A comparison of methods for calculating tight-binding bond energies

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Abstract
The maximum entropy (ME) method has been compared with the square root terminator (SRT) and Gaussian quadrature (GQ) methods, and some variants of them, for the calculation of tight-binding bond energies based on the recursion method. It is found that with a reasonable estimate of the band edges, preferably too wide rather than too narrow a band, There is no generally preferable method from the point of view of how accurately the exact bond energies are reproduced with from three to six recursion levels. The ME methods are more stable if the chosen bandwidth is too great, but are no better than the SRT methods for too narrow a band. The ME densities of states have a simple analytic form, readily integrated by standard real integration packages. There are numerical difficulties in integrating the SRT densities of states from the band edges, but these can be overcome by contour integration, which avoids the square root singularities. A disadvantage of the ME methods is their extra computational cost and numerical problems for higher numbers of levels (moments). For calculating relative structural energies, the GO method is superior to either of the others for more than five recursion levels. Overall, the SRT method looks the least useful of the three for applications to atomistic relaxation.

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