Second virial coefficients of asymmetric top molecules

A short self-contained derivation is given for the second virial coefficient B-2(T) of a gas consisting of identical interacting asymmetric rigid rotors. The resulting expression is correct through h(2). First, the canonical partition function is derived by means of an h expansion of exp[-H/(k(B)T)] due to Friedmann [Adv. Chem. Phys. 4, 225 (1962)]. The present work applies angular momentum operators and known facts from angular momentum theory. It is considerably more accessible than Friedmann's exposition, which is not based on angular momentum operators, but instead on explicit derivatives with respect to Euler angles. The partition function obtained from the h expansion is applied to the derivation of an expression for B-2(T) that is identical in appearance to the expression for symmetric rotors of T Pack [J. Chem. Phys. 78, 7217 (1983)]. The final equation in this work is valid for rigid rotors of any symmetry. (c) 2005 American Institute of Physics.