A closed form for the second virial coefficient of the Woolley potential

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Abstract
The second virial coefficient B(T) of the Woolley potential (r/re= phi -1n/exp(-e>>1( phi -1),V/D=( phi -1)2-1) is evaluated in closed form in terms of the parabolic cylinder functions. The large-argument (positive and negative) expansions of these functions lead to simple asymptotic formulae for B(T) at low and high temperatures, which are given explicitly for n=6. At low temperatures, in the case of H2, a study of the accuracy and range of validity of the first- (B(1)) and second- (B(2) order asymptotic expressions of B(T) shows that B(1) has an accuracy of less than 10% and B(2) of less than 3% for kT/D=T*-1 in marked contrast to the T-1/4 behaviour for the Lennard-Jones (12,6) potential which is obtained from the Woolley potential for e1=0 and n=6.