Correlation times for molecular reorientation

The dependence of the reduced reorientational correlation times, τ n *, for linear and spherical-top molecules on the angular velocity correlation time, τω*, is evaluated and conveniently presented for four different models of molecular reorientational thermal motion—the extended diffusion model, the Langevin model, the Ivanov model, and the strong collision model. In particular the theories of Sack [2] and Fixman and Rider [6] are compared. They are not the same for spherical molecules in the Langevin model. Some new results are also given for the Langevin model for the almost-free-molecule limit. The results are relevant to molecular gases, liquids and crystals. It is concluded that if experimental values of, say, τ1*/τ2* only, are available, this gives little information about the model unless τω* ⪸ 1/2 but may do about τω*. For τω* ≪ 1 all models except the last approach the Hubbard limit, τ n *τω*→n(n + 1). Information about the mechanism of molecular reorientation is only possible, even if τ n *(τω*) is known, when τω* ⪸ 1/2, depending on the accuracy of the data and excepting the physically unlikely strong collision model. On the other hand, the limit of τ n */τω* as τω*→∞ is usually very model-dependent but the limit is surely in the quantummechanical regime.