Verlet modified

The Verlet modified (1980) (Ref. 1) closure for hard sphere fluids, in terms of the cavity correlation function, is (Eq. 3)

$y(r)=\gamma (r)-A\frac{1}{2}{\gamma }^2(r)[\frac{1}{1+B\gamma (r)/2}]$

where several sets of values are tried for A and B (Note, when A=0 the HNC is recovered). Later (Ref. 2) (1981) 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:

$y(r)=\gamma (r)-A\frac{1}{2}{\gamma }^2(r)[\frac{1+\lambda \gamma (r)}{1+\mu \gamma (r)}]$

with $A=0.80$, $\lambda =0.03496$ and $\mu =0.6586$.

References

1. [MP_1980_41_0183]
2. [MP_1981_42_1291]