From the inhomogeneous functional derivation formalism of Percus, we derive here a perturbation equation on correlation functions which represents a generalization of the hard sphere equation of Barker, Henderson, and Smith. It is particularly suited to the expansion from the hard spheres to the soft spheres due to fast numerical convergence. To render our development independent of machine simulation input, we use the Verlet–Weis hard sphere construction. Comparison of our calculations with the Monte Carlo (MC) results on two types of soft spheres, the inverse‐12 model and the repulsive part of the Lennard‐Jones (LJ) potential due to the Weeks–Chandler–Andersen (WCA) division, shows that this theory improves over the widely used WCA approximation and the Percus–Yevick (PY) theory for the radial distribution functions. For the shorter‐ranged LJ repulsion, superior agreement with MC data on equilibrium properties and radial distribution functions is obtained for temperatures T<2.8 and all densities. A mixed theory combining the perturbation equation and the PY approximation is found to work well for the inverse‐12 potential for xT−1/4<0.63.

1.
L. L.
Lee
,
J. Chem. Phys.
62
,
4436
(
1975
).
2.
J. K. Percus in The Equilibrium Theory of Classical Fluids, edited by H. L. Frisch and J. L. Lebowitz (Benjamin, New York, 1964);
J. K.
Percus
and
G. J.
Yevick
,
Phys. Rev.
110
,
1
(
1958
).
3.
L.
Verlet
and
J.‐J.
Weis
,
Phys. Rev. B
5
,
939
(
1972
).
4.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
,
J. Chem. Phys.
54
,
5237
(
1971
);
D.
Chandler
and
J. D.
Weeks
,
Phys. Rev. Lett.
25
,
149
(
1970
);
H. C.
Andersen
,
J. D.
Weeks
, and
D.
Chandler
,
Phys. Rev. A
4
,
1597
(
1971
).
5.
J. A.
Barker
and
D.
Henderson
,
J. Chem. Phys.
47
,
2856
(
1967
);
J. A.
Barker
and
D.
Henderson
,
47
,
4714
(
1967
).,
J. Chem. Phys.
6.
L. L.
Lee
and
D.
Levesque
,
Mol. Phys.
26
,
1351
(
1973
).
7.
P.
Hutchinson
and
W. R.
Conkie
,
Mol. Phys.
24
,
567
(
1972
).
8.
W. G.
Hoover
,
D. G.
Gray
, and
K. W.
Johnson
,
J. Chem. Phys.
55
,
1128
(
1971
);
W. G.
Hoover
,
D. A.
Young
and
R.
Grover
,
J. Chem. Phys.
56
,
2207
(
1972
); ,
J. Chem. Phys.
W. G.
Hoover
,
M.
Ross
,
K. W.
Johnson
,
D.
Henderson
,
J. A.
Barker
and
B. C.
Brown
,
J. Chem. Phys.
52
,
4931
(
1970
); ,
J. Chem. Phys.
W. G. Hoover, G. Stell, E. Goldmark, and G. D. Degani, “Generalized van der Waals Equation of State” (preprint, 1975).
9.
J.‐P.
Hansen
,
Phys. Rev. A
2
,
221
(
1970
);
J.‐P.
Hansen
and
J.‐J.
Weis
,
Mol. Phys.
23
,
853
(
1972
).
10.
J.‐J. Weis, Monte Carlo calculations of the Lennard‐Jones repulsion potential (3.3) (private communication, 1976).
11.
F. P.
Buff
and
F. M.
Schindler
,
J. Chem. Phys.
29
,
1075
(
1958
).
12.
B. A.
Lowry
,
H. T.
Davis
, and
S. A.
Stuart
,
Phys. Fluids
7
,
402
(
1964
).
13.
K. E.
Gubbins
,
W. R.
Smith
,
M. K.
Tham
, and
E. W.
Tiepel
,
Mol. Phys.
22
,
1089
(
1971
). We note that the first‐order term in their perturbation expansion involves already g3 and g4,(also ∂g2/∂p), while our expansion, based on Percus’ method, involves g3 only in first order.
14.
D.
Henderson
,
J. A.
Barker
, and
W. R.
Smith
,
Utilitas Mathematica,
1
,
211
(
1972
);
W. R.
Smith
and
D.
Henderson
,
Mol. Phys.
24
,
778
(
1972
).
15.
J. G.
Kirkwood
,
J. Chem. Phys.
3
,
300
(
1935
).
16.
J. L.
Lebowitz
and
J. K.
Percus
,
Phys. Rev.
122
,
1675
(
1961
);
J. L.
Lebowitz
and
J. K.
Percus
,
J. Math. Phys.
4
,
116
,
248
(
1963
).
17.
V. Volterra, Theory, of functionals and of integral and of integrodifferential equations (Dover, New York, 1959).
18.
E.g., B. J.
Alder
and
C. E.
Hecht
,
J. Chem. Phys.
50
,
2032
(
1969
).
19.
D.
Henderson
and
E. W.
Grundke
,
J. Chem. Phys.
63
,
601
(
1975
).
20.
Our modification on the Henderson‐Grundke method lies essentially in using a more exact formula in the Fourier transform of the δg(r) correction term of Verlet and Weis. See Eq. (25) and (30), Ref. 19.
21.
M. S.
Wertheim
,
Phys. Rev. Lett.
10
,
321
(
1963
),
M. S.
Wertheim
,
J. Math. Phys.
5
,
643
(
1964
);
E.
Thiele
,
J. Chem. Phys.
39
,
474
(
1963
).
22.
N. P.
Carnahan
and
K. E.
Starling
,
J. Chem. Phys.
51
,
635
(
1969
).
23.
See, e.g.,
L. L.
Lee
and
H. M.
Hulburt
,
J. Chem. Phys.
58
,
44
and
(
1973
).
24.
Our results for the WCA ĝss(r) properties differ slightly from those of Verlet and Weis (Ref. 3). This may be due to the different ways of approximating the y(r).
25.
MC values estimated from Ref. 9.
26.
This should be useful for the perturbation theories for anisotropic fluids. See, e.g.,
G.
Stell
,
J. C.
Rasaiah
, and
H.
Narang
,
Mol. Phys.
23
,
393
(
1972
);
L.
Verlet
and
J.‐J.
Weis
,
Mol. Phys.
28
,
665
(
1974
); ,
Mol. Phys.
K. E.
Gubbins
and
C. G.
Gray
,
Mol. Phys.
23
,
187
(
1972
); ,
Mol. Phys.
J. C.
Rasaiah
,
B.
Larsen
, and
G.
Stell
,
J. Chem. Phys.
63
,
722
(
1975
);
K. C.
Mo
and
K. E.
Gubbins
,
J. Chem. Phys.
63
,
1490
(
1975
); ,
J. Chem. Phys.
G. N.
Patey
and
J. P.
Valleau
,
J. Chem. Phys.
61
,
534
(
1974
); ,
J. Chem. Phys.
G. N.
Patey
and
J. P.
Valleau
,
64
,
170
(
1976
).,
J. Chem. Phys.
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