Statistical mechanics of linear molecules I: Percus-Yevick and convolution-hypernetted-chain approximations

It is shown how the Percus-Yevick and convolution-hypernetted-chain approximations for dense fluids of linear molecules can be brought into practically applicable forms by using cartesian tensor formalism and pertubation theory. The possibility of expanding the intermolecular potential and the correlation functions is discussed in detail. Also, exact reductions for the Ornstein-Zernike relation in real space and for the Percus-Yevick equation are given. Some other approaches to the statistical mechanics of linear molecules are critically discussed. It is shown in particular, that the mean spherical model is an inconsistent type of perturbation theory. The necessary cartesian tensor formulae are given in appendices as well as formally exact expressions for the second virial coefficient and for the Fourier-transformed Ornstein-Zernike relation.