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Theory and implementation

In chemistry, the CN is the total number of neighbours of a central atom in a molecule or ion. The definition used in nMOLDYN is somewhat different and can be seen as an extension of as the former definition. Indeed, in nMOLDYN, the CN is not defined over one defined central atom but around the centers of gravity of a set of group of atoms. So, if only one group made of only atom is selected for the analysis, then, the definition is the same as the original definition. In that context, the CN is defined as:

| (4.191)

where is the number of groups of atoms, is the number of species found in the system and is the CN defined for specie I defined as the number of atoms of species I found in a shell of width dr at a distance r of the center of gravity of the group of atom g.

nMOLDYN allows one to compute the CN on a set of equidistantly spaced distances at different times:

| (4.192)

where and are respectively the number of distances and times at which the CN is evaluated and

| (4.193)

is the number of atoms of specie I found within at frame f from the center of gravity of group g.

From these expression, several remarks can be done. Firstly, the Eqs 4.192 and 4.193 can be restricted to intramolecular and intermolecular distances only. Secondly, these equations can be averaged over the selected frames providing a time averaged intra and intermolecular CN. Finally, the same equations (time-dependent and time-averaged) can be integrated over to provide a cumulative CN. nMOLDYN computes all these variations.

The concept of CN is useful for structure-related analysis. It can reveal for instance some packing effects that may have occured during the simulation.

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