Earlier, I constructed a possible model of hydronium hydroxide, or H3O+.OH– One way of assessing the quality of the model is to calculate the free energy difference between it and two normal water molecules and compare the result to the measured difference. Here I apply a further test of the model using isotopes.

Imperial College London

Henry Rzepa

[Earlier](http://www.ch.imperial.ac.uk/rzepa/blog/?p=16118){target="_blank"
rel="noopener"}, I constructed a possible model of hydronium hydroxide,
or H~3~O^+^.OH^-- ^One way of assessing the quality of the model
is to calculate the free energy difference between it and two normal
water molecules and compare the result to the measured difference. Here
I apply a further test of the model using isotopes.

Pure water has pH 7, which means equal concentrations for both
\[H~3~O^+^\] and  \[OH^--^\] of 10^-7^M. Converting this to a free
energy one gets ΔG~298~ 19.088 kcal/mol. Now the pD of pure deuterium
oxide is
[reported](http://www.madsci.org/posts/archives/2005-08/1125410589.Ch.r.html){target="_blank"
rel="noopener"} as 7.435, equivalent to ΔG~298~ 20.274, an isotope
effect on the free energy of ΔΔG~298~
=**[1.186]{style="color:#FF0000;"}** kcal/mol. How does the theoretical
model (ωB97XD/Def2-TZVPPD/SCRF=water^‡^) previously
reported\[cite\]10.14469/ch/191999\[/cite\],\[cite\]10.14469/ch/191998\[/cite\]
do? The value obtained is**[
1.215]{style="color:#FF0000;"}**,\[cite\]10.14469/hpc/407\[/cite\] an
apparent error of only 0.029 kcal/mol. I am quite pleased with the close
correspondence; at least the model is capable of reporting good isotope
effects on the ionisation equilibrium of pure water!

Finally, with some confidence assured, one might apply this to tritonium
tritoxide. Tritiated water is so radioactive it would boil in an
instant, probably well before its pT could be measured. ΔΔG~298~ is
calculated as **[1.798]{style="color:#FF0000;"}** kcal/mol. Will this
estimate ever be challenged by experiment?

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

‡ It is assumed no isotope effect acts on the dielectric constant of
water and hence the continuum model used here to model it. In fact the
isotope effect on this property is modest; ε~298~ = 77.94, compared with
78.36 for normal water.\[cite\]10.6028/jres.060.060\[/cite\]

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.146139.99408){rel="noopener"
target="_blank"}.

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Earlier, I constructed a possible model of hydronium hydroxide, or H
<sub>
 3
</sub>
O
<sup>
 +
</sup>
.OH^– ^One way of assessing the quality of the model is to calculate the free energy difference between it and two normal water molecules and compare the result to the measured difference. Here I apply a further test of the model using isotopes.

Messaggi di Rogue Scholar

Deuteronium deuteroxide. The why of pD 7.435.