Appendix

Abstract

Let I₁; I₂, and I₃ be the three principal moments of inertia of the molecule. The rotational partition function of a single molecule is given by ${q_r} = {h^{ - 3}}\int {\int {{\text{exp(}}} } - \beta {E_k})d\phi d\phi d\psi d{P_\phi }d{P_\theta }d{P_\psi }$ (9.1) where E_k is the rotational kinetic energy of the molecule ${E_k} = (1/2)\sum\limits_{i = 1}^3 {{I_i}} {w_i}^2$ (9.2) and the w_i are the components of the angular velocity of the molecule along the principal axes. The integration in (9.1) is carried out over all the orientations (expressed in terms of the three Euler angles) and their conjugate momenta.