Complexity analysis of simulations with analytic bond-order potentials

The modeling of materials at the atomistic level with interatomic potentials requires a reliable descriptionof different bonding situations and relevant system properties. For this purpose, analytic bond-orderpotentials (BOPs) provide a systematic and robust approximation to tight binding calculations at reducedcomputational cost. This paper presents a formal analysis of the computational complexity of analytic BOPsimulations based on a detailed assessment of the computationally most intensive parts. Different algorithmsand implementations are presented and compared along with optimisations for efficient numerical processing.Systematic benchmarks show that a recent implementation of analytic BOPs reaches the theoreticalscaling limits with regard to the number of atoms and the number of moments