Block bond-order potential as a convergent moments-based method

The theory of a bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of $\sigma$ and $\pi$ bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a moments-based method with a low number of moments. Our use of the Lanczos basis simplifies the calculations of the band energy and forces, which allows the application of the method to the molecular dynamics simulations of large systems. As an illustration of this convergent $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ method we apply the block bond-order potential to the large-scale simulation of the deformation of a carbon nanotube.