PMMCS Potential (Pedone)¶

Interactive example

See the Potential Settings notebook for a worked example of configuring electrostatics across all three potentials.

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

Default 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, PppmConfig

# 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,
)

# Default: DSF electrostatics, melt pre-equilibration enabled
potential = generate_potential(structure_dict, potential_type="pmmcs")

# PPPM with custom cutoff, no melt block
potential = generate_potential(
    structure_dict,
    potential_type="pmmcs",
    melt=False,
    electrostatics=PppmConfig(
        long_range_cutoff=12.0,
        kspace_accuracy=1e-5,
    ),
)

`melt` — high-temperature pre-equilibration¶

When melt=True, the generator appends a 10 000-step Langevin NVE/limit block at 4000 K:

fix langevinnve all langevin 4000 4000 0.01 48279
fix ensemblenve all nve/limit 0.5
run 10000
unfix langevinnve
unfix ensemblenve

This relaxes unfavourable atomic contacts that are common in randomly packed starting structures before the main melt–quench run. The nve/limit 0.5 cap prevents runaway atom velocities if two atoms are placed too close together. Set melt=False when the starting structure is already equilibrated or when you want full control over the thermostat schedule.

Electrostatics options¶

amorphouspy supports four Coulomb solvers via the InteractionConfig subclasses (DsfConfig, WolfConfig, PppmConfig, EwaldConfig). The choice affects which LAMMPS directives are emitted:

Method	`pair_style` fragment	`kspace_style`	Recommended cutoff
`dsf` (default)	`coul/dsf <alpha> <cutoff>`	—	8.0 Å
`wolf`	`coul/wolf <alpha> <cutoff>`	—	8.0 Å
`pppm`	`coul/long <cutoff>`	`pppm <accuracy>`	12.0 Å
`ewald`	`coul/long <cutoff>`	`ewald <accuracy>`	12.0 Å

DSF and Wolf are real-space methods. They require a damping parameter alpha (Å⁻¹, default 0.25) that controls how quickly the interaction is damped. Larger alpha allows a shorter long_range_cutoff but at the cost of accuracy near the cutoff. DSF shifts both the potential and the force to zero at the cutoff; Wolf shifts only the potential.

PPPM and Ewald are reciprocal-space methods. The alpha parameter is ignored. The default long_range_cutoff widens to 12.0 Å because without DSF-style damping the real-space part decays more slowly. A kspace_style line is appended after the pair coefficients; kspace_accuracy (default 1e-5) tunes the accuracy of the long-range Fourier sum at the cost of k-space solver time.

The short-range cutoff (Morse + repulsive wall) is fixed at 5.5 Å and is not user-configurable. Only the Coulomb cutoff (long_range_cutoff) can be overridden via the config classes.

What the generator produces¶

The PMMCS generator creates LAMMPS configuration lines that: 1. Define the hybrid/overlay coul/* 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 5. Optionally append the melt pre-equilibration block

Technical Details¶

Short-range cutoff¶

The Morse + repulsive term uses a fixed 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