B. Bildstein et G. Kahl, TRIPLET CORRELATION-FUNCTIONS FOR HARD-SPHERES - COMPUTER-SIMULATION RESULTS, The Journal of chemical physics, 100(8), 1994, pp. 5882-5893
We present results for the triplet distribution function g(3)(r,s,t) o
f hard-spheres obtained in extensive molecular-dynamics simulations; t
he packing fractions we have investigated range from 0. 15 to 0.45. Th
e simulation data have been compared to results for g(3) (r,s,t) which
we calculated via some recently proposed analytical and numerical met
hods; two of these methods are based on density-functional theory and
the Wertheim-Thiele solution of the Percus-Yevick equation; another me
thod, proposed by Barrat, Hansen, and Pastore uses a factorization ans
atz for the pair direct correlation function and the last approximatio
n is based on a formal density expansion of g(3) (r,s,t), truncated af
ter second order. Furthermore we compared, simulation results to data
obtained by the ''source-particle method'' (or PY3 method) proposed a
few years ago by Attard. Attard's method shows an extremely good agree
ment not only for general configurations, but in particular for partic
les at direct contact; this approximation has to be considered as the
most reliable method available for the numerical determination of the
triplet-structure of a simple liquid. Concerning the results of the ot
her methods discrepancies with the simulation data are observed in par
ticular near the contact and for very close triplet-configurations. Ap
art from Attard's approximation the second order density expansion giv
es the best agreement. For less close configurations, i.e., if particl
es are separated by 1.5 to 2 hard-sphere diameters, the results of all
the methods investigated practically coincide.