What's mean the magnitude of the imaginary frequency of a transition state ?

zako

Hi everybody,
* I would like to ask about the meaning of the magnitude of the imaginary frequency of a transition state and what's important about it?
* What does mean imaginary frequency should higher than 100 cm-1?

zako

Thank you very much dear liyuanhe211

liyuanhe211

A transition state should have one and only one imaginary frequency (i.e. negative force constant) while the derivative is zero. One should verify the structure met those conditions and the mode corresponds to the imaginary frequency has the desired vibration mode. In most cases, looking at the vibration of the imaginary frequency can tell you whether the TS is correct (to be sure, do an IRC).

The magnitude of the imaginary frequency tells you how steep the curve drops around the highest point (basically so, also affected by the mass term). Most chemical reactions involve one or more bond-breaking / bond-forming, and most covalent bonds are quite "stiff", thus the top of the curve along the direction of the imaginary frequency should be quite steep. A magnitude less than 100 cm-1 corresponds to a very flat (soft) surface, thus one says that the TS you found is most likely not a bond-changing event.  

However, do not just look at the numbers. In my experience, it's not that rare to have a correct, bond-changing TS to have an imaginary frequency with magnitude less than 100 cm-1 (I even have one less than 10 cm-1 and later confirmed to be correct). These processes usually have (at least) one side of the minima having electronic energy very close to TS, making the area around the TS relatively flat.