# Verlet modified

The **Verlet modified** ^{[1]} closure relation for hard sphere fluids,
in terms of the cavity correlation function, is (Eq. 3)

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 (^{[2]} 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.