Relation between the kernel polynomial method and the bond-order potential

Abstract

The kernel polynomial method and the bond-order potential are two well-known linear scaling approaches in constructing interatomic potentials. They have been developed from different backgrounds in parallel, and the link between them has not been analyzed before. This Brief Report will demonstrate their close link by deriving the kernel polynomial method in the similar procedure that the analytic bond-order potential was constructed. An expression of bond order can also be derived from the kernel polynomial method; subsequently, the kernel polynomial method has a similar force expression as the analytic bond-order potential. Finally we will show that the kernel polynomial method, like the analytic bond-order potential, is also able to explain the structural trend across the nonmagnetic transition-metal series.