Posts Tagged ‘Chemical elements’

Smoke and mirrors. All is not what it seems with this Sn2 reaction!

Thursday, April 4th, 2019

Previously, I explored the Graham reaction to form a diazirine. The second phase of the reaction involved an Sn2′ displacement of N-Cl forming C-Cl. Here I ask how facile the simpler displacement of C-Cl by another chlorine might be and whether the mechanism is Sn2 or the alternative Sn1. The reason for posing this question is that as an Sn1 reaction, simply ionizing off the chlorine to form a diazacyclopropenium cation might be a very easy process. Why? Because the resulting cation is analogous to the cyclopropenium cation, famously proposed by Breslow as the first example of a 4n+2 aromatic ring for which the value of n is zero and not 1 as for benzene.[1] Another example of a famous “Sn1” reaction is the solvolysis of t-butyl chloride to form the very stable tertiary carbocation and chloride anion (except in fact that it is not an Sn1 reaction but an Sn2 one!)

Here is the located transition state for the above, using Na+.6H2O as the counter-ion to the chloride. The calculated free energy of this transition state is 3.2 kcal/mol lower than the previous Sn2′ version (FAIR data collection, 10.14469/hpc/5045), with an overall barrier to reaction of 26.5 kcal/mol. This compares to ~24.5 kcal/mol obtained by Breslow for solvolysis of the cyclopropenyl tosylate. Given the relatively simple solvation model I used in the calculation (only six waters to solvate all the ions, and a continuum solvent field for water), the agreement is not too bad.

The animation above is of a normal vibrational mode known as the transition mode (click on the image above to get a 3D rotatable animated model). The calculated vectors for this mode (its energy being an eigenvalue of the force constant matrix) are regularly used to “characterise” a transition state. I will digress with a quick bit of history here, starting in 1972 when another famous article appeared.[2] The key aspect of this study was the derivation of the first derivatives of the energy of a molecule with respect to the (3N) geometrical coordinates of the atoms, using a relatively simply quantum mechanical method (MINDO/2) to obtain that energy. Analytical first derivatives of the MINDO/2 Hamiltonian were then used to both locate the transition state for a simple reaction and then to evaluate the second derivatives (the force constant matrix) using a finite difference method. That force constant matrix, when diagonalized, reveals one negative root (eigenvalue) which is characteristic of a transition state. The vectors reveal how the atoms displace along the vibration, and should of course approximate to the path to either reactant or product.

Since that time, it has been a more or less mandatory requirement for any study reporting transition state models to characterise them using the vectors of the negative eigenvalue. The eigenvalue invariably expressed as a wavenumber. Because this comes from the square root of the mass-weighted negative force constant, it is often called the imaginary mode. Thus in this example, 115i cm-1, the i indicating it is an imaginary number. The vectors are derived from quadratic force constants, which is a parabolic potential surface for the molecule. Since most potential surfaces are not quadratic, it is recognized as an approximation, but nonetheless good enough to serve to characterise the transition state as the one connecting the assumed reactant and product. Thousands of published studies in the literature have used this approach.

So now to the animation above. If you look closely you will see that it is a nitrogen and not a carbon that is oscillating between two chlorines (here it is the lighter atoms that move most). The vectors confirm that, with a large one at N and only a small one at C. So it is Sn2 displacement at nitrogen that we have located? 

Not so fast. This is a reminder that we have to explore a larger region of the potential energy surface, beyond the quadratic region of the transition state from which the vectors above are derived. This is done using an IRC (intrinsic reaction coordinate). Here it is, and you see something remarkable.

The Cl…N…Cl motions seen above in the transition state mode change very strongly in regions away from the transition state. On one side of the transition state, it forms a Cl…C bond, on the other side a Cl…N.

It is also reasonable to ask why the paths either side of the transition state are not the same? That may be because with only six explicit water molecules, three of which solvate the sodium ion, there are not enough to solvate equally the chloride anions either side of the transition state. As a result one chlorine does not behave in quite the same way as the other. The addition of an extra water molecule or two may well change the resulting reaction coordinate significantly.

