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.

Previously, I [looked
at](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15924){target="_blank"} models
of how ammonia could be protonated by water to form ammonium hydroxide.
The energetic outcome of my model matched the known equilbrium in water
as favouring the unprotonated form (p*K*b \~4.75). I add here two amines
for which R=Me~3~Si and R=CN. The idea is that the first will assist
nitrogen protonation by stabilising the positive centre and the second
will act in the opposite sense; an exploration if you like of how one
might go about computationally designing a
non-steric [superbasic](https://en.wikipedia.org/wiki/Superbase){target="_blank"}
amine that becomes predominantly protonated when exposed to water (p*K*b
\<1)^†^ and is thus more basic than hydroxide anion in this medium.

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/NH3OH.svg){.aligncenter
.size-full .wp-image-15936 decoding="async" width="440"}

Before reporting any calculations, let us see what the CSD (Cambridge
structure database) might contain. The search query is simple, a
3-coordinate amine forming a 4-coordinate quaternary nitrogen^†^ with
one N-H and a positive (formal) charge on the N, and a 1-coordinate
oxygen with one O-H and a negative charge on the O. With the constraints
R \< 10%, no disorder and no errors, one gets as many as 15
hits,\[cite\]10.14469/hpc/361\[/cite\] several of which also apparently
contain separate water molecules in the crystal. A warning bell (perhaps
several) sounds, since if R \< 5%, the number of hits drops to just 2;
these are clearly difficult structures to refine!^‡^ So there is some
tantalising evidence that in the solid state at least, the quaternary
ammonium group (with at least one N-H), water and a hydroxide
anion might be capable of co-existence. As noted below^†^ some
fascinating 2-coordinate amines have also been reported as
having superbasic properties.

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/nh+o-.jpg){.aligncenter
.size-full .wp-image-15936 decoding="async" width="150"}

**R=CN:** the well known compound
[cyanamide](https://en.wikipedia.org/wiki/Cyanamide){target="_blank"} is
known to act only as an acid and its basic properties are never quoted.
Shown below is the reaction path for transfer of a proton from water to
the amine using an 8-water model (n=8) in which two bridges can serve to
help stabilize any ionic form. The energy required to do so however is
at least 24 kcal/mol (ωB97XD/Def2-TZVPPD/SCRF=water) which indicates
that no protonated amine is formed. This can be attributed to the
electron withdrawing cyano group strongly destablising any adjacent
positive ammonium centre and thus effectively completely inhibiting its
formation.

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

**R=Me~3~Si:** this too is already
known\[cite\]10.1016/j.jorganchem.2006.09.021\[/cite\],\[cite\]10.5517/CCNDXZX\[/cite\]
but only in the presence of the non-coordinating counter-anion
B(C~6~F~5~)~4~ crystallised from non-protic solution. An ionised form
can now be located using the model above. This has the structure shown
below; note the very short hydrogen bonds associated with the hydroxide
anion and the possibility of forming only two water bridges across the
ion-pair. The relative free energy of the ion-pair (table below) shows
it to be if anything less basic than ammonia. 

![NH3-8](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/04/me3sinh3oh.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/nh.log;spin 3;');"
width="350"}

| | | | |
|----------|----------------------------------------|----------------------------------------------------------------------------|-----------------------------------------|
| n=8 | R=H | R=SiMe~3~ | R=CN |
| ΔΔG~298~ | 7.0\[cite\]10.14469/ch/191946\[/cite\] | 7.6\[cite\]10.14469/ch/191987\[/cite\],\[cite\]10.14469/ch/191982\[/cite\] | \>24\[cite\]10.14469/ch/191983\[/cite\] |

NBO (natural bond orbital) analysis might here  be a useful metric of
basicity. Hence Me~3~SiNH~2~...H~2~O  suggests that donation from the N
lone pair into an antiperiplanar Si-C bond is quite large (E(2) = 11.9
kcal/mol), although alternative donation by nitrogen into the H-O σ\*
bond  of the water is much higher (33.4 kcal/mol). 

Perhaps the basicity of simple amines is related to their ability to
form stabilizing water bridges across the ion-pair? With trimethylsilyl
substituents, this feature (and hence the basicity) is partially or even
fully suppressed as in *e.g.* tris(trimethylsilyl)amine.The pKb of the
latter appears to be unreported\[cite\]10.1039/tf9646001257\[/cite\] but
it does seem to be only weakly basic and \"*inert to
H~2~O*\",\[cite\]10.1002/zaac.19603030502\[/cite\] a property attributed
instead to multiple character in the Si-N bonds. 

I will in a future post look at the alternative class of phosphazenium
amines which do manage to achieve
superbasicity.\[cite\]10.5517/CC12MRFW\[/cite\]

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

^†^A phosphazenium 3-coordinate
amine\[cite\]10.1002/anie.198711671\[/cite\] was in 1991 claimed to be
the strongest metal-free neutral base. This has now been superceded by
combining this base motif with that of a sterically operating
proton sponge.\[cite\]10.1021/ja409760z\[/cite\],\[cite\]10.5517/CC12MRFW\[/cite\]
I will report the computational modelling of these systems in a later
post.

^‡^One of the structures identified with R\<10% is
UBEJIU\[cite\]10.1021/jm991140q\[/cite\] and which is worth showing
below. Note the apparent close contact of the type N-H...H-O
(1.416-1.463Å) rather than the expected N-H...OH.  If correct (this
feature is not mentioned in the article itself) it would be classified
as a ***dihydrogen bond***, a type normally only found in situations
such as B-H...H-N. There are a number of other inconsistencies which
must be resolved if this structure is to stand as correct.

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

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

Previously, I looked at models of how ammonia could be protonated by water to form ammonium hydroxide.

Messaggi di Rogue Scholar

Hydronium hydroxide: the why of pH 7.

Ways to encourage water to protonate an amine: superbasing.