Summary: correlating in silico TS energies with ee values

Thanks for everyone for their replies.  The following is a summary of the
 responses
 given to my initial question.  In short I had asked if there were any methods
 available
 to correlate experimental ee values with TS energies obtained in silico.  Hope
 this can
 help others as well.
 Hi Joe,
 The critical number you would need is the activation energy, i.e. the difference
 between
 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.
 http://www.shodor.org/UNChem/advanced/kin/arrhenius.html
 Then, you would need to test the correlation of the calculated activation
 energies with
 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
 respective
 reaction rates. If thermodynamically controlled, then the product energies
 (energies of
 reaction) should control the product ratios. This approach has been applied in a
 paper
 by: Malwitz, N., Reaction Kinetic  Modeling from PM3 Transition State
 Calculations, J.
 Phys. Chem., Vol 99,
  No. 15, 1995 p. 5291
  Regards,
  David Gallagher
  CAChe Group, Fujitsu
  Portland, Oregon
 Hi,
 This comes out of the Eyring or Arrhenius equations, which
 you find in any basic physical chemistry text book.  Arrhenius: k = A
 exp(-Ea/RT); I
 prefer Eyring, but they give the same results when you're looking at relative
 rates.
 As a first approximation assume that the constant(s) are equal for both paths
 (usually
 including the entropy, a fairly strong approximation...).  I assume that you're
 looking
 at an irreversible step, then the ratio of products, r, can be obtained simply
 as the
 ratio of rate constants, r = exp(DEa/RT), where DEa is the difference in
 transition
 state energy (all the constants disappear in the division).  When you have the
 ratio,
 the ee is easily obtained from ee = (r-1)/(r+1), which is the excess divided by
 the
 total, the definition of ee.
          /Per-Ola
 Joe,
 The enantiomeric excess can be expressed as a ratio which means that you should
 be able
 to predict the ration from using the dG values at the dtationary point (TS).  At
 a
 minimum, you need to do frequency calculations in  order to obtain dG values.
 You know
 that one can consider that a pair of diastereomeric transition states (and they
 have to
 be to have different TS energies as enantiomeric TS have equivalent energies)
 can be
 considered to be an equilibrium reaction so K# = exp[-DG/RT]. So you can compare
 TS
 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
 isomers.
  I hope this helps...
  Mark
 Hi,
 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
 calculate
 that as the end of an IRC run (or DRC with some handwaving), depending on the
 program
 you are using. Then use the apparent DeltaEdagger in the Arrhenius equation.
 Or use
 the delta(deltaEdagger) as a measure of the relative ratios of the isomers.This
 should
 lead (at worst) to a prediction of the predominant isomer, assuming kinetic
 control of
 the reaction. Delta(deltaE) (from the two ends of the IRC) can be used as a
 prediction
 of the predominant isomer, assuming thermodynamic control.
  Sb
 Hi,
 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
 obtained
 under a kinetic control or under thermodynamic control. If the experimental
 conditions
 are such that you obtain the thermal equilibrium for your products then you
 should use
 their energies to calculate their proportions. (Bearing in mind that enantiomers
 have
 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
 rate
 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
 term :
 [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:
 [A]/[B]=exp(-(Delta_E(TS-A)-Delta_E(TS-B))/RT)
  hope this helps,
  Paul.
 Joe,
         Please take a look at the following publication from Ken Houk's group.
         I did the calculations for stereoselective hydroborating agents - mono
 and
 di-isopinanylcampheylboranes.  We used a hybrid QM/MM method at that time due to
 the
 difficulty of using a complete QM approach for the system. If you read the paper
 and
 references carefully, you should see some formulas showing how to convert
 relative
 energies into enantiomeric excess values.
         There is also an earlier publication (of which I am a co-author) -
 should be
 Tetrahedron, or something similar listed in the Science paper.  Sorry, I do not
 a copy
 of the paper with me at the moment.
         Contact me or Ken Houk (UCLA) if you have further questions.
         Regards,
         Jim Metz