The overall message is that there are two ways to characterise a computed reaction path. One involves looking at the motions of all the atoms just in the narrow region of the transition state. Most reported literature studies do only this. When the full path is explored with an IRC, a different picture can emerge, as here. The Cl…N…Cl Sn2 mode is replaced by a Cl…C/N…Cl mode. This example however is probably rare, with most reactions the transition state vibration and the IRC do actually agree!

References

  1. R. Breslow, "SYNTHESIS OF THE s-TRIPHENYLCYCLOPROPENYL CATION", Journal of the American Chemical Society, vol. 79, pp. 5318-5318, 1957. https://doi.org/10.1021/ja01576a067
  2. J.W. McIver, and A. Komornicki, "Structure of transition states in organic reactions. General theory and an application to the cyclobutene-butadiene isomerization using a semiempirical molecular orbital method", Journal of the American Chemical Society, vol. 94, pp. 2625-2633, 1972. https://doi.org/10.1021/ja00763a011

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The shortest known CF…HO hydrogen bond.

Sunday, March 24th, 2019

There is a predilection amongst chemists for collecting records; one common theme is the length of particular bonds, either the shortest or the longest. A particularly baffling type of bond is that between the very electronegative F atom and an acid hydrogen atom such as that in OH. Thus short C-N…HO hydrogen bonds are extremely common, as are C-O…HO.‡ But F atoms in C-F bonds are largely thought to be inert to hydrogen bonding, as indicated by the use of fluorine in many pharmaceuticals as inert isosteres.[1] Here I do an up-to-date search of the CSD crystal structure database, which is now on the verge of accumulating 1 million entries, to see if any strong C-F…HO hydrogen bonding may have been recently discovered.

The search query uses the CF…HO distance as one variable, and the C-F-H angle as the second. The first diagram shows just intermolecular interactions, up to a distance of 2.7Å which is the sum of the van der Waals radii of the two elements. The hot spot occurs at this value, and an angle of ~95°.

The intra-molecular plot shows a similar value for the most common F…H distance, with the interesting variation that the angle subtended at F is about 80°. The outlier at the short end of the spectrum (arrow) was observed in 2014[2] with the structure shown below. It is indeed the current record holder by some margin! This length by the way is however a great deal longer than the shortest O…HO hydrogen bonds, which can be in the region of 1.2Å (with the proton sometimes symmetrically disposed between the two oxygen atoms). The value is also very similar to the record holder for the shortest C-H…H-C interaction.

It is always useful to check up on crystallographic hydrogen atom positions using a quantum calculation, so here is one at the ωB97XD/Def2-TZVPP level (Data DOI: 10.14469/hpc/5131) which replicates the values nicely.

ωB97XD/Def2-TZVPP Calculation

A QTAIM analysis of the critical points shows that the F…H BCP has a high value of ρ(r) (most hydrogen bonds only reach about 0.03 au).

NBO analysis indicates the  E(2) perturbation energy for donation from an F lone pair into the H-O σ* orbital is 21.2 kcal/mol, which indicates a strong  H-bond (typical C-O…HO values are 18-22 kcal/mol). The F…H bond order is 0.05.

This molecule has another interesting property, also noted in the original article;[2] the shift in wavenumber of the O-H stretching vibration. Most hydrogen bonds are characterised by the shift (mostly red and recently discovered blue shifts) that occurs in the OH group when it hydrogen bonds. These shifts are typically 100-200 cm-1 but in this molecule there is no shift, which is described as “exceptional”.

The 1H NMR shift of the OH proton is observed at δ 4.8 ppm, with the value calculated here (ωB97XD/Def2-TZVPP) being 4.75 ppm. A very large H-F coupling was observed of 68 Hz, again a very high value for a “through space” hydrogen bond.

So another record for the molecule makers to try to break!

‡Respectively 7142 and 31428 intermolecular (3859 and 10602 intra) examples using the same search parameters as above, with the shortest values being ~1.28 and ~1.2Å.

