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Theory and implementation
The PDF is an example of a pair correlation function, which describes how, on average,
the atoms in a system are radially packed around each other. This proves to be a particularly effective way of describing
the average structure of disordered molecular systems such as liquids. Also in systems like liquids, where there is
continual movement of the atoms and a single snapshot of the system shows only the instantaneous disorder, it is extremely
useful to be able to deal with the average structure.
The PDF is useful in other ways. For example, it is something that can be deduced experimentally from x-ray or neutron
diffraction studies, thus providing a direct comparison between experiment and simulation. It can also be used in
conjunction with the interatomic pair potential function to calculate the internal energy of the system, usually quite
accurately.
Mathematically, the PDF can be computed using the following formula:
 |
(4.186) |
where
is the number of selected species,
and
are respectively the numbers of atoms of species
I and J,
and
respectively the weights for species I and J
(see Section 4.2.1 for more details) and
is the partial PDF for
and
species that can be defined as:
 |
(4.187) |
where
is the density of atom of specie J and
is the mean number of atoms of specie
J in a shell of width dr at distance r of the atom
of specie I.
From the computation of PDF, two related quantities are computed in nMOLDYN, the Radial-Distribution Function (RDF) defined as:
 |
(4.188) |
and the Total-Correlation Function (TCF) defined as:
 |
(4.189) |
where
is the average atomic density defined as:
 |
(4.190) |
where N is the total number of atoms of the system and
the volume of the simulation box.
In nMOLDYN, the PDF, the RDF and the TCF are further splitted into an intra-and inter-molecular parts
which added together give respectively the total PDF, RDF and TCF.
Next: Parameters
Up: Pair Distribution Function
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pellegrini eric
2009-10-06