Posts Tagged ‘Properties of water’

Autoionization of hydrogen fluoride.

Sunday, April 24th, 2016

The autoionization of water involves two molecules transfering a proton to give hydronium hydroxide, a process for which the free energy of reaction is well known. Here I ask what might happen with the next element along in the periodic table, F.

I have been unable to find much about the autoionization of HF in the literature; the pH of neat HF appears unreported (unlike that of H2O, which of course is 7). Even the dielectric constant of liquid HF[1],[2] seems to vary widely, the largest reported being ~84. It is suggested that liquid HF is much less ordered than e.g. water, and this suggests that a single static model is unlikely to be entirely realistic. Nonetheless, I thought it might be informative to take the model I previously constructed for water and try applying it to HF. Here is part of the geometry optimisation cycle[3] from the original edited water model. I used ωB97XD/Def2-TZVPPD/SCRF=water for the model. Why continuum water as the solvation treatment? Well, standard parameters for liquid HF are not available (perhaps given the variation in dielectric) and since the upper bound might be similar to water, I decided to use that to see what I got. Clearly however an approximation.

The low energy final geometry corresponds to 10 HF molecules and lies about 16 kcal/mol lower (in total energy) than the cyclic structure containing H2F+.F– species connected by two (HF)3 bridges and two further non-bridge HF molecules hydrogen bonding to the H2F+ and the F–. In fact the ionic structure turns out to be a transition state for proton shifting along the chain to create (HF)10, with a free energy barrier of 9.2 kcal/mol above the neutral form.[4] This difference between ionic and non-ionic forms is considerably less than that for water as previously indicated. Note also how much shorter the hydrogen bonding H…F distances are in the HF cluster.

So unlike water, where the hydronium hydroxide is a clear minimum in the potential with a small but distinct barrier (~3.5 kcal/mol[5]) to proton transfer, with HF at the same level of theory the barrier is zero. Perhaps the difference might be because whereas hydronium hydroxide can support three stabilizing (H2O)3 bridges, only two (HF)3 bridges are possible with H2F+.F–. It might also be higher levels of theory (or better/larger models of the HF cluster) could well give a barrier for the process, but this does tend to suggest that the dynamics of HF liquid may suggest quite different lifetimes for autoionized forms of HF compared to water. Liquid HF is clearly just as complicated a liquid as is H2O, certainly much less is known about it.

References

  1. R.H. Cole, "Dielectric constant and association in liquid HF", The Journal of Chemical Physics, vol. 59, pp. 1545-1546, 1973. https://doi.org/10.1063/1.1680219
  2. P.H. Fries, and J. Richardi, "The solution of the Wertheim association theory for molecular liquids: Application to hydrogen fluoride", The Journal of Chemical Physics, vol. 113, pp. 9169-9179, 2000. https://doi.org/10.1063/1.1319172
  3. H.S. Rzepa, "H 10 F 10", 2016. https://doi.org/10.14469/ch/192032
  4. H.S. Rzepa, "H 10 F 10", 2016. https://doi.org/10.14469/ch/192034
  5. H.S. Rzepa, "H22O11", 2016. https://doi.org/10.14469/ch/192022

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Deuteronium deuteroxide. The why of pD 7.435.

Friday, April 22nd, 2016

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.

Pure water has pH 7, which means equal concentrations for both [H3O+] and  [OH–] of 10-7M. Converting this to a free energy one gets ΔG298 19.088 kcal/mol. Now the pD of pure deuterium oxide is reported as 7.435, equivalent to ΔG298 20.274, an isotope effect on the free energy of ΔΔG298 =1.186 kcal/mol. How does the theoretical model (ωB97XD/Def2-TZVPPD/SCRF=water‡) previously reported[1],[2] do? The value obtained is 1.215,[3] 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. ΔΔG298 is calculated as 1.798 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; ε298 = 77.94, compared with 78.36 for normal water.[4]

References

  1. H.S. Rzepa, "H 22 O 11", 2016. https://doi.org/10.14469/ch/191999
  2. H.S. Rzepa, "H 22 O 11", 2016. https://doi.org/10.14469/ch/191998
  3. H. Rzepa, "Deuteronium deuteroxide; free energy differences.", 2016. https://doi.org/10.14469/hpc/407
  4. C. Malmberg, "Dielectric constant of deuterium oxide", Journal of Research of the National Bureau of Standards, vol. 60, pp. 609, 1958. https://doi.org/10.6028/jres.060.060

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Oxane oxide: a tautomer of hydrogen peroxide.

