Chemistry 324 - Spring 2008

The instructions for this assignment can be found here.

To summarize, you were asked to predict the regiochemistry of the following cycloaddition using FMO (note: the left and right-hand products will be referred to as meta and ortho, respectively):

Then you were asked to compare the FMO predictions to those based on calculated energy barriers. Finally, you were asked to look at other properties of the transition states (geometry, electron distribution) that might support the overall picture. My results follow …

Frontier MO Analysis

The key to this analysis is to locate the relevant orbitals, identify the dominant FMO interaction, and predict regiochemistry.

The molecular formulas tell us that each molecule contains two orthogonal pi systems. The two pi systems play different roles - one participates in the cycloaddition, the other is a spectator - but we can be overlook this distinction because each pi system contains the same information. In other words, it doesn’t matter if I select HOMO or HOMO-1 as the donor orbital because

they are degenerate. Likewise, it doesn’t matter if I select LUMO or LUMO+1 as the acceptor orbital. Furthermore, it doesn’t matter if my donor and acceptor orbitals are orthogonal because this won’t change the outcome of my analysis.

Some caution is still required. I should actually look at my orbital surfaces in order to characterize each orbital’s nodal pattern. I should never rely solely on orbital energies to assign donor and acceptor roles.

The relevant nitrile oxide (1,3-dipole component) orbitals are shown below.

• Donor (HOMO, -10.16 eV, orbital coefficients C -.32, N -.09, O +.54). Things to notice:
  • The MO contains one “pi” node (Ignore the node between the two C). This is what we expect for the second MO in any linear conjugated system.
  • The isosurface suggests that C makes a larger contribution than O. The orbital coefficients, however, say otherwise. Remember that orbital decay increases with increasing electronegativity: C < N < O. So even though O makes a larger contribution to the MO than C does, the MO decays faster (looks smaller) near O. When in doubt, always check the orbital coefficients.

• Acceptor (LUMO, +5.11 eV, orbital coefficients C +.57, N -.59, O +.25). Things to notice:
  • The MO contains two “pi” nodes. This is what we expect for the third MO in any linear conjugated system.
  • N makes the largest contribution to this orbital (see orbital coefficient). However, N is not one of the reacting atoms. Pay attention only to the reacting atoms.

The relevant alkyne (dipolaraphile) orbitals are:

• Donor (HOMO, -11.67 eV, orbital coefficients CH -.29, CCN -.30). Things to notice:
  • The MO contains one “pi” node overall (second orbital in linear conjugated system), but no nodes within the alkyne (CC π).
  • The orbital coefficients on the two carbons are essentially identical. This MO cannot be used to predict regioselectivity.

• Acceptor (LUMO, +2.98 eV, orbital coefficients CH +.62, CCN -.48). Things to notice:
  • The MO contains two “pi” nodes (third orbital in linear conjugated system), and one node inside the alkyne (CC π*).
  • The terminal C makes a slightly larger contribution to the MO (this is not readily apparent from the isosurface).

Putting it all together, we find that the dominant interaction involves the nitrile oxide HOMO (donor) and alkyne LUMO (acceptor) and we expect O to add to the terminal C of the alkyne. That is, we expect the methyl and cyano groups to be adjacent in the final product.

Calculated Energy Barriers

HF/3-21G energies for the reactants and transition states, and calculated energy barriers, are listed below. Reactant energies were obtained from equilibrium geometry models. Transition state energies were obtained from models generated by transition state searches. IR frequency calculations were used to verify that the transition state models were stationary points (one imaginary vibration frequency).

• nitrile oxide -205.51566 au
• alkyne -167.61366 au
• meta transition state -373.08533 au
  • meta energy barrier = 27.6 kcal/mol
• ortho transition state -373.09821 au
  • ortho energy barrier = 19.5 kcal/mol

Naturally these calculated barrier should be taken with several grains of salt:

• the HF method fails to include electron correlation
• the 3-21G basis set does not place enough basis functions on each atom
• the barriers reflect only calculated changes in electronic energy and do not incorporate changes in nuclear kinetic energy
• likewise, entropy and solvent effects have been ignored.

That said, the calculated Δ(ΔE*) is large and consistent with the FMO analysis. The ortho product should form more rapidly.

