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 …

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The emphasis of my treatment of frontier MO theory has been on its application, not its theoretical foundation. When it comes to FMO, I hope that you will to be able to use it and read articles in which others refer to it.

Of course, I could say a lot more about orbitals if time permitted. If you feel like you would like to spend some extra time on this material (and this applies to everything that we cover), please come see me. Physical organic chemistry is one of my favorite subjects (nerd! nerd!) and I am more than happy to talk about any aspect of it.

Today’s PowerPoint (revised W, Feb 27)

Authors often file additional material with their papers that does not get published in the journal proper. This material is referred to as supporting (or supplementary) information and often contains important additions to the basic paper.

For example, the experiment-based papers that appear in a rapid-publication journal like Organic Letters usually contain only summaries of the research. Detailed experimental procedures, spectroscopic data, and crystallographic data, are published on-line as supplements.

Nearly all journals expect computational chemists to provide supporting information for their papers. At the very least, the chemist is expected to provide lists of the atomic Cartesian coordinates for each model, but other model properties may be demanded too.

A coordinate list can serve two purpose. First, it makes it possible for another scientist to repeat the calculation and check it for errors. Also, and from our point of view more important, a coordinate list can be converted into a “3-D” model so we don’t have to rely solely on the small flat figures in the journal to see what is going on.

You can use Spartan to view published models if you know how to convert the data in the supporting info into a file format that Spartan recognizes. The conversion procedure that I followed for paper #4 can be briefly summarized as:

1. Download & open supporting information
2. Copy atom coordinates to clipboard
3. Paste atom coordinates into a text file
4. Save text file with .xyz extension
5. Open file in Spartan

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A few days ago I showed you how to model an energy profile for internal rotation. As part of that exercise, we tried (quickly) calculating a profile using AM1 and I said the results weren’t believable. I have also asked you to calculate some profiles using HF/3-21G. Are these more believable? Let’s see…

Truth = MP2/6-31G*

I have calculated energy profiles for internal rotation in 1,3-butadiene using 5 different tools: MMFF (a molecular mechanics force field), AM1 (semi-empirical QM), HF/3-21G and HF/6-31G (two versions of Hartree-Fock QM), and MP2/6-31G* (a post-Hartree-Fock QM tool). Of these, MP2 should give the most reliable results, so let’s just assume the results are reliable.

E relative (kcal/mol) vs. CCCC dihedral angle (^o) for MMFF, AM1, & MP2

MMFF energies are pretty good. AM1 are not. The AM1 curve is in the right ballpark, but all kinds of important details are incorrect: no skewed minimum, no cis (eclipsed) maximum, trans → skew barrier much too small.

E relative (kcal/mol) vs. CCCC dihedral angle (^o) for HF/3-21G, HF/6-31G* & MP2

The 3 models agree very closely. The agreement is especially good at large angles (180 > dihedral > 120), then subtle disagreements (error ~0.3 kcal/mol) appear.

The behavior of both Hartree-Fock models is very reassuring, but I have a sad fact to relate: the reliability of any approximate tool (and HF is definitely an approximation) varies from one molecule to the next. What works out so well for 1,3-butadiene, might or might not work for acrolein.

When you generate a list of models, e.g., conformers, there are two ways to get information about them. One is tedious, but obvious. The other is very fast, but relies on obscure buttons.

Tedious & (perhaps) obvious

The obvious part: whenever you examine any model, you can always get its energy by selecting Display: Properties and you can always get the value of a dihedral angle by selecting Geometry: Measure dihedral (there is also a blue button you can use) and selecting 4 atoms.

The tedious part: you will have to repeat this for each molecule in your list. In addition, each energy and each angle will have to be written on a piece of paper and then (yawn) typed into Excel.

Very fast (uses obscure buttons)

First, select Display: Spreadsheet. To add relative energies, select the molecule that you think/know has the lowest energy, click the top of a blank column in the sheet, click Add…, and click rel. E (and kcal/mol). This adds a column of energy data to your sheet.

Second, use Geometry: Measure dihedral (or the blue button) to get the value of the dihedral angle that interests you. When this value is displayed, a little red-&-yellow “P” button will appear next to the value in the lower right-hand corner of the window. Click the “P”. This adds a column of dihedral data to your sheet.

Third, and the best part, click-drag in the sheet to select the data you want (you probably will need to drag the edges of the spreadsheet window to make it larger). Select Edit: Copy and then paste the data into Excel.

I have posted some background information on energy calculations here (required reading).

I have also repeated the calculations that you performed in class and posted the results below. The comparison of reactions, and the comparison of different methods for calculating reaction enthalpies, are very interesting. But let’s start with the raw data first.

AM1 Reaction enthalpies (298 K)

1. Number under molecule is its AM1 heat of formation (kcal/mol)

2. Number on right (bold) is the AM1 reaction enthalpy (kcal/mol). Some of my numbers (which I trust completely) are different from what you reported. Since I don’t have your heats of formation, I can’t account for any discrepancies.

3. Consistent with your predictions, the addition of CO2 is not nearly as favorable as the addition of ethylene. However, the additions of CO2 and MeCN are both predicted to be exothermic.