Friday, April 15th, 2016

 If H3N+-O– is viable compared with its tautomer H2N-OH when carrying water bridges, then why not try H2O+-O– vs HO-OH?

There are no examples to be found in crystal structures! The solvated structure of H2O+-O– is modified directly from that of H3N+-O– and the computed (ωB97XD/6-311++G(d,p)/SCRF=water) structure[1] is shown below. Noteworthy is that the hydrogen bonds at the O+ end are far stronger than those to at the O– end.

NH3-8

The corresponding hydrated hydrogen peroxide is 16.3 kcal/mol lower in free energy; this compares favourably with the value for water itself and suggests that oxane oxide might also be capable of isolation inside a suitable hydrogen bond stabilising cavity.

References

  1. H.S. Rzepa, "H20O11", 2016. https://doi.org/10.14469/ch/192005

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Azane oxide, a tautomer of hydroxylamine.

Friday, April 15th, 2016

In the previous post I described how hydronium hydroxide or H3O+…HO–, an intermolecular tautomer of water, has recently been observed captured inside an organic cage[1] and how the free-standing species in water can be captured computationally with the help of solvating water bridges. Here I explore azane oxide or H3N+-O–,‡ a tautomer of the better known hydroxylamine (H2N-OH).

The usual search[2] of the Cambridge structure database reveals only two (related) entries[3],[4] the second reported in 2015.[5].

NH3-8
NH3-8

Now, location of hydrogen atoms is always a bit tricky, but here we see two species H3N+-OH…–O-+NH3 connected by a strong hydrogen bond of 1.54Å (click on the above image to see this packing). However, it is noteworthy that the N-O bonds for each of these species are exactly the same length (1.412Å); one might have imagined that whether the oxygen carries a proton or not would affect its bond length to nitrogen. There is here a strong hint that energetically the azane oxide might be relatively low in energy relative to hydroxylamine and perhaps that the zwitterionic form might be favoured when captured with hydrogen bonds.

So certainly time for a computational exploration of this species. I am using the three water bridges as before, each comprised of three water molecules and the ωB97XD/6-311++G(d,p)/SCRF=water method. In fact the structure optimises[6] to a delightful propeller-like geometry in which bridges are formed from both two AND three waters across the ion-pair, with overall three-fold C3 symmetry (i.e. chiral! Indeed, this species has a predicted optical rotation of 40° at 589nm).

NH3-8

Hydroxylamine itself has a less symmetric arrangement of hydrogen bonds[7], with a free energy in fact very similar (within 1 kcal/mol) to the ion-pair isomer. Here, a stochastic (statistical) exploration of all the various arrangements of water would be needed to be confident that the lowest energy form had been located. I would note that the N-O bond lengths in the ion-pair and neutral forms are respectively 1.399 and 1.435Å.

NH3-8

Certainly, this very brief computational look at azane oxide suggests that concentrations of this species in aqueous solutions of hydroxylamine might be appreciable (detectable). Its "trapping" inside a suitably designed cavity must be a realistic possibility (the cavity used to trap hydronium hydroxide probably does not have the correct dimensions for this purpose), as indeed illustrated in the two crystal structures noted above.

‡ I have represented this species in ionic form, but you may find text books showing it in dative form, or H3N→O. My personal inclination is to always prefer the ionic form, if only because it enables connections/analogies such as the one here to hydronium hydroxide to be more easily made.

