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357. LINEAR and NONLINEAR: A Set of Programs to
Calculate the Classical Pressure Second Virial of
Linear and Nonlinear Molecules
by Sohail Murad, School of Chemical Engineering, Olin
Hall, Cornell University, Ithaca, New York 14853
The classical second virial of a linear molecule can be
shown to be
(1)
where
B2(T) = second virial coefficient
NA = Avagodro's number
R = center-center distance between two
molecules
(qi,fi) = orientation of molecule i in Euler
angles
fij = fj - fi
b = 1/kT, where k is the Boltzman constant
f(R;a) = pair potential, where a is the
orientation of the two molecules
The program evaluates the four-fold integral using a
third degree nonproduct formula developed by Stroud.
The integral is thus evaluated as
(2)
where are the coordinates where the function f (x) is
sampled. For an n-dimensional hypercube of width 2,
centered at the origin, these have been shown to be
(3)
where s = 1, 2, ...n/2 for n even. If n is odd, these
are defined as
(4)
Before this method can be used, a retransformation of
variables has to be carried out. Moreover, to achieve
the required accuracy, the region of integration Sn has
to be divided into a large number of such hypercubes.
To use the program, the user must supply a subroutine,
FUN, which defines the pair potential f(R;a) needed in
equation (1). The sample subroutine is for a site-site
nitrogen potential suggested by Cheung and Fowles. All
calculations are carried out in reduced units, and
subroutine FUN must also be in reduced form. (The
reducing parameters s and e should normally be the
parameters for the most important part of the pair
potentials.)
FORTRAN IV (IBM)
Lines of Code: 420
Recommended Citation: S. Murad, QCPE 11, 357 (1978).
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