D-INTERPOLATION OF VIRIAL COEFFICIENTS

Zheng Zhen and John Loeser Department of Chemistry Oregon State University Corvallis, OR 97331-4003 

Dimensional interpolation is used to approximate the configuration space integrals required in the computation of higher-order hard sphere virial coefficients. Simple analytic results can he obtained at D = 

D — and D oo the smooth and generic dimension-dependence of the integrals enables one to interpolate reasonably accurate D = 3 values (rms error 1%) from the dimensional limit results. The interpolated integrals can be used either on their ovm, or in conjunction with an integral equation approximation which sums some subset of the required integrals exactly (such as the hypemetted-chain or Percus-Yevick methods) the combination methods are invariably better than either dimensional interpolation or integral equations alone. Interpolation-corrected Percus-Yevick values can be computed quite easily at arbitrary order however, errors in higher-order values are 

It is most convenient to treat the equation of state in dimensionless form. This may be done by writing the compressibility factor z = pV/NkT) as a function of the packing fraction (rj = Nvo/V, where Vo is the volume of a sphere). Consider first a hard sphere fluid in D = l. A one-dimensional sphere is a line segment, so this is nothing but a fluid of hard rods interacting along a line. Clearly the fluid should approach ideality (z — 1) at very low density (rj 0), and should become incompressible z — oo) at closest packing ( — 1). In fact, the equation of state is known exactly [4], and is just 

As shown in Fig. 1, hard sphere fluids in D 1 exhibit a fluid- solid phase transition. (Because there are no attractive forces, however, there is no liquid-vapor transition). In the fluid region, the equation of state can be expanded as a Taylor series in the packing fraction, 

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