Ammonium hydroxide (NH4+…OH–) can be characterised quantum mechanically when stabilised by water bridges connecting the ion-pairs.

Imperial College London

Henry Rzepa

Ammonium hydroxide (NH~4~^+^...OH^--^) can be [characterised quantum
mechanically](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15924){target="_blank"
rel="noopener"} when stabilised by water bridges connecting the
ion-pairs. It is a small step from there to **hydronium hydroxide**, or
H~3~O^+^...OH^--^. The measured concentrations \[H~3~O^+^\] ≡
\[OH^--^\] give rise of course to the well-known pH 7 of pure water, and
[converting](http://chemwiki.ucdavis.edu/Core/Organic_Chemistry/Fundamentals/What_is_the_pKa_of_water%3F){target="_blank"
rel="noopener"} this ionization constant to a free energy indicates that
the solvated ion-pair must be some \~19.1 kcal/mol higher in free energy
than water itself.^♣^ So can a quantum calculation reproduce pH7 for
water?

Let me start by saying that locating a stable minimum
for H~3~O^+^...OH^--^ is non-trival. I have been trying to find a
structure on and off for a little while now, but all my erstwhile
attempts have resulted in barrierless proton transfers back to
H~2~O...OH~2~.^†^ So I now decided on a more systematic approach by
running a CSD (Cambridge structure database) search, defining the
species H~3~O^+^ and specifying that the oxygen sustain one
additional hydrogen bond, as
per H~3~O^+^....H.\[cite\]10.14469/hpc/370\[/cite\]^ ^This produced 69
hits, with the distribution of O...H distances shown below indicating
that a wide spectrum of hydrogen bond lengths to this oxygen appears
possible.

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/h3o..h.jpg){.aligncenter
.size-full .wp-image-15936 decoding="async" width="400"}

Restricting the search to  H~3~O^+^....H-O  and specifying that the last
O is bonded to just one atom^‡^ reduces this to one
hit.\[cite\]10.1002/chem.201406383\[/cite\] If you click on the image
below or visit here\[cite\]10.5517/CC13Q0F8\[/cite\] you will see the
hydrogen bonding pattern in this unique example is of the type
(ROH...H)~3~O^+^...HO^--^(...HOR)~3~ with overall three-fold symmetry.
The \"bridge\" across the ion pair in this case is formed from hydrogen
bonds to -CH~2~OH groups
in 1,3,5-tris(hydroxymethyl)-2,4,6-triethylbenzene.

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/h3ooh.jpg){.aligncenter
.size-full .wp-image-15936 decoding="async"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2016/04/BUGMAT.mol;spin 3;');"
width="400"}

This structure immediately poses the question of whether water bridges
could replace the organic bridge in the species above, to enable the
elusive water-solvated hydronium hydroxide to finally be characterised
as a *bona-fide* minimum in a quantum mechanical potential. By
analogy one would need three bridges, each to be comprised of 3H~2~O. In
other words a system containing  eleven water molecules.  An
ωB97XD/6-311++G(d,p)/SCRF=water calculation indeed reveals this
C~3~-symmetric arrangement is a minimum with a
calculated\[cite\]10.14469/ch/191994\[/cite\] free energy (298K) 23.3
(23.5/Def2-TZVPPD) kcal/mol above that of the corresponding water
cluster\[cite\]10.14469/ch/191995\[/cite\] in which a proton transfer
has neutralised the ion pair. The error of +4.2 kcal/mol is probably due
to a combination of incomplete basis set (calculations with better bases
are under way), incomplete correction for solvation (continuum) as well
as the limited size of the explicit water cluster (nine supporting water
molecules) and other aspects such as the DFT method itself and the RRHO
partition function approximations for thermal corrections. It would be a
useful calibrant of all these aspects to explore whether these various
corrections would converge to the known value or not.

The calculated geometry\[cite\]10.14469/ch/191994\[/cite\] reveals a
H~3~O...HO hydrogen bond \~2.14Å, well within the range shown in the
crystal structure distribution above.

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/hydronium-hydroxide.jpg){.aligncenter
.size-full .wp-image-15936 decoding="async"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2016/04/hydronium-hydroxide.log;frame 164;spin 3;');"
width="400"}

With the basic model for hydronium hydroxide identified, one can now
explore how to improve both the accuracy of the model in reproducing the
\"pH 7\" observable and how indeed one might engineer a more superbasic
variation.

