Imperial College London

Henry Rzepa

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](http://dx.doi.org/10.1021/ja028812d "Quantum Mechanical Predictions of the Stereoselectivities of Proline-Catalyzed Asymmetric Intermolecular Aldol Reactions"){target="_blank"}.

In the last 12 years or so, the area of enantioselective organocatalysis
has [blossomed](http://dx.doi.org/10.1021/ja300415t){target="_blank"},
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).

[![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/Houk.svg "Houk"){.aligncenter
.wp-image-6478 loading="lazy" decoding="async" width="350"
height="158"}](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/Houk.svg)

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](http://dx.doi.org/10.1021/ja300415t){target="_blank"} 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](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2300){target="_blank"}
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
    ΔG~298~^†^.
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.  

    ::: {#attachment_6482 .wp-caption .aligncenter style="width: 254px"}
    ![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/6a-SR-original.jpg "6a-SR-original"){.wp-image-6482
    loading="lazy" decoding="async"
    aria-describedby="caption-attachment-6482"
    onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2012/04/6a.log;frame 1; zoom 100;connect (atomno=1) (atomno=11) partial;connect (atomno=28) (atomno=27) partial;connect (atomno=28) (atomno=17) partial;vectors on;vectors 4;vectors scale 5.0; color vectors yellow; vibration 20;animation mode loop;');"
    width="244" height="214"}
    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.

::: {#attachment_6481 .wp-caption .aligncenter style="width: 254px"}
![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/6a-SR.jpg "6a-SR"){.wp-image-6481
loading="lazy" decoding="async"
aria-describedby="caption-attachment-6481"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('green');jmolApplet([450,450],'load wp-content/uploads/2012/04/6a.log;frame 67; zoom 100;connect (atomno=1) (atomno=11) partial;connect (atomno=28) (atomno=27) partial;connect (atomno=28) (atomno=17) partial;vectors on;vectors 4;vectors scale 5.0; color vectors yellow; vibration 20;animation mode loop;');"
width="244" height="214"}

(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)]{style="color: green;"
    title="Click to view 3D model"
    onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('green');jmolApplet([450,450],'load wp-content/uploads/2012/04/6a.log;frame 67; zoom 100;connect (atomno=1) (atomno=11) partial;connect (atomno=28) (atomno=27) partial;connect (atomno=28) (atomno=17) partial;vectors on;vectors 4;vectors scale 5.0; color vectors yellow; vibration 20;animation mode loop;measure 1 11;measure 28 27;measure 28 17;');"},
    [(R,R)]{style="color: red;" title="Click to view 3D model"
    onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('orange');jmolApplet([450,450],'load wp-content/uploads/2012/04/6b.log;frame 99; zoom 100;connect (atomno=1) (atomno=11) partial;connect (atomno=28) (atomno=27) partial;connect (atomno=28) (atomno=17) partial;vectors on;vectors 4;vectors scale 5.0; color vectors yellow; vibration 20;animation mode loop;measure 1 11;measure 28 27;measure 28 17;');"},
    [(S,S)]{style="color: red;" title="Click to view 3D model"
    onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('pink');jmolApplet([450,450],'load wp-content/uploads/2012/04/6c.log;frame 149; zoom 100;connect (atomno=31) (atomno=18) partial;connect (atomno=8) (atomno=2) partial;connect (atomno=2) (atomno=1) partial;vectors on;vectors 4;vectors scale 5.0; color vectors yellow; vibration 20;animation mode loop;measure 31 18;measure 8 2;measure 1 2;');"}
    and [(R,S)]{style="color: red;" title="Click to view 3D model"
    onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('pink');jmolApplet([450,450],'load wp-content/uploads/2012/04/6d.log;frame 49; zoom 100;connect (atomno=18) (atomno=4) partial;connect (atomno=8) (atomno=2) partial;connect (atomno=2) (atomno=1) partial;vectors on;vectors 4;vectors scale 5.0; color vectors yellow; vibration 20;animation mode loop;measure 18 4;measure 2 8;measure 2 1;');"} \[click
    on preceding links to view models\] are
    [0.0](http://hdl.handle.net/10042/to-13916){target="_blank"},
    [6.0](http://hdl.handle.net/10042/to-13917){target="_blank"},
    [5.7](http://hdl.handle.net/10042/to-13918){target="_blank"} and
    [5.4](http://hdl.handle.net/10042/to-13915){target="_blank"} 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.

[![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/6c.gif "6c"){.aligncenter
.size-full .wp-image-6532 loading="lazy" decoding="async" width="273"
height="210"}](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/6c.gif)[![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/6c.svg "6c"){.aligncenter
.wp-image-6533 loading="lazy" decoding="async" width="233"
height="134"}](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/04/6c.svg)

------------------------------------------------------------------------

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


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.

Rogue Scholar Beiträge

Stereoselectivities of Proline-Catalyzed Asymmetric Intermolecular Aldol Reactions.