Summary: correlating in silico TS energies with ee values
- From: Joe Harriman <s808o/at/unb.ca>
- Subject: Summary: correlating in silico TS energies with ee
- Date: Thu, 10 Jun 2004 10:43:23 -0300
Thanks for everyone for their replies. The following is a summary of the
given to my initial question. In short I had asked if there were any methods
to correlate experimental ee values with TS energies obtained in silico. Hope
help others as well.
The critical number you would need is the activation energy, i.e. the difference
the transition state energy and the reactants ground state energy (ideally free
energies including the entropic term). This should correlate with the energy of
activation (Ea) from the Arrhenius equation.
Then, you would need to test the correlation of the calculated activation
some experimentally-derived numbers to:
1) establish that the model and theory-level does reasonably reproduce your
experimentally observed results
2) to create a 'calibration' equation to more accurately estimate
activation energies for new reaction paths
If kinetically controlled, then the product ratios should be related to the
reaction rates. If thermodynamically controlled, then the product energies
reaction) should control the product ratios. This approach has been applied in a
by: Malwitz, N., Reaction Kinetic Modeling from PM3 Transition State
Phys. Chem., Vol 99,
No. 15, 1995 p. 5291
CAChe Group, Fujitsu
This comes out of the Eyring or Arrhenius equations, which
you find in any basic physical chemistry text book. Arrhenius: k = A
prefer Eyring, but they give the same results when you're looking at relative
As a first approximation assume that the constant(s) are equal for both paths
including the entropy, a fairly strong approximation...). I assume that you're
at an irreversible step, then the ratio of products, r, can be obtained simply
ratio of rate constants, r = exp(DEa/RT), where DEa is the difference in
state energy (all the constants disappear in the division). When you have the
the ee is easily obtained from ee = (r-1)/(r+1), which is the excess divided by
total, the definition of ee.
The enantiomeric excess can be expressed as a ratio which means that you should
to predict the ration from using the dG values at the dtationary point (TS). At
minimum, you need to do frequency calculations in order to obtain dG values.
that one can consider that a pair of diastereomeric transition states (and they
be to have different TS energies as enantiomeric TS have equivalent energies)
considered to be an equilibrium reaction so K# = exp[-DG/RT]. So you can compare
Equilibrium constants K#(1)/K#(2) = exp[(DG(2)-DG(1))/RT]
> From this it is easy to see how you could predict ration of optical
I hope this helps...
All other things equal, the energies can be treated as classical
barriers relative to the ground-state for the start of the reaction. I would
that as the end of an IRC run (or DRC with some handwaving), depending on the
you are using. Then use the apparent DeltaEdagger in the Arrhenius equation.
the delta(deltaEdagger) as a measure of the relative ratios of the isomers.This
lead (at worst) to a prediction of the predominant isomer, assuming kinetic
the reaction. Delta(deltaE) (from the two ends of the IRC) can be used as a
of the predominant isomer, assuming thermodynamic control.
First, I am not an expert in this area, and I will be very much
interested in the summary of all the answers that
you will get.
That said, I think that it depends on wether the two enantiomeric products are
under a kinetic control or under thermodynamic control. If the experimental
are such that you obtain the thermal equilibrium for your products then you
their energies to calculate their proportions. (Bearing in mind that enantiomers
the same energy, then you should get ee=0.) Assuming that you are under kinetic
control, I would suggest using the Transition State Theory that states that the
constant is proportional to exp(-Delta_G(TS)/RT). Then you can see that the
concentration of each product is proportionnal to k and thus to this exponential
[A]/[B]=exp(-(Delta_G(TS-A)-Delta_G(TS-B))/RT) If you think that the entropic
contribution is the same for both TS, you can write:
hope this helps,
Please take a look at the following publication from Ken Houk's group.
I did the calculations for stereoselective hydroborating agents - mono
di-isopinanylcampheylboranes. We used a hybrid QM/MM method at that time due to
difficulty of using a complete QM approach for the system. If you read the paper
references carefully, you should see some formulas showing how to convert
energies into enantiomeric excess values.
There is also an earlier publication (of which I am a co-author) -
Tetrahedron, or something similar listed in the Science paper. Sorry, I do not
of the paper with me at the moment.
Contact me or Ken Houk (UCLA) if you have further questions.