Posts Tagged ‘City: Aachen’

Hypervalence revisited. The odd case of hexamethyl selenium.

Tuesday, November 7th, 2017

One thread that runs through this blog is that of hypervalency. It was therefore nice to come across a recent review of the concept[1] which revisits the topic, and where a helpful summary is given of the evolving meanings over time of the term hypervalent. The key phrase “it soon became clear that the two principles of the 2-centre-2-electron bond and the octet rule were sometimes in conflict” succinctly summarises the issue. Two molecules that are discussed in this review caught my eye, CLi6 and SeMe6. The former is stated as “anomalous in terms of the Lewis model“, but as I have shown in an earlier post, the carbon is in fact not anomalous in a Lewis sense because of a large degree of Li-Li bonding. When this is taken into account, the Lewis model of the carbon becomes more “normal”. Here I take a look at the other cited molecule, SeMe6.

I should start by summarising what I think are two fundamental ways in which electrons can be added to the valence shell of a main group element.

  • If an s/p basis only is used for the (main group) valence shell, then once eight electrons have populated the four bonding molecular orbitals constructed from this basis, additional electrons can then go into the four antibonding orbitals. This simple concept is often taught as an explanation for why the bond orders across the range N≡N, O=O, F-F and Ne…Ne decrease regularly (in fact one could also add CC to the left of this series, which is thought to have a weak quadruple bond). The Lewis octet is maintained throughout.
  • The second fundamental possibility is to expand the valence shell basis set to s/p/d or s/s/p/p (the second s or p-shell is the Rydberg level, i.e. 3s for carbon) or even s/s/p/p/d. That would be a true Lewis octet expansion, which depends on identifying significant Rydberg occupancy. This latter is in fact very rare, and few examples have been conclusively identified. One such as been discussed on this blog  and more examples were presented at the Aachen bond Slam in September 2017. Unlike the first mechanism (which reduces bond orders), this one actually increases bond orders and any bonds where the atomic orbital contributions have a significant Rydberg component can be considered as “Hyperbonds“.

One can then address the issue of hypervalency (and any octet expansion) by analysing the basis set contributions of the orbitals. These orbitals can be either canonical molecular orbitals or localised (NBO) orbitals. If a single determinant wavefunction is appropriate, then the orbitals would be doubly occupied (for closed shell species). If the molecule has multi-reference character, then of course fractional electron occupancy of these orbitals may be required (as would e.g. be the case for ozone, O3, another molecule asserted in the review as hypervalent[1]).

There are other ways of analysing the wavefunction. The one discussed at length in the review[1] is from an atomic charge map, but also mentioned is an ELF partitioning. This derives not from an orbital population but from the distribution of a function (ELF) calculated from the electron density itself. It was this latter method that was cited for SeMe6. The ELF method partitions electrons into so-called basins, which can be monosynaptic (lone pairs and ionic bonds), disynaptic (covalent bonds) and more rarely trisynaptic (3-centre bonds). Using this analysis, six disynaptic octahedrally-arranged ELF basins were located for  SeMe6  (“in which the Se–C bonds are relatively non-polar, can have electron populations exceeding 8 at the central atom”[1]) and for which the total integration cames to 11.34e (FAIR Data DOI for this calculation can be see at 10.14469/hpc/3219).

The key phrase is “non-polar”, since the Lewis concept relates to shared electron pair or covalent hypervalency. It was this aspect that I focused on seven years back in looking at whether e.g. IF7 was hypervalent (along with I(CN)7). These were too ionic to reveal disynaptic covalent ELF basins. So in an effort to reduce the polarity, I tried II7 and At.At7, on the grounds that these homonuclear molecules might be less polar. The seven I-I or At-At ELF disynaptic basins integrated to totals of 6.55 and 6.47e respectively; there was no evidence of “octet expansion” for either central halogen. Instead of course, the six electrons in the octet-excess needed to create seven I-I bonds actually populate I-I antibonding orbitals, as per method 1 above. Accordingly the I-I bond orders reduce from 1.0 to e.g. 0.47 for the axial substituents and 0.37 for the five equatorial groups.

