5.2 Pair Correlation Function

An average of this quantity represents the relative frequency, or

In a fluid we usually have ; only in the presence of external fields or near surfaces varies in a non-trivial manner.

Let us proceed to the ``pair correlation function'' (PCF)

This is the

To determine , proceed like this:

- Divide the range of -values (at most , where is the side length of the basic cell) into intervals of length .
- A given configuration
is scanned to
determine, for each pair , a ``distance channel''number

- In a histogram table the corresponding value is then incremented by . This procedure is repeated every, say, MD steps (or MC steps).
- At the end of the simulation run the histogram is normalized according to 5.1.

Significance of in fluid physics:

- The average of any quantity that depends on the pair
potential may be expressed as an integral over .

Example: pressure (see also 1.2)

- Theory: analytical approximations to for a given pair potential .[KOHLER 72],[HANSEN 86]
- Experiment: the Fourier transform of , the
``scattering law''

is just the relative intensity of neutron or X-ray scattering at a scattering angle with

Plot the PCF and see whether it resembles the one given in
Figure 5.1.

F. J. Vesely / University of Vienna