Interaction site models for molecular fluids

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Abstract
A detailed study is made of the atom-atom (i.e. site-site) correlation functions—especially the direct correlation function—for the interaction site model (ISM) of Andersen and Chandler. The work is based on the observation of Høye and Stell that the site-site Ornstein-Zernike-like equation of Chandler and Andersen can be regarded as a rewritten version of the usual Ornstein-Zernike equation for particle-particle correlations, where the particles are identified with the atoms that constitute the ISM molecules. Our new results include (i) new compressibility theorems in terms of the site-site direct correlation functions, and (ii) for ISM diatomics (both polar and non-polar) full asymptotic (i.e. large-r) characterization of the site-site direct correlation function based on the assumption that the corresponding particle-particle direct correlation function behaves asymptotically like the particle-particle potential times -1/k B T (k B = Boltzmann's constant and T = absolute temperature). Further asymptotic results are also given for a wider class of ISMs, in particular for triatomics. All our asymptotic results (except those for two classes of homonuclear symmetric n-atomics) are in fundamental disagreement with assumptions of the reference interaction site approximation (RISA) and the more general interaction site approximation (ISA), both originally proposed by Chandler and Andersen, as well as with all subsequently proposed approximations of which we are aware. (iii) A characterization is given of a family of ISMs containing point charges that is solvable in a class of linear approximations, including the ISA, as well as an approximation that is asymptotically faithful to the results noted in the preceding item. The family of ISMs considered includes models that have heretofore lacked analytic solution. (iv) The relation between the exact analytic solution of the Chandler-Andersen RISA and its approximate solution according to the widely-used Lowden-Chandler ansatz is examined on the basis of the particle-particle picture. It is pointed out how the relatively good liquid density agreement and the relatively poor low density agreement between the two solutions can be easily understood within this framework.