Martynov Vompe

The Martynov-Vompe (Refs. 1 and 2) closure

$B=-a(\ln y^{*})-b(\ln y^{*}{)}^2$

where

$y^{*}(r)=\ln y(r)-\beta {\mathrm{\Phi }}_p$

where ${\mathrm{\Phi }}_p$ is the perturbative part of the pair potential (Note: in the Weeks-Chandler-Anderson separation for the Lennard-Jones system, the `perturbative part' is the attractive part). Martynov and Vompe have used the $d{p}_v-d{P}_c$ and $dU-dP$ thermodynamic consistencies in constructing their closures (Ref. 3).

References

1. G. A. Martynov and A. G. Vompe "Differential condition of thermodynamic consistency as a closure for the Ornstein-Zernike equation", Physical Review E, 47 pp. 1012 - 1017 (1993)
2. A. G. Vompe and G. A. Martynov "The bridge function expansion and the self-consistency problem of the Ornstein–Zernike equation solution", Journal of Chemical Physics 100 pp. 5249-5258 (1994)
3. Lloyd L. Lee, Dhananjay Ghonasgi, and Enrique Lomba "The fluid structures for soft-sphere potentials via the zero-separation theorems on molecular distribution functions", Journal of Chemical Physics 104 pp. 8058-8067 (1996)