Posts Tagged ‘Hydride’

A Theoretical Method for Distinguishing X‐H Bond Activation Mechanisms.

Wednesday, July 25th, 2018

Consider the four reactions. The first two are taught in introductory organic chemistry as (a) a proton transfer, often abbreviated PT, from X to B (a base) and (b) a hydride transfer from X to A (an acid). The third example is taught as a hydrogen atom transfer or HAT from X to (in this example) O. Recently an article has appeared[1] citing an example of a fourth fundamental type (d), which is given the acronym cPCET which I will expand later. Here I explore this last type a bit further, in the context that X-H bond activations are currently a very active area of research.

To help understand these four types, I have colour-coded the electron pair constituting the X-H covalent bond in red.

  1. In mechanism (a), this electron pair stays with X, thus liberating a proton which is captured by the base.
  2. The hydride transfer (b) is so-called because in fact this electron pair travels together with the proton, hence the term hydride or H–.
  3. Hydrogen atom transfers as in (c) in effect transfer both a proton and one electron to another atom (oxygen in the example above), leaving behind one electron on X. The electron and the proton are said to travel together as a “true” hydrogen atom.
  4. The fourth mechanism (d) is fundamentally different from (c) in that whilst the electron and the proton travel in concert (at the same time), they do not travel together. In this example the proton travels to the oxygen, whilst the electron travels to the iron centre, in the process reducing its oxidation state. This mode is now called a concerted proton-coupled electron transfer, or cPCET as above.

The tool employed to distinguish between mechanisms (c) and (d) is the IBO or intrinsic bond orbital localisation scheme.[2] One practical advantage of such a scheme over better known localisation methods such as NBO (Natural bond orbitals) is that IBOs can be made to transform smoothly during the course of a reaction, as followed by say an IRC (Intrinsic reaction coordinate). NBOs may instead show discontinuous behaviour along a reaction IRC. Klein and Knizia have located transition states for examples of both (c) and (d) above and studied the IBOs along such IRCs. The two IBO reaction transformations are very different, as illustrated below (used, with permission, from the article itself). For the HAT type (X=C above), an α-spin IBO morphs from a C-H bond into a H-O bond, whilst the β-spin counterpart morphs from being located on the C-H bond into a carbon-centered radical. For the cPCET mode, the α-spin IBO morphs from C-H to a C-centered radical, but the β-spin region grows onto an iron d-orbital. It is in fact even more complex than the diagram above implies, since some reorganisation of the O-Fe region occurs and the H…:O region is still anti-bonding at the transition state.

We can see from this that mechanistic reaction analysis is starting to track the “curly arrows” we conventionally use to represent reactions in some detail, as well as informing us about the relative detailing timing of the various curly arrows used. Of course this latter aspect cannot be easily represented by conventional curly arrows. It seems timely to revisit the vast corpus of organic and organometallic “curly arrow pushing” to starting adding such information!

References

  1. J.E.M.N. Klein, and G. Knizia, "cPCET versus HAT: A Direct Theoretical Method for Distinguishing X–H Bond‐Activation Mechanisms", Angewandte Chemie International Edition, vol. 57, pp. 11913-11917, 2018. https://doi.org/10.1002/anie.201805511
  2. G. Knizia, "Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts", Journal of Chemical Theory and Computation, vol. 9, pp. 4834-4843, 2013. https://doi.org/10.1021/ct400687b

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Hypervalent Helium – not!

Friday, February 16th, 2018

Last year, this article[1] attracted a lot of attention as the first example of molecular helium in the form of Na2He. In fact, the helium in this species has a calculated‡ bond index of only 0.15 and it is better classified as a sodium electride with the ionisation induced by pressure and the presence of helium atoms. The helium is neither valent, nor indeed hypervalent (the meanings are in fact equivalent for this element). In a separate blog posted in 2013, I noted a cobalt carbonyl complex containing a hexacoordinate hydrogen in the form of hydride, H–. A comment appended to this blog insightfully asked about the isoelectronic complex containing He instead of H–. Here, rather belatedly, I respond to this comment!

The complex [HCo6(CO)15]– has a calculated bond index at the hydrogen of 0.988 and a calculated NMR chemical shift of 21.6 ppm (ωB97XD/Def2-TZVPPD calculation) compared to a measured value of 23.2 ppm. Despite being six-coordinate, the hydride has a bond index that does not exceed one (it is not hypervalent).

