Welcome to rdfpy’s documentation!¶

rdfpy is a Python library for fast computation of 2D and 3D radial distribution functions.

Installation¶

rdfpy can be installed using pip:

pip install rdfpy

Introduction and Examples¶

What are Radial Distribution Functions?¶

The radial distribution function (RDF) (or pair correlation function) characterises the structure of a system of particles. If we select an arbitrary particle as the origin, the RDF describes the number of particles we would observe relative to the bulk density of the system, as a function of distance. This is calculated and averaged over every particle in the structure being considered. The formal definition of the RDF is

\[g_{i}(r) = \frac{n_{i}(r)}{4 \pi r^{2}\delta r \rho}\]

where \(n_{i}(r)\) is the number of particles between distances \(r\) and \(\delta r\), and \(\rho = \frac{N}{V}\) is the number density. Dividing by \(\rho\) ensures that the RDF is centred around 1 when the density of particles observed at some distance does not deviate from the bulk density.

Example: RDF of a Crystal Structure¶

In this example, we use rdfpy to compute the RDF of crystalline Ti. The Crystallographic Information File (CIF) can be obtained from here, and is provided by the Materials Project. First we import the rdf function from rdfpy, as well as pymatgen for obtaining atom coordinates from the CIF file, and numpy.

We then load the structure and create a supercell so that there are enough atoms in the crystal to compute an RDF from. Also, to make the resulting function smoother, we add some noise to the coordinates.

import numpy as np
from rdfpy import rdf
from pymatgen import Structure

structure = Structure.from_file('/path/to/Ti_mp-46_computed.cif')
structure.make_supercell(10)

coords = structure.cart_coords
noise = np.random.normal(loc=0.0, scale=0.05, size=(coords.shape))
coords = coords + noise

Finally we use rdfpy to compute the RDF from the coordinates, specifying the step size parameter dr:

g_r, radii = rdf(coords, dr=0.05)

Plotting g_r against radii results in the following function.

Licence¶

The MIT License (MIT)

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.