rdf namespace
#include <code/cpp/include/rdf.hpp>

Defines RDF-specific functions. This calculates the bulk radial distribution function.

The radial distribution function $g(r)$ , or pair distribution function. It can be used to illuminate features of short-range and long-range order. The RDF is the probability of finding a particle at a distance of $r$ from a tagged reference particle, relative to that of an ideal gas. For a system of $N$ particles, the pair correlation function for $N(N-1)$ pairs is:

\[ \rho_N^{(2)}(r,r') = ⟨\sum_{i=1}^{N} \sum_{j=1,j \neq i}^{N} \delta (r-r_i) \delta (r'-r_j) \langle \]

The code essentially bins distances between pairs of particles, and normalizes the resulting histogram is normalized with respect to an ideal gas. The algorithm for the calculation of $g(r)$ may be divided into the following steps:

  1. Initialization: The $g(r)$ array is initialized to zero.
  2. Sampling: The histogram is added to for a particular bin, if the distance of a pair of atoms falls within the $r$ associated with the bin.
  3. Normalization: Every bin of the $g(r)$ array is normalized by the product of the number of ideal gas particles in that bin, and the number of particles and number of frames.

Changelog