References

  1. M. Stapf, W. Seichter, and M. Mazik, "Unique Hydrogen‐Bonded Complex of Hydronium and Hydroxide Ions", Chemistry – A European Journal, vol. 21, pp. 6350-6354, 2015. https://doi.org/10.1002/chem.201406383
  2. H. Rzepa, "Search for Azane oxide", 2016. https://doi.org/10.14469/hpc/380
  3. Fischer, Dennis., Klapotke, Thomas M.., and Stierstorfer, Jorg., "CCDC 1054611: Experimental Crystal Structure Determination", 2015. https://doi.org/10.5517/cc14ddqn
  4. Fischer, D.., Klapotke, T.M.., and Stierstorfer, J.., "CCDC 827687: Experimental Crystal Structure Determination", 2012. https://doi.org/10.5517/ccws8lh
  5. D. Fischer, T.M. Klapötke, and J. Stierstorfer, "1,5‐Di(nitramino)tetrazole: High Sensitivity and Superior Explosive Performance", Angewandte Chemie International Edition, vol. 54, pp. 10299-10302, 2015. https://doi.org/10.1002/anie.201502919
  6. H.S. Rzepa, "H 21 N 1 O 10", 2016. https://doi.org/10.14469/ch/192000
  7. H.S. Rzepa, "H 21 N 1 O 10", 2016. https://doi.org/10.14469/ch/192001

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Hydronium hydroxide: the why of pH 7.

Thursday, April 14th, 2016

Ammonium hydroxide (NH4+…OH–) can be characterised quantum mechanically when stabilised by water bridges connecting the ion-pairs. It is a small step from there to hydronium hydroxide, or H3O+…OH–. The measured concentrations [H3O+] ≡ [OH–] give rise of course to the well-known pH 7 of pure water, and converting 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 H3O+…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 H2O…OH2.† So I now decided on a more systematic approach by running a CSD (Cambridge structure database) search, defining the species H3O+ and specifying that the oxygen sustain one additional hydrogen bond, as per H3O+….H.[1] 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

Restricting the search to  H3O+….H-O  and specifying that the last O is bonded to just one atom‡ reduces this to one hit.[2] If you click on the image below or visit here[3] you will see the hydrogen bonding pattern in this unique example is of the type (ROH…H)3O+…HO–(…HOR)3 with overall three-fold symmetry. The "bridge" across the ion pair in this case is formed from hydrogen bonds to -CH2OH groups in 1,3,5-tris(hydroxymethyl)-2,4,6-triethylbenzene.

NH3-8

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 3H2O. In other words a system containing  eleven water molecules.  An ωB97XD/6-311++G(d,p)/SCRF=water calculation indeed reveals this C3-symmetric arrangement is a minimum with a calculated[4] free energy (298K) 23.3 (23.5/Def2-TZVPPD) kcal/mol above that of the corresponding water cluster[5] 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[4] reveals a H3O…HO hydrogen bond ~2.14Å, well within the range shown in the crystal structure distribution above.

NH3-8

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

Addendum 2: Shown below is the intrinsic reaction cooordinate (IRC) calculated[6] 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
NH3-8
NH3-8

♣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 H3O+ or OH– have been reported[7] but not as an ion-pair.

‡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.

References

  1. H. Rzepa, "Crystal structures containing the hydronium cation", 2016. https://doi.org/10.14469/hpc/370
  2. M. Stapf, W. Seichter, and M. Mazik, "Unique Hydrogen‐Bonded Complex of Hydronium and Hydroxide Ions", Chemistry – A European Journal, vol. 21, pp. 6350-6354, 2015. https://doi.org/10.1002/chem.201406383
  3. Stapf, Manuel., Seichter, Wilhelm., and Mazik, Monika., "CCDC 1034049: Experimental Crystal Structure Determination", 2015. https://doi.org/10.5517/cc13q0f8
  4. H.S. Rzepa, "H22O11", 2016. https://doi.org/10.14469/ch/191994
  5. H.S. Rzepa, "H 22 O 11", 2016. https://doi.org/10.14469/ch/191995
  6. H.S. Rzepa, "H22O11", 2016. https://doi.org/10.14469/ch/192002
  7. M.K. Ghosh, T.H. Choi, and C.H. Choi, "Like-charge ion pairs of hydronium and hydroxide in aqueous solution?", Physical Chemistry Chemical Physics, vol. 17, pp. 16233-16237, 2015. https://doi.org/10.1039/c5cp02182k

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How many water molecules does it take to form ammonium hydroxide from ammonia and water?

