Posts Tagged ‘Atom’

What are the highest bond indices for main group and transition group elements?

Sunday, March 4th, 2018

A bond index (BI) approximately measures the totals of the bond orders at any given atom in a molecule. Here I ponder what the maximum values might be for elements with filled valence shells.

Following Lewis in 1916[1] who proposed that the full valence shell for main group elements should be 2 (for the first two elements) and 8 (the “octet“), Bohr (1922[2]), Langmuir (1919-1921[3]) and Bury (1921[4]) extended this rule to include 18 (the transition series) and 32 (the lanthanides and actinides). If we assume no contributions from higher Rydberg shells (thus 3s, 3p, 3d for carbon etc) and an electron pair model for orbital population (which amounts to the single-determinantal model), then the maximum bond index for hydrogen (and helium) would be 1, it would be 4 for main group elements, and then what?

For the special case of hydrogen, I have previously identified (for a hypothetical species) a bond index of 1.33, due mostly to a high Rydberg occupancy of 1.19e. The more normal BI is <1.0, as noted for this hexacoordinated hydride system. My current estimate for the maximum bond index for main group elements is <4.5. Thus for SF6, it has the value of ~4.33 and that includes a modest occupancy of Rydberg shells of 0.36e = 0.18 BI. Exclude these and it is close to 4.

Move on from group 16 to group 6 and you get compounds such as Me4CrCrMe44- or ReMe82- where the metal bond indices are ~6.5.‡ Compounds such as Cr(Me)6 (BI = 5.6)  and W(Me)6 (BI = 6.1) are rather lower. This is a long way from 18/2 = 9. The lanthanides and actinides[5] are unlikely to reveal many large BIs (32/2= 16 maximum value) since they are often ionic and the wavefunctions may be too complex to allow a simple index such as a BI to be safely computed.

So if we are hunting for record BIs, the transition elements are the place to hunt. Can a BI of 6.5 be beaten? Can it even approach 9, its maximum value? Does anyone know of candidate molecules? 

‡FAIR Data doi: 10.14469/hpc/3352.

References

  1. G.N. Lewis, "THE ATOM AND THE MOLECULE.", Journal of the American Chemical Society, vol. 38, pp. 762-785, 1916. https://doi.org/10.1021/ja02261a002
  2. N. Bohr, "Der Bau der Atome und die physikalischen und chemischen Eigenschaften der Elemente", Zeitschrift f�r Physik, vol. 9, pp. 1-67, 1922. https://doi.org/10.1007/bf01326955
  3. I. Langmuir, "Types of Valence", Science, vol. 54, pp. 59-67, 1921. https://doi.org/10.1126/science.54.1386.59
  4. C.R. Bury, "LANGMUIR'S THEORY OF THE ARRANGEMENT OF ELECTRONS IN ATOMS AND MOLECULES.", Journal of the American Chemical Society, vol. 43, pp. 1602-1609, 1921. https://doi.org/10.1021/ja01440a023
  5. P. Pyykkö, C. Clavaguéra, and J. Dognon, "The 32‐Electron Principle", Computational Methods in Lanthanide and Actinide Chemistry, pp. 401-424, 2015. https://doi.org/10.1002/9781118688304.ch15

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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 »