The application of the M"obius inversion formula to the embedded-atom method

TL;DR

This paper introduces a systematic lattice-inversion method for deriving analytical long-range embedded-atom potentials, which converge faster than previous models and are validated through various material property calculations.

Contribution

It presents a novel analytical approach using Möbius inversion for embedded-atom potentials, establishing a link with the universal binding energy model.

Findings

Potentials converge exponentially faster than previous models

Accurate predictions of elastic constants and phonon dispersions

Validated potentials for phase stability and melting temperatures

Abstract

We present a systematical method for obtaining analytical long-range embedded-atom potentials based on the lattice-inversion method. The potentials converge faster (exponentially) than Sutton and Chen's power-law potentials (Philos. Mag. Lett. 61, 2480(1990)). An interesting relationship between the embedded-atom method and the universal binding energy equation of Rose et al. (Phys. Rev. B 29, 2963 (1984)) is also pointed out. The potentials are tested by calculating the elastic constants, phonon dispersions, phase stabilities, surface properties and melting temperatures of the fcc transition metals.