Posts Tagged ‘Ammonium’

Organocatalytic cyclopropanation of an enal: (computational) mechanistic understanding.

Saturday, August 25th, 2018

Symbiosis between computation and experiment is increasingly evident in pedagogic journals such as J. Chemical Education. Thus an example of original laboratory experiments[1],[2] that later became twinned with a computational counterpart.[3] So when I spotted this recent lab experiment[4] I felt another twinning approaching.

The reaction under consideration is that between dec-2-enal and 2,4-dinitrobenzyl chloride as catalysed by an α,α-diphenylprolinol trimethylsilyl ester with addition of further base (di-isopropylamine?). The proposed mechanism can be seen in figure 7‡ of the journal article[4] and also scheme 2 of an earlier article.[5] The following is my interpretation of their published mechanism (the compound numbering is the same as in Figure 7).

  1. The initiating step is the condensation between the alkyl enal (1) and the prolinol derivative (3), with elimination of water and the formation of a positive iminium cation (5). One might wonder at this stage what the counter ion to this cation is.
  2. 5 then reacts with 2,4-dinitrobenzyl chloride (2) with apparent elimination of HCl to form 6. This corresponds to 1,4-Michael addition to 5 with the formation of the first new  C-C bond and the creation of two new stereogenic centres.
  3. 6 then cyclises to form a second new C-C bond and a third new stereogenic centre as in 7.
  4. 7 is then hydrolysed to give the final product 4.

A total of three (starred) stereogenic centres are therefore created in 4, implying 23 = 8 steroisomers, arranged as four diastereomers and their enantiomers. A computational mechanistic analysis might strive to cast light on the following questions.

  • Is the sequence shown in figure 7 reasonable? If not can a more reasonable cycle be constructed that has energetics corresponding to a facile reaction at 0°C?
  • What are the predicted relative yields of the four possible diastereomeric products and do they match those observed?
  • If  R=α,α-diphenylprolinol trimethylsilyl ester, then this fourth chiral centre increases the total number of stereoisomers to 16, arranged in eight pairs of diastereomers. Does this result in the diastereomers of 4 forming with an excess of one enantiomer over the other (an ee ≠ 0)?

This post addresses just the first question (R=R’=H, R”=isopropylamine) leaving the other two questions for later analysis.

My analysis (figure above)♥ of the mechanism, as cast for computational analysis†, differs in various details from Figure 7/Scheme 2 of the published articles.[4],[5]

  1. The issue of defining a counterion to 5 is solved by in fact starting the cycle with proton abstraction from 2 by di-isopropylamine♦ to form a benzylic anion, as stabilized by the 2,4-dinitro groups and with the positive counter-ion being the protonated amine base.
  2. The next step is reaction between 1 and 3 to form an aminol 10, a tetrahedral intermediate.
  3. To remove water from this to form an iminium cation 5, one has to protonate the hydroxy group and this can now be done using the cationic ammonium species formed in step 5 above.
  4. The benzylic anion can now react with the iminium cation to form the first C-C bond and the first two stereocentres via 1,4-Michael addition to form 6
  5. The species 6 can now eliminate chloride anion to form the cyclopropyl iminium cation/anion pair 7, generating the 3rd stereogenic centre.
  6. Hydrolysis forms the product 4 and returns the system to the starting point in the catalytic cycle.
  7. Also included is whether an alternative mechanism is viable, involving elimination of Cl– from 8 to form a “carbene”, which could then potentially add to the alkene in 1.

Species (transition state)

FAIR Data DOI
10.14469/hpc/4642

ΔG273.15, Hartree
(ΔΔG‡273.15, kcal/mol)

Structure
(click for 3D model)
Reactants -1837.174744♣ (0.0)
TS1 -1837.150502 (15.2)
TS2 -1837.154923 (12.4)
TS3 -1837.147927 (16.8)
TS4 -1837.175723 (-0.6)
TS5 -1837.101534 (45.9)

The (relative) free energies of the transition states at the B3LYP+GD3BJ/6-311G(d,p)/SCRF=chloroform level shown in the table above (click on the thumbnail images to show the 3D model of each transition state) reveal that the highest point corresponds to TS3, a C-C bond forming reaction. This is noteworthy because it constitutes the reaction between an ion-pair, albeit ions which are both heavily stabilized by delocalisation. Since the reaction is known to proceed over 3 hours at 0°C, the activation barrier of 16.8 kcal/mol is also entirely reasonable. TS5, the putative formation of a carbene from the benzyl chloride, has a very high barrier and in fact cyclises to form 9. This pathway can therefore be safely ignored.

