Subject: SUMMARY: How to measure stability?

From: "T. Koch" <[email-masked]>
Date: Thu, 14 Dec 1995 17:25:36 +0100 (MET)

Dear netters,

some times ago I posted a question concerning the stabilty of computed 
molecules.
I received some answers and would like to thank all who responded. Now I 
post the answers I got. If there are any additional opinions on this 
topic I would appreciate to receive your mail.

The original posting was:

  I have a question which should be of considerable interest for 
computational chemists. The question is: How do I measure computationally 
the stability of organic molecules?
  I study some molecules which presumably have not yet been prepared. And I 
would like to know if these molecules have a chance to exist. What I did 
so far is the most simple and obvios method: I compared the absolute 
electronic energy with the same quantity on a known and more or less 
stable isomer. But from the results I got I think that this is only a 
crude approximation on a "measure" of stability and reactivity.
  What I didn't examine yet but could be quite sensible (I think) is doing 
a CI or MCSCF calculation and looking at the energy gap between the 
frontier orbitals and comparing it to known isomers.
  Another way could be an examination of the computed IR-spectrum. Are 
there very low frequencies (shallow dips in the potential engergy 
surface) which could lead to "new" molecules?
  Is there a way to determine "centers of reactivity" ?

The answers are:

From: Ernest Chamot <[email-masked]>

>I have a question which should be of considerable interest for 
>computational chemists. The question is: How do I measure computationally 
>the stability of organic molecules?

Actually, your initial approach should give you a decent estimate of the
thermodynamic stability (especially the RELATIVE thermodynamic stability),
but as you point out it is a poor measure of the KINETIC stability/reactivity:

>so far is the most simple and obvios method: I compared the absolute 
>electronic energy with the same quantity on a known and more or less 
>stable isomer. But from the results I got I think that this is only a 
>crude approximation on a "measure" of stability and reactivity.

This thermodynamic stability would give you a good idea of whether the
reactions you are proposing to synthesize the new compound will work, but
not whether the new compound will be isolable before conversion into
something else.

In the past I've considered each bond individually and calculated the energy
barrier for each bond homolysis in systems where bond homolysis was the only
reasonable mode of decomposition.  You could similarly consider all
reasonable reactions (homolysis, heterolysis, cyclic ring reversions,
dimerizations, etc.) one by one, but if you have a very complicated system
this could be daunting.  (Using CI or MCSCF may get you a more accurate
answer, but if it reduces the number of possibilities you can test, I think
it would reduce rather than increase your confidence that you understand the
stability of your system.)  What one needs, of course, is a good enough idea
of the entire potential energy surface, to be able to identify the
lower(est) saddle points serving as barriers between your molecule and
conversion into some other isomer/products.  This is sort of what you would
be doing with:

>  Another way could be an examination of the computed IR-spectrum. Are 
>there very low frequencies (shallow dips in the potential engergy 
>surface) which could lead to "new" molecules?
>  Is there a way to determine "centers of reactivity" ?

I think it would be a good idea to pursue, but not just looking at the
lowest energy frequencies: one vibrational mode may start out steeper than
the others, but crossover a transition state to some other products before
going through as high a maximum.  The low frequencies would be good starting
points though.  I haven't tried following a specific eigenvector from a
ground state as such (I'm usually either starting from a transition state or
near to a stationary geometry), but I would think Intrinsic Reaction
Coordinate (or DRC) searches following each of the lower frequencies from
the computed IR-spectrum would be a good way to probe for the preferred
"centers of reactivity" without having to explicitly define the center of
reactivity a priori.