Supporting analysis - transition state geometry

Geometry & orbital overlap. According to the FMO analysis, the ortho transition state should create better CO orbital overlap. This should manifest itself as a shorter CO distance in the ortho transition state. The distances for the forming (partial) single bonds are:

• ortho transition state: 1.870 (CO) and 2.455 Å (CC)
• meta transition state: 2.032 (CO) and 2.286 Å (CC)

consistent with our prediction.

Geometry & asynchronicity. According to the FMO analysis, the ortho transition state is characterized by a “large-large” (CO) and a “small-small” (CC) pair of orbital overlaps. The meta at transition state, on the other hand, is characterized by two “large-small” orbital overlaps. Therefore, the ortho transition state should be more asynchronous. This is borne out by the calculated transition state geometries (see above).

Geometry & Hammond postulate. The HF/3-21G energies of the products (equilibrium geometry models) and the corresponding reaction energies are:

• ortho product -373.25670 au (ΔE = -79.9 kcal/mol)
• meta product -373.24611 au (ΔE = -73.2 kcal/mol)

According to the Hammond postulate, the transition states for these exothermic reactions should be reactant-like. Furthermore, we can expect that the transition state for the more exothermic ortho reaction will be more reactant-like.

A large number of geometrical changes occur during these reactions. Some of these are relevant, but others are not. For example, a cycloaddition necessarily brings the two reactants close together so the interatomic distances used in the previous sections are not reliable guides to whether a transition state is reactant-like or product-like (and, we noted that these distances can be explained in other ways). It is better to look at geometry changes that occur within each reactant. There are many distances and angles that we could look at, but here are some that appear in the nitrile oxide:

• CN distance. Reactant = 1.136 Å. Products = 1.452 (ortho) and 1.438 Å (meta). The transition state distances are clearly reactant-like, 1.152 (ortho) and 1.161(meta) Å, and the shorter ortho distance is clearly more reactant-like.
• NO distance. Reactant = 1.317 Å. Products = 1.289 (ortho) and 1.294 Å (meta). The transition state distances are clearly reactant-like, 1.333 (ortho) and 1.311 Å (meta), and the longer ortho distance is clearly more reactant-like.
• CNO bond angle. Reactant = 180°. Products = 104.9° (ortho) and 105.5° (meta). The transition states appear to be slightly closer to products than reactant by this measure, 140.9° (ortho), and 139.6° (meta).
• CCN bond angle. Reactant = 180°. Products = 122.1° (ortho) and 121.3° (meta). This angle makes the transition states look reactant-like, 165.3° (ortho), and 158.7° (meta), and the ortho transition state looks more reactant-like.

Although there is not unanimous agreement on the position of the transition state (and I have not reported any parameters for the alkyne), it would seem that, on balance, the data support the Hammond postulate.

Supporting analysis - charge transfer

The dominant FMO interaction involves a nitrile oxide donor MO and an alkyne acceptor MO. Therefore, in the transition state, we expect to see positive charge accumulate on the nitrile oxide and negative charge accumulate on the alkyne.

Since the reactants are both neutral, the simplest (but most tedious) way to assess this prediction is to look at the overall charge on each “reactant” in the transition state. In other words, I will sum the atomic charges of all of the alkyne atoms, including the hydrogen and cyano group. Fortunately, it is not necessary to sum the atomic charges for the nitrile oxide (which contains more atoms) because the transition state has no net charge. (Note: atomic charges are obtained by selecting Display: Properties and then selecting the atom of interest. The following values are based on Natural Charges.)

• Reactant: alkyne = 0, nitrile oxide = 0
• Transition state
  • ortho: alkyne = -0.17, nitrile oxide = +0.17
  • meta: alkyne = -0.10, nitrile oxide = +0.10
• Product
  • ortho: alkyne = +0.20, nitrile oxide = -0.20
  • meta: alkyne = +0.22, nitrile oxide = -0.22

The direction of electron transfer in the transition state is nitrile oxide → alkyne and is consistent with the FMO prediction. Interestingly, the direction of electron transfer reverses as the transition state changes into product. This is not unexpected. The dominant FMO interaction may control the approach to the transition state, but it involves only one electron pair and other electron pairs must eventually participate in the reaction.

In conclusion, while we might have concerns about the low level theory used to construct these models, the fact that several properties of the models (energy, geometry, and electron distribution) seem to be internally consistent, i.e., they can all be rationalized using a single theory, increases our confidence in the qualitative validity of these results.