**Addendum 1:** The NCI (non-covalent-interaction) analysis of
the hydronium hydroxide water complex is shown below. The blue regions
indicate strong hydrogen bonds, with cyan being weaker. In fact, the
covalent/non-covalent threshold normally taken for an  NCI analysis
 (0.05 au) had to be increased to 0.10 for this example (the default
threshold was already treating the HO...H interactions as covalent
rather than non-covalent).

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/nci-h3ioh.jpg){.aligncenter
.size-full .wp-image-15936 decoding="async"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2016/04/11_den.cub.xyz;isosurface wp-content/uploads/2016/04/11_den.cub.jvxl translucent;zoom 150;');"
width="400"}

**Addendum 2:** Shown below is the intrinsic reaction cooordinate (IRC)
calculated\[cite\]10.14469/ch/192002\[/cite\] for the proton transfer
from the hydronium hydroxide ion-pair to form neutral water, revealing a
barrier of \~3kcal/mol and exothermicity of 23 kcal/mol and how the
dipole moment evolves.

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/PT.svg){.aligncenter
.size-full .wp-image-15936 decoding="async" width="450"}  
![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/DM.svg){.aligncenter
.size-full .wp-image-15936 decoding="async" width="450"}  
![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/PTb.gif){.aligncenter
.size-full .wp-image-15936 decoding="async" width="440"}

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

^♣^Dissociation/equilibrium constants are rarely converted into free
energies in text books and elsewhere. I would argue here that one gets a
better intuitive feeling for such systems if expressed as energies. In
this case, such a self-ionization energy for water might also be a
useful way of calibrating how any given quantum mechanical procedure
might perform in terms of the solvation model etc.

^†^Recent calculations of like-charge pairs of either H~3~O^+^ or OH^--^
have been reported\[cite\]10.1039/C5CP02182K\[/cite\] but not as an
ion-pair. The temperature dependence of the autoionization has also been
reported\[cite\]10.1063/1.1878712\[/cite\] as involving, *inter alia*,
changes in the coordination number of the OH^--^ with temperature.

^‡^It is implicit when one talks about *connecting bonds* that the
weaker hydrogen bonds do not qualify. Of course there is a whole
spectrum of hydrogen bonding strengths; ones involved in ion-pairs for
example can be up to 3 times stronger than those to neutral systems.

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.146372.26960){rel="noopener"
target="_blank"}.

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


Ammonium hydroxide (NH

 4


 +

…OH

 –

) can be characterised quantum mechanically when stabilised by water bridges connecting the ion-pairs.

Hydronium hydroxide: the why of pH 7.

[Earlier](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15295){target="_blank"
rel="noopener"} I explored models for the heteroaromatic electrophilic
protiodecarboxylation of an 3-substituted indole, focusing on the role
of water as the proton transfer and delivery agent. Next,
came [models](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15415){target="_blank"
rel="noopener"} for both water and the general **base**
catalysed ionization of indolinones. Here I explore general
**acid** catalysis by evaluating the properties of two possible models
for decarboxylation of 3-indole carboxylic acid, one involving proton
transfer (PT) from neutral water in the presence of covalent un-ionized
HCl (**1**) and one with PT from a protonated water resulting
from ionised HCl (**2**).

[![Indole
diazocoupling](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/01/decarbox2.svg){.aligncenter
.size-full .wp-image-14967 decoding="async" style="text-align: justify;"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/01/decarbox2.svg)

The original study\[cite\]10.1039/P29770000281\[/cite\] noted that the
rate of decarboxylation fitted well to the kinetic expression: [rate =
{a + b\[L~3~O^+^\]/(1 +
c\[L~3~O^+^\])}\[indole\]]{style="color:#FF0000;"}, where L can be H
or D. Experimentally, \[L~3~O^+^\] is controlled by adding a strong
general acid such as HCl, which when the
[appropriate](http://www.ch.imperial.ac.uk/rzepa/blog/?p=13394){target="_blank"
rel="noopener"} number of water molecules are
added\[cite\]10.1002/chem.201504016\[/cite\] fully ionizes to
H~3~O^+^.OH^--^. Now for B3LYP+D3/Def2-TZVPD/SCRF=water calculations:

- Model **1 **takes the pure water model and adds HCl (blue above) *via*
  hydrogen bonding to the H~2~O that is transferring the proton to the
  indole ring. Three water molecules are hydrogen bonding to the
  carboxylate oxygens to create a bicyclic network in which a ring of
  either 8 or 10 atoms can act as the proton relay structure. The
  question now arises whether the proton relay takes the longer (red)
  route or the slightly shorter green route.
- Isomeric model **2** uses H~3~O^+^ for proton transfer, with an
  adjacent Cl^--^ to complete the ion-pair.