Sunday, March 20th, 2016

This is a corollary to the previous post‡ exploring how many molecules are needed to ionise HCl. Here I am asking how many water molecules are required to form the ionic ammonium hydroxide from ammonia and water.

As Wikipedia will inform you, "it is actually impossible to isolate samples of NH4OH (more formally the ion-pair NH4+OH– ) as these ions do not comprise a significant fraction of the total amount of ammonia except in extremely dilute solutions (my italics)". In fact, the ionization constant Kb = [NH4+][OH–]/[NH3][H2O] is ~1.8 x 10-5 (pKb 4.75) equivalent to a free energy difference of  ~6.5 kcal/mol between the two forms.† This is in stark contrast to solutions of e.g. HCl in water, where essentially all of the HCl is ionised to hydronium chloride or H3O+Cl– by addition of just ~4-5 water molecules. So what is the water model required to compute this known behaviour of ammonia? Here, this will be ωB97Xd/Def2-TZVPPD/SCRF=water, i.e. a continuum water model is already included and we add n further discrete water molecules to enhance it.

For n=0 or 2, the ion-pair is not an explicit minimum (although it appears to be a "hidden intermediate"[1]). Values of e.g. n=4,6,8 allow the formation of two or three "bridges" comprising two or three water molecules connecting the N and O atoms by hydrogen bonds and this additional solvation enables location of a transition state for proton transfer between O and N. This implies an equilibrium can be established as NH3 + H2O ⇌* NH4+.OH– with the ion-pair now a genuine minimum stabilized by those ion-pair bridges. Note in particular how the hydrogen bond lengths involving the water salt-bridge in the ion-pair are shorter than for the neutral water-ammonia complex.

NH3-8

The contact ion-pair is nevertheless a very shallow minimum when surrounded by 4 or more explicit waters, the barrier from proton transfer from N being less than a vibrational quantum, and so the lifetime of the contact ion-pair is very much defined by the proton dynamics of the system..

4

8

For n=8, the dipole moment changes along the IRC for proton transfer between N and O as might be expected for the collapse of a contact ion-pair.

8dm

The relative free energies of the ion-pair and the un-ionized pair are shown below, the former being the higher. The values correspond approximately to the known ionization constant. As more explicit water molecules are added, there is a hint that the proportion of ion-pairs might actually decrease relative to neutral ammonia. However, these calculations are for a contact ion-pair and not a solvent-separated ion pair, the latter form possibly being the more appropriate form for extremely dilute solutions (see above). Modelling the latter type of ion-pair is not as straightforward as the contact variety;  as the ion separation increases, so the propensity for barrierless proton transfers increases, ultimately leading back to the contact form. So to understand if it is correct that in extremely dilute solutions there is no remaining neutral ammonia, probably only a full molecular dynamics treatment of such a system is likely to give further insights.

n 4 6 8
 ΔΔG298 6.4[2] 5.9[3] 7.0[4]

To summarise, in order to compute the formation of the ammonium hydroxide ion pair from ammonia and water, one has to include an additional four or more explicit water molecules in the calculation. This model confirms that in the resulting equilibrium, only a tiny proportion of the ammonia becomes ionised. With such a base model in place, one can now proceed to investigate how addition of substituents on the nitrogen might impact upon such ionisation, i.e. to form a stronger or a weaker base.

‡A more complete analysis followed.[5] *If you are wondering how to produce a reversible arrow, see here. †This is only approximate, since the concentration of water needs renormalising.

 

References

  1. https://doi.org/
  2. H.S. Rzepa, and H.S. Rzepa, "H13NO5", 2016. https://doi.org/10.14469/ch/191950
  3. https://doi.org/
  4. H.S. Rzepa, and H.S. Rzepa, "H21NO9", 2016. https://doi.org/10.14469/ch/191946
  5. A. Vargas‐Caamal, J.L. Cabellos, F. Ortiz‐Chi, H.S. Rzepa, A. Restrepo, and G. Merino, "How Many Water Molecules Does it Take to Dissociate HCl?", Chemistry – A European Journal, vol. 22, pp. 2812-2818, 2016. https://doi.org/10.1002/chem.201504016

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