Subject: SUMMARY: TS imaginary freq. value

From: val <[email-masked]>
Date: Thu, 04 Mar 1999 21:41:50 +0300

Dear CCL'ers,

 The original question and the replies received up to now are shown 
 below. My big thanks to to Stefan Fau, Alexander Bagatur'yants,
 Marcel Swart and E. Lewars.

    best regards,
    Valentin.

--------------------------------------------------q---

I have got a Transition State (TS) structure with unusually low 
imaginary frequency value, about 17 CM**-1.
However, the gradient convergence criterion is satisfied, Hessian
is correct (only one imaginary freq.), visualization of the normal
mode gives right picture and Intrinsic Reaction Coordinate 
optimization connects the TS to reactants and products.

Is this enough to proof that the saddle point is true TS of the 
reaction of interest?

Does it make any sense to take into account the value of the 
imaginary frequency? In what range should it be for the most
common cases?

Any references on TS imaginary frequency value interpretation
are really welcome.

Thanks in advance, I will summarize as usual.

sincerely yours,
Valentin.
------------------------------------------------------

--------------------------------------------------r1--
Dear Valentin,

I think you did anything to ensure that your structure IS a TS 
connecting your educts and products. You certainly did more than some 
people do in recent publications. If you are interested in exact values 
for the lower frequencies, you need a geometry that is very good, i.e. 
the displacements should be inside the limits, too. (With Gaussian DFT
you can increase the integration grid to "ultrafine". A subsequent 
optimization with this grid needs only a few cycles to converge.)

The absolute value of your imaginary frequency is quite low, most bond 
breaking processes have values in the range of hundreds i cm^-1. We know 
values of 20i cm^-1 from rotations of M-CH3 or M-PH3 bonds, but since 
you did the IRC you are on the safe side.

The value of the imaginary frequency gives you information about the 
curvature of the potential energy surface at the TS along the imaginary 
mode. It is a local quantity that may be used to guess the shape of the 
"energy wall" separating educts and products, but the energies of the 
optimized points of your IRC give the same information quantitatively.

In my view an imaginary frequency of 17i cm^-1 is not very different from 
a "normal" frequency of 17 cm^-1. It is just imaginary instead of real.

Stefan
______________________________________________________________________
Dr. Stefan Fau
Fachbereich Chemie, AK Frenking
Philipps-Universität Marburg
35032 Marburg, Germany
[email-masked]
------------------------------------------------------

--------------------------------------------------r2--
Dear Valentin,

Certainly, this is the correct TS that correspond to the reaction that you
are interested in.

The region of TS is a domain of strong anharmonicity. In addition, the
nature of your TS may be different. For example, two valleys can differ only
in the conformation(s) of the reacting molecule(s). The other reason for the
extreme flattnes of your PES in the TS region can be associated with a low
activation barrier, at least on the one side of your reaction.

Anyway, there is no apparent restriction on the value of the imaginary
frequency characterizing a TS as well as in the case of a real frequency of
a minimum (or a TS).

Best wishes,
Yours

Prof. Alexander Bagatur'yants
Photochemistry Center, Russian Academy of Sciences
ul. Novatorov 7a, Moscow, 117421 Russia
Phone: (007-095)-936-2588 Fax: (007-095)-936-1255
E-mail: [email-masked]
Home page: http://www.icp.rssi.ru/eng/bagat/bagat.htm
------------------------------------------------------

--------------------------------------------------r3--
A normal imaginary frequency is of the range of 300 - 800 CM**-1,
but the value depends much on the QM method you use.
Do you use semi-empirical (i.e. AM1/PM3) methods ?
This because I have some limited experience with TS's in MOPAC93,
and if I remember correctly, the TS frequency was smaller than with ab
initio methods.

Sincerely,

Marcel Swart.

==============================================================
Marcel Swart

Theoretical Chemistry (MSC)
Molecular Dynamics (GBB)

University of Groningen
Chemistry Department
Room 18.45
Nijenborgh 4
9747 AG Groningen
The Netherlands
tel : 31 - (0)50 - 3634377
fax : 31 - (0)50 - 3634441

E-mail : [email-masked]
WWW: http://theochem.chem.rug.nl/~marcel/
==============================================================

------------------------------------------------------

--------------------------------------------------r4--
1999 Feb 23
REPLY TO VALENTIN ANANIKOV, Re IMAG FREQ (BELOW)

Hello, If you have an imaginary frequency (one and only one), then *at that
level of theory* the species is a transition state (a first-order saddle point).
So your structure is indeed a TS (at that level of theory). QED.
 As you point out, 17i ("-17") cm-1 seems small for an imag freq. It's probably
OK, however, for a low-energy rotation; you don't say what the vibration
(rotation?) corresponds to--an almost free rotor (low-energy torsional barrier),
or pyramidalization of a group that is barely flat? In any case the small value
of the imag freq indicates the barrier to the reaction represented by the TS
is very low. The reactant going to this TS hovers on the edge of existence
-- at the level of theory that you used (for a rotation or pyramidalization
the "reaction" is trivial and represents just a conformational change).
You do say that visualization and an IRC job confirm it's the TS you want.

  TS freqs are commonly in the range of roughly 300i -- 1500i cm-1, with the
bigger values involving H migration (as in HNC --> HCN).

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