Hartree-Fock/3-21G Reaction enthalpies (0 K)

1. Number on right is the HF/3-21G reaction enthalpy at 0 K (kcal/mol). This combines the total energy and the zero-point energy (ZPE), but does not include PV work (< 1 kcal/mol) or the effects of warming from 0 K to 298 K (typically < 1 kcal/mol).

2. The HF/3-21G enthalpies are very different from the AM1 enthalpies. In fact, the differences are so large, they cannot be due to the different temperatures that were assumed. The two tools give similar qualitative results for ethylene vs. CO2 vs. MeCN, but the quantitative agreement is poor.

Better Energies

Mark Twain once said that a man with two watches never knew what time it was. The same can be said about someone who has used two tools for calculating energies. Which answer is right? Is either answer right?

One way to answer these questions is to change tools and re-calculate the energies. Since other tools will use different approximations, we might learn whether AM1 or HF/3-21G was more reliable. An even better approach is to use a tool that uses fewer approximations. The following table shows two sets of reaction enthalpies (0 K) obtained using a post-Hartree-Fock tool (MP2) and a density functional theory-based tool (B3LYP).

The results are quite surprising.

1. The energies obtained with the higher-level tools agree with each other for two reactions, but not the third (the simple Diels-Alder). The addition of CO2 is predicted to be endothermic and the reaction enthalpies for CO2 and MeCN are very different from each other.

2. The energies obtained with the higher-level tools do not agree with the lower-level energies. Neither AM1 nor HF/3-21G is quantitatively reliable. This is especially the case when the types of chemical bonds in the reactants and products are different (the next section shows a case where AM1 and HF/3-21G do much better).

3. Even qualitative predictions can be risky. The low-level tools predicted 3 exothermic reactions. Wrong! The low-level tools predicted fairly similar behavior for CO2 and MeCN (reaction enthalpies differ by < 10 kcal/mol). Wrong! The low-level tools were correct, however, in predicting a very exothermic Diels-Alder reaction for ethylene.

Endo v. Exo (Isomer energies)

The previous section shows that reaction enthalpies are hard to calculate reliably when the starting materials and products contain different kinds of bonds.

Reliable energies can be obtained, however, when the same kinds of bonds appear on both sides of the reaction arrow, as in the following epimerization:

The energy of the endo isomer relative to the exo isomer (obtained using the same 4 tools described above) is listed below:

All of the calculated energies fall within a 1.5 kcal/mol range showing that low-level and high-level tools can give consistent results for certain systems. Unfortunately, the range energies includes zero, so one tool (MP2) predicts the endo isomer as more stable while the others predict the exo isomer as more stable.

When calculated energy differences are as small as these, one should include all relevant energy corrections (ZPE, warming to 298 K, and so on). I haven’t done this. The three ab initio energies are relative “total” energies only.

Round off your energy (at the end of the calculation)

Computers calculate very precisely and produce results with lots of figures after the decimal point. The accuracy of these calculations tends to be abysmal, however, so there is no need to get carried away and include lots of figures in the final energies. If you look at my tables and figures, you will see that I generally round reaction enthalpies (but not molecular energies) to +/- 0.1 kcal/mol. This level of precision is higher than the accuracy of most thermochemical measurements (typically 1-2 kcal/mol) and much higher than the accuracy of my calculated enthalpies.

On the other hand, while you can round off your final result, you should not round off the preliminary values. The rule-of-thumb is to always carry at least one digit past the one that you think will be uncertain. This means recording AM1 heats of formation to the closest 0.01 kcal/mol and recording ab initio total energies to the closest 0.00001 au (10^-5).

On Fri (Feb 1) we used transition state models to follow atoms from reactants to products in Diels-Alder reactions. This exercise had several goals and you might reflect on how well it worked:

• Learn 2 techniques for building transition state models
  • Build reactants or products, define bond changes, search transition state library
  • Build reactants or products, constrain (a part of) the geometry to resemble the transition state, calculate best positions for the remaining atoms
• Learn the basic structural features of the Diels-Alder transition state
• Learn to differentiate endo positions from exo positions in the transition state

Another goal of the exercise was to learn how to correlate reactant geometry with product geometry. You may not have realized that the Diels-Alder reaction can produce a large number of isomers and there is a correlation between transition state geometry and product geometry.

A non-specific cycloaddition between a heavily substituted diene and a heavily substituted dienophile can generate as many as 32 possible cyclohexenes. There are 2 possible regioisomers, and there are 4 chiral carbons in each regioisomer, so there are 2^4 (= 16) stereoisomers of each regioisomer.

The Diels-Alder reaction is stereospecific. Groups that are effectively cis in the starting materials (G & e, B & c, etc.) must end up cis in the product. Therefore, the Diels-Alder reaction can only generate 8 possible isomers, and only 4 stereoisomers of each regioisomer.

Each of the products shown above comes from a different transition state. You can see this more easily by looking at the 4 “ortho” regioisomers derived from E-1,3-pentadiene and acrylonitrile (CH2=CHCN).

As the following models reveal, each of the “ortho” products comes from a different transition state geometry. The cis products are derived from endo transition states that bring together different faces of the starting materials. The trans products are derived from exo transition states.

One last thought: if either starting material is symmetric, the number of possible product isomers will decrease, but the number of possible transition state geometries will stay exactly the same. This means you will need to consider more than transition state geometry for each product.