Are diazomethanes hypervalent molecules? Probably, but in an unexpected way!

December 23rd, 2017

A recently published review on hypervalency[1] introduced a very simple way of quantifying the effect. One of the molecules which was suggested to be hypervalent using this method was diazomethane. Here I take a closer look.

The new method is called the valence electron equivalent γ. It is defined as “the formal shared electron count at a given atom, obtained by any combination of valid ionic and covalent resonance forms that reproduces the observed charge distribution”. These atom charge maps can be obtained from various kinds of quantum mechanical calculation; the one adopted in the review was Bader’s QTAIM analysis.

Three resonance forms used to estimate γ for the atoms in diazomethane are shown below. According to Durrant[1], “if γ(X) > 8, neither form of the octet rule is obeyed and the atom is hypervalent”. His procedure gives γ(N) = 10 (table 3 and also structure 27a[1]), suggesting that the third resonance form shown below is the most appropriate.

As a result, the nitrogen is to be considered hypervalent, with five formal covalent bonds and hence a ten shared-electron valence shell. If such hypervalence is to be considered as more than just a convenient representation and to have a deeper underlying foundation, similar conclusions should ideally emerge from other ways of analysing the wavefunctions for such species. Here I try the NBO (Natural Bond Orbital) and ELF (Electron localization Function) analyses of two types of wavefunction using both DFT (density functional theory) ωB97XD/Def2-TZVPP and multi-reference CASSCF(12,12)/Def2-TZVPP Hamiltonians.‡

Firstly, the NBO method, which localizes electron pairs. There are four bonding NBOs associated with the central nitrogen and a modest contribution from a fifth, the terminal nitrogen lone pair (bottom).

The carbon has four NBOs comprising one “non-bonding lone pair”, two C-Hs, a C-N and one partial C-N (bottom). This partitioning can be quantified using Wiberg atom bond indices: C, 3.716; N 3.802; N 2.907 (the C-N and N=N bond orders are 1.425 and 2.368). Note that the “non-bonding carbon lone pair” would not contribute to the C bond index, which is already 3.72. Is numerical evidence perhaps emerging that the carbon may exceed the octet in its valence shell? In contrast, the central nitrogen, with a bond index of 3.802, but not having any associated “non-bonding lone pair”, does not look to exceeding the octet. It seems well short of achieving γ(N) = 10, equivalent to a bond index of 5 as shown in the resonance form above.

Now for ELF, which is derived from the electron density and the basin locations from its kinetic energy density. The values are the integrations for the individual ELF basins, of which 0.498*2 = 0.996 is the monosynaptic basin for the carbon lone pair noted above. The total for this carbon comes to 8.16, the adjacent nitrogen 6.59 and the terminal nitrogen 7.52e. 

The CASSCF(12,12) values are respectively are 8.18, 6.50 and 7.50e, which are very similar. So these two types of electron partitioning show no evidence that the central nitrogen has γ(N) = 10; it’s actually ~6.5, which is a long way short of 10! However, γ(C) = ~8.2, which does exceed the octet, if only very modestly. Perhaps this can best be summarised with the following representation based on the bond orders, which indicates three shared covalent bonds to carbon, a partial (dashed) C-N interaction and a lone pair implied by the minus sign, the total of which exceeds γ(C) = ~8. It all boils down really to whether that “lone pair” of electrons on the carbon is truly a non-bonding electron pair or whether it should be considered a fully covalent pair associated also with the nitrogen. Certainly, there appears to be no evidence from NBO or ELF that this is the case.

The next logical question to ask is whether the effect can be “optimised” such that γ(C) > 8 or even >> 8. I will address this in the next post.

‡FAIR data for all calculations is available at DOI: 10.14469/hpc/3476

References

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

Tags:
Posted in Hypervalency, Interesting chemistry | No Comments »

Ammonide: an alkalide formed from ammonia and resembling an electride.

December 17th, 2017

Alkalides are anionic alkali compounds containing e.g. sodide (Na–), kalide (K–), rubidide (Rb–) or caeside (Cs–). Around 90 examples can be found in the Cambridge structure database (see DOI: 10.14469/hpc/3453  for the search query and results). So what about the ammonium analogue, ammonide (NH4–)? A quick search of Scifinder drew a blank! So here I take a look at this intriguingly simple little molecule.‡

It can be formed by adding two electrons to the ammonium cation; NH4+ + 2e ↠ NH4–. One might be encouraged to do this since the LUMO (lowest unoccupied molecular orbital, below) of the ammonium cation has A1 symmetry and so can accept two electrons without the penalty of Jahn-Teller distortions. These electrons will apparently expand the valence electron “octet” around the nitrogen from 8 to 10; a hypervalent species then?

