Condensed Matter Physics, 2010, vol. 13, No. 1, p. 13002:110
DOI:10.5488/CMP.13.13002
Title:
Convenient formulae for some integrals in perturbation theory
Author(s):

D. Henderson
(Department of Chemistry and Biochemistry, Brigham Young University, Provo UT 84602)

The free energy and pressure of a fluid, as given by
perturbation theory, involve integrals of the hard sphere
correlation functions and their density derivatives. In most
applications a straightforward procedure would be to obtain these
integrals, possibly numerically, using the formulae and computer
codes for the hard sphere correlation functions, given previously
[Mol. Phys., 2007, 106, 2; Condens. Matter Phys., 2009,
12, 127], followed by numerical differentiation with respect
to the
density and a possible compounding of errors. More sophisticated
methods are given in this paper, which is the second in a planned
trilogy, drawn from the author's lecture notes. Three representative
model fluids are considered. They are the squarewell fluid, the
Yukawa fluid, and the LennardJones fluid. Each model fluid is
popular for theoretical and engineering calculations and can
represent a simple fluid such as argon. With the methods presented
here, numerical integration and differentiation are not necessary
for the squarewell and Yukawa fluids. Numerical integration cannot
be easily avoided in the case of the LennardJones fluid. However,
numerical differentiation with respect to the density is not
required.
Key words:
perturbation theory, inverse temperature expansion, compressibility approximations, analytic methods
PACS: 02.30.Qy, 02.30.Rz, 05.20.Jj, 05.70.Ce, 64.30.+t