The next stage would be to investigate the stereochemical implications of this mechanism (atoms in 4 marked with a *) using the actual substituents for R and R’. Because the mechanism includes ion-pairs throughout, this does actually present some tricky issues. Unlike molecules with covalent bonds, where the shapes are relatively easy to predict, ion-pairs are more flexible and can often adopt a variety of poses, the relative energy of which is frequently determined simply by the magnitudes of their dipole moments.[6] If I manage to sort this out, I will report back here.

‡I would love to show you figure 7 here, but the publisher asserts that I would need to pay them $87.75 to do so and so you will have to acquire the article yourself to see it.

†Various guiding rules include constructing the entire catalytic cycle using exactly the same number of atoms so that the cycle can show only relative (free) energies and using neutral ion-pair models rather than just charged species alone.

♥Almost all the chemical diagrams on this blog for some ten years now have been in SVG (scalable vector graphics) format. Most modern web browsers for a number of years now have had excellent support for SVG. Until recently SVG could not be generated directly from a drawing program such as e.g. ChemDraw. Instead I saved as EPS (encapsulated postscript) and then used a program called Scribus to convert to SVG. In fact with Chemdraw V18.0, the direct conversion to SVG seems to be working very well, including honoring color maps. To scale up a diagram, click on it to open a new browser window containing only it and then use the browser zoom-in control to magnify it. Unlike e.g. a pixel image, SVG images magnify/scale correctly.

♣This relates to metadata as described in this post in performing a global search of any species matching this Gibbs Energy.

♦If the mechanism is set up without any base, then proton abstraction must occur directly from the benzyl chloride. Under these circumstances, the barrier for proton removal is 27.5 kcal/mol, whilst that for C-C bond formation is only 13.6.

References

  1. A. Burke, P. Dillon, K. Martin, and T.W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", Journal of Chemical Education, vol. 77, pp. 271, 2000. https://doi.org/10.1021/ed077p271
  2. J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", Journal of Chemical Education, vol. 78, pp. 1266, 2001. https://doi.org/10.1021/ed078p1266
  3. K.K.(. Hii, H.S. Rzepa, and E.H. Smith, "Asymmetric Epoxidation: A Twinned Laboratory and Molecular Modeling Experiment for Upper-Level Organic Chemistry Students", Journal of Chemical Education, vol. 92, pp. 1385-1389, 2015. https://doi.org/10.1021/ed500398e
  4. M. Meazza, A. Kowalczuk, S. Watkins, S. Holland, T.A. Logothetis, and R. Rios, "Organocatalytic Cyclopropanation of (<i>E</i>)-Dec-2-enal: Synthesis, Spectral Analysis and Mechanistic Understanding", Journal of Chemical Education, vol. 95, pp. 1832-1839, 2018. https://doi.org/10.1021/acs.jchemed.7b00566
  5. M. Meazza, M. Ashe, H.Y. Shin, H.S. Yang, A. Mazzanti, J.W. Yang, and R. Rios, "Enantioselective Organocatalytic Cyclopropanation of Enals Using Benzyl Chlorides", The Journal of Organic Chemistry, vol. 81, pp. 3488-3500, 2016. https://doi.org/10.1021/acs.joc.5b02801
  6. J. Clarke, K.J. Bonney, M. Yaqoob, S. Solanki, H.S. Rzepa, A.J.P. White, D.S. Millan, and D.C. Braddock, "Epimeric Face-Selective Oxidations and Diastereodivergent Transannular Oxonium Ion Formation Fragmentations: Computational Modeling and Total Syntheses of 12-Epoxyobtusallene IV, 12-Epoxyobtusallene II, Obtusallene X, Marilzabicycloallene C, and Marilzabicycloallene D", The Journal of Organic Chemistry, vol. 81, pp. 9539-9552, 2016. https://doi.org/10.1021/acs.joc.6b02008

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Ammonide: an alkalide formed from ammonia and resembling an electride.

