Tight Binding Models

Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can b...

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Bibliographic Details
Published inarXiv.org
Main Authors Elena, Alin M, Meister, Matthias
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.04.2005
Subjects
Binding
Computer simulation
Dependence
Derivatives
Quantum mechanics
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Summary:Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a computer program they obviate the need to type all the required derivatives of all occuring matrix elements by hand.
ISSN:2331-8422
DOI:10.48550/arxiv.0504719