# Qualitatively, How do MEAM Potentials Work?

I have frequently come across MEAM potentials in my work, but I lack an intuitive understanding of what they do.

What's a good qualitative description of a MEAM potential function?

In short, it is a semi-empirical approach to atom/atom interaction for periodic systems.

It is based on the embedded atom method (EAM) idea where "the energy of a given atom is taken as one half the energy in two-body bonds with its neighboring atoms plus the energy to embed the atom in the electron density at its site arising from all the other atoms" [1,2].

The MEAM is a modification of EAM [3]. The main modifications were the ad hoc inclusion of the differences between metallic and covalent bonding [3].

It had been applied to FCC, BCC, diamond cubic, and gaseous materials [4] and to HPC metals [5].

[1] M.S. Daw and M.I. Baskes, Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals, Phys. Rev. Lett. 50 1285 (1983). DOI: 10.1103/PhysRevLett.50.1285
[2] M.S. Daw and M.I. Baskes, Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B. 29 644 (1984). DOI: 10.1103/PhysRevB.29.6443
[3] M.I. Baskes, J.S. Nelson, and A.F. Wright, Semiempirical modified embedded-atom potentials for silicon and germanium, Phys. Rev. B. 40, 6085 (1989). DOI: 10.1103/PhysRevB.40.6085
[4] M.I. Baskes, Modified embedded-atom potentials for cubic materials and impurities, Phys. Rev. B. 46, 2727 (1992). DOI: 10.1103/PhysRevB.46.2727
[5] M.I. Baskes and R.A. Johnson, Modified embedded atom potentials for HCP metals, Modelling Simul. Mater. Sci. Eng. 2 147 (1994). DOI: 10.1088/0965-0393/2/1/011

• I like the first line and second paragraph, but could you give an overview of what the bonds could be considered to be for example? What's the qualitative explanation of the potential function $\Phi_{ij}$? Or of the embedding function $F(\bar{\rho}_i)$? Nov 23 '21 at 12:13

To add on to the answer given by Camps above, I will explain a bit more about the Semi-Empirical nature of the potentials.

The idea is based on density functional theory, and approximates the electron density of orbitals around the nucleus using some functional form. In the Baskes paper the form chosen is a decaying exponential.

In the original EAM there are four of these functions, which are known as partial electron densities, representing the four orbital shells: s, p, d, f. Each of these is approximated as a sphere originating at the nucleus. This proved to be too simplistic a model, and so in MEAM the partial electron densities are altered to give them directionality depending on the atoms local environment. In a sense the partial densities become perturbations of the originals from the EAM formalism. Each partial electron density can be considered a correction to the basic approximation of the EAM partial electron densities.

The total electron density at any point is the combination of these partial electron densities. The embedding function describes the change in energy that occurs when placing an atom into a position surrounded by the electron density given by its neighbours. The potential function $$\Phi_{ij}$$ is chosen to match physical constants and so far as I'm aware could be any kind of formalism so long as it gets you the right values.

This is the first time I've really looked at this, so corrections are welcome!