|       |                     |                                                                                                                                                       |                                                                        |
|-------|---------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------|
| Model | ΔG^‡^~298~ (0.044M) | DataDOIs                                                                                                                                              | k^H^/k^[D]{style="font-size: 11px;"}^\[cite\]10.14469/hpc/204\[/cite\] |
| 1     | 27.4                | \[cite\]10.14469/ch/191792\[/cite\],^‡^\[cite\]10.14469/ch/191795\[/cite\],^†^\[cite\]10.14469/ch/191794\[/cite\],\[cite\]10.14469/ch/191767\[/cite\] | 5.69                                                                   |
| 2     | 16.8^‡^ (14.8)^†^   | \[cite\]10.14469/ch/191795\[/cite\],\[cite\]10.14469/ch/191790\[/cite\],\[cite\]-\[/cite\]                                                            | 2.45                                                                   |

^‡^[Reactant as a non-ionised covalent HCl.]{style="font-size:10px;"}
^†^[reactant as an isomeric ionized H~3~O^+^.Cl^-- ^ beng 2.0 kcal/mol
higher in energ within this solvation model. [Note added in proof. A
significantly lower form of the reactant has subsequently been located
which increases the free energy barrier to 22.1 kcal (vis 22.0 actually
measured!). Diacussion of this can be seen in the [associated post
here](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15505){target="_blank"
rel="noopener"}.]{style="color:#FF0000;"}]{style="font-size:10px;"}

1.  An IRC for Model 1 shows that the proton relay takes the red path,
    whereas without the HCl the green path is followed.

     

     

     

    [![Indole
    diazocoupling](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/01/HCL-cova.gif){.aligncenter
    .size-full .wp-image-14967 decoding="async"
    style="text-align: justify;"
    width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/01/HCL-cova.gif)

    The transition state free energy however is ..

2.  10.6^‡ ^or 12.6^†^ kcal/mol **higher** than model **2 **(click on
    the image below to load a 3D model). The general acid catalysed
    model is therefore preferred. The difference in free energy between
    the two models corresponds to a rate acceleration of
    \>10^6^,^ ^which is indeed similar to that
    observed\[cite\]10.1039/P29770000281\[/cite\].

![Decarboxylation using a general acid
catalyst](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/01/Model2.jpg){.aligncenter
.size-full .wp-image-14967 decoding="async"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2016/01/model2.log;frame 3;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;');"
style="text-align: justify;" width="400"}

The clincher comes with calculation\[cite\]10.14469/hpc/204\[/cite\] of
the kinetic isotope effects (KIE). For general acid catalysis, they were
measured as k^H^/k^D^ \~2.5.\[cite\]10.1039/P29770000281\[/cite\]

- For model 1, using an un-ionised reactant and un-ionised transition
  state, the calculated KIE is 5.69 (very similar to that [calculated
  for the water catalysed
  reaction](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15295){target="_blank"
  rel="noopener"}, 5.66) but not a good fit to experiment.
- For model 2, using the same un-ionised reactant but an ionised
  transition state, KIE = 2.04, a much better fit.
- For model 2, using ionised reactant AND transition state, KIE =
  [[**2.45**]{style="color:#FF0000;"}]{style="font-size:14px;"}, an even
  better fit to experiment.

So we now have a model for the general acid catalysed decarboxylation of
a 3-indole carboxylate which agrees with both the kinetic behaviours and
the isotope effects measured for this reaction. Since the barrier is a
relatively large one, proton tunnelling may play a lesser role in this
interpretation, and the stage is set to use this model to *e.g.* explore
how isotope effects are indeed influenced by tuning the reactivity using
ring substitutents, the original purpose of my researches all those
years ago. Perhaps the catch phrase *I've started so I'll start* is now
more apposite.

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.145337.72789){rel="noopener"
target="_blank"}.

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


Earlier I explored models for the heteroaromatic electrophilic protiodecarboxylation of an 3-substituted indole, focusing on the role of water as the proton transfer and delivery agent. Next, came models for both water and the general

 base

catalysed ionization of indolinones.

Messaggi di Rogue Scholar

Hydronium hydroxide: the why of pH 7.

I’ve started so I’ll finish. Kinetic isotope effect models for a general acid as a catalyst in the protiodecarboxylation of indoles.