# Chemical time scales

In calculating UV/VIS spectra with computational procedures (say, TD-DFT), it is commonly assumed that the geometry of the ground-state is still valid also for the excited state due to the short time scale (I more or less took this statement from here).

So I asked myself, are there good references on time scales for chemical processes? Some phenomena may be obviously faster than others, but others (say, two molecular excitations) may be not that obvious to compare.

I am looking for something simple, like a table (or tables) with examples.

• The CH stretch vibration of a CH bond (a very fast vibration) is ~3000 cm-1 which means one vibration takes around 10 fs. Rotations of small molecules are around 10 ps to 1 ns. Going through a transition state without any barrier is around 60fs ( 1/(kB*T/h)). So for basically everything that occurs faster than some fs the atoms (or better the cores) will lag behind. – DSVA Jan 30 '17 at 17:15
• Thanks for your comment @DSVA! What about excitations/emissions? They surely span a lot in terms of time. When can I safely assume the excited state is not going to rearrange itself? – Felipe S. S. Schneider Jan 30 '17 at 19:04
• As a rule of thumb, excited state lifetimes are not often less than a picosecond, several hundreds of ps to many nanoseconds is more typical. e.g. trans-stilbene 70 ps , pyrene 100's ns. Of course there are exceptions particularly when quenching by electron transfer occurs. So most excited states do have time to respond to their new potential before they decay. – porphyrin Jan 30 '17 at 21:52
• If you want to simulate emission spectroscopy, you should optimize your excited states... (hint: stokes shift etc) – Fl.pf. Jan 31 '17 at 10:32

## 1 Answer

According to the Franck-Condon principle which you are implicitly referring to, absorption is indeed very fast compared to all other processes.

If you are looking for time scales of photophysical processes, I can suggest you for example B. Valeur's book "Molecular Fluorescence: Principles and Applications", chapter 3 (Characteristics of fluorescence emission). You'll find this list of characteristic times:

• absorption: $10^{-15}$ s
• vibrational relaxation: $10^{-12} - 10^{-10}$ s
• $\ce{S_1}$ lifetime (fluorescence): $10^{-10} - 10^{-7}$ s
• intersystem crossing: $10^{-10} - 10^{-8}$ s
• internal conversion: $10^{-11} - 10^{-9}$ s
• $\ce{T_1}$ lifetime (phosphorescence): $10^{-6} - 1$ s

as well as examples of molecules with their photophysical data.

For chemical processes, it depends on many things, such as concentration, diffusion rates... and you would need to precise your question (type of photochemical reaction, type of quenching, etc.).

• True, thanks for sharing. That's what I was looking for, I will accept this answer. – Felipe S. S. Schneider Feb 1 '17 at 16:03