Pair distribution function: Difference between revisions

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See Eq. 5.10 of Ref. 1:
See Eq. 5.10 of Ref. 1:


:<math>\ln g(r_{12}) + \frac{\Phi(r_{12})}{kT} - E(r_{12}) = n \int \left(g(r_{13}) -1 - \ln g(r_{13}) -  \frac{\Phi(r_{13})}{kT} - E(r_{13})  \right)(g(r_{23}) -1)  ~{\rm d}r_3</math>
:<math>\ln g(r_{12}) + \frac{\Phi(r_{12})}{kT} - E(r_{12}) = n \int \left(g(r_{13}) -1 - \ln g(r_{13}) -  \frac{\Phi(r_{13})}{kT} - E(r_{13})  \right)(g(r_{23}) -1)  ~{\rm d}{\mathbf r}_3</math>


where <math>r_{12} = |{\mathbf r}_2 - {\mathbf r}_1|</math>.
where, ''i.e.'' <math>r_{12} = |{\mathbf r}_2 - {\mathbf r}_1|</math>.
==See also==
==See also==
*[[Radial distribution function]]
*[[Radial distribution function]]

Revision as of 16:09, 10 July 2007

For a fluid of particles, enclosed in a volume at a given temperature (canonical ensemble) interacting via the `central' intermolecular pair potential , the two particle distribution function is defined as

where , where is the Boltzmann constant.

Exact convolution equation for

See Eq. 5.10 of Ref. 1:

where, i.e. .

See also

References

  1. J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics 28 pp. 169-199 (1965)