PMMCS Potential (Pedone)¶

The PMMCS potential, developed by Pedone et al., is the most broadly applicable force field in amorphouspy. It uses a Morse-type short-range interaction combined with a repulsive \(r^{-12}\) wall and damped-shifted-force (DSF) Coulomb interactions.

Reference¶

A. Pedone, G. Malavasi, M.C. Menziani, A.N. Cormack, U. Segre. "A New Self-Consistent Empirical Interatomic Potential Model for Oxides, Silicates, and Silica-Based Glasses", J. Phys. Chem. B 110, 11780–11795 (2006). DOI:10.1021/jp0611018

Functional Form¶

The total pairwise interaction energy is:

\[ V(r_{ij}) = D_{ij} \left[1 - e^{-a_{ij}(r_{ij} - r_0)}\right]^2 - D_{ij} + \frac{C_{ij}}{r_{ij}^{12}} + \frac{q_i q_j}{r_{ij}} \]

where:

Symbol	Description
\(D_{ij}\)	Morse potential well depth (eV)
\(a_{ij}\)	Morse potential width parameter (Å⁻¹)
\(r_0\)	Morse equilibrium distance (Å)
\(C_{ij}\)	Repulsive wall coefficient (eV·Å¹²)
\(q_i, q_j\)	Partial atomic charges

The Coulomb term uses the damped shifted force (DSF) method with a damping parameter of 0.25 Å⁻¹ and a cutoff of 8.0 Å. DSF provides accurate electrostatic energies without the expense of Ewald summation, making it efficient for amorphous systems.

LAMMPS pair style: hybrid/overlay coul/dsf 0.25 8.0 pedone 5.5

Charges¶

All atomic charges are fixed (composition-independent):

Element	Charge (\(e\))
O	−1.2
Si	+2.4
Al	+1.8
Na	+0.6
Ca	+1.2
Mg	+1.2
K	+0.6
Li	+0.6

Note: The oxygen charge is always −1.2 regardless of composition. This is a defining feature of the PMMCS potential.

Supported Elements¶

The PMMCS potential supports 28 elements (plus oxygen), making it the broadest of the three potentials:

Category	Elements
Alkali metals	Li, Na, K
Alkaline earth	Be, Mg, Ca, Sr, Ba
Transition metals	Sc, Ti, Zr, Cr, Mn, Fe, Fe3+, Co, Ni, Cu, Ag, Zn
Post-transition	Al, Si, Ge, Sn
Pnictogens	P
Rare earth	Nd, Gd, Er
Anion	O

Usage¶

from amorphouspy import get_structure_dict, generate_potential

# Works with any composition using supported elements
structure_dict = get_structure_dict(
    {"SiO2": 60, "Al2O3": 10, "Na2O": 15, "CaO": 10, "MgO": 5},
    target_atoms=3000,
)

potential = generate_potential(structure_dict, potential_type="pmmcs")

# The potential DataFrame contains LAMMPS configuration
print(potential["Config"].iloc[0][:5])  # First 5 LAMMPS commands

What the generator produces¶

The PMMCS generator creates LAMMPS configuration lines that: 1. Define the hybrid/overlay coul/dsf pedone pair style 2. Set atomic charges via set type ... charge ... 3. Define Morse parameters for all element pairs via pair_coeff 4. Set the repulsive wall coefficient \(C_{ij}\) for close-range interactions

Technical Details¶

Short-range cutoff¶

The Morse + repulsive term uses a cutoff of 5.5 Å. This is shorter than BJP (8.0 Å) and SHIK (10.0 Å), making PMMCS simulations somewhat faster per timestep.

When to use PMMCS¶

Multi-component glasses with elements beyond Ca-Al-Si-O
Exploratory studies where element coverage matters more than potential accuracy for a specific system
Rapid screening of compositions (fast short-range cutoff)
Systems with rare earth or transition metal dopants

Limitations¶

Fixed oxygen charge may not accurately capture composition-dependent charge transfer effects
Parameters for some element pairs may be less well-validated than others
The \(r^{-12}\) repulsive wall is a simplification compared to more physically motivated forms