References

  1. S. Purser, P.R. Moore, S. Swallow, and V. Gouverneur, "Fluorine in medicinal chemistry", Chem. Soc. Rev., vol. 37, pp. 320-330, 2008. https://doi.org/10.1039/b610213c
  2. M.D. Struble, C. Kelly, M.A. Siegler, and T. Lectka, "Search for a Strong, Virtually “No‐Shift” Hydrogen Bond: A Cage Molecule with an Exceptional OH⋅⋅⋅F Interaction", Angewandte Chemie International Edition, vol. 53, pp. 8924-8928, 2014. https://doi.org/10.1002/anie.201403599

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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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Pyrophoric metals + the mechanism of thermal decomposition of magnesium oxalate.

Sunday, March 19th, 2017

A pyrophoric metal is one that burns spontaneously in oxygen; I came across this phenomenon as a teenager doing experiments at home. Pyrophoric iron for example is prepared by heating anhydrous iron (II) oxalate in a sealed test tube (i.e. to 600° or higher). When the tube is broken open and the contents released, a shower of sparks forms. Not all metals do this; early group metals such as calcium undergo a different reaction releasing carbon monoxide and forming calcium carbonate and not the metal itself. Here as a prelude to the pyrophoric reaction proper, I take a look at this alternative mechanism using calculations.


There are ~60 crystal structures of metal oxalates, of which several are naturally occurring minerals (Fe, humboldtine[1], Ca, Weddellite[2], Li[3], Na[4], K[5], Cs[6]. The natural geometry of the oxalate di-anion is planar (torsion 0 or 180°) but a small number are twisted such as the caesium oxalate.

The kinetics of pyrolysis of a number of metal  oxalates were studied some years ago (Ca[7], Li[8]) indicating barriers ranging from 53-68 kcal/mol. One proposed mechanism is as shown in this article.[7]

It was surmised from the kinetic analysis that the k1 activation step (rotation about the C-C bond from planar to twisted) was ~12 ± 20 kcal/mol, whilst steps k2 or k3 had the much higher activation energy noted above. A search (of Scifinder) for quantum mechanical “reality checks” of this mechanism revealed a blank and so I apply such a check here using Mg as the metal.

The carbonyl extrusion step (ωB97XD/Def2-TZVPPD/SCRF=water, DOI: 10.14469/hpc/2320) was studied with a water solvent field applied in an effort to mimic the solid state crystal structure of the species as a better representation of the ionic lattice than a pure vacuum calculation.An IRC (intrinsic reaction coordinate, DOI: 10.14469/hpc/2324) reveals the start-point geometry still has a very small negative force constant (-38 cm-1, DOI: 10.14469/hpc/2321) which now corresponds to a small rotation about the C-C bond to give a C2-symmetric conformation:

But the barrier for this process is tiny and nothing like the ~12 ± 20 kcal/mol inferred from the kinetic analysis. Perhaps most of the incentive to pack into a totally planar geometry comes from the interactions in the ionic lattice. The calculated free energy barrier (ΔG298‡ 54.7 kcal/mol, ΔG755‡ 55.1 kcal/mol) is within the reported measured range.

The mechanism for production of pyrophoric metal itself is likely to be far more complex, involving (inter alia) electron transfer from oxygen to metal. If I find anything I will report back here.

