Subject: Re: CCL:the meanings of the magnitude of the imaginary frequency?

From: elewars <elewars)at(trentu.ca>
Date: Wed, 13 Aug 2003 12:09:32 -0400

2003 August 13

Hello,

Re "...any meaning for the magnitude of the imaginary frequency at the transition
state."

The magnitude of a frequency is an indication of the curvature of the PES along
the direction corresponding to the normal-mode vibration for the freq. If the
curvature is strong, you can expect a large freq, if it is gentle (PES along that
direcvtion almost flat) you can expect a low freq. The imag. freq. corresponds to
the curvature in the transition state region along the reaction coordinate. In the
reaction A--> TS -->B, a low A --> B barrier tends to correspond to a small
curvature along the reaction coord. in the region of the TS, and so the imag.
freq. will be likely to be small. Conversely, a big A --> B barrier tends to
correspond to a large reaction coord. curvature near the TS, and to a large imag.
freq. But since vibrational freqs. are the *mass-weighted* eigenvalues of the
force constant matrix (second deriv. matrix, "curvature matrix") the masses of the
atoms involved in the vibration also affect the freqs. A freq. (imaginary or
otherwise) corresponding to movement of an H atom will be bigger than almost any
other freq. (look at the equation for a simple harmonic oscillator).

You could do a few calculations on TSs  for reactions of known activation E to
check out the truth of the above.

People sometimes try to judge the stability of a potentially kinetically unstable
molecule (with no imaginary freqs) from the value of the lowest-frequency
vibration corresponding to a decomposition mode.

In a very rough way (i.e. other things being about equal) a lower imag. freq
probably corresponds to a smaller barrier. Thus the B3LYP/6-31G* freq for
cyclic-C6H6--> 3 HCCH is 617i cm-1, while that for cyclic-N6 --> 3N2 is 323i cm-1
(barriers ca. 740 and 1 kJ mol-1).

E. Lewars
===========

wangyan wrote:

> Dear ccler,
>
> I want to know whether there is any meanings for the
> magnitude of the imaginary frequency at the transition
> state. It is well known that the more the stretching
> frequency of the zeolitec OH group, the stronger the
> O-H bond. Is it still suitable for the imaginary
> frequency ? Does it mean that the transition state
> which have higher imaginary frequency is more stable
> than that which have low imaginary frequency ?
>
> any information is welcome. thanks in advance.
>
> best regards
>
> wangyan
>
> !!!!!!!!!!!!!!!!wangyan
> !!!!!!!!!!!!!!!!wangyanemail)at(dicp.ac.cn
> !!!!!!!!!!!!!!!!!!!!2003-08-13
>
> -= This is automatically added to each message by mailing script =-
> To send e-mail to subscribers of CCL put the string CCL: on your Subject: line
> and send your message to:  CHEMISTRY)at(ccl.net
>
> Send your subscription/unsubscription requests to: CHEMISTRY-REQUEST)at(ccl.net
> HOME Page: http://www.ccl.net   | Jobs Page: http://www.ccl.net/jobs
>
> If your mail is bouncing from CCL.NET domain send it to the maintainer:
> Jan Labanowski,  jkl)at(ccl.net (read about it on CCL Home Page)
> -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+