### Coordination analysis This modifier performs two types of computations:

• It counts the number of neighbors for each particle that are within a given cutoff range around its position. This information, the so-called coordination number of the particle, will be stored in the `Coordination` output property by the modifier, where is available for subsequent operations, for example selecting particles that have a certain number of neighbors using the Expression selection modifier or visualizing the coordination numbers using the Color coding modifier.

• In addition, the modifier computes the radial pair distribution function (radial PDF, or simply RDF) for the particle system as a whole. The radial pair distribution function g(r) measures the probability of finding a particle at distance r given that there is a particle at position r=0; it is essentially a histogram of inter-particle distances. The pair distribution function is normalized by the average number density of particles (i.e. the total number of particles in the simulation cell divided by its volume). See the Wikipedia for more information on this distribution function.

#### Element-wise RDFs The Compute partial RDFs option lets the modifier compute separate radial distribution functions for all pair-wise combinations of particle types or elements. The computed partial RDFs will be normalized such that the summation of the partial RDFs, weighted by the product of the two corresponding elemental concentrations, yields the total RDF. For example, for a binary system with two particle species ɑ and β, the modifier computes a set of three partials functions gɑɑ, gɑβ and gββ, which add up to the total distribution as follows:

g(r) = cɑ2 gɑɑ(r) + 2 cɑcβ gɑβ(r) + cβ2 gββ(r)

Here, the cɑ and cβ denote the concentrations of the two species in the system and the factor 2 in the mixed term appears due to gɑβ(r) and gβɑ(r) being always identical.

#### Time-averaged RDF

In the current program version, the Coordination analysis modifier can only calculate the instantaneous RDF for the current simulation frame. To calculate an average RDF over all frames of a simulation trajectory, you can use OVITO's scripting capabilities and let the Coordination analysis calculate the RDF for each frame and then average the histogram data over all frames with a few lines of Python code. See the corresponding section of the scripting manual for an example.