One interesting property of the centroid of the ELF basins is that you can infer the polarity of the bond from its position along the bond axis. For II7, the centroids are displaced towards the central iodine, indicating it is more electronegative, and away from the terminal iodine, indicating it is the electropositive partner. I mention this since the ELF basins for SeMe6 show the centroids to be strongly displaced towards the carbon and away from the Se (0.38/0.62), indicating that this molecule is in fact polar and NOT non-polar as was asserted. 

To follow-up this latter observation, I did an NBO analysis of the wavefunction for SeMe6 (FAIR Data DOI: 10.14469/hpc/3220). This reveals the following properties.

  • Se populations: [core]4S( 1.30)4p( 3.04)4d( 0.06)5p( 0.01) of which Rydberg = 0.06516, natural charge on Se, 1.60224
  • C populations:  [core]2S( 1.20)2p( 3.65)3S( 0.01)3p( 0.01) of which Rydberg = 0.01838, natural charge on C -0.86670
  • H populations:  1S( 0.80)
  • Total Rydberg population: 0.20556
  • Wiberg Se-C bond orders:  0.6689
  • Wiberg bond indices:  Se 4.0431, C 3.8252,  H 0.9621

So according to this orbital-based analysis, SeMe6 is in effect a partially ionic compound with no evidence of significant Rydberg occupancies and hence no evidence of any octet expansion at Se. Thus we see two different interpretations emerging, depending on the analytical method used:

  1. SeMe6 is a polar molecule with no hypervalent attributes as judged using orbital analysis.
  2. As a polar molecule, it has six methyl carbanion-like substituents in which the carbon “lone pairs” all point towards the Se, manifesting as disynaptic ELF basins and indicating a total valence-basin octet-expanded population of 11.34e at Se. Even though this octet expansion originates mostly from the carbon atomic orbitals, the disynaptic nature of these valence basins means that the Se could indeed be defined as hypervalent.

Well, SeMe6 has turned out to be rather less clear-cut than implied by the assertion “in which the Se–C bonds are relatively non-polar”. There are however possible modifications to SeMe6 that might yet make it less polar. These may be the subject of a follow-up post.

References

  1. M.C. Durrant, "A quantitative definition of hypervalency", Chemical Science, vol. 6, pp. 6614-6623, 2015. https://doi.org/10.1039/c5sc02076j

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Two new types in the chemical bonding zoo: exo-bonds and hyper-bonds?

Wednesday, September 6th, 2017

The chemical bond zoo is relatively small (the bond being a somewhat fuzzy concept, I am not sure there is an actual count of occupants). So when two new candidates come along, it is worth taking notice. I have previously noted the Chemical Bonds at the 21st Century-2017: CB2017 Aachen conference, where both were discussed.

  1. The first now has a name, the exo-bond, one example of which is the C2 diatomic. The hint that a quadruple bond could be formulated between the two carbon atoms goes back a little while[1] (see Table 1), but revived interest really took off after ~2010, around the time my blog on the topic also appeared. You can see the abundance of post 2010 articles in the bibliography at the Aachen bond-slam. At the conference, four speakers all agreed using rather different methods that there was indeed “something” additional to a C≡C triple bond and that this “something” might be worth ~15-30 kcal/mol of stabilization.† The debate centered around whether this term deserved to be called a bond, or whether it should be downgraded to merely that of biradicaloid stabilizations.‡ The more conventional population of a σ*-antibond it was argued would not result in such stabilizations. Since many kinds of bonds have stabilization energies of similar magnitude, not least the weaker hydrogen bonds, agostic bonds, halogen bonds etc, let us for the sake of argument call it a bond here. Because four electrons might occupy the same space along the σ-symmetric C-C axis, they experience significant so-called static correlation∞ which results in partition into one electron pair occupying the central region (the endo-bond) and the other pair in the outer region (the exo-bond).  This separation decreases the Pauli electron repulsions along the entire C-C axis region.  An example of an exo-bond is found in [1.1.1] propellane, where the notional central C-C bond is thought to actually occupy the region outside the central C-C bond axis, but largely in this example because of angular strains. In this case however, the propellane bond is not competing with an endo-bond along the same axis. We might conclude therefore that the convention of characterising a bond using the separation between the two nuclei (the bond-length) is rather stressed when one has two different bonds along the axis of the nuclei, one of which is obviously “longer” than the other.