From: Pascal HEBANT <[email-masked]>

>  Is there a way to determine "centers of reactivity" ?
 You can use Fukui functions that are easy to compute from HF or DFT
calculations. see among other references  :

J. L. Gázquez, Hardness and softness in Density Functional Theory  in
Chemical Hardness , Coll. Structure and Bonding (Springer-Verlag, Berlin,
1993)

R. G. Parr et W. Yang, Density Functional Theory of atoms and molecules ,
(Oxford University Press, New York, 1989)

P. K. Chatteraj et R. G. Parr, Density Functional Theory of chemical
hardness  in Chemical Hardness , Coll. Structure and Bonding
(Springer-Verlag, Berlin, 1993)

From: Jason Lye <[email-masked]>

Our group has recently begun to look at predicting the regioselectivity of 
certain nucleophilic and electrophilic reactions.  Most techniques use a 
weighted frontier orbital approach.  Some references that you might want to
read are:

K. Fukui, T. Yonezawa, C. Nataga, Journal of Chemical Physics, Vol 26, No.4
 Pages 831-841, (1957)

K. Fukui, T. Yonezawa, C. Nataga, H. Shingu, 
Journal of Chemical Physics, Vol 22, No.8, Pages 1433-1442, (1954)

K. Fukui, T. Yonezawa, C. Nataga, Bulletin of the Chemical Society of Japan,
Vol. 27, Pages 423-427, (1954)

Also, we have learned that other factors besides frontier orbital density are
often involved.  These may include steric effects and also electrostatic 
repulsion/attractions between the two reagents.

From: "E. Lewars" <[email-masked]>

With regard to the recent question by Thorsten Koch "How do I measure the
stability of organic molecules? ...I compare absolute electronic energy with...
a known and more or less stable isomer."  There were also queries about the
relevance of frontier orbitals and calculated IR frequencies.

  *Stability* can refer to (1) the tendency of an isolated molecule to react,
perforce by isomerizing or by dissociating, or it can refer to (2) the tendency
of a molecule to react with another (possibly identical) molecule.

  Considering (1):
  The calculated freqs (i.e. the calc IR spectrum) provide information about
the reactivity of the isolated molecule.  If there are no imaginary ("negative")
freqs, the molecule can exists *as far as that particular level of calc is
concerned*, that is, it is a relative minimum on the potential energy surface;
it sits in a well and jiggles its all-real vibrational modes, escaping from
the well at a rate that, ignoring wierd things like tunneling, depends (at
least approximately) on the height of the barrier separating it from the
nearest other well (or nearest plateau, for dissociation).
  A low-freq vibration corresponding to bond cleavage should make one suspect
that at some higher computational level this freq will become imaginary, and
the bond will actually break.  A low-freq "vibration" that coresponds to a
torsional mode would, if it were coaxed into being imaginary at a higher level,
correspond to a conformational change: the molecule might still exist, but might
not, say, be flat as in the input geom, but rather puckered (e.g. flat D4h
cyclobutane may prefer to be D2d).
  The stability of a real molecule (a relative minimum) can be quantified by
calculating the rate at which it goes over the lowest barrier separating it
>from its isomerization or dissoaciation product(s).  Of course, if it's
substantially the lowest-energy species on the PES then you don't have to worry
about this.  Stability is most intelligible if expressed as half-life at some
temperature (like room temp, where most of us live).

  Considering (2):
  Comparison of the frontier orbitals (HOMO and LUMO) with those of known,
similar molecules is probably wothwhile, since reaction with electrophiles
and nucleophiles will be governed (to the ubiquitious first approximation)
by the energies of these orbitals.

Some references to calulations on the stabilities/existence of exotic organic
molecules are:
Oxirene and substituted oxirenes--
Vacek,..., Schaefer,..., J Phys Chem 98 (1994) 8660.
Fowler, Galbraith, Vacek and Schaefer, J Am Chem Soc 116 (1994) 9311.
Scott, Nobes, Schaefer and Radom, J Am Chem Soc 116 (1994) 10159

N6 (e.g. hexaazabenzene), N8, etc--
Engelke, J Am Chem Soc  115 (1993) 2961
Engelke, J Org Chem 57 (1992) 4841
Engelke and Stine, J Phys Chem 94 (1990) 5689 ["Is N8 Cubane Stable?]
Engelke, J Phys Chem 94 (1990) 6924                            /|\
Engelke, J Phys Chem 96 (1992) 10789                            |
Engelke, J Phys Chem 93 (1989) 5722                             |
                                                             STABLE
Benzooxirene--
Lewars, THEOCHEM 1996

CO2 polymers--
Lewars, THEOCHEM 1996

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