## 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 @V06627@ $$\eta$$. The rotational correlation time can be obtained from the decay of the @F02453@ or @P04569@ @AT06776@ and is related to the average molecular @R05411@, $$D_{\text{r}}$$, in turn related to the hydrodynamic molecular volume of the @FT07380@, $$V$$, and to $$\eta$$ (see Note 3).
Notes:
1. Mathematical definition: $$r(t) = r_{\text{0}}\, exp\! \left ( -\frac{t}{\tau_{\text{c}}} \right )$$ with $$r(t)$$ the @ET07370@ at time $$t$$ and $$r_{\text{0}}$$ the fundamental @ET07370@.
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 @S06027@–@E01914@ relationship is used for the calculation of $$D_{\text{r}}$$, i.e., $$D_{\text{r}} = R\, T/6\, V\eta$$ with $$R$$ the @G02579@, $$T$$ 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 @F02453@ @P04712@ methods. Compare with @RT07475@.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 416 [Terms] [Paper]