Subject: Imaginary frequency and rate constant

From: "Ivar Martin" <[email-masked]>
Date: Wed, 24 May 95 11:12:30 EST

Dear CCL people,

Last week I posted the question about imaginary frequency at TS
and rate constant calculation. The original question was:

     As it is expected, MOPAC calculates one and only one negative
vibrational frequency at TS. The value lies (-300 - -150 cm-1). Is it 
correct to use this frequency as pre-exponent factor (frequency factor) in 
Arrhenius rate constant equation? The reaction I study is C-C single bond
forming (or splitting) reaction.

     I got several responses from people who asked me kindly to 
     share the answers I might get:
                                     J. Pat Cannady
                                     Rene Fournier
                                     Jerzy M Rudzinski
                                     Robert W. Zoellner
                                     Emiel Rorije
                                     Henk Verhaar
                                     Sanja Sekusak

     Unfortunately, I didn't get any explanation to this question
from CCL. What I only have is my own understanding that the
exponential part of the Arrhenius rate constant equation gives the
number of molecules in TS.

  (N_TS/N_GS)=exp[-deltaG#/(R*T)]

       where N_TS - number of molecules in transition state
             N_GS - number of molecules in ground state

If the imaginary frequency is the measure of translational
movement of atoms bearing this imaginary vibrational mode in TS,
why not to use this frequency as pre-exponent frequency factor
in Arrhenius equation!

Also, I have the opinion of Prof. Arvi Rauk from the University of 
Calgary who said: ... the imaginary frequency only measures the curvature 
of the reaction coordinate at the transition state. It may 
be used in the Bell formula for a quantum mechanical 
tunnelling correction to the classical rate which would only 
be a funcion of the barrier height ...

I'm pretty sure there should be people in CCL who could give
exhaustive explanation.
_______________________________
Dr. Ivar Martin
Department of Bioorganic Chemistry           tel: +372 2 526510
Institute of Chemistry                       fax: +372 2 536371
Akadeemia tee 15 EE0026                   e-mail: [email-masked]
Tallinn, ESTONIA

---

From: <[email-masked]>
Date: Wed, 24 May 1995 16:22:11 +0200 (DFT)

On Wed, 24 May 1995, Ivar Martin wrote:

>  .....     
>   .....    
> Also, I have the opinion of Prof. Arvi Rauk from the University of > If the imaginary frequency is the measure of translational

BDear Colleague,

The existence of an "immaginary frequency" at the TS is a reformulation
of the fact, that the enrgy has a maximum (and not a minimum) along a
given (normal) coordinate. Although it is expressed in frequency units,
it is really a measure of the curvature of that point only, and has
nothing to do directly with any reaction rate. The "quasi-termodinamic"
formulation of Eyring's "absolute reaction rate" or "transitiuon state"
theory was a great-scale misunderstanding, which caused very much harm
to science. 20 years ago I wrote: "The activated complexes are not true
chemical species, do not fulfil the conditions defining a canonic
ensemble, and therefore cannot be considered as independent subjects of
the canonic distribution." (J. Chem. Phys. 60, 2564, 1974). This also
means that there is no meaning to attribute any termodynamic quantities
to the TS.

This does not mean that there can be no modern variants of transition
state theory, which are free of the deffects of the old one.

Best regards,

Yours sincerely,

Prof. Istvan Mayer

            e-mails: [email-masked]  
                     [email-masked]
                     [email-masked]

Central Research Institute for Chemistry
of the Hungarian Academy of Sciences
H-1525 Budapest, P.O.Box 17
Hungary