Cluster expansion

About: Cluster expansion is a research topic. Over the lifetime, 1605 publications have been published within this topic receiving 37221 citations.

New reference equation of state for associating liquids

Abstract: An equation of state for associating liquids is presented as a sum of three Helmholtz energy terms: Lennard-Lones (LJ) segment (temperature-dependent hard sphere + dispersion), chain (increment due to chain formation), and association (increment due to association). This equation of state has been developed by extending Wertheim’s theory obtained from a resummed cluster expansion. Pure component molecules are characterized by segment diameter, segment-segment interaction energy, for example, Lennard-Jones u and E, and chain length expressed as the number of segments. There are also two association parameters, the association energy and volume, characteristic of each site-site pair. The agreement with molecular simulation data is shown to be excellent at all the stages of development for associating spheres, mixtures of associating spheres, and nonassociating chains. The model has been shown to reproduce experimental phase equilibrium data for a few selected real pure compounds.

Generalized cluster description of multicomponent systems

Abstract: A general formalism for the description of configurational cluster functions in multicomponent systems is developed. The approach is based on the description of configurational cluster functions in terms of an orthogonal basis in the multidimensional space of discrete spin variables. The formalism is used to characterize the reduced density matrices (or cluster probability densities) and the free energy functional obtained in the Cluster Variation Method approximation. For the particular representation chosen, the expectation values of the base functions are the commonly used multisite correlation functions. The latter form an independent set of variational parameters for the free energy which, in general, facilitates the minimization procedure. A new interpretation of the Cluster Variation Method as a self-consistency relation on the renormalized cluster energies is also presented.

Optimized Cluster Expansions for Classical Fluids. II. Theory of Molecular Liquids

Abstract: The optimized cluster expansion methods developed in the first article of this series (I) are generalized to apply to molecular fluids. These methods make use of summations of ring and chain cluster diagrams. The summations are performed explicitly for certain classes of molecular models. The molecules in these classes contain several ``interaction sites,'' and the total interaction between two molecules is a sum of site‐site potentials that depend on the scalar distances between sites on the two molecules. The principal results of this work are computationally simple techniques for calculating the thermo‐dynamic properties and pair correlation functions of molecular fluids in which the intermolecular interactions are highly angular dependent. The techniques should be reliable since they arise from the same approximations that have been shown to be very accurate when applied to simple fluids.

Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory

Abstract: The symmetry‐adapted‐cluster (SAC) expansion of an exact wavefunction is given. It is constructed from the generators of the symmetry‐adapted excited configurations having the symmetry under consideration, and includes their higher‐order effect and self‐consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open‐shell systems as well as closed‐shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher‐order effect and the self‐consistency effect. We have expressed some existing open‐shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo‐orbital theory which is an extension of open‐shell orbital theory in the SAC expansion formula.