Posts Tagged ‘aqueous solutions’

George Olah and the norbornyl cation.

Friday, March 10th, 2017

George Olah passed away on March 8th. He was part of the generation of scientists in the post-war 1950s who had access to chemical instrumentation that truly revolutionised chemistry. In particular he showed how the then newly available NMR spectroscopy illuminated structures of cations in solvents such “Magic acid“. The obituaries will probably mention his famous “feud” with H. C. Brown over the structure of the norbornyl cation (X=CH2+), implicated in the mechanism of many a solvolysis reaction that characterised the golden period of physical organic chemistry just before and after WWII. 

The dispute between Olah and Brown was not played on a pitch using quite the same goal posts. Olah did much of his work in magic acid and Brown did his in aqueous solutions. I was involved in a tiny way when the discussion about the precise character of the norbornyl cation was reaching its peak in the mid 1970s. At the time, I was working with Michael Dewar, who was himself not shy in joining in the fun and sometimes very acrimonious disputes at conferences. We contributed by calculating the so-called core-electron carbon ESCA spectrum.[1] History records that we came down on the wrong side,‡ by suggesting that this form of spectroscopy supported Brown rather than Winstein/Olah on the basis of a 6:1 spectral deconvolution (classical) rather than 5:2 (non-classical). More recently of course the crystal structure of the parent cation itself has been shown to be non-classical[2] (there are other crystal structures which differ in respect to having one or more additional methyl groups[3]). For a 3D model of norbornyl cation, see DOI: 10.5517/CCZ21LN. This still leaves the issue (very slightly) open for the structure of the solvated cation when formed in water! 

When I started to teach a course in molecular modelling, I touched briefly on how modelling could contribute and whilst updating the notes in the 1990s, wondered why the boron analogue had never been so studied (X=BH2). Unlike the crystallographically difficult norbornyl ion-pair, the iso-electronic boron species would be neutral and not need a counter-ion. Perhaps it might be a more manageable molecule? Checking the Cambridge structural database, such a species has never been reported!† So here as my homage to Olah, I report its calculated structure (b2plypd3/Def2-TZVPP, DOI: 10.14469/hpc/2236).

The norbornyl cation has symmetrical C-C bridging distances of ~1.80±0.02Å and a basal C-C distance of ~1.39±0.02Å. The calculated values for the boron equivalent are 2.16Å and 1.36Å respectively, with all positive force constants. B-C bonds are normally 1.66-1.72Å, significantly longer than C-C bonds, which makes the longer B-C lengths in this example unsurprising. More interestingly, the species has one vibrational normal mode (ν 203 cm-1) which corresponds to the [1,2] shift of the BH2 group across the basal C-C. For a classical species, this vibrational motion would correspond to a transition state (an imaginary vibration) but for a non-classical species it is of course real. In this sense it is analogous to the so-called real Kekulé mode in non-classical benzene, which “equilibrates” the two classical Kekulé structures. The corresponding calculated vibration for the norbornyl cation itself is ν 194 cm-1 (DOI: 10.14469/hpc/2238).

Of course, the entire controversy over the structure of this species is littered with comparisons between not quite similar systems, differing in a methyl group more or less. So morphing a C+ to a B might be seen as quite a large change. But perhaps if it had been crystallised in say the 1960s, would the subsequent debates have taken a different turn?

‡ We were also wrong about the symmetry of the Diels-Alder cyclisation, which is nowadays accepted to be synchronous rather than asynchronous for simple  Diels-Alder reactions. But that is another story.

†GAXLIA is perhaps the closest analogue.[4],

References

  1. M.J.S. Dewar, R.C. Haddon, A. Komornicki, and H. Rzepa, "Ground states of molecules. 34. MINDO/3 calculations for nonclassical ions", Journal of the American Chemical Society, vol. 99, pp. 377-385, 1977. https://doi.org/10.1021/ja00444a012
  2. F. Scholz, D. Himmel, F.W. Heinemann, P.V.R. Schleyer, K. Meyer, and I. Krossing, "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation", Science, vol. 341, pp. 62-64, 2013. http://dx.doi.org/10.1126/science.1238849
  3. T. Laube, "Redetermination of the Crystal Structure of the 1,2,4,7‐<i>anti</i>‐tetramethylbicyclo[2.2.1]heptan‐2‐yl cation at 110 K", Helvetica Chimica Acta, vol. 77, pp. 943-956, 1994. https://doi.org/10.1002/hlca.19940770407
  4. P.J. Fagan, E.G. Burns, and J.C. Calabrese, "Synthesis of boroles and their use in low-temperature Diels-Alder reactions with unactivated alkenes", Journal of the American Chemical Society, vol. 110, pp. 2979-2981, 1988. https://doi.org/10.1021/ja00217a053

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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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Why are α-helices in proteins mostly right handed?