References

  1. T. Echigo, and M. Kimata, "Single-crystal X-ray diffraction and spectroscopic studies on humboldtine and lindbergite: weak Jahn–Teller effect of Fe2+ ion", Physics and Chemistry of Minerals, vol. 35, pp. 467-475, 2008. https://doi.org/10.1007/s00269-008-0241-7
  2. C. Sterling, "Crystal structure analysis of weddellite, CaC2O4.(2+x)H2O", Acta Crystallographica, vol. 18, pp. 917-921, 1965. https://doi.org/10.1107/s0365110x65002219
  3. https://doi.org/
  4. G.A. Jeffrey, and G.S. Parry, "The Crystal Structure of Sodium Oxalate", Journal of the American Chemical Society, vol. 76, pp. 5283-5286, 1954. https://doi.org/10.1021/ja01650a007
  5. Dinnebier, R.E.., Vensky, S.., Panthofer, M.., and Jansen, M.., "CCDC 192180: Experimental Crystal Structure Determination", 2003. https://doi.org/10.5517/cc6fzcy
  6. Dinnebier, R.E.., Vensky, S.., Panthofer, M.., and Jansen, M.., "CCDC 192182: Experimental Crystal Structure Determination", 2003. https://doi.org/10.5517/cc6fzf0
  7. F.E. Freeberg, K.O. Hartman, I.C. Hisatsune, and J.M. Schempf, "Kinetics of calcium oxalate pyrolysis", The Journal of Physical Chemistry, vol. 71, pp. 397-402, 1967. https://doi.org/10.1021/j100861a029
  8. D. Dollimore, and D. Tinsley, "The thermal decomposition of oxalates. Part XII. The thermal decomposition of lithium oxalate", Journal of the Chemical Society A: Inorganic, Physical, Theoretical, pp. 3043, 1971. https://doi.org/10.1039/j19710003043

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VSEPR Theory: A closer look at bromine trifluoride, BrF3.

Tuesday, February 14th, 2017

I analysed the bonding in chlorine trifluoride a few years back in terms of VSEPR theory. I noticed that several searches on this topic which led people to this post also included a query about the differences between it and the bromine analogue. For those who posed this question, here is an equivalent analysis.

The calculation is done at the same level as before (ωB97XD/6-311++D(d,p)) for consistency (DOI: 10.14469/hpc/2160)

Click for 3D

  1. Basins 8 and 9 have electron populations of 2.33e (2.07e for the chlorine analogue) with an angle subtended at Br of 159°. The greater electron population and hence electron pair repulsion has the effect of increasing the angle compared to Cl (154°). The coordination is even more square pyramidal than with Cl.
  2. Basin 7 has a population of 0.73e, this time less than Cl (0.87e). 
  3. Basins 11 and 12 are 0.82e. With Cl, this single basin was replaced by a pair of split basins, each pair summing to 0.91e (the same effect happens with F-F). The angle 4-2-3 is 172° (174° for Cl) which suggests a slightly increased 2-electron-3-centre interaction between e.g. atoms 1-4 or 1-3 compared to Cl.
  4. The total basin count surrounding the Br is therefore 7.03e, compared to 6.84e with Cl, which suggests Br is slightly more electronegative in this context than Cl.

Bromine has a habit of springing surprises, but not so much in this example.

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Na2He: a stable compound of helium and sodium at high pressure.

Saturday, February 11th, 2017

On February 6th I was alerted to this intriguing article[1] by a phone call, made 55 minutes before the article embargo was due to be released. Gizmodo wanted to know if I could provide an (almost)† instant‡ quote. After a few days, this report of a stable compound of helium and sodium still seems impressive to me and I now impart a few more thoughts here.

The discovery originates from 17 authors based in 17 different institutions, an impressive illustration of global science and cooperation. I illustrate with this diagram, to be found not in the main article body but in its supporting information and for which the caption reads:


Computed charge density (eÅ-3) of Na2He at 300 GPa, plotted in the [110] plane of the conventional cell. The color bar gives the scale.

The nuclei carry of course the greatest charge density, but the density labelled “2e” is not nuclear-centered. This is typical of species known as electrides, where positive cations are associated with just electrons acting as the counter-anion and about which there was an extensive debate earlier on this blog. There is much discussion in the article[1] about the essential role of the He atoms in bringing about the formation of such an electride, an effect that is summarised in a second diagram also found in the supporting information:

I found myself thinking that it would be great to have the first diagram represented as a movie, evolving as the pressure is increased from say ambient to 300 GPa, and presumably showing the “2e” feature (which means diamagnetic electrons) forming as the pressure increases. Would their evolution be abrupt (a step change) or gradual as the pressure increases and the interatomic distances all decrease? As I understand it, this chemical phenomenon is due not so much to the usual coulombic attraction between positive nuclei and negative charge density from the electronic wavefunction leading to e.g. covalent bonds, but to electron repulsions induced by decreasing nuclear separations resulting in electride-like ionisation and hence electron localisation into the “interstitial cavities” of the lattice. Without pressure, you would just have sodium and helium atoms!

