Imperial College London

Henry Rzepa

I return to this reaction one more time. Trying to explain why it is
enantioselective for the epoxide product poses peculiar difficulties.
Most of the substituents can adopt one of several conformations, and
some exploration of this conformational space is needed.

![sharpless-binuclear](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/12/sharpless-binuclear.svg){.aligncenter
.size-full .wp-image-8659 decoding="async"}

Amongst the conformational possibilities are the two rotations shown
below. The blue rotates the ester with respect to the Ti-O-C unit, and
the red rotates within the ester group itself. In fact the conformations
of esters almost invariably adopt the first conformation shown,
a *s-cis* orientation where one lone pair from the alkoxy group is
*anti* to the axis of the carbonyl group (red rotation). Crystal
structures of binuclear titanoxy compounds show both options for the
blue
rotation.![sharpless-conf](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/sharpless-conf.svg){.aligncenter
.size-full .wp-image-8851 decoding="async"}

One might imagine that there are two rotations about the C-O and O-Ti
bonds in the iPr-O-Ti fragment as well. Whilst some of the many
permutations are precluded simply on steric grounds, this still leaves a
lot of possibilities. I have certainly not explored anything like the
full set, but felt it worth reporting two conformations which have lower
energies than the ones I [reported in this
post](http://www.ch.imperial.ac.uk/rzepa/blog/?p=8658){target="_blank"}.
If I find any yet lower in energy, I will add a postscript here.

<table class="aligncenter" data-border="0" data-align="center">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="odd">
<td colspan="2">New conformations (hydrogens removed for clarity)</td>
</tr>
<tr class="even">
<td><div id="attachment_8854" class="wp-caption aligncenter"
style="width: 230px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/R-new.jpg"
class="size-full wp-image-8854" decoding="async"
aria-describedby="caption-attachment-8854"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/01/R-4114.42426997-0.1118467333-4113.701664.log;frame 2;connect (atomno=9) (atomno=97) PARTIAL;connect (atomno=9) (atomno=96) PARTIAL;connect (atomno=9) (atomno=10) PARTIAL;connect (atomno=9) (atomno=2) PARTIAL;connect (atomno=1) (atomno=2) NONE;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 20;animation mode loop;&#39;);"
width="220" alt="R. Click for 3D" />
<p>(R). Click for 3D</p>
</div></td>
<td><div id="attachment_8855" class="wp-caption aligncenter"
style="width: 230px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/S-new.jpg"
class="size-full wp-image-8855" decoding="async"
aria-describedby="caption-attachment-8855"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/01/S-4114.42823719-0.1164206556-4113.702163.log;frame 6;connect (atomno=9) (atomno=97) PARTIAL;connect (atomno=9) (atomno=96) PARTIAL;connect (atomno=9) (atomno=10) PARTIAL;connect (atomno=9) (atomno=2) PARTIAL;connect (atomno=1) (atomno=2) NONE;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 20;animation mode loop;&#39;);"
width="220" alt="S Click for 3D." />
<p>(S). Click for 3D.</p>
</div></td>
</tr>
<tr class="odd">
<td colspan="2">Old conformations</td>
</tr>
<tr class="even">
<td><div id="attachment_8671" class="wp-caption aligncenter"
style="width: 220px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/12/Ti2-R.jpg"
class="size-full wp-image-8671" decoding="async"
aria-describedby="caption-attachment-8671"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2012/12/R-4113.685522.log;frame 2;connect (atomno=10) (atomno=9) PARTIAL;connect (atomno=9) (atomno=96) PARTIAL;connect (atomno=9) (atomno=9) PARTIAL;connect (atomno=27) (atomno=35) PARTIAL;connect (atomno=35) (atomno=28) PARTIAL;connect (atomno=1) (atomno=2) NONE;vectors on;vectors 4;vectors scale 5.0; color vectors magenta; vibration 20;animation mode loop;&#39;);"
width="210" />
<p>(R). Click for 3D.</p>
</div></td>
<td><div id="attachment_8672" class="wp-caption aligncenter"
style="width: 220px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/12/Ti2-S.jpg"
class="size-full wp-image-8672" decoding="async"
aria-describedby="caption-attachment-8672"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2012/12/S-4113.690260.log;frame 2;connect (atomno=9) (atomno=97) PARTIAL;connect (atomno=9) (atomno=96) PARTIAL;connect (atomno=9) (atomno=10) PARTIAL;connect (atomno=9) (atomno=2) PARTIAL;connect (atomno=1) (atomno=2) NONE;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 20;animation mode loop;&#39;);"
width="210" alt="(S). Click for 3D" />
<p>(S). Click for 3D</p>
</div></td>
</tr>
</tbody>
</table>

