The isomerization of chorismate can be envisioned to happen by a few different mechanisms. Maybe the C-O bond breaks homolytically first, and the allyl radical attaches to the six-membered ring? Maybe the bond breaking and bond making are concerted? In the latter case two different transition states are possible depending on the orientation of the vinyl ether arm. If the conformation of the vinyl ether arm before the reaction is such that the carboxylate points toward the larger portion of the six-membered ring, the bicyclic transition state is said to be in the endo form. If the carboxylate points toward the CH between the bond-forming and bond-breaking centers in the the bicyclic transition state, the configuration is said to be exo. Because the endo and exo form cannot inter-convert without breaking a (partial) bond, they are geometric isomers. If we plan to use transition state analogs to inhibit chorismate mutase, it is important to know which isomer forms in the active site of the enzyme. We will assume for a moment that the form in he enzyme active site is the lowest energy form. Thus, we need to determine the structures and energies of the two alternative transition states. Conversely, experimental inhibition studies with different stereoisomers of transition state analogs can be used to elucidate the stereo-chemistry of the enzymatic transition state.
Locating reaction transition states can be difficult, and the key usually is in starting in the point that is not too far from the transition state. With some effort, one can manually change the structure of chorismate to look like a transition state, and then locate the transition state for the chorismate isomerization using MOPAC and the PM3 method. A computational chemistry program Gaussian offers a more convenient method, called the Synchronous Transit-Guided Quasi-Newton (STQN) method in which the the initial structure of transition state is interpolated from the structures of the reactant and the product. However, the structures of chorismate and prephenate that you have optimized are not well-suited for such an interpolation because these represent the extended conformations. A conformation near the transition state (a near attack conformation) would be a much better starting point. Because editing and minimization of molecular geometries to generate such near attack conformers is tedious, you can download suitable structures of chorismate and prephenate. Copy these structures into a new file according to instructions at http://www.gaussian.com/g_whitepap/qst2.htm. Use # PM3 Opt=QST2 for keywords to request a QST2 calculation using the PM3 Hamiltonian with Gaussian. Insert appropria te title sections, such as Chorismate ready to react and Prephenate after bond formation. Specify -1 for charge and 1 for the spin multiplicity for each structure; there is no redundant input in our case. Check that you have appropriately used empty lines between title sections and molecule specifications; there should also be an empty line at the very end of the file. Save this file as chor_prep_qst2.dat. Submit the job by typing into Unix shell g03 < chor_prep_qst2.dat > chor_prep_qst2.log
Open Gaussian log file with MOLDEN by typing molden -A chor_prep_qst2.log and click on the Geom. Conv. button. The graph displays the success of the geometry optimization. You can click on Movie to animate the structural changes during optimization. Examine the final structure of the transition state and record the bond-forming (C-C) and bond breaking (C-O) distances. But how can we be sure that the structure found really is a transition state? This is done by calculating the second derivative matrix: if the structure is a saddle point all its first derivatives must be zero, and all but one second derivative should be positive. The one negative second derivative corresponds to the reaction coordinate and can be visualized as a molecular vibration that takes the reactant into a product. To calculate the second derivatives and vibrational frequencies for the optimized structure with Gaussian, open the ZMAT Editor in MOLDEN, select Gaussian, and select Submit. Select -1 for Charge and edit the first Keyword line to read: #P PM3 Freq. Give a meaningful Job Name, such as Chor_TS_PM3, and Submit the calculation. Hit OK twice to acknowledged the job setup and submission. You may close MOLDEN. The calculation will take less than a minute. Verify that the calculation completed (tail Chor_TS_PM3.log) and open the frequency job with MOLDEN (molden -A Chor_TS_PM3.log). Change the Draw Mode to Solid: Ball & Stick and hit the Norm. Mode box. Change the Scale Factor to 0.2, hit Enter, and click on the first (negative) frequency. Observe the molecular vibration that takes chorismate into prephenate.
In semi-empirical calculations, the heat of formation of the transition state is listed as "Energy=" in the Gaussian log file. You can get the value by typing grep 'Energy= ' Chor_TS_PM3.log into the Unix shell. Gaussian reports energies in Hartrees per particle; multiply this value by 627.51 to get the answer in more familiar kcal/mol units. Using this value, and the heat of formation of chorismate, calculate the activation energy.