Imperial College London

Henry Rzepa

Infra-red spectroscopy of molecules was introduced 110 years ago by
Coblentz\[cite\]10.1103/PhysRevSeriesI.20.273\[/cite\] as the first
*functional group* spectroscopic method (" *The structure of the
compound has a great influence on the absorption spectra. In many cases
it seems as though certain bonds are due to certain groups.*"). It hangs
on in laboratories to this day as a rapid and occasionally valuable
diagnostic tool, taking just minutes to measure. Its modern utility
rests on detecting common functional groups, mostly based around
identifying the nature of double or triple bonds, and to a lesser extent
in differentiating between different kinds of C-H
stretches\[cite\]10.1002/chem.201200547\[/cite\] (and of course OH and
NH). One common use is to identify the environment of carbonyl groups,
C=O. These tend to come in the form of aldehydes and ketones, esters,
amides, acyl halides, anhydrides and carbonyls which are part of small
rings. The analysis is performed by assigning the value of the C=O
stretching wavenumber to a particular range characteristic of each type
of compound. Thus ketones are said to inhabit the range of \~1715-1740
cm^-1^ and simple esters come at \~1740-1760 cm^-1^, some 20-30 cm^-1^
higher. Here I try to analyse how this difference arises.

The analysis is based on trying to understand how the components of an
ester interact with each other, and in particular how the alkyl oxygen
interacts with the carbonyl group. Three electronic interactions in
particular can be focused on (below). The first two of these weaken the
C=O bond; the last strengthens it. [So which effect wins
out](http://hdl.handle.net/10.6084/m9.figshare.640654)?

![s-cis-ester1](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/02/s-cis-ester1.svg){.aligncenter
.size-full .wp-image-9607 decoding="async"}

1.  The donation of an in-plane σ lone pair (Lp~σ~) on the alkyl oxygen
    into the C=O σ\* acceptor (red arrows) 
2.  The donation of an out-of-plane π lone pair (Lp~π~) into the C=O π\*
    acceptor (blue arrows)
3.  The donation of an in-plane σ lone pair (Lp~σ~) on the acyl oxygen
    into the C-O σ\* acceptor (green arrows) 

I will start with computational models, which have the advantage that
one can dissect how the vibrations arise. The first two rows show a
comparison of the experimental gas phase
values\[cite\]10.1063/1.461230\[/cite\] with a standard "medium
level" ωB97XD/6-311G(d,p) calculation. The discrepancy amounts to
\~100-114 cm^-1^. 

|                                                   |                                                                                          |                                                                                             |
|---------------------------------------------------|------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------|
| The carbonyl stretch in esters and ketones        |                                                                                          |                                                                                             |
| Method:                                           | Ester                                                                                    | Ketone                                                                                      |
| Expt (gas phase)\[cite\]10.1063/1.461230\[/cite\] | 1761^‡^                                                                                  | 1737^‡^                                                                                     |
| Harmonic ωB97XD/6-311G(d,p)                       | [1860](http://hdl.handle.net/10.6084/m9.figshare.599005){target="_blank" rel="noopener"} | [1851](http://hdl.handle.net/10.6084/m9.figshare.640514){target="_blank" rel="noopener"}    |
| Anharmonic ωB97XD/6-311G(d,p)                     | 1832^†^                                                                                  | [1828](http://hdl.handle.net/10.6084/m9.figshare.640654){target="_blank" rel="noopener"}^†^ |
| Harmonic ωB97XD/aug-cc-pvQZ                       | [1836](http://hdl.handle.net/10.6084/m9.figshare.640100){target="_blank" rel="noopener"} | [1831](http://hdl.handle.net/10042/23919){target="_blank" rel="noopener"}                   |
| Harmonic CCSD(T)/6-311G(d,p)                      | [1826](http://hdl.handle.net/10.6084/m9.figshare.640467){target="_blank" rel="noopener"} | [1792](http://hdl.handle.net/10.6084/m9.figshare.640106){target="_blank" rel="noopener"}    |
| Corrected CCSD(T)/6-311G(d,p)                     | \~1774                                                                                   | \~1749                                                                                      |
| Expt (gas phase)                                  | 1761                                                                                     | 1737                                                                                        |
| Reduced CCSD(T)/6-311G(d,p)                       | 1764                                                                                     | 1743                                                                                        |

