Abstract
The Mayerf-function for purely hard particles of arbitrary shape satisfiesf 2(1, 2)=−f(1, 2). This relation can be introduced into the graphical expansion of the direct correlation functionc(1, 2) to obtain a graphical expression for the case of exact coincidence, in position and orientation, of two identical hard cores. The resulting expression forc(1, 1)+1 contains only graphsG fromc(1), the sum of irreducible graphs with one labeled point. Relative to its coefficient inc(1),G occurs inc(1, 1) with an additional factorR c which is 1 for the leading graph in the expansion and of the form 2−2L(G) for all other graphs. HereL(G)=0, 1, 2,..., is a nonnegative integer. Topological analysis is used to derive an expression forL(G) in terms of the connectivity properties ofG.
Similar content being viewed by others
References
L. Boltzmann,Wissenschaftliche Abhandlungen [Reprinted Chelsea, New York, 1968],
W. W. Wood and J. D. Jacobson,J. Chem. Phys. 27:720 (1957).
T. E. Wainwright and B. J. Alder, AEC Report Contract No. W-7405-eng-48, Radiation Laboratory at Livermore, University of California;Nuovo Cimento 9 (Suppl. X):116 (1957).
H. Reiss, H. L. Frisch, and J. L. Lebowitz,J. Chem. Phys. 31:369 (1959).
D. M. Tully-Smith and H. Reiss,J. Chem. Phys. 53:4015 (1970); Erratum,54:3661 (1971).
J. J. Vieceli and H. Reiss,J. Chem. Phys. 57:3746 (1973);J. Stat. Phys. 7:143 (1973); 8:299 (1973).
H. Reiss and R. V. Casberg,J. Chem. Phys. 61:1107 (1974).
M. J. Mandell and H. Reiss,J. Stat. Phys. 13:107, 113 (1975).
R. M. Gibbons,Mol. Phys. 17:81 (1969).
B. Barboy and W. M. Gelbart,J. Stat. Phys. 22:685 (1980), and references cited therein.
J. E. Kilpatrick,Adv. Chem. Phys. 20:39 (1971).
F. H. Ree and W. G. Hoover,J. Chem. Phys. 40:939 (1964).
F. H. Ree and W. G. Hoover,J. Chem. Phys. 41:1635 (1964).
F. H. Ree and W. G. Hoover,J. Chem. Phys. 46:4181 (1967).
K. W. Kratky,J. Stat. Phys. 27:533 (1982);29:129 (1982).
B. Mulder, Thesis, Utrecht (1986).
J. K. Percus and G. J. Yevick,Phys. Rev. 110:1 (1958).
J. M. van Leeuwen, J. Groeneveld, and J. deBoer,Physica 25:792 (1959).
M. S. Green,J. Chem. Phys. 33:1403 (1960).
E. Meeron,J. Math. Phys. 1:192 (1960).
G. S. Rushbrooke,Physica 26:1425 (1960).
T. Morita and K. Hiroike,Prog. Theor. Phys. 23:1103 (1960).
L. Verlet,Nuovo Cimento 18:77 (1960).
M. S. Wertheim,Phys. Rev. Lett. 10:321 (1963);J. Math. Phys. 5:643 (1964).
E. Thiele,J. Chem. Phys. 38:1959 (1963).
M. Klein,J. Chem. Phys. 39:1388 (1963).
A. Perera, P. G. Kusalik, and G. N. Patey,J. Chem. Phys. 87:1295 (1987).
D. Frenkel and B. M. Mulder,Mol. Phys. 55:1171, 1193 (1985).
J. W. Perram, M. S. Wertheim, J. L. Lebowitz, and G. O. Williams,Chem. Phys. Lett. 105:277 (1984).
G. Stell, inThe Equilibrium Theory of Classical Fluids, H. L. Frisch and J. L. Lebowitz, eds. (Benjamin, New York, 1964).
W. G. Hoover and J. C. Poirier,J. Chem. Phys. 37:1041 (1962).
E. Meeron and A. J. Siegert,J. Chem. Phys. 48:3139 (1968).
D. Henderson and E. W. Grundke,Mol. Phys. 24:669 (1972).
M. S. Wertheim,J. Math. Phys. 8:927 (1967).
M. S. Wertheim,J. Stat. Phys. 35:19, 35 (1984); 42:459, 477 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wertheim, M.S. Coincidence theorem for the direct correlation function of hard-particle fluids. J Stat Phys 52, 1367–1387 (1988). https://doi.org/10.1007/BF01011654
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01011654