The **R**adial **D**istribution **F**unction, **R.D.F.** , *g*(*r*), also called pair distribution function or pair correlation function, is the elementary tool used to extract the structural information from numerical simulations.

**Figure 1:**Space discretization for the evaluation of the radial distribution function.

Considering an homogeneous repartition of the particles in space, the *g*(*r*) represents the probability to find a particle in the shell *dr* at the distance *r* of another particle [Fig. 1].

By discretizing the space in intervals *dr* [Fig. 1] it is possible to compute for a given atom, the number of atoms *dn*(*r*) at a distance between *r* and *r* + *dr* of this atom:

where *N* represents the total number of particles, *V* the volume and where g(*r*) is the radial distribution function.

In this notation the volume of the shell of thickness *dr* is approximated *V*_{shell} = *π*(*r* + *dr*)^{3} - *πr*^{3} 4*π* *r*^{2} *dr*.

By distinguishing the chemical species it is possible to compute the partial radial distribution functions *g*_{αβ}(*r*):

where *c*_{α} represents the concentration of species *α*.

These functions give the density probability for an atom of the *α* species to have a neighbor of the *β* species at a given distance *r*.

**Figure 2:**Partial radial distribution functions of glassy GeS

_{2}at 300 K.

Figure [Fig 2] illustrates the results of the calculation of the partial radial distribution functions for gGeS_{2} at 300 K, and allows to visualize the characteristics of the repartition of the chemical species.

Since version 1.1 the R.I.N.G.S. code also gives access to the reduced distribution functions **G**_{αβ}(*r*) defined by:

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