The structure of liquids can be studied by either neutron or X-ray scattering. The most common way to describe liquid structure is by a radial distribution function. However, this is not easy to obtain from a scattering experiment.
gmx rdf calculates radial distribution functions in different ways. The normal method is around a (set of) particle(s), the other methods are around the center of mass of a set of particles (-com) or to the closest particle in a set (-surf). With all methods, the RDF can also be calculated around axes parallel to the z-axis with option -xy. With option -surf normalization can not be used.
The option -rdf sets the type of RDF to be computed. Default is for atoms or particles, but one can also select center of mass or geometry of molecules or residues. In all cases, only the atoms in the index groups are taken into account. For molecules and/or the center of mass option, a run input file is required. Weighting other than COM or COG can currently only be achieved by providing a run input file with different masses. Options -com and -surf also work in conjunction with -rdf.
If a run input file is supplied (-s) and -rdf is set to atom, exclusions defined in that file are taken into account when calculating the RDF. The option -cut is meant as an alternative way to avoid intramolecular peaks in the RDF plot. It is however better to supply a run input file with a higher number of exclusions. For e.g. benzene a topology, setting nrexcl to 5 would eliminate all intramolecular contributions to the RDF. Note that all atoms in the selected groups are used, also the ones that don't have Lennard-Jones interactions.
Option -cn produces the cumulative number RDF, i.e. the average number of particles within a distance r.