Soft Sphere Potential¶

The soft sphere potential is a simple repulsive interaction used primarily for structure generation and packing optimization.

Theory¶

Potential Form¶

The pairwise energy between atoms \(i\) and \(j\) is:

\[ u_{ij}(r) = \begin{cases} \frac{\epsilon}{\alpha} \left(1 - \frac{r_{ij}}{\sigma}\right)^\alpha & \text{if } r_{ij} < \sigma \\ 0 & \text{if } r_{ij} \geq \sigma \end{cases} \]

Where:

\(r_{ij}\): Distance between atoms \(i\) and \(j\)
\(\sigma\): Particle diameter (cutoff distance)
\(\epsilon\): Energy scale
\(\alpha\): Stiffness exponent

Force¶

The force is derived from the potential:

\[ \mathbf{F}_{ij} = -\nabla u_{ij} = -\frac{\epsilon}{\sigma} \left(1 - \frac{r_{ij}}{\sigma}\right)^{\alpha-1} \frac{\mathbf{r}_{ij}}{r_{ij}} \]

for \(r_{ij} < \sigma\), and \(\mathbf{F}_{ij} = 0\) otherwise.

Usage¶

Basic Example¶

from a2c_ase.potentials.soft_sphere import SoftSphere
from ase import Atoms
import numpy as np

# Create atoms
atoms = Atoms(
    'Si8',
    positions=np.random.random((8, 3)) * 10,
    cell=[10, 10, 10],
    pbc=True
)

# Create calculator
calculator = SoftSphere(
    sigma=2.5,      # Particle diameter (Å)
    epsilon=1.0,    # Energy scale (eV)
    alpha=2,        # Stiffness exponent
    skin=0.2       # Neighbor list skin
)

# Attach and compute
atoms.calc = calculator
energy = atoms.get_potential_energy()
forces = atoms.get_forces()

Parameters¶

Parameter	Type	Default	Description
`sigma`	float	1.0	Particle diameter (Å)
`epsilon`	float	1.0	Energy scale (eV)
`alpha`	int	2	Stiffness exponent
`skin`	float	0.2	Neighbor list skin (Å)