{"id":16118,"date":"2016-04-14T07:38:47","date_gmt":"2016-04-14T06:38:47","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=16118"},"modified":"2023-09-17T07:28:09","modified_gmt":"2023-09-17T06:28:09","slug":"hydronium-hydroxide-the-why-of-ph-7","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=16118","title":{"rendered":"Hydronium hydroxide: the why of pH 7."},"content":{"rendered":"
\n

\n\tAmmonium hydroxide (NH4<\/sub>+<\/sup>…OH–<\/sup>) can be characterised quantum mechanically<\/a> when stabilised by water bridges connecting the ion-pairs. It is a small step from there to hydronium hydroxide<\/strong>, or H3<\/sub>O+<\/sup>…OH–<\/sup>. The measured concentrations [H3<\/sub>O+<\/sup>] ≡ [OH–<\/sup>] give rise of course to the well-known pH 7 of pure water, and converting<\/a> 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.♣<\/sup> So can a quantum calculation reproduce pH7 for water?\n<\/p>\n

\n\tLet me start by saying that locating a stable minimum for H3<\/sub>O+<\/sup>…OH–<\/sup> 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 H2<\/sub>O…OH2<\/sub>.†<\/sup> So I now decided on a more systematic approach by running a CSD (Cambridge structure database) search, defining the species H3<\/sub>O+ <\/sup>and specifying that the oxygen sustain one additional hydrogen bond, as per H3<\/sub>O+<\/sup>….H.[1]<\/a><\/span> <\/sup>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.\n<\/p>\n

\n\t\"NH3-8\"\n<\/p>\n

\n\tRestricting the search to  H3<\/sub>O+<\/sup>….H-O  and specifying that the last O is bonded to just one atom‡<\/sup> reduces this to one hit.[2]<\/a><\/span> If you click on the image below or visit here[3]<\/a><\/span> you will see the hydrogen bonding pattern in this unique example is of the type (ROH…H)3<\/sub>O+<\/sup>…HO–<\/sup>(…HOR)3<\/sub> with overall three-fold symmetry. The "bridge" across the ion pair in this case is formed from hydrogen bonds to -CH2<\/sub>OH groups in 1,3,5-tris(hydroxymethyl)-2,4,6-triethylbenzene.\n<\/p>\n

\n\t\"NH3-8\"\n<\/p>\n

\n\tThis 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<\/em> minimum in a quantum mechanical potential. By analogy one would need three bridges, each to be comprised of 3H2<\/sub>O. In other words a system containing  eleven water molecules.  An ωB97XD\/6-311++G(d,p)\/SCRF=water calculation indeed reveals this C3<\/sub>-symmetric arrangement is a minimum with a calculated[4]<\/a><\/span> free energy (298K) 23.3 (23.5\/Def2-TZVPPD) kcal\/mol above that of the corresponding water cluster[5]<\/a><\/span> 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.\n<\/p>\n

\n\tThe calculated geometry[4]<\/a><\/span> reveals a H3<\/sub>O…HO hydrogen bond ~2.14Å, well within the range shown in the crystal structure distribution above.\n<\/p>\n

\n\t\"NH3-8\"\n<\/p>\n

\n\tWith 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.\n<\/p>\n

\n\tAddendum 1: <\/strong>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).\n<\/p>\n

\n\t\"NH3-8\"\n<\/p>\n

\n\tAddendum 2:<\/strong> Shown below is the intrinsic reaction cooordinate (IRC) calculated[6]<\/a><\/span> 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.\n<\/p>\n

\n\t\"NH3-8\"
\n\t\"NH3-8\"
\n\t\"NH3-8\"\n<\/p>\n

\n

\n\t♣<\/sup>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.\n<\/p>\n

\n\t†<\/sup>Recent calculations of like-charge pairs of either H3<\/sub>O+<\/sup> or OH–<\/sup> have been reported[7]<\/a><\/span> but not as an ion-pair. The temperature dependence of the autoionization has also been reported[8]<\/a><\/span> as involving, inter alia<\/em>, changes in the coordination number of the OH–<\/sup> with temperature.\n<\/p>\n

\n\t‡<\/sup>It is implicit when one talks about connecting bonds<\/i> 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.\n<\/p>\n

