Subject: Activation Barrier vs Stability

From: "David Anick" <[email-masked]>
Date: Sun, 18 Jun 2000 20:30:00 -0400

Dear CCL subscribers,

I would be interested in opinions, examples, best guesses,
references, or published data related to the following two
questions.  I will be happy to summarize responses.

(1) I have a unimolecular "rearrangement" reaction for which I
have computed state A ("reactant"), state B ("product"), and
the T-state.  All three are converged to nicely by optimization
programs, with A and B being PES minima and the TS a 1st order
saddle.  The electronic energy of A is below that of the TS by
3 kcal/mol, but when I compute and add in the ZPE's, state A
has slightly higher energy than the TS (by ~ 0.2 kcal/mol).
State B is of considerably lower energy than either, even after
ZPE corrections.
 What does this mean?  Would the molecule quickly tunnel
out of state A at 0 K?  Can I consider A to be a stable (even
if short-lived) state of the molecule, or must it be viewed as
an unstable intermediate or transitional state?  Would it be
correct to use the energy difference between A and B, to talk
about a Boltzmann distribution of a population into states
A and B, or would it all be basically B?

(2) Like (1) in that there is a unimolecular reaction A -> B,
but now both A and B have energies below the TS (including
the ZPE corrections).  My question is, is there a ball park
estimate for the temperature T at which A becomes unstable,
in terms of the activation barrier (i.e. DG =3D G(TS) - G(A)).
I'm open to opinions about how "unstable" should be defined,
but an operational definition could be "half-life of A less than
a minute".  I think this comes down to predicting the pre-
Arrhenius factor, and there will be a wide range answers
depending on the reaction, but I wonder if anyone can offer
gross generalizations, e.g. "small organic molecules for which
such a rearrangement pathway exists, are typically unstable
above temp DG/10kB", or the like.  The DG's (with ZPE included)
I'm looking at are between 2 and 10 kcal/mol, and the reactions
involve the movement of 3 to 6 second row atoms.

Thank you very much for taking the time to read this.  Any
and all responses will be much appreciated.

Sincerely,

David Anick MD PhD
[email-masked]