Sunday, December 17th, 2017

Alkalides are anionic alkali compounds containing e.g. sodide (Na–), kalide (K–), rubidide (Rb–) or caeside (Cs–). Around 90 examples can be found in the Cambridge structure database (see DOI: 10.14469/hpc/3453  for the search query and results). So what about the ammonium analogue, ammonide (NH4–)? A quick search of Scifinder drew a blank! So here I take a look at this intriguingly simple little molecule.‡

It can be formed by adding two electrons to the ammonium cation; NH4+ + 2e ↠ NH4–. One might be encouraged to do this since the LUMO (lowest unoccupied molecular orbital, below) of the ammonium cation has A1 symmetry and so can accept two electrons without the penalty of Jahn-Teller distortions. These electrons will apparently expand the valence electron “octet” around the nitrogen from 8 to 10; a hypervalent species then?

So what are the (calculated) properties of NH4–? The energy of the now HOMO (highest occupied molecular orbital) at the ωB97XD/Def2-TZVPPD/solvent=water level is -3.6eV, a respectable electron affinity (the additional electrons are said to be bound). More insight can be obtained from the NBO analysis, which produces localized versions of the molecular orbitals. There are four equivalent NBOs, one of which is shown below.

Each is bonding along one H-N bond, mildly anti-bonding along the other three N-H bonds, but again bonding in the H-H regions! This matches the observations made earlier that when more electrons are pumped into normally valent main group molecules, they will occupy the antibonding levels. This is accompanied by a reduction in the bond orders associated with the central atom. In this case, the N-H bond orders are reduced from 0.79 to 0.602 and the total bond index at the nitrogen is reduced from 3.16 to 2.408. The bond index at hydrogen is at first sight increased from 0.79 to a surprising 1.0003, but this is explained because the H-H bond orders are 0.1328 (three for each H), which brings the H index up to 1.0. The N-H vibration (A1 symmetric) is 3466 cm-1 for NH4+  which is reduced to 2659 for NH4–.†

So it appears that adding two electrons to the ammonium cation induces H-H bonding! More insight can be obtained from an ELF analysis of the electron density basins.

The above shows four attractors (as they are called) centered at the hydrogen nuclei, with 2.053e each (4*2.053 = 8.212e). The remaining ~2e are located in basins (green) centered at two different types of attractors. One is along the axis of each N-H bond and exo to it (0.316e) and the other sits on top of any set of three hydrogens (0.103e), 1.68e in total. The value of the ELF function at the attractor is shown above. You should realize that ELF=1.0 corresponds to perfectly localized electrons (for which the kinetic energy density is zero) and ELF=0.5 would correspond to a free-electron gas. The ELF value of e.g. 0.77 is getting close to an electron gas, and in fact corresponds to what we call an electride.

So, the nitrogen valence shell electron octet is not actually exceeded! The additional two electrons in ammonide sit beyond the nitrogen, in H-H regions. Whether or not it is a viable species for detection remains to be established, but even its computed bonding properties have proved interesting and it deserves to join the alkalide family. 

Postscript

Ammonide exists in a shallow well in the potential energy surface, shown below, with the dissociation to ammonia and hydride anion being exothermic.

The intrinsic reaction coordinate shows one interesting feature at  IRC ~-1.1 which corresponds to repulsion between the hydride and the lone pair of the nitrogen atom resulting in inversion of configuration during the latter stages of the IRC.

‡FAIR data collection; 10.14469/hpc/3455. †Perhaps unsurprisingly, these values are somewhat basis set dependent. Thus a ωB97XD/Def2-QZVPPD/Water calculation gives the following values: bond index at N, 1.998, N-H bond index, 0.4995, H-H bond index 0.1689, H bond index 1.0062, total Rydberg population, 0.2738, ν(A1) 2686 cm-1. The ELF basins are H, 2.039, exo-basins 0.282 and 0.141 (total 1.692). The improved basis set better describes the diffuse regions beyond the N-H bonds.

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Ammonium tetraphenylborate and the mystery of its π-facial hydrogen bonding.

Friday, March 10th, 2017

A few years back, I did a post about the Pirkle reagent[1] and the unusual π-facial hydrogen bonding structure[2] it exhibits. For the Pirkle reagent, this bonding manifests as a close contact between the acidic OH hydrogen and the edge of a phenyl ring; the hydrogen bond is off-centre from the middle of the aryl ring. Here I update the topic, with a new search of the CSD (Cambridge structure database), but this time looking at the positional preference of that bond and whether it is on or off-centre. 