\n

Acknowledgments<\/h4>\n

This post has been cross-posted in PDF format at Authorea<\/a>.<\/p>\n

References<\/h2>\n
  1. H. Rzepa, \"Crystal structures containing the hydronium cation\", 2016. https:\/\/doi.org\/10.14469\/hpc\/370<\/a>\n\n<\/li>\n
  2. M. Stapf, W. Seichter, and M. Mazik, \"Unique Hydrogen\u2010Bonded Complex of Hydronium and Hydroxide Ions\", Chemistry \u2013 A European Journal<\/i>, vol. 21, pp. 6350-6354, 2015. https:\/\/doi.org\/10.1002\/chem.201406383<\/a>\n\n<\/li>\n
  3. Stapf, Manuel., Seichter, Wilhelm., and Mazik, Monika., \"CCDC 1034049: Experimental Crystal Structure Determination\", 2015. https:\/\/doi.org\/10.5517\/cc13q0f8<\/a>\n\n<\/li>\n
  4. H.S. Rzepa, \"H22O11\", 2016. https:\/\/doi.org\/10.14469\/ch\/191994<\/a>\n\n<\/li>\n
  5. H.S. Rzepa, \"H 22 O 11\", 2016. https:\/\/doi.org\/10.14469\/ch\/191995<\/a>\n\n<\/li>\n
  6. H.S. Rzepa, \"H22O11\", 2016. https:\/\/doi.org\/10.14469\/ch\/192002<\/a>\n\n<\/li>\n
  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<\/i>, vol. 17, pp. 16233-16237, 2015. https:\/\/doi.org\/10.1039\/c5cp02182k<\/a>\n\n<\/li>\n
  8. T. Yagasaki, K. Iwahashi, S. Saito, and I. Ohmine, \"A theoretical study on anomalous temperature dependence of pKw of water\", The Journal of Chemical Physics<\/i>, vol. 122, 2005. https:\/\/doi.org\/10.1063\/1.1878712<\/a>\n\n<\/li>\n<\/ol>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    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–. 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Of course, pure water consists of three potential catalysts, water itself or [H2O], and the products of autoionisation, [OH-] and\u00a0[H3O+]. The latter are in much smaller concentration, equivalent to a penalty of\u2026","rel":"","context":"In "reaction mechanism"","block_context":{"text":"reaction mechanism","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1086"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2021\/04\/ketyl-hydroxyl.gif?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":15924,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=15924","url_meta":{"origin":16118,"position":1},"title":"How many water molecules does it take to form ammonium hydroxide from ammonia and water?","author":"Henry Rzepa","date":"March 20, 2016","format":false,"excerpt":"This is a corollary to the previous post\u2021 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\u2026","rel":"","context":"In "General"","block_context":{"text":"General","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16320,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=16320","url_meta":{"origin":16118,"position":2},"title":"Autoionization of hydrogen fluoride.","author":"Henry Rzepa","date":"April 24, 2016","format":false,"excerpt":"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\u2026","rel":"","context":"In "Interesting chemistry"","block_context":{"text":"Interesting chemistry","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=4"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16308,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=16308","url_meta":{"origin":16118,"position":3},"title":"Deuteronium deuteroxide. The why of pD 7.435.","author":"Henry Rzepa","date":"April 22, 2016","format":false,"excerpt":"Earlier, I constructed a possible model of hydronium hydroxide, or H3O+.OH-\u00a0One way of assessing the quality of\u00a0the model is\u00a0to\u00a0calculate\u00a0the free energy difference between it and two normal water molecules\u00a0and compare\u00a0the result to\u00a0the measured\u00a0difference. Here I apply a further test of the model using isotopes. Pure water has pH 7, which\u2026","rel":"","context":"In "Interesting chemistry"","block_context":{"text":"Interesting chemistry","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=4"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16208,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=16208","url_meta":{"origin":16118,"position":4},"title":"Azane oxide, a tautomer of hydroxylamine.","author":"Henry Rzepa","date":"April 15, 2016","format":false,"excerpt":"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 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-,\u2021\u2026","rel":"","context":"In "General"","block_context":{"text":"General","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":23522,"url":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=23522","url_meta":{"origin":16118,"position":5},"title":"A computational mechanism for the aqueous hydrolysis of a ketal to a ketone and alcohol.","author":"Henry Rzepa","date":"April 1, 2021","format":false,"excerpt":"The previous post was about an insecticide and made a point that the persistence of both insecticides and herbicides is an important aspect of their environmental properties. Water hydrolysis will degrade them, a typical residency time being in the order of a few days. I noted in passing a dioxepin-based\u2026","rel":"","context":"In "reaction mechanism"","block_context":{"text":"reaction mechanism","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?cat=1086"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ch.ic.ac.uk\/rzepa\/blog\/wp-content\/uploads\/2021\/03\/R-1024x699.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]}],"jetpack_likes_enabled":false,"authors":[{"term_id":2661,"user_id":1,"is_guest":0,"slug":"admin","display_name":"Henry Rzepa","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/897b6740f7f599bca7942cdf7d7914af5988937ae0e3869ab09aebb87f26a731?s=96&d=blank&r=g","0":null,"1":"","2":"","3":"","4":"","5":"","6":"","7":"","8":""}],"_links":{"self":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/16118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=16118"}],"version-history":[{"count":75,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/16118\/revisions"}],"predecessor-version":[{"id":26505,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=\/wp\/v2\/posts\/16118\/revisions\/26505"}],"wp:attachment":[{"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16118"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fppma_author&post=16118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}