CellCluster Development for the Pair Distribution Function: Application to Rigid Disks at High Density
Abstract
A technique, modeled after the cellcluster theory for the partition function, is developed for estimating the molecular pair distribution function. This technique, while general, is thought to be particularly applicable to highdensity crystalline systems. Attention is focused on Ω(ζ), the average number of pairs that have a distance between centers less than or equal to ζ. In the highdensity crystalline limit, Ω(ζ) for a system of N_{μ}dimensional rigid spheres has the following expansion, in the neighborhood of η=0,
2Ω/N=2μη+bη^{2}+cη^{3}+...,
η=(ζσ)/(aσ),
where a is the distance between lattice sites and σ is the diameter of a sphere. The exact development for a onedimensional system is given wherein the technique can be demonstrated to be convergent. For twodimensional rigid disks all contributions from fourparticle or fewer cell clusters to the constants b and c were calculated. The resulting series through fourth order is
b=2(192/217)1.6069+0.3763+...=0.1154+...,
c=0(216/217)+1.09860.6638+...=0.5606+....
 Publication:

Journal of Chemical Physics
 Pub Date:
 December 1966
 DOI:
 10.1063/1.1727478
 Bibcode:
 1966JChPh..45.4190L