Imperial College London

Henry Rzepa

According to Guggemos, Slavicek and Kresin, about
5-6\![cite\]10.1103/PhysRevLett.114.043401\[/cite\]. This is one of
those simple ideas, which is probably quite tough to do experimentally.
It involved blasting water vapour through a pinhole, adding HCl
and measuring the dipole-moment induced deflection by an electric field.
They found "***evidence for a noticeable rise in the dipole moment
occurring at ***[[[[[***[[n]{#MathJax-Span-30 .mi}[≈]{#MathJax-Span-31
.mo}[5]{#MathJax-Span-32 .mn}]{#MathJax-Span-29
.mrow}[--]{#MathJax-Span-33 .mi}***[***6***".]{#MathJax-Span-34
.mn}]{#MathJax-Span-28 .mrow}]{#MathJax-Span-27 .mrow}]{#MathJax-Span-26
.math}]{#MathJax-Element-3-Frame .MathJax}]{.aps-inline-formula}

Modelling the structures takes little time. So here are some
ωB97XD/6-311++G(2d,2p) gas phase models. I state at the outset that
these are not dynamic-stochastic models, averaged over many
conformations, but a static picture of individual poses. As usual, click
on individual images to obtain an interactive 3D model (Java
required).^‡^

n=1.\[cite\]10.14469/ch/189758\[/cite\] Dipole moment 3.7D

![hcl+1h2o](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-1h2o.jpg){.aligncenter
.size-full .wp-image-13396 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/1H2O.log;frame 27;spin 3;');"
width="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-1h2o.jpg 424w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-1h2o-300x152.jpg 300w"
sizes="(max-width: 424px) 100vw, 424px"}

n=2.\[cite\]10.14469/ch/189760\[/cite\] Dipole moment 2.4D. Note how the
O...H bond becomes shorter.

![hcl+2h2o](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-2h2o.jpg){.aligncenter
.size-full .wp-image-13397 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/2H2O.log;frame 144;spin 3;');"
width="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-2h2o.jpg 417w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-2h2o-300x292.jpg 300w"
sizes="(max-width: 417px) 100vw, 417px"}

n=3.\[cite\]10.14469/ch/189759\[/cite\] Dipole moment 2.5D. Note how the
key O..H bond is contracting rapidly, as are the other H-bond
interactions. This is the cyclic polarisation effect, where each bond
influences the others. We are starting to approach the formation of
H~3~O^+^ and Cl^--^!

![hcl+3h2o](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-3h2o.jpg){.aligncenter
.size-full .wp-image-13398 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/3H2O.log;frame 100;spin 3;');"
width="200"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-3h2o.jpg 448w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-3h2o-300x294.jpg 300w"
sizes="(max-width: 448px) 100vw, 448px"}

n=4.\[cite\]10.14469/ch/189763\[/cite\] Dipole moment 2.3 D, We have two
ways to add the next water molecule, firstly to try to stabilise the
H~3~O^+^. Nope.

![hcl+4h2o](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-4h2o.jpg){.aligncenter
.size-full .wp-image-13403 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/4H2Oi.log;frame 2;spin 3;');"
width="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-4h2o.jpg 591w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-4h2o-300x195.jpg 300w"
sizes="(max-width: 591px) 100vw, 591px"}

n=4,\[cite\]10.14469/ch/189763\[/cite\] Dipole moment 1.1 D. Better by
solvating the Cl^--^! The proton originally attached to the Cl is now
starting its transfer to the water to form that hydronium cation, but
the dipole moment is not yet large.

![hcl+4h2o1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-4h2o1.jpg){.aligncenter
.size-full .wp-image-13406 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/4H2O.log;frame 2;spin 3;');"
width="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-4h2o1.jpg 642w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/hcl-4h2o1-300x214.jpg 300w"
sizes="(max-width: 642px) 100vw, 642px"}

n=5.\[cite\]10.14469/ch/189756\[/cite\] Dipole moment 4.7D. The
ionisation is almost complete and the dipole moment is on the increase.

![5](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/5.jpg){.aligncenter
.size-full .wp-image-13412 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/5H2O.log;frame 104;spin 3;');"
width="250"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/5.jpg 392w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/5-196x300.jpg 196w"
sizes="(max-width: 392px) 100vw, 392px"}

n=6.\[cite\]10.14469/ch/189761\[/cite\] The dipole moment is up to 8.2D
and the three H-O bonds of the hydronium cation are almost all equal in
length.

![6](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/61.jpg){.aligncenter
.size-full .wp-image-13417 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/6H2O.log;frame 2;spin 3;');"
width="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/61.jpg 616w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/61-300x277.jpg 300w"
sizes="(max-width: 616px) 100vw, 616px"}

A cautionary observation though. The isomer below for
n=6\[cite\]10.14469/ch/189764\[/cite\] is lower in energy by ΔG -1.2
kcal/mol, and its dipole moment is only 2.5D! The charges (summed onto
heavy atoms) show the chloride to have -0.88 and the hydronium cation
+0.88, so it is a true ion-pair, despite its dipole moment.

![6a](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/6a.jpg){.aligncenter
.size-full .wp-image-13421 decoding="async"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/02/6H2Oi.log;frame 52;spin 3;');"
width="250"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/6a.jpg 496w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/02/6a-266x300.jpg 266w"
sizes="(max-width: 496px) 100vw, 496px"}

So these calculations do indeed appear to confirm that 5-6 water
molecules are required to ionise HCl. But it does raise the interesting
issue that even for n=6, there are poses for the assembly which have low
dipole moments. Clearly of course the observed dipole moment is a
dynamic average over many conformations of similar energy but the
prediction that some of these may have low dipole moments should be
noted.

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^‡^ If you right-click in the 3D model area, you can bring down a list
of vibrational modes for each complex from the first item of the pop-up
menu that appears (labelled model). You might wish to e.g. explore how
the H-Cl stretch vibration changes as the ionisation increases.

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.142410.09040){rel="noopener"
target="_blank"}.

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According to Guggemos, Slavicek and Kresin, about 5-6![cite]10.1103/PhysRevLett.114.043401[/cite]. This is one of those simple ideas, which is probably quite tough to do experimentally. It involved blasting water vapour through a pinhole, adding HCl and measuring the dipole-moment induced deflection by an electric field.

Publicaciones de Rogue Scholar

How many water molecules does it take to ionise HCl?