Select one of the projects below for study. In several cases, collaboration is possible; where it is suggested, you may both submit the same report, which should be written by both of you jointly. (The way research really is done.)

1. The reaction of alkenes with molecular bromine, Br₂, to yield vicinal dibromides, is suggested to proceed by initial formation of a charge transfer complex between bromine and the alkene p-system, followed by conversion of the complex to a cyclic bromonium ion. Thus, in principal, the rates of reaction of alkenes might be controlled by (1) the electrical potential at the p-bond; (2) the energy of the alkene HOMO; or (3) the stability of the bromonium ion. Some relative rate data are tabulated below. Select either (1) and (2), or (3), perform appropriate ab initio, calculations, and test the hypotheses. In your report, Justify your choice of basis set.

2. Trivalent nitrogen in amines is tetrahedral, and thus capable of supporting chirality. Enantiomeric structures typically are not observed, however, because the nitrogen undergoes rapid inversion through a trigonal, planar, achiral intermediate of D_3h symmetry.

1. Compute the barrier to inversion of nitrogen in CH₃NH₂. (Think: what will the transition state look like?)

   Then consider either of the explorations below:

2. It has been suggested that substituents might be found that would increase the barrier, either by stabilizing the tetrahedral structure or by destabilizing the planar one. Select substituents to test each of these possibilities, and repeat the barrier determination. (Think about orbital interactions with the nitrogen unshared pair!)

3. Another possible way of achieving the effects in part (b) is to incorporate the nitrogen into a ring. Explore this possibility with computation.

3. Some experimental evidence exists indicating that whereas PH₃ undergoes pyramidal inversion as described above for NH₃, substitution of successive fluorines for hydrogens may shift the mechanism toward a square planar, C_2v transition state. Explore this possibility with computation.

4. The possible modes of interaction of an adjacent substituent with a carbon reactive intermediate (carbocation, radical, carbanion) are shown below:

Select one reactive intermediate and explore how its stability is affected by X = Li (sigma-donor, pi-acceptor), CH₃ ( sigma- and pi-donor), NH₂ (sigma-acceptor, pi-donor) and CN (sigma- and pi-acceptor). Use a series of isodesmic reactions to generate stabilization energies for each group, relative to X = H.

5. GAUSSIAN and Spartan '04, but not Spartan '02, permit the calculation of ¹³C shielding tensors. In Gaussian, this requires the inclusion of the keyword NMR in a single point calculation that uses an optimized geometry. In Spartan, one clicks the NMR button when setting up the single point calculation. If one compares the tensors for TMS and the molecules of interest, one can predict the ¹³C chemical shifts relative to TMS. The accuracy is typpically about 5 ppm. The minimum basis set capable of giving good results is 6-31G*. Best of all would be a B3LYP/6-31G* optimization, followed by a single point at this basis.

Select one of the sets of molecules below, calculate chemical shifts relative to TMS (which you also will need to calculate), and find experimental data to compare. Discuss any trends in chemical shift.

1. butane, 2-butene, 2-butyne;

2. 1-aminopropane, 1-propanol, 1-fluoropropane.

6. Relative gas phase basicities are tabulated below for several amines, in the form of the energy change for the reaction:

BH⁺ + NH₃ = B + NH₄⁺

1. Compute the energy change with full geometry optimization at the 6-31G* level;

2. Use the C-T solvation module to calculate the solvation energies at this geometry;

3. Correct the 6-31G* energies for solvation; the result should approximate the solution basicities of the amines.

7. The reaction of Fe (II) with H₂O₂ produces hydroxyl radicals resulting in what is called Fenton chemistry. The Fe (II) initially is four-coordinate, and the question has been raised whether it coordinates to a single O of the H₂O₂, becoming five-coordinate, or to both O simultaneously, thus becoming six-coordinate. Using water for the other four ligands, and the 3-21G* basis set in Spartan, try to resolve this question.

8. Select one of the molecules below. Create a Z-matrix, and use it to do a 6-31G* geometry optimization and frequency calculation with Gaussian. Be sure you employ symmetry in the construction of the Z-matrix. Your report should include the Z-matrix and the total energy obtained from the calculation.

• cis-2-butene

• square planar AlCl₄^-

• the anti-conformer of butane

• cyclopentadienyl anion

9. Write isodesmic reactions that could be used to obtain the enthalpy of formation of one of the pairs of molecules below. Carry out the necessary calculations at the 6-31G* level of theory. Compare your result to the experimental value.

• propene and cyclopropane

• 1,3-cyclohexadiene and 1,3,5-hexatriene

10. An advantage of computation over experiment is that one can visualize transition states. Consider the reaction of hydroxyl radical with methanol, which could involve the radical abstracting either a carbon-bound hydrogen or the oxygen-bound one. Using UHF calculations at the 6-31G* level, compute the overall energy change for each process (DH of reaction), remembering zero-point corrections. Then locate the transition state for each abstraction. How do you characterize it as the transition state ? Assuming that the activation energy is accurately represented as the difference between the initial state and the transition state, which reaction should be faster? This project can be done with either Spartan or Gaussian.

11. The enzyme liver alcohol dehydrogenase (LADH) oxidizes ethanol to acetaldehyde. The initial step involves a transfer of a hydride from the a-carbon of ethanol to the 4- position of the pyridinium ring of nicotine adenine dinucleotide (NAD+):

Modeling the entirety of NAD+ would be too much for our computers, but you should be able to handle the nicotinamide portion, with, for example, a methyl on nitrogen in place of the ribose.

Calculate DH for this reaction. Try to locate the transition state; if you succeed, calculate the activation energy for the transfer.

12. Returning to a project from the molecular mechanics page: Copper (II) complexes of N-methylamino acids have the general structure shown below for N-methylalanine.

Are the ligands around copper placed square planar or tetrahedral? With two stereogenic centers, this kind of complex can exist in diastereomeric forms. What is the energy difference between them (this is important because such complexes are sometimes used to resolve racemic amino acids).

The redox potentials of enzymes with Cu++ bound by amino acids depend on the geometry around the Cu. You can employ Koopman's theorem to calculate the redox potential of the diastereomeric complexes (the copper is typically reduced to Cu+).