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Density

Textbook guide to local and grid number densities — where matter sits in space, beyond the isotropic \(g(r)\).

Conventions

  • Density in Å⁻³; length Å.
  • LocalDensity needs a NeighborList; GaussianDensity smears onto a grid without one.

1. Two density pictures

  • LocalDensity — per-particle scalar: number density inside a sphere of radius r_max about each particle. Interfaces, voids, packing variations.
  • GaussianDensity — continuous field \(\rho(\mathbf{r})\) on a fixed 3-D grid by Gaussian smearing of width sigma. Visualization and adsorption maps.

Too small a length scale → shot noise; too large → washed-out features. Match r_max / sigma to a physical length (first \(g(r)\) minimum, interface width).

2. Usage

import numpy as np
import molpy as mp

rng = np.random.default_rng(0)
xyz = rng.uniform(0.0, 20.0, size=(200, 3))
frame = mp.Frame()
frame["atoms"] = {"x": xyz[:, 0], "y": xyz[:, 1], "z": xyz[:, 2]}
frame.box = mp.Box.cubic(20.0)

from molpy.compute import NeighborList, LocalDensity, GaussianDensity

nlist = NeighborList(cutoff=4.0)(frame)
local = LocalDensity(r_max=4.0)([frame], [nlist])
grid = GaussianDensity(nx=64, ny=64, nz=64, sigma=1.0)([frame])

Optional diameter on LocalDensity applies a particle-size correction (0.0 counts centres only).

3. Pitfalls

  1. r_max / sigma not matched to structure → noise or over-smoothing.
  2. Free box → periodic box required.
  3. Comparing densities across systems without reporting the smoothing length.

See also