where the radial distribution function is expressed as (Eq. 1)
and where several sets of values are tried for A and B (Note, when A=0 the hyper-netted chain is recovered).
Later Verlet used a Padé (2/1) approximant ( Eq. 6) fitted to obtain the best hard sphere results by minimising the difference between the pressures obtained via the virial and compressibility routes:
with , and where the radial distribution function for hard spheres is written as (Eq. 1)
where is the hard sphere diameter.