The search (February 2017 database, DOI:10.14469/hpc/2233) is shown above, QA = N, O, F, Cl and other constraints are R < 0.01, no errors, no disorder. Two distances are plotted, one (DIST1) is from the H to the ring centroid and the second (DIST2) from the H to an edge carbon atom. The colour code relates to ANG1, the angle subtended at the centroid. A value of 90° would indicate the H is orthogonal to the plane of the aromatic ring.

You can see from the above that the yellow dots correspond to ~90° and that by and large the H…centroid distances are shorter than the H…C distances. 

The above is another representation of this search, again showing that the preferred angle is 90°, although there is a fair bit of scatter. The extreme outliers may be crystallographic errors, but one point caught my eye and is circled in red above; ammonium tetrafluoroborate (3D model DOI: 10.5517/CC4V6TZ). This has a very short distance from the H to the centroid (2.07Å), shorter than the Pirkle reagent that we looked at all those years back. The authors[3] note that “The N-H…Ph distances, H…M 2.067Å … are exceptionally short (M = aromatic midpoint)” but also that “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system.” This implies that such bonds are largely agnostic about whether they bind to the centroid of the ring or to its edge and that the most probable position might arise simply because of crystal packing. An interesting variation on this molecule is a crystal that includes a further 5NH3 in addition to ammonium tetraphenylborate (3D model DOI: 10.5517/cc7bly2). Here an ammonia intervenes between the ammonium cation and a phenyl ring, resulting in a binding of the ammonia with two NHs closer to the edge of the ring and one NH interacting in parallel mode.

Time therefore for a calculation, using B3LYP+GD3BJ/Def2-TZVPP, the functional being chosen because the dispersion contribution is not built in, but uses what is currently thought to be the best representation of these attractions. The issue now is what molecular unit to use? This is an ionic structure and so a periodic boundary model is most appropriate, but given its size I reduced this to two models comprising smaller discrete fragments.

  1. A unit just comprising the simple ion pair. This leaves two of the four N-H bonds devoid of hydrogen bonding (DOI:10.14469/hpc/2234). The optimisation adopts a pose where two NH groups are directed towards a carbon atom rather than the ring centroid. How much of this is due to the smallness of this model?
  2. A unit comprising a double ion pair, which allows one ammonium group to participate with all four NH groups across four phenyl rings and exhibiting six NH interactions in total with six rings (DOI: 10.14469/hpc/2235). The NH hydrogen vectors all interact with ring carbons rather than the ring centroid.

This brief computational exploration has covered only one method (the B3LYP DFT procedure), albeit with what is thought to be a good dispersion attraction term added and a reasonable basis set. It does seem to show that hydrogen bonds interacting with the centroid of a phenyl ring are not the preferred mode, which is instead an interaction with the edge of the ring. The quote above, “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system” suggests that whilst the average position might be the centroid, a true hydrogen bond to the centroid might be rarer than thought. Although most of the crystallographic examples located in the searches above deem to show a preference for the ring centroid, this might be more apparent than real. 

References

  1. H.S. Rzepa, M.L. Webb, A.M.Z. Slawin, and D.J. Williams, "? Facial hydrogen bonding in the chiral resolving agent (S)-2,2,2-trifluoro-1-(9-anthryl)ethanol and its racemic modification", Journal of the Chemical Society, Chemical Communications, pp. 765, 1991. https://doi.org/10.1039/c39910000765
  2. H.S. Rzepa, M.H. Smith, and M.L. Webb, "A crystallographic AM1 and PM3 SCF-MO investigation of strong OH ⋯π-alkene and alkyne hydrogen bonding interactions", J. Chem. Soc., Perkin Trans. 2, pp. 703-707, 1994. https://doi.org/10.1039/p29940000703
  3. T. Steiner, and S.A. Mason, "Short N<sup>+</sup>—H...Ph hydrogen bonds in ammonium tetraphenylborate characterized by neutron diffraction", Acta Crystallographica Section B Structural Science, vol. 56, pp. 254-260, 2000. https://doi.org/10.1107/s0108768199012318

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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.

NH3-8

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. 

NH3-8

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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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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