1) Read the Abstract and Introduction of a paper by Allen, Csaszar, and Horner "The Puckering Inversion Barrier and Vibrational Spectrum of Cyclopentene. A Scaled Quantum Mechanical Force Field Algorithm" and summarize what was known about the experimental geometry of cyclopentene in 1992. Express the experimental puckering barrier from a semirigid bender analysis in kJ/mol units. Why did these scientists use MP2 geometry optimization instead of PM3 geometry optimization?
2) You practiced setting up and running what seemed like a simple semiempirical calculation. Specifically, you requested that the program PC GAMESS / Firefly take your input structure for cyclopentene, and optimize it using a second derivative-based method. In this case, the Hessian is calculated numerically at the starting geometry. During the optimization, the first step is taken according to a Newton-Rhapson method. However, in subsequent steps, the Hessian is not recomputed based on the current geometry, but updated based on a previous Hessian and current forces using the Powell scheme (instead of BFGS this time). The calculation continues like this until the forces become smaller than the threshold values (e.g. MAXIMUM GRADIENT reaches below 0.0001). The calculation also stops if the number of optimization steps reaches the maximum number (NSTEP=20 by default). When started in the region near the minimum, such calculations are expected to converge fairly rapidly to the minimum. However, a closer inspection suggests that the minimum was not found in this case; the calculation ended with a message:
1 ***** FAILURE TO LOCATE STATIONARY POINT, TOO MANY STEPS TAKEN *****
UPDATED HESSIAN, GEOMETRY, AND VECTORS WILL BE PUNCHED FOR RESTART
**** THE GEOMETRY SEARCH IS NOT CONVERGED! ****
Carefully examine the progress of the optimization with MOLDEN. Notice that you can click on the points along the geometry optimization path to see the molecular geometry at that point. Carefully analyze the output file of your calculation with a text editor. Notice that before the first optimization step is being taken, the Hessian is calculated numerically (e.g. by finite difference method) and a large part of the input reports about the calculation of the Hessian. The actual optimization starts after a line
...... END OF NUMERICAL HESSIAN CALCULATION ....
Read the $STATPT section of the GAMESS manual, draw your conclusions about why the optimization failed, and change your input file so that the calculation will be successful. You should see a message ***** EQUILIBRIUM GEOMETRY LOCATED ***** in a successfully finished calculation. You should be able to come up with at least two independent ways to fix the problem with cyclopentene.
Similarly, make the vinylcyclopropene calculation work. Based on the heat of formation values for the optimized geometry for the reactant and the product, calculate PM3 isomerization energy for this reaction. Compare the result with the experimental data. Discuss the accuracy of PM3 in calculating the molecular structures and the isomerization energy in this example.
1) Read pages 375-377 of the review paper Allylic Strain in Six-Membered Rings and the Introduction Chapter of The Influence of Allylic Strain on Structure and Reactivity. Write an essay that summarizes what is a allylic strain. Build initial structures for axial and equatorial forms of 1,6-dimethyl-cyclohexene and optimize each at PM3 level. Is this allylic strain sufficient for guiding the stereoselective addition to the double bond? Justify your answer.
2) The successful application of semiempirical methods requires a good understanding of their limitations. For example, before starting a large research project that aims at the prediction of isomerization energies of complex organic molecules, one should ask which of several available semiempirical methods is most suitable. As the speed of different semiempirical methods is quite similar, the accuracy for a particular type of problem is most important. Test the accuracy of AM1 and PM3 semiempirical methods for the isomerization of branched organic molecules into less-branched isomers. For this task, pick total of six reactions from Tables 3 and 5 of the paper Performance of B3LYP Density Functional Methods for a Large Set of Organic Molecule by Tirado-Rives and Jorgensen that best represent reactions where branching changes significantly. Optimize each structure using your choice of a minimization method. You can use any program of your choice, the instructions below assume that you are using PC GAMESS / Firefly. Verify that the calculation converged successfully by checking the output from Unix command grep EQUILIBRIUM filename.out. The Unix command grep will search the file 'filename.out' for word 'EQUILIBRIUM' and return lines containing this word. If the optimization converged, you should see:
1
If the geometry optimization failed, change your input (e.g. construct a better z-matrix by manually adjusting bond lengths/angles, or by using a different optimization method based on what you learned from the Level 1 assignment) until the geometry search converges. If the geometry optimization converged successfully, check the value for the heat of formation for the optimized structure. This time, search for 'HEAT' with grep. You will see several values corresponding to structures along the search path; the last value corresponds to the optimized structure. The 'HEAT OF FORMATION' is the standard enthalpy for this molecule. Calculate isomerization enthalpies for each reaction for AM1 and PM3 methods. Calculate the absolute error based on your AM1 result and the experimental data. Calculate the absolute error based on your PM3 result and the experimental data. Calculate the mean absolute error for AM1 and PM3. Make your recommendation about the most appropriate computational method for studying isomerization reactions in larger molecules based on your result and data in the paper by Tirado-Rives and Jorgensen.
As discussed in the review Allylic 1,3-Strain as a Controlling Factor in Stereoselective Transformations by Reinhard Hoffmann one of the challenges of organic synthesis is stereoselective creation of new stereocenters by transforming a prochiral center in reactant into a chiral group in the product. In general, prochiral center such as sp2 carbon can be approached from either side, and two isomers will form. If the probability of approach from to sides are the same, a racemic mixture is obtained. If the probability of approach form one side is higher than the probability of approach from the other side, the product is enriched in one of the isomers. A successful stereoselective creation will yield a large excess of the desired isomer.
Reaction involving nonchiral reactants in non-chiral environment in the absence of chiral catalysts or polarized light always yields a racemic mixture. However, stereoselective creation of a new stereocenter in a molecule that already contains one stereocenter is possible. One elegant approach here takes advantage of allylic strain.
The Claisen rearrangement is a [3,3] sigmatropic rearrangement in which an allyl vinyl ether is converted to a carbonyl group concomitantly with the formation of a new carbon-carbon bond. In an analogous thio-Claisen rearrangement, allyl vinyl thioether rearranges into sulfoxide. Claisen rearrangement is an efficient and frequently used strategy for creation of new carbon-carbon bonds.
Consider the stereoselective synthesis of a methyl ether of 2-[(1S)-1,2,2-trimethylpropyl]-4-pentene(dithioic) acid from (S)-3,4,4-trimethyl-1-(methylthio)-1-(2-propenylthio-(Z)-1-pentene. Build the structure of the reagent in several conformations and minimize each using either PM3 method in PC GAMESS / Firefly, or the PM3/PDDG method in BOSS (see the BOSS user manual). Identify conformers with a geometry that supports the thio-Claisen rearrangement; try to find one reactant conformation that would lead to the formation of (1S,2S) diastereomer, and one reactant conformetion that would lead to (1S,2R) diastereomer. Calculate the energies of these "near attack conformers" with respect to the lowest energy structure. In any case, you will need a reasonably good starting geometry; your optimizations are likely to fail if the initial geometry is too far from a reasonable structure.
Build the two possible diastereomers (1S,2S) and (1S,2R) of the reaction product and mininimize their structures. Calculate the energy difference between two diastereomers and estimate which is the thermodynamically more favored diastereomer. Calculate the isomerization enthalpy and discuss if the reaction is expected to be enthalpically favorable. Estimate the equilibrium constant assuming that molar volumes and entropies of the reactant and product are the same. Briefly discuss the utility of computational modeling for planning stereoselective transformations based on allylic strain