    Which brings us to representations; e.g. Chemdraw now allows drawing of quadruple bonds and so it can be drawn thus quite simply.

    The second form breaks the century-old convention that all bonds along a diatomic axis are drawn in the same manner, by isolating the exo-bond to make the point clear. Perhaps we should stick to the first, but be prepared to explain the underlying complexity of the quantum mechanical symmetries as we do to students with σ/π/δ/φ bonds, which are another mechanism for avoiding having bonds in exactly the same regions. I know the story has not yet ended; but is it time to at least speculate when the text-books will start to reflect/discuss the exo-bond?

  2. The second I dub the hyper-bond. This goes back to G. N. Lewis and his famous octet rule for main group elements, the expansion of which was subsequently described by the term hypervalent. That term has become rather confused with hypercoordinate, since hypervalent is often used to describe hypercoordinate species such as PCl5, SF6 or I.I7. But this does rather break the original definition, since few if indeed any of these hypercoordinate molecules have a significantly expanded octet shell. At the Aachen meeting, a molecule fitting the original definition was presented, appearing first in early form on this blog. Put simply, a wavefunction for CH3F2- can be calculated (ωB97XD/Def2-QZVPPD/SCRF=water, DOI: cb3n ) for which the two additional electrons populate a molecular orbital with significant contributions from the 3s/3p valence shell AOs (atomic orbitals) for both carbon and fluorine. The alternative would have been to populate the anti-bonding C-H or C-F orbitals composed of 2s/2p valence shell AOs. The former results in a total population of these higher valence shells of 1.55e and makes the C-F (Wiberg) bond order >1 (1.14) and the total Wiberg bond indices >4 for carbon (4.162) and >1 for F (1.275). The resulting HOMO (highest occupied molecular orbital) or NBO (they are very similar) looks as below. It takes the approximate form of a torus or cylinder wrapping the inner C-F bond, a second layer to the C-F bond if you wish. 

    Normal valence shell F-C σ-orbital defining the regular C-F bond.

    Higher valence shell F-C σ-orbital defining the C-F hyper-bond.

    Rather than the entire molecule being defined as hypervalent, only one (in this case localized) orbital is given the term and the other orbitals are conventional.

In both cases the molecules are either very reactive (C2) or with such a low barrier to fragmentation (into CH3– and F– for CH3F2-) that detection of the latter is unlikely. But these are interesting Gedanken experiments in quantum mechanics, which in turn catalyse the development of new techniques and in some cases might even lead to the design and isolation of new types of molecules.

†The known thermochemistry of the two reactions; HC≡CH → HC≡C + H•; HC≡C• → CC + H• is ~17 kcal/mol less endothermic for the second step, suggesting some factor is needed to account for the additional stabilization when CC is formed.

‡The singlet to triplet excitation energy for C2 is ~+30 kcal/mol, so the biradicaloid electrons are certainly spin-coupled.

∞Other “difficult” correlated molecules include Be2 and B2.

References

  1. R.S. Mulliken, "Note on Electronic States of Diatomic Carbon, and the Carbon-Carbon Bond", Physical Review, vol. 56, pp. 778-781, 1939. https://doi.org/10.1103/physrev.56.778

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WATOC 2017 report.

Tuesday, August 29th, 2017

The triennial conference is this year located in Munich. With 1500 participants and six parallel sessions, this report can give only a flavour of proceedings.