Saturday, April 9th, 2011

Understanding why and how proteins fold continues to be a grand challenge in science. I have described how Wrinch in 1936 made a bold proposal for the mechanism, which however flew in the face of much of then known chemistry. Linus Pauling took most of the credit (and a Nobel prize) when in a famous paper in 1951 he suggested a mechanism that involved (inter alia) the formation of what he termed α-helices. Jack Dunitz in 2001 wrote a must-read article on the topic of “Pauling’s Left-handed α-helix” (it is now known to be right handed).  I thought I would revisit this famous example with a calculation of my own and here I have used the ωB97XD/6-311G(d,p) DFT procedure to calculate some of the energy components of a small helix comprising (ala)6 in both left and right handed form.

Firstly, it is important to note that Pauling was apparently not aware of the absolute handedness of amino acids (which are (S) in CIP terminology). This had in fact only been established a few months before Pauling’s publication by Bijvoet, and news of this might not have reached Pauling. So Pauling guessed (or perhaps, he had already built his models, and did not have time to reconstruct them) and his famous α-helix diagram turned out to be the enantiomer of the real McCoy. As with DNA itself, the helix bears a diastereomeric relationship to the chirality of the amino acids; both have to be inverted to get the proper enantiomer (which is what Pauling did). The secret that Pauling had discovered was hydrogen bonding, and particular, weak N-H…O=C interactions (Wrinch had thought it was strong covalent N-C-OH bonding instead). Of course, there are other effects at work, which include van der Waals or dispersion interactions, electrostatic effects resulting from the large dipoles in peptides (not least due to the zwitterionic character), the planarity of the peptide bond itself, the potential for other types of hydrogen bond (e.g. C-H…O) and entropic effects. I have split some of these down for left and right handed forms of DNA in another post.

It turns out calculating most of these effects on an even-handed basis is not that easy. Only the recent advent of dispersion-corrected DFT procedures, together with solvation algorithms that allow for accurate geometry optimisation and subsequent evaluation of free energies allows such a calculation to be performed. Hitherto, it has been mostly molecular mechanics that has been used (which itself relies on many parameters from quantum mechanics, such as atom charges, and explicitly identifying interactions for hydrogen bonding). By returning to a quantum-mechanical model, some of these assumptions inherent in the mechanics method need not be made.

We showed in 1991 that an effective solvation treatment required for the zwitterionic form of amino acids in aqueous solutions would ideally comprise not only a self-consistent-reaction-field, but also explicit water molecules as solvent. Here only the former solvation term is included, but expanding the model to include water is certainly possible. Both the zwitterionic and the neutral forms of (ala)6 are included below, so that the effect of a large dipole on the structure and relative helical stability can be estimated. One notes that (even in a dielectric cavity corresponding to water), the extended zwitterions are high energy species.  In a protein, they of course would be stabilized by the immediate environment of the ions. The right-handed helix clearly comes out as more stable (by about 1 kcal/mol per residue, see also DOI: 10.1021/ja960665u),  but this is not really due to either dispersion effects or entropy and must therefore arise largely from the hydrogen-bond like interactions. Ionizing the termini to form a zwitterion increases the propensity for a right handed helix slightly.

Relative thermodynamic energies (kcal mol-1) of (ala)6 α-helices
System Total energy Dispersion ΔΔH298 Δ(T.ΔS298) ΔΔG298
Left, neutral 0.0
 0.0 0.0 0.0 0.0
Right, neutral -4.0
 +0.2 -4.0 0.9 -4.9
Left, zwitterion 0.0 0.0 0.0 0.0 0.0
Right, zwitterion -7.1 0.1 -6.3 1.7 -8.0

Shown below are the calculated structures. The chains have (inter alia) unusual bifurcated hydrogen-bonding interactions, between one carbonyl group and two N-H groups (show as atom with halo). These are not quite the models that Linus Pauling built!

Left handed. Click for 3D

Right handed. Click for 3D

Left handed zwitterion. Click for 3D

Right handed zwitterion. Click for 3D

For a more objective analysis of the interactions within the system, a QTAIM analysis is shown below.

Left helix. Bond critical points in green. Click for 3D.

Right helix. Click for 3D

Whilst the overall conclusion is that theory agrees well with the experimental observation that peptide sequences tend to coil into right rather than left handed helices,  the reasons they do so is a little more subtle than simple model building alone can reveal.  As the AIM shows, a plethora of unusual and weaker interactions occur within these helices, a full analysis of which must await presentation elsewhere.

An NCI analysis reveals strong hydrogen bonds as blue-shaded surfaces.

NCI surface. Click for 3D.

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