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} | :<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. .