Cellhyphen;Cluster Development for the Pair Distribution Function: Application to Rigid Disks at High Density

摘要

A technique, modeled after the cellhyphen;cluster 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 highhyphen;density crystalline systems. Attention is focused on OHgr;(zgr;), the average number of pairs that have a distance between centers less than or equal to zgr;. In the highhyphen;density crystalline limit, OHgr;(zgr;) for a system ofNmgr;hyphen;dimensional rigid spheres has the following expansion, in the neighborhood of eegr;=0,2OHgr;sol;Nequals;2mgr;eegr;plus;beegr;2plus;ceegr;3plus;middot;middot;middot;,eegr;equals;lpar;zgr;minus;sgr;rpar;sol;lpar;aminus;sgr;rpar;,whereais the distance between lattice sites and sgr; is the diameter of a sphere. The exact development for a onehyphen;dimensional system is given wherein the technique can be demonstrated to be convergent. For twohyphen;dimensional rigid disks all contributions from fourhyphen;particle or fewer cell clusters to the constantsbandcwere calculated. The resulting series through fourth order isbequals;2minus;lpar;192sol;217rpar;minus;1.6069plus;0.3763plus;middot;middot;middot;equals;minus;0.1154plus;middot;middot;middot;,cequals;0minus;lpar;216sol;217rpar;plus;1.0986ndash;0.6638plus;middot;middot;middot;equals;minus;0.5606plus;middot;middot;middot;.