The urge to obtain this intriguing electronic wavefunction for myself now appeared (wavefunctions are rarely if ever included in supporting information). To do this you must have atom coordinates available, But such data was not to be found in the supporting information. It was eventually tracked down (by a crystallographer; thanks Andrew!) to the caption in Figure 2.

However, you probably do need to be a crystallographer to convert this data into a set of coordinates. This was done and is here deposited as a CIF file for you to play with if you wish (DOI:10.14469/hpc/2154)[2]. I have reduced the packing of the unit cell obtained from this CIF file (198 atoms) to just 60 and you can enjoy them by clicking on the diagram below. I should point out that if one uses a program that can recognise the periodic lattice such as Crystal (used in the article discussed here), there is no need to make such reductions, but in this instance I wanted to use a program such as Gaussian in discrete (non-periodic) mode, for which the calculation (B3LYP/Def2-SVPD) has DOI: 10.14469/hpc/2156[3] and where you can also find a wavefunction file to play with if you wish.

Click for 3D model

An ELF analysis for this non-periodic wavefunction looks as below. The ELF basins labelled “2e” located in the centre of the cube show an integrated electron population of ~1.9e and correspond to the localised electron pairs noted in the article above.

Click for 3D

The basins on the boundaries of this non-periodic unit show reduced integrations (red arrows below, 0.08 – 1.7e) and are artefacts of the non-periodic approximation introduced.

The ionization into an electride is brought about by the close proximity of the atoms as induced by high pressure. Releasing the pressure would allow the ionized electrons to re-attach themselves to the valence shell of the sodium atoms, thus destroying the unique properties of the system. It is certainly true that this system challenges our normal concepts of what a molecule is. The presence of He is essential and yet its electrons are hardly involved in the re-organised wavefunction. I cannot wait for more examples to be discovered!

†To meet the 55 minute deadline, I was given about 15 minutes thinking time!

‡Instant responses on social media now seem a sine qua non of the political world, so why not the scientific one?!

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. Rzepa, "Na2He: a stable compound of helium and sodium at high pressure.", 2017. https://doi.org/10.14469/hpc/2154
  3. H. Rzepa, "He20Na40", 2017. https://doi.org/10.14469/hpc/2156

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Posted in Bond slam, crystal_structure_mining, Interesting chemistry | 11 Comments »

Allotropic halogens.

Sunday, April 26th, 2015

Allotropes are differing structural forms of the elements. The best known example is that of carbon, which comes as diamond and graphite, along with the relatively recently discovered fullerenes and now graphenes. Here I ponder whether any of the halogens can have allotropes.

Firstly, I am not aware of much discussion on the topic. But ClF3 is certainly well-known, and so it is trivial to suggest BrBr3, i.e. Br4 as an example of a halogen allotrope. Scifinder for example gives no literature hits on such a substance (either real or as a calculation; it is not always easy nowadays to tell which). So, is it stable? A B3LYP+D3/6-311++G(2d,2p) calculation reveals a free energy barrier of 17.2 kcal/mol preventing Br4 from dissociating to 2Br2.[1] The reaction however is rather exoenergic, and so to stand any chance of observing Br4, one would probably have to create it at a low temperature. But say -78° would probably be low enough to give it a long lifetime; perhaps even 0°.

Br4c
Br4

So how to make it? This is pure speculation, but the red colour of bromine originates from (weak, symmetry forbidden) transitions, with energies calculated (for the 2Br2 complex) as 504, 492nm. Geometry optimisation of the first singlet excited state of 2Br2 produces the structure below, not that different from Br4.
2Br2-excited

 

At least from these relatively simple calculations, it does seem as if an allotrope of bromine might be detectable spectroscopically, if not actually isolated as a pure substance.

References

  1. H.S. Rzepa, "Br4", 2015. https://doi.org/10.14469/ch/191228

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