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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). |