Posts Tagged ‘steric exchange energy’

The conformation of acetaldehyde: a simple molecule, a complex explanation?

Friday, February 8th, 2013

Consider acetaldehyde (ethanal for progressive nomenclaturists). What conformation does it adopt, and why? This question was posed of me by a student at the end of a recent lecture of mine. Surely, an easy answer to give? Read on …

acetaldehyde

There really are only two possibilities, the syn and anti. Well, I have discovered it is useful to start with a search of the Cambridge data base. With R=H or C, X unspecified,  acyclic and T ≤ 175K, two searches were performed. The first identified the torsion around O=C-C-H. This clearly shows a maximum at 120° (with twice the probability), and a smaller one at 0°. This matches syn; the anti conformation above would be expected to have peaks at 60° and 180°; the latter in particular is singularly missing.

acetaldehyde-180

An alternative search is to define the distance between the oxygen and the H. For the syn conformer, distances of ~2.5 and 3.1Å are expected; for the anti conformer, 2.7 and 3.3Å. Again, syn matches better. Remember, searches based on the position of a hydrogen are less reliable than most, so these distributions provide only a statistical indication.

acetaldehyde-dist

Now for a (ωB97XD/6-311G(d,p) calculation of the rotational barrier. The minima occur at torsions of 0, 120 and 240°, matching syn, although the barrier is very low.

acet-rot

Now to try to find explanations. The standard one finds this in three effects:

  1. Donation from two C-H bonds (R=H above) into the π*C=O NBO orbital (in the manner that was used to explain the cis-orientation of the two methyl groups in cis-butene). 
  2. Donation from the single co-planar C-H bond into the σ*C=O NBO orbital (blue bonds above)
  3. Pauli bond-bond repulsions between two filled NBOs. 

Effect 1 has an NBO perturbation energy E(2) of 7.0 kcal/mol for the syn conformer and 6.45 for the anti. The explanation is the π*C=O NBO “leans outward”, overlapping better with the C-H bonds in the syn than in the anti.  the One up to the syn! Effect 2 has values of 1.3 for the syn and 4.1 for the anti. The latter now has the edge. But wait, there are other (smaller) interactions. The syn has an antiperiplanar orientation of the two C-H bonds shown above (X=H,red), E(2) = 3.3 vs 0.6 for the corresponding syn-planar orientation in the anti-conformation. It’s now a tie; neck-and-neck.

Effect three suggests that the disjoint NLMO steric exchange energy is 54.34 for the anti and 53.88 (i.e. lower) for the syn. It is vaguely disappointing that no absolutely clear-cut explanation emerges. But then the difference (in total free energy) is only 1.4 kcal/mol. But even this small difference in energy can manifest in fairly clear-cut conformational preferences obtained from crystal structures. Ultimately of course, all effects in chemistry are reducible to the sum of lots of small effects (in other words unpredictable until one does the sum). 

I cannot end without mentioning the largest of all the NBO interactions, namely the in-plane lone pair on the oxygen as donor and the aldehyde proton C-H as acceptor (X=H). This has values of 29.3 for syn and 28.8 kcal/mol for anti. This manifest (inter alia) in a greatly reduced C-H vibrational wavenumber (ν 2982 for syn, 2900 cm-1 for anti) compared to the methyl C-H values (~3043-3164).

So this tiny little molecule ended up a little less obvious than might have seemed at the outset. One can find interesting things in even the tiniest of things! 


HC...C-H alignment. Click for  3D.

HC…C-H alignment. Click for 3D.

 

HC...C-H alignment. Click for  3D.

O=C*…C-H alignment. Click for 3D.

Stereoselectivities of Proline-Catalyzed Asymmetric Intermolecular Aldol Reactions.

Sunday, April 22nd, 2012

Astronomers who discover an asteroid get to name it, mathematicians have theorems named after them. Synthetic chemists get to name molecules (Hector’s base and Meldrum’s acid spring to mind) and reactions between them. What do computational chemists get to name? Transition states! One of the most famous of recent years is the Houk-List.

