*From*: Joe Harriman <s808o/at/unb.ca>*Subject*: Summary: correlating in silico TS energies with ee values*Date*: Thu, 10 Jun 2004 10:43:23 -0300

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