## rotational correlation time, $$\tau_{\text{c}}$$, $$\theta$$

https://doi.org/10.1351/goldbook.RT07474
Parameter describing the time dependence of the tumbling of a molecular entity in a medium of @[email protected] $$\eta$$. The rotational correlation time can be obtained from the decay of the @[email protected] or @[email protected] @[email protected] and is related to the average molecular @[email protected], $$D_{\text{r}}$$, in turn related to the hydrodynamic molecular volume of the @[email protected], $$V$$, and to $$\eta$$ (see Note 3).
Notes:
1. Mathematical definition: $$r(t) = r_{\text{0}}\, \text{exp}\! \left ( -\frac{t}{\tau_{\text{c}}} \right )$$ with $$r(t)$$ the @[email protected] at time $$t$$ and $$r_{\text{0}}$$ the fundamental @[email protected]
2. In the case of a spherical emitting species reorienting itself in a homogeneous fluid, $$\tau_{\text{c}} = \frac{1}{6D_{\text{r}}}$$.
3. Often, the @[email protected]–@[email protected] relationship is used for the calculation of $$D_{\text{r}}$$, i.e., $$D_{\text{r}} = R\, T/6\, V\eta$$ with $$R$$ the @[email protected], $$T$$ the absolute temperature and $$V$$ the hydrodynamic molecular volume. However, the use of this relationship at a molecular level is questionable, and $$D_{\text{r}}$$ should be independently determined by time-resolved @[email protected] @[email protected] methods. Compare with @[email protected]
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 416 [Terms] [Paper]