So here is the neutral helium analogue. The He bond index emerges as 0.71 at the geometry of the hydride complex. Compare this with the bond index of 0.15 calculated for Na2He and it would be fair to say that at this geometry, the helium in [HeCo6(CO)15] would have a greater claim to be a molecular compound. Back in 2010, extrapolating from a series of posts here, I had speculated[2] about other molecular species of He, including the di-cation below. This has a He bond index of 0.54, rather less than that in [HeCo6(CO)15] but much more than in Na2He. It is also vibrationally stable.

But now, [HeCo6(CO)15] goes “pear-shaped” (why do pears have such a bad press?). I started a process of optimizing the geometry of this complex (ωB97Xd/Def2-TZVPPD). Slowly, the He started to creep out of the centre of the complex and emerge from the cavity. After about 100 steps it reached the geometry shown below, at which point the Wiberg bond index has dropped to 0.62 and still going down. I think it might take a few more steps to be completely expelled, but I have stopped the geometry optimisation at this stage.

So helium appears not to be valent in [HeCo6(CO)15]. However, I have yet to try Ne, which is both larger and softer. I will post results here.

‡All data at 10.14469/hpc/3587.

References

  1. X. Dong, A.R. Oganov, A.F. Goncharov, E. Stavrou, S. Lobanov, G. Saleh, G. Qian, Q. Zhu, C. Gatti, V.L. Deringer, R. Dronskowski, X. Zhou, V.B. Prakapenka, Z. Konôpková, I.A. Popov, A.I. Boldyrev, and H. Wang, "A stable compound of helium and sodium at high pressure", Nature Chemistry, vol. 9, pp. 440-445, 2017. https://doi.org/10.1038/nchem.2716
  2. H.S. Rzepa, "The rational design of helium bonds", Nature Chemistry, vol. 2, pp. 390-393, 2010. https://doi.org/10.1038/nchem.596

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Posted in Hypervalency | 4 Comments »

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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The mechanism of borohydride reductions. Part 1: ethanal.

Sunday, April 12th, 2015

Sodium borohydride is the tamer cousin of lithium aluminium hydride (LAH). It is used in aqueous solution to e.g. reduce aldehydes and ketones, but it leaves acids, amides and esters alone. Here I start an exploration of why it is such a different reducing agent.
BH4

Initially, I am using Li, not Na (X=Li), to enable a more or less equal comparison with LAH, with water molecules to solvate rather than ether (n=2,3,5) and R set to Me. First, n=2, for which the IRC is shown below. In this model, we will assume that the carbonyl has not first reacted with water to form a gem-diol. The free energy barrier is 9.6 kcal/mol (ωB97XD/6-311+G(d,p)/SCRF=water) which corresponds to a very fast reaction at room temperatures.

BH4a
The immediate product is, if anything, more interesting than the transition state[1] with quite a stretched length for the newly formed C-H bond and predicted stretching wavenumber for this bond of 2137 cm-1. This effect is similar to that seen for the LAH reduction of cinnamaldehyde, and is due to stereoelectronic antiperiplanar alignment of the oxyanionic oxygen lone pair with the C-H bond. This species is also some 6.5 kcal/mol higher in energy than the reactant, and is clearly not the final product of the reaction (which must contain e.g. B-O bonds), the mechanism for which will not be investigated here immediately.
BH4-2p
For n=3, we see new solvation patterns, including a dihydrogen bond formed between water and the borohydride at the transition state; ΔG† is 10.0 kcal.mol.

Click for 3D.

Click for 3D.

Finally, n=5, where the TS is showing a cage-like structure of complex weak interactions, ΔG† is 11.3 kcal.mol. We see a model where inclusion of explicit solvent molecules can have a significant influence on the size of the barrier obtained.

Click for 3D

Click for 3D


BH4-5

NCI surface. Click for 3D.

NCI surface. Click for 3D. Blue=strong attractions, green=weak.

n ΔG298‡ FAIR Data citation
2 9.6 [2]
3 10.0 [3]
5 11.3 [4]

With a mechanistic prototype now identified, it is time to start varying some of the parameters, such as X and R. This will enable us to assess the models built here to see if they reflect reality.

References

  1. H.S. Rzepa, and H.S. Rzepa, "C 2 H 12 B 1 Li 1 O 3", 2015. https://doi.org/10.14469/ch/191186
  2. H.S. Rzepa, and H.S. Rzepa, "C 2 H 12 B 1 Li 1 O 3", 2015. https://doi.org/10.14469/ch/191188
  3. H.S. Rzepa, and H.S. Rzepa, "C 2 H 14 B 1 Li 1 O 4", 2015. https://doi.org/10.14469/ch/191189
  4. H.S. Rzepa, and H.S. Rzepa, "C 2 H 18 B 1 Li 1 O 6", 2015. https://doi.org/10.14469/ch/191192

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Posted in reaction mechanism | 2 Comments »