In the last 12 years or so, the area of enantioselective organocatalysis has blossomed, and an important example involves the asymmetric amino acid (S)-proline (below, shown in green). As its enamine derivative (below, shown in blue), it can catalyse the aldol condensation with an aldehyde or ketone to form two new adjacent stereogenic centres resulting from C-C bond formation (shown below as (R) and (S) as attached to the carbons connected to the red bond).

The Houk-List transition state was located for this reaction, and as a useful model for rationalising the stereospecificity of this reaction it has become justly famous (although to be fair, other models have also been proposed). The challenge is to identify the factors selecting for just one stereoisomer (S,R in this case) over the other three (a similar challenge is described in this post for the heterotactic polymerisation of lactide). Houk, List and co-workers constructed their model (the example shown below is for R=isopropyl)  as follows.

  1. They employed a B3LYP/6-31G(d) density functional model.
  2. The geometry of the transition state was located for all four diastereomeric transition states using this method. Importantly, this geometry was for the gas phase, which provided a value for ΔG298.
  3. These free energies were then corrected for the (relative) solvation energies of the four transition states. This was essential, since in the mechanism shown above, a neutral reactant gives a zwitterionic product, via a partially ionic transition state (indeed, the dipole moment of these transition states is around 10D). 
  4. The resultant Houk-List model then predicted that of the four isomeric transition states, the lowest was (as shown above) the (S,R) diastereomer.
  5. This particular transition state geometry has an interesting feature involving a 9-membered ring, large enough to accommodate a linear proton transfer without strain, by virtue of a trans double bond motif (the C=N bond). The (S,S) and (R,S) isomers have a cis motif instead at this location.

    Houk-List transition state. Original geometry.

Well, this transition state is now nine years old. Unlike asteroids, or mathematical theorems, or indeed molecules and their reactions, a transition state is a slightly more ephemeral object. Its features and properties do rather depend on the particular quantum model used to construct it. There is one feature of the model, necessary in 2003, but no longer so in 2012. This was the use of a gas-phase optimised geometry, augmented at that geometry with a so-called single-point solvation energy correction. Nowadays, the solvation correction is included in the energy used in the geometry optimisation, which now properly reflects the effect of the solvation. Re-optimisation with this inclusion, at the ωB97XD/6-311G(d,p)/SCRF=dmso level thus updates the original Houk-List geometry.

(S,R) Houk-List transition state, updated geometry. Click for 3D

  1. The most significant changes involve the O…H—O bond lengths. Respectively 1.13/1.31Å in the original, they change to 1.06/1.40Å at the new level.
  2. The forming C-C bond changes in length from 1.89 to 2.05Å (the latter, it has to be said, being a much more “normal” value for a transition state). 
  3. Whilst these might not seem very great changes, we do not yet know how they might impact upon the relative free energies of the four transition states. Houk and List reported the (S,R), (R,R), (S,S) and (R,S) relative free energies as 0.0, 6.7, 7.8 and 4.6 kcal/mol. The updated values for (S,R), (R,R), (S,S) and (R,S) [click on preceding links to view models] are 0.0, 6.0, 5.7 and 5.4 kcal/mol [click on preceding links to view calculation archives], which represent only minor changes to these energies.
  4. The (S,S) diastereoisomer is an interesting outlier. The transition state normal mode wave numbers are -373, -481, -815 and -402 cm-1 respectively and the O…H…O bond lengths for (S,S) are 1.18 and 1.20Å, a rather more symmetrical proton transfer than the other three.

Which brings us to the main point; what is the origin of the diastereoselectivity? An NBO analysis can compare the total steric exchange energy (due to Pauli bond-bond repulsions) of the four isomers, which  turns out to be respectively 1214, 1221, 1235 and 1229 kcal/mol. In other words, the favoured isomer has the smallest steric exchange energy. Of course this one term is not the only contributing factor, and a more elaborate analysis will no doubt provide further insight.

So an update to the Houk-List transition state reveals the general characteristics are intact and it is still a very useful model for analysing stereoselectivity in proline organocatalysis.

Postscript:  The Intrinsic reaction coordinate  (for (S,S) ) is shown below.