Imperial College London

Henry Rzepa

The journal of chemical education has many little gems providing
inspiration for laboratory experiments. Jonathan Piard reports one based
on the reaction below\[cite\]10.1021/ed4005003\[/cite\]; here I
investigate the mechanism of this transformation.

[![spiropyran](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiropyran4.svg){.aligncenter
.size-full .wp-image-13335 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiropyran4.svg)  
There are two things going on here; an electrocyclic ring opening
involving breaking the C-O bond, with a *cis/trans* isomerism of the
alkene (concurrent or consecutive). A crystal structure of the dinitro
analogue establishes the *trans*
stereochemistry\[cite\]10.1039/A902379H\[/cite\]. This product
zwitterion is highly coloured (blue-purple) unlike the colourless
reactant. The rate at which this colour clears can be easily measured in
a UV/visible spectrometer, and from this activation parameters are
inferred as a function of the solvent.

Photochemically, this reaction is too complex to study quickly using
computation, but the thermal back reaction is much easier. Applying the
ωB97XD/6-311G(d,p)/SCRF=solvent procedure and using the C-O bond as a
reaction coordinate results in the following transition
state\[cite\]10.14469/ch/189540\[/cite\] IRC
profile\[cite\]10.14469/ch/189573\[/cite\] for DMSO as solvent, here
connecting to the *cis*-alkene. The thermal forward barrier for the
C...O cleaving is \~12 kcal/mol. More significantly, the back reaction
is only \<2 kcal mol, which is very much lower than that
reported\[cite\]10.1021/ed4005003\[/cite\] (\~22 kcal/mol) and makes the
*cis*-alkene very much a transient species and therefore **not**
the coloured species being measured.

[![C-O-cleave](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/C-O-cleave.svg){.aligncenter
.size-full .wp-image-13315 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/C-O-cleave.svg)

A second transition state involving C=C bond rotation is
located\[cite\]10.14469/ch/189546\[/cite\] and this yields the following
IRC\[cite\]10.14469/ch/189648\[/cite\] to form the *trans*-alkene, with
activation parameters listed below. It is entirely probable however that
the forward photochemical reaction follows a different course involving
conical intersections; an interesting study in its own right, but beyond
the scope of this post.

[![cis-trans](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/cis-trans.gif){.aligncenter
.size-full .wp-image-13349 loading="lazy" decoding="async" width="469"
height="282"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/cis-trans.gif)

|                                                                           |                       |                                 |                                  |
|---------------------------------------------------------------------------|-----------------------|---------------------------------|----------------------------------|
| Measured and computed activation parameters for the thermal back reaction |                       |                                 |                                  |
| Solvent                                                                   | ΔG~298~, kcal mol^-1^ | ΔH, kcal mol^-1^                | ΔS, cal K^-1^ mol^-1^            |
| DMSO, measured                                                            | 22.0                  | [26.4]{style="color: #ff0000;"} | [+14.6]{style="color: #ff0000;"} |
| toluene, measured                                                         | 19.0                  | [14.3]{style="color: #ff0000;"} | [-15.6]{style="color: #ff0000;"} |
| DMSO, calc\[cite\]10.14469/ch/189546\[/cite\]                             | 21.2                  | 20.4                            | +2.6                             |
| toluene, calc\[cite\]10.14469/ch/189579\[/cite\]                          | 18.6                  | 19.1                            | +1.8                             |

The next issue surrounds the effect of solvent. Most spectacular are
those of the activation parameters for the thermal back-reaction. The
measured activation entropy ΔS changes with solvent by
[**Δ30.2**]{style="color: #ff0000;"} cal, and the enthalpy ΔH by
[**Δ12.1**]{style="color: #ff0000;"} kcal, which are enormous solvent
effects. Are they in fact real? It is reassuring at least that the
calculated free energy agrees pretty closely with the measured values.
So too does the decrease in ΔG in changing the solvent from DMSO to
toluene (3.0 kcal/mol measured, 2.6 calculated).

There is little sign of a large solvent effect in the calculated values.
This could be for three reasons.

1.  The first is that adding explicit, hydrogen-bonded solvent molecules
    to the system is essential. As the zwitterionic character is lost
    when the *trans*-alkene starts to rotate, the system will become
    less ionic, and hence shed solvent molecules and gain entropy. If
    the solvent is not capable of hydrogen bonding, as say toluene,
    these will not be shed and the entropy will not increase at the
    transition state. It is difficult however to reconcile this picture
    with the apparent large loss of entropy for toluene as solvent.
2.  The second reason is because of a complete change in mechanism, one
    not modelled here.
3.  For completeness, one should also mention that the measured values
    might simply be in error, either due to typographical mistakes or
    indeed in numerical analysis.

I will conclude with the colour. It is possible to compute the
electronic excitations across the range 180-580nm, and I show below a
*difference spectrum* (for DMSO as solvent) with the product +ve and the
reactant  -ve. You can see the spectacular red-shift for the highly
conjugated zwitterion! The absolute value of λ~max~ is not red-shifted
enough (by about 65 nm), but the effect remains real.  
[![spiro](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiro.jpg){.aligncenter
.size-full .wp-image-13332 decoding="async" width="440"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiro.jpg 1048w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiro-300x210.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiro-1024x717.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiro-900x630.jpg 900w"
sizes="(max-width: 1048px) 100vw, 1048px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/spiro.jpg)

The above experiment is for undergraduate chemistry laboratories. I
suggest that a computational reality check could also easily be included
into such a lab, and would certainly help give students a broader
perspective.

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The journal of chemical education has many little gems providing inspiration for laboratory experiments. Jonathan Piard reports one based on the reaction below[cite]10.1021/ed4005003[/cite]; here I investigate the mechanism of this transformation. There are two things going on here;

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