  1. Edward Valeev talked about the scaling problem in coupled cluster theories, the so-called gold standard for computing the energy and properties of small molecules. The problem is that the number of basis functions N describing the atomic basis set for the atoms scales from between N6 to N10 in terms of computer time, with similar behaviour for the memory required for the calculation. He described methods based on natural pair orbitals and localisation schemes which can achieve linear scaling, ie N1 for the energy, quite a break through! Using reasonable basis sets, CCSD(T)-like energies for molecules with 100s of atoms were reported. During the Q&A time afterwards (the tight schedules associated with so many speakers means questions are often limited to 1-2, with very short answers) a question was posed about the prospects for first and second derivatives for the method. This means that e.g. reaction mechanisms can then be probed with unprecedented energetic accuracy. The answer was non-committal, but if these derivatives do arrive, it will revolutionise our ability to understand mechanisms.
  2. Which brings me nicely to Jeremy Harvey, who talked about calculating accurate overall rate constants for complex mechanistic cycles. The rate equations are solved for the steady state condition and include concentrations of all species and the energies are obtained using CCSD(T)-F12 theory (a modification which allows better basis set scaling without increased computation time) as single point geometries. He described an example where the barrier associated with a postulated mechanism was about 6 kcal/mol higher than derived from the observed rate. This was sufficient to induce them to explore alternative mechanisms, which were indeed located with an appropriately lower barrier. I have used the value of ~10 kcal/mol as my mechanistic test on this blog, and it’s really nice to see this value being reduced further.
  3. Yet again this theme emerged with Yitzhak Apeloig, who asked about the mechanism for C=Si bond rotations in substituted systems recently made in his group. The energy of this rotation is low enough to be observed in NMR spectra. But when the energy of C=Si bond rotation is computed it comes out about 10 kcal/mol too high. Again alternative mechanisms were explored and it turns out that a 1,2 migration from R2C=SiR2 to form a carbylidene species, R-C-SiR3, rotation and then 1,2 again to reformulate the R2C=SiR2 system came up with the goods.
  4. Peter Scheiner talked about how attractions between molecules can be induced by dispersion. He described how Ph3C-CPh3 is an unknown molecule (dissociating into Ph3P• radicals) but when 4,6-di-tert-butyl groups are placed on all the phenyl rings, the dispersion attractions between them can account for ~60 kcal/mol (!), more than enough to stabilise the system. I have already described some of this work in a post here. The prospects are very exciting for more dispersion-stabilised molecules to emerge. During Q&A, a question was posed about what other atom pairs other than H…H might be brought into ultra-short contact by these attractive dispersion forces; we may expect further examples to emerge in the near future.
  5. Ken Houk gave a fascinating glimpse into the post-transition state world of reaction dynamics, as applied to Diels Alder cycloadditions and Cope rearrangements. The reactions are characterised by the residency times of the dynamic trajectories in the region of the transition state as short (~4 fs), medium (20-40fs) and long (80+fs), these times mapping on to what we used to call “synchronous”, “asynchronous” and “stepwise”. A good example is the so-called bis-pericyclic reaction of cyclopentadiene where the trajectories pass through a transition state but then bifurcate into two (in this case) equivalent pathways. He discussed other examples where the trajectories follow either a 2+4 cycloaddition pathway or a 4+6 alternative pathway and how the number of trajectories for each can be influenced by either solvent (water) or an enzyme. Ken described several 20-40fs trajectories as corresponding to “dynamic stepwise” reactions, which during Q&A was suggested are equivalent to the term “hidden intermediate” pathways coined by Dieter Cremer and as revealed in many posts here from the intrinsic reaction coordinates or IRCs. This is a clear growth area and expect many more examples of reaction dynamics to be applied to many exciting systems in the future.
  6. Leo Radom talked about very simple molecules, H3CX and the effects on the bond dissociation energy (BDE) of the C-H bonds if the group X is either strongly or weakly protonated (the latter via a hydrogen bond), or deprotonated (again strongly or weakly via a hydrogen bond from hydroxide anion). This is important in several enzymic pathways, where the CH bond might be activated in a similar manner by the enzyme. He also talked about similar effects on the ionisation potential. I noticed a connection between this theme and what might be called the electron affinity of H3CX. If you want to see what the connection is, go visit the Aachen bond Slam, about which I have previously blogged! 

I will stop with an observation that all the notes above were taken in real-time during the talks, which all emerged as Powerpoint slides, having an average residency time on the screen of perhaps 1-2 minutes each. References were invariably given as full journal citations (authors, journal, year, volume, pages) rather than as DOIs, and given the time constraints I did not try to capture them. Hence the lack of citations above to the presenters’ work. The slide displays are traditionally not made available to audiences‡ and photography of the screen or recording is considered very bad form. Conferences are not really about FAIR data, which I have described often on this blog.

I hope these six examples give one flavour of what is happening at WATOC 2017. If another interesting collection emerges, I may describe it here.

‡But see e.g. doi: b9r9 for an Aachen talk.

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