n the realizability of pair correlation functions

ceton, NJ The pair correlation function g2ðrÞ provides a basic geometric descriptor for man systems. It must obey two necessary conditions: (i) non-negativity for all distances non-negativity of its associated structure factor SðkÞ for all k. Here we utilize an stochastic construction algorithm for particle configurations to establish conditions (i) and (ii) are also sufficient, i.e., g2ðrÞ is in fact realizable. Two types of target pair co functions have been investigated in one, two, and three dimensions for hard-core specifically a unit step function, and a contact d plus step pair correlation function indicate that the former target function is realizable up to a terminal density set by condition (ii), at which the particle core packing fraction equals 2 d in d dim Furthermore, results are consistent with the proposition that for d41 the contact d function is realizable up to a terminal density due to condition (ii) at which the fraction of cores is ðd þ 2Þ=2dþ1 [Torquato and Stillinger, J. Phys. Chem. B 106 (2