Calculation of binding energy from moments via Jacobi polynomials

Moments contain essential information for the density of states, and they can be readily computed within the tight-binding framework; therefore, it is desirable to obtain the bond energy from the moments. A linear-scaling moment-based potential via orthogonal polynomials (LMPO) was proposed recently by (Qin, 2010) [29]. Arbitrary orthogonal polynomials can be implemented within the LMPO. This paper will concentrate on Jacobi polynomials, and these polynomials have finite support intervals. In order to match these support intervals with the band edges of the density of states, the band edges need to be obtained first, ideally from the moments. Algorithms obtaining the band edges from the moments are analysed, and a more convergent algorithm is proposed. Then the combination of this band edge algorithm and the LMPO is examined on an s-band system and a d-band tungsten system. As demonstrated from the results, even though the band edges are not fully converged within only a limited number of moments, this combined method is able to converge to the tight-binding results in terms of binding energy. Consequently, this can significantly reduce the computation time.