Structural theory of liquid-vapour critical point with application to hard-core Yukawa fluids

March, Perrot and Tosi [Mol. Phys. 93, 355 (1998)] proposed three structural integrals I ₀, I ₁ and I ₂ to account for the liquid-vapour critical point (LVCP) based on the virial expression for the pressure. The interrelations between these integrals are obtained from the universality of LVCP. We extend the work of March et al. and suggest another structural integral I ₃. We also provide analytical expressions for I _n (n = 0, 1, 2, 3) for hard-core Yukawa fluids based on the series mean spherical approximation. The location of LVCP parameters versus the intermolecular potential range parameter is accurately calculated for three different equations of states. We find good agreement when compared with computer simulation results only for the compressibility equation of state within the mean density approximation. The universality of the critical compressibility ratio at the LVCP is discussed in detail.