So what are the (calculated) properties of NH4–? The energy of the now HOMO (highest occupied molecular orbital) at the ωB97XD/Def2-TZVPPD/solvent=water level is -3.6eV, a respectable electron affinity (the additional electrons are said to be bound). More insight can be obtained from the NBO analysis, which produces localized versions of the molecular orbitals. There are four equivalent NBOs, one of which is shown below.

Each is bonding along one H-N bond, mildly anti-bonding along the other three N-H bonds, but again bonding in the H-H regions! This matches the observations made earlier that when more electrons are pumped into normally valent main group molecules, they will occupy the antibonding levels. This is accompanied by a reduction in the bond orders associated with the central atom. In this case, the N-H bond orders are reduced from 0.79 to 0.602 and the total bond index at the nitrogen is reduced from 3.16 to 2.408. The bond index at hydrogen is at first sight increased from 0.79 to a surprising 1.0003, but this is explained because the H-H bond orders are 0.1328 (three for each H), which brings the H index up to 1.0. The N-H vibration (A1 symmetric) is 3466 cm-1 for NH4+  which is reduced to 2659 for NH4–.†

So it appears that adding two electrons to the ammonium cation induces H-H bonding! More insight can be obtained from an ELF analysis of the electron density basins.

The above shows four attractors (as they are called) centered at the hydrogen nuclei, with 2.053e each (4*2.053 = 8.212e). The remaining ~2e are located in basins (green) centered at two different types of attractors. One is along the axis of each N-H bond and exo to it (0.316e) and the other sits on top of any set of three hydrogens (0.103e), 1.68e in total. The value of the ELF function at the attractor is shown above. You should realize that ELF=1.0 corresponds to perfectly localized electrons (for which the kinetic energy density is zero) and ELF=0.5 would correspond to a free-electron gas. The ELF value of e.g. 0.77 is getting close to an electron gas, and in fact corresponds to what we call an electride.

So, the nitrogen valence shell electron octet is not actually exceeded! The additional two electrons in ammonide sit beyond the nitrogen, in H-H regions. Whether or not it is a viable species for detection remains to be established, but even its computed bonding properties have proved interesting and it deserves to join the alkalide family. 

Postscript

Ammonide exists in a shallow well in the potential energy surface, shown below, with the dissociation to ammonia and hydride anion being exothermic.

The intrinsic reaction coordinate shows one interesting feature at  IRC ~-1.1 which corresponds to repulsion between the hydride and the lone pair of the nitrogen atom resulting in inversion of configuration during the latter stages of the IRC.

‡FAIR data collection; 10.14469/hpc/3455. †Perhaps unsurprisingly, these values are somewhat basis set dependent. Thus a ωB97XD/Def2-QZVPPD/Water calculation gives the following values: bond index at N, 1.998, N-H bond index, 0.4995, H-H bond index 0.1689, H bond index 1.0062, total Rydberg population, 0.2738, ν(A1) 2686 cm-1. The ELF basins are H, 2.039, exo-basins 0.282 and 0.141 (total 1.692). The improved basis set better describes the diffuse regions beyond the N-H bonds.

Tags: , , , , , , , , , , , , ,
Posted in Hypervalency | 2 Comments »

Identification of a simplest hypervalent hydrogen fluoride anion.

December 8th, 2017

An article with the title shown above in part recently appeared.[1] Given the apparent similarity of HF1- to CH3F1- and CH3F2-, the latter of which I introduced on this blog previously, I thought it of interest to apply my analysis to HF1-.

The authors[1] conclude that “the F atom of HF− is negative and hypervalent and the bonding is more covalent than ionic“. So, firstly an NBO analysis. Shown below is the singly occupied NBO (ωB97XD/Def2-TZVPPD calculation, FAIR data DOI: 10.14469/hpc/3274)

The nature of this orbital is that most of it is located beyond the hydrogen and a node is apparent between the F and H (it is H-F antibonding). The Wiberg bond index for both H and F is 0.48, as is the F-H bond order. This matches with the observation of one electron in an orbital which is H-F antibonding. NBO analysis also indicates that the atomic orbital contributions to F[core]2S(1.93)2p(5.77)3S(0.05)3p(0.04)3d(0.01) and H 1S(0.96)2S(0.12)2p(0.10) show modest Rydberg character on the hydrogen, less on the fluorine. By this criterion, it is the hydrogen and not the fluorine that is hypervalent!

Next, the ELF analysis (respectively FAIR data DOI: DFT 10.14469/hpc/3377  and CASSCF(7,8) 10.14469/hpc/3394). 

DFT CASSCF(7,8)

Both these methods reveal a monosynaptic ELF basin located away from the H, with an integration of about 1 electron. The F lone pairs form a torus around the F and the total of electrons around the fluorine is <8. So again no evidence from ELF that the fluorine is hypervalent.