The conformations differ in the regions indicated with a red arrow; the
([R](http://hdl.handle.net/10042/22377){target="_blank"}) being 10.1 and
the ([S](http://hdl.handle.net/10042/22376){target="_blank"}) 7.5
kcal/mol lower in ΔG~298~. Note how a change in conformation of just one
group can "knock-on" to other groups. The relative energies (kcal/mol)
of these two new conformations are shown below, broken down into three
components.

|            |              |                              |             |
|------------|--------------|------------------------------|-------------|
| Enantiomer | Total energy | Attractive dispersion energy | Free energy |
| R          |  +2.2        |  +2.9                        |  +0.3       |
| S          |  0.0         |  0.0                         |  0.0        |

As before, (S) wins out clearly in terms of the dispersion attractions,
which appears to be also reflected in the total energy of each system
(in other words, differentiation from non-dispersion terms is not
large). The free energy includes the entropy calculated from the normal
vibrational modes using the rigid-rotor-harmonic-oscillator
approximation. Whilst it too shows (S) to be the lower in energy, the
distinction is less clear-cut than with the old conformations. One is
often warned that the RRHO oscillator approximation is not good for
molecules with many free rotors (which normally means about single
bonds), although one normally might expect that comparing two very
similar systems will result in a lot of cancellation of errors. But this
result here does suggest that for the Sharpless system, which has many
free-rotor groups, free energies might need taking with an extra dose of
caution. I would also add that one does need to optimise the geometry of
transition states for such systems with extraordinary accuracy; for
these two examples, one does need to achieve values for the six "zero"
translations and rotations of \< 10 cm^-1^, which can involve heroic
efforts (as it did here!). 

I end by reiterating my earlier conclusion. The Sharpless seems to be an
example of a reaction which achieves stereospecificity by the
[accumulation of many very tiny
effects](http://www.ch.imperial.ac.uk/rzepa/blog/?p=221){target="_blank"}
(the dispersion attractions), and hence the use of a
dispersion-corrected method is absolutely critical. It may also in part
involve accumulation of another set of small effects contributing to the
total entropy and hence free energy. What it appears **not to be** is a
manifestation of a small number of larger effects (*e.g.*
stereoelectronic alignments) which can be "named". Chemistry by and
large is always an attempt to achieve simple explanations by use of the
latter; in other words developing simple heuristics or rules that can be
transferred between systems. Where you have an effect that is in effect
an accumulation of many terms, it is much more difficult to express this
as simple transferable rules. Chemistry at such a level then is reduced
simply to computing the sum of these small effects, rather than relying
on simple rules. Have we perhaps reached this level with the Sharpless
per-epoxidation? Would it be such fun if it were?

::: {.wp_orcid_field}
[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
rel="author"}
:::


I return to this reaction one more time. Trying to explain why it is enantioselective for the epoxide product poses peculiar difficulties. Most of the substituents can adopt one of several conformations, and some exploration of this conformational space is needed. Amongst the conformational possibilities are the two rotations shown below.

Messaggi di Rogue Scholar

Sharpless epoxidation, enantioselectivity and conformational analysis.