Tight-Binding Theory in the Computational Materials Science

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The tight-binding (TB) theory and TB molecular dynamics (TBMD) are now popular and valuable computational schemes available to materials scientists. The simplicity and transparency of the TB schemes enables us to get clear physical insights into the complicated phenomena. In the present review article, the calculational methods of the TB theory and TBMD are outlined and their applications to the important problems in the material sciences will be presented. Recently, linear scaling O(N) (order of N) TB methods have been developed for large scale computer simulations; we analyze the main ideas involved in these O(N) TB methods and their different implementations. The divide-and-conquer techniques for linear-scaling quantum mechanical calculations are reviewed, in conjunction with the catalytic activity of biological molecules. In addition, I also address the genetic and fuzzy algorithms coupled to the TB theory which allows us to find complicated final structures quite efficiently from simple initial structures.

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