A recent theory of Haymet, Rice, and Madden (HRM) for the pair and triplet correlation functions is tested at liquid state densities against new molecular dynamics results for the Lennard‐Jones (12,6) fluid. The HRM integral equation, based on the Born–Green equation and a topological reduction of the diagrammatic expansion of the triplet correlation function, has been solved for a high temperature state (T*=2.74, ρ*=0.80) and is found to give triplet correlation functions in good agreement with the molecular dynamics results. For a lower‐temperature state (T*=0.73, ρ*=0.85), where numerical difficulties have thus far frustrated attempts to obtain a self‐consistent solution of the HRM integral equation, direct tests of the HRM closure are made using molecular dynamics pair correlation functions to evaluate the diagrams. Although some striking qualitative features of the triplet correlations are correctly described by the HRM closure for this low‐temperature state, the HRM approach is not in quantitative agreement with the molecular dynamics results. Test calculations indicate that the principle source of these errors is the neglect of important higher‐order diagrams for the triplet correlation function. A reorganization of the diagrammatic series is suggested which may identify the most important of these neglected diagrams. Additional computer simulation results are also reported for the purely repulsive Weeks–Chandler–Andersen (WCA) ‘‘reference’’ fluid and for the underlying hard sphere fluid. The similarity of the pair structures of these fluids, noted by WCA, is also found to hold with high accuracy for the triplet structures. It is suggested that these similarities may be exploited in applying the methods of HRM to the hard sphere fluid.
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1 January 1983
Research Article|
January 01 1983
Triplet correlation functions in the Lennard‐Jones fluid: Tests against molecular dynamics simulations
William J. McNeil;
William J. McNeil
Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
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William G. Madden;
William G. Madden
Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
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A. D. J. Haymet;
A. D. J. Haymet
Department of Physics, Harvard University, Cambridge, Massachusetts 02138
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Stuart A. Rice
Stuart A. Rice
The Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637
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J. Chem. Phys. 78, 388–398 (1983)
Article history
Received:
May 20 1982
Accepted:
June 10 1982
Citation
William J. McNeil, William G. Madden, A. D. J. Haymet, Stuart A. Rice; Triplet correlation functions in the Lennard‐Jones fluid: Tests against molecular dynamics simulations. J. Chem. Phys. 1 January 1983; 78 (1): 388–398. https://doi.org/10.1063/1.444514
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