There are several possible causes for such errors:

1.  [The calculation is for harmonic frequencies; whereas those measured
    are anharmonic. ]{style="line-height: 13px;"}
2.  DFT-level force constants at modestly sized basis set levels are
    known to be too large compared with a complete basis set calculation
    (CBS). It used to be the practice in fact to routinely scale the
    force constants down by \~10% to correct for this effect.
3.  The correlation treatment in a DFT approach is incomplete (an error
    which may in fact be also absorbed into the 10% correction noted
    above).

So to really get to the root of why an observed ester carbonyl stretch
is higher than that of the equivalent ketone, we have to get a handle on
these effects above. 

1.  [One can calculate cubic and quartic force constants to get an
    estimate of the effect of anharmonicity on the (harmonic/quadratic)
    values, which emerges as 23-28 cm^-1^ ]{style="line-height: 13px;"}
2.  Upping the level of the basis set to aug-cc-pVQZ (close to, but not
    quite a CBS) reveals further corrections of 20-24 cm^-1 ^. 
3.  Replacing the DFT method with a CCSD(T)-level treatment of the
    dynamic correlation gives corrections of 34 and 59
    cm^-1 ^respectively for ester and ketone. Assuming the corrections
    can be treated additively, one can apply the first two to the third,
    producing "corrected" CCSD(T)/6-311G(d,p) values which are only
    about 12-13 cm^-1^ higher than the observed value. This remaining
    discrepancy is probably due to the difference between aug-cc-pvQZ
    and a complete basis set (CBS) and any remaining errors in the
    correlation modelled by CCSD(T). We can be assured now that our
    theory is reproducing experiment very well.

Now that we can assess the accuracy of our computational methods, we
need to try to relate the results to the C=O bond itself. Does turning a
ketone into an ester really make it stronger? To directly compare the
C=O bond of two different molecules, we need to eliminate the effects of
mixing the C=O normal stretching mode with similar energy modes arising
from other parts of the molecule. A simple way of estimating this is to
set the mass of all but two of the atoms to a very small value
(0.00001), leaving only the masses of the C and O as normal; this is
shown as a reduced frequency in the table above. The harmonic
CCSD(T)/6-311G(d,p) C=O "pure" mode reduces to 1764 for methyl ethanoate
and 1743 cm^-1^ for propanone. So after all of this, at least we now
know that the force constant for the C=O stretch really is stronger for
an ester. The green arrows seem to win out over the blue/red ones.

One calculation too many? The (Wiberg) bond order for the C=O bond can
be derived from the wavefunctions. Its value is 1.635 for ester, and
1.681 for ketone (CCSD/6-311G(d,p)) or 1.766/1.848 (ωB97XD/aug-cc-pvQZ).
This is the opposite to that inferred from the carbonyl stretch, and
hence favours the blue/red arrows over the green arrows. I set out in
this post to try to bring clarity to how an adjacent oxygen influences
how we think of the properties of the C=O functional group, but as
happens quite often, the answer you get depends on the measurement you
make.

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

‡ The solution values in e.g. acetonitrile are reduced by \~20 cm^-1^,
reaching the values often quoted in text books for these functional
groups. † The effect on C-H values is greater, *e.g.* a reduction from
3186 to 2967 cm^-1^.

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.142795.57236){rel="noopener"
target="_blank"}.

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:::


Infra-red spectroscopy of molecules was introduced 110 years ago by Coblentz[cite]10.1103/PhysRevSeriesI.20.273[/cite] as the first
<em>
 functional group
</em>
spectroscopic method (“
<em>
 The structure of the compound has a great influence on the absorption spectra.
</em>

Messaggi di Rogue Scholar

Why is the carbonyl IR stretch in an ester higher than in a ketone?