Posts Tagged ‘Acid dissociation constant’

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.

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♣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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Ways to encourage water to protonate an amine: superbasing.

Friday, April 8th, 2016

Previously, I looked at 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 (pKb ~4.75). I add here two amines for which R=Me3Si 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 amine that becomes predominantly protonated when exposed to water (pKb <1)† and is thus more basic than hydroxide anion in this medium.

NH3-8

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,[1] 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.

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R=CN: the well known compound cyanamide 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

R=Me3Si: this too is already known[2],[3] but only in the presence of the non-coordinating counter-anion B(C6F5)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. 

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n=8 R=H R=SiMe3 R=CN
ΔΔG298 7.0[4]

7.6[5],[6]

>24[7]

NBO (natural bond orbital) analysis might here  be a useful metric of basicity. Hence Me3SiNH2…H2O  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[8] but it does seem to be only weakly basic and "inert to H2O",[9] 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.[10]

†A phosphazenium 3-coordinate amine[11] 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.[12],[10] I will report the computational modelling of these systems in a later post.

‡One of the structures identified with R<10% is UBEJIU[13] 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

References

  1. H. Rzepa, "Substituted ammonium hydroxides", 2016. https://doi.org/10.14469/hpc/361
  2. Y. Sarazin, J.A. Wright, and M. Bochmann, "Synthesis and crystal structure of [C6H5Hg(H2NSiMe3)][H2N{B(C6F5)3}2], a phenyl–mercury(II) cation stabilised by a non-coordinating counter-anion", Journal of Organometallic Chemistry, vol. 691, pp. 5680-5687, 2006. https://doi.org/10.1016/j.jorganchem.2006.09.021
  3. Sarazin, Y.., Wright, J.A.., and Bochmann, M.., "CCDC 608250: Experimental Crystal Structure Determination", 2007. https://doi.org/10.5517/ccndxzx
  4. H.S. Rzepa, and H.S. Rzepa, "H21NO9", 2016. https://doi.org/10.14469/ch/191946
  5. H.S. Rzepa, and H.S. Rzepa, "C 3 H 29 N 1 O 9 Si 1", 2016. https://doi.org/10.14469/ch/191987
  6. H.S. Rzepa, and H.S. Rzepa, "C 3 H 29 N 1 O 9 Si 1", 2016. https://doi.org/10.14469/ch/191982
  7. H.S. Rzepa, "CH20N2O9", 2016. https://doi.org/10.14469/ch/191983
  8. E.W. Abel, D.A. Armitage, and G.R. Willey, "Relative base strengths of some organosilicon amines", Transactions of the Faraday Society, vol. 60, pp. 1257, 1964. https://doi.org/10.1039/tf9646001257
  9. J. Goubeau, and J. Jimenéz‐Barberá, "Tris‐(trimethylsilyl)‐amin", Zeitschrift für anorganische und allgemeine Chemie, vol. 303, pp. 217-226, 1960. https://doi.org/10.1002/zaac.19603030502
  10. Kögel, Julius F.., Oelkers, Benjamin., Kovačević, Borislav., and Sundermeyer, Jörg., "CCDC 1002088: Experimental Crystal Structure Determination", 2014. https://doi.org/10.5517/cc12mrfw
  11. R. Schwesinger, and H. Schlemper, "Peralkylated Polyaminophosphazenes— Extremely Strong, Neutral Nitrogen Bases", Angewandte Chemie International Edition in English, vol. 26, pp. 1167-1169, 1987. https://doi.org/10.1002/anie.198711671
  12. J.F. Kögel, B. Oelkers, B. Kovačević, and J. Sundermeyer, "A New Synthetic Pathway to the Second and Third Generation of Superbasic Bisphosphazene Proton Sponges: The Run for the Best Chelating Ligand for a Proton", Journal of the American Chemical Society, vol. 135, pp. 17768-17774, 2013. https://doi.org/10.1021/ja409760z
  13. P. Vianello, A. Albinati, G.A. Pinna, A. Lavecchia, L. Marinelli, P.A. Borea, S. Gessi, P. Fadda, S. Tronci, and G. Cignarella, "Synthesis, Molecular Modeling, and Opioid Receptor Affinity of 9,10-Diazatricyclo[4.2.1.1<sup>2,5</sup>]decanes and 2,7-Diazatricyclo[4.4.0.0<sup>3,8</sup>]decanes Structurally Related to 3,8-Diazabicyclo[3.2.1]octanes", Journal of Medicinal Chemistry, vol. 43, pp. 2115-2123, 2000. https://doi.org/10.1021/jm991140q

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