In fact this analysis resembles one feature of CLi6. With nominally 12e apparently contributing to the shared C-Li shell, CLi6 was described as hypervalent.[2] In fact ~3e of these are “expelled” from the shared C-Li regions into Li-Li regions, where they contribute only to lithium valency and not to the carbon valency. With HF1-, the additional electron apparently responsible for the hypervalency contributes only to the H, but not to the F valencies. With CH3F2-, the two injected electrons do appear to contribute to the C-F bond, making it a true hyperbond.

So based on the above, I cannot entirely agree with the assertion that “the F atom of HF− is negative and hypervalent”[1], but I might suggest that something more unusual is happening, the hydrogen is (mildly) hypervalent! 

References

  1. M. Liu, H. Chen, C. Chin, T. Huang, Y. Chen, and Y. Wu, "Identification of a Simplest Hypervalent Hydrogen Fluoride Anion in Solid Argon", Scientific Reports, vol. 7, 2017. https://doi.org/10.1038/s41598-017-02687-z
  2. H. Kudo, "Observation of hypervalent CLi6 by Knudsen-effusion mass spectrometry", Nature, vol. 355, pp. 432-434, 1992. https://doi.org/10.1038/355432a0

Tags:
Posted in Hypervalency | No Comments »

FAIR data ⇌ Raw data.

December 7th, 2017

FAIR data is increasingly accepted as a description of what research data should aspire to; Findable, Accessible, Inter-operable and Re-usable, with Context added by rich metadata (and also that it should be Open). But there are two sides to data, one of which is the raw data emerging from say an instrument or software simulations and the other in which some kind of model is applied to produce semi- or even fully processed/interpreted data. Here I illustrate a new example of how both kinds of data can be made to co-exist.

I will start with a recent publication[1] with the title Crystallographic Snapshot of an Arrested Intermediate in the Biomimetic Activation of CO2. The nature of this intermediate caught the eye of another research group, who responded with their own critique[2]‡ along with the comment “However, since we have no access to the original crystallographic data …” They might have been referring to the semi-processed data (containing the so-called hkl structure factors) but they may also have been alluding to the raw image data captured directly from the diffractometer cameras. That traditionally has not been available via the CSD (Cambridge structural database), but would be required for a complete re-analysis of the crystal structure. Now the first example of how both FAIR (processed) data and raw data can co-exist has appeared.

The latest version of the CSD database shows an entry resulting from the following publication[3] and the deposited data has its own DOI there (10.5517/ccdc.csd.cc1n9ppb). That entry in turn has a DOI pointer to the Raw data (10.14469/hpc/2300) held in a different location and the pointer is reciprocated (⇌) with the latter pointing back to the former. Both datasets point to the original article, thus completing a holy triangle.†

There is more. The Raw dataset (10.14469/hpc/2300) declares it is a member of a superset, called Crystal structure data for Synthesis and Reactions of Benzannulated Spiroaminals; Tetrahydrospirobiquinolines (10.14469/hpc/2297) where you can find information about six other related structures. That collection is in turn a member of a superset called Synthesis and Reactions of Benzannulated Spiroaminals; Tetrahydrospirobiquinolines (10.14469/hpc/2099) where DOIs to other types of data associated with this project can be found, such as Computational data (10.14469/hpc/2098) and NMR data (10.14469/hpc/2294). Although a human can with some determination follow these associations up, down and across, the system is designed to also be followed by automated algorithms that could traverse this web quickly and efficiently.

So you can now see that a crystal structure held in the CSD could be the starting point for a journey of FAIR data discovery, in manner that has not hitherto been possible. How quickly the CSD will become populated by links to Raw (and other) data remains to be seen. I have not yet discovered any mechanism for specifying a CSD query which stipulates that Raw data must be available, but no doubt this will come.

To end, back to the Biomimetic Activation of CO2 referred to at the start. With no access to the original data, recourse was made to computational modelling.[2] Which where  I came in, since I wanted access to the original (computational) data. Sadly it did not appear to be available with the article,[2] in much the same manner as the original complaint. Perhaps, when FAIR data becomes fully accepted as part of how science is done nowadays, such complaints will become ever rarer!

‡In fact the original authors did respond[4] with an acknowledgement that their original conclusions were not correct.

†Almost. The article [3] cites DOI: 10.14469/hpc/2099 (Ref 28), but it does not cite DOI: 10.5517/ccdc.csd.cc1n9ppb because the latter had not been minted yet at the time the final proofs were corrected, and there is no mechanism to add it at a later stage.

References

  1. S.L. Ackermann, D.J. Wolstenholme, C. Frazee, G. Deslongchamps, S.H.M. Riley, A. Decken, and G.S. McGrady, "Crystallographic Snapshot of an Arrested Intermediate in the Biomimetic Activation of CO<sub>2</sub>", Angewandte Chemie International Edition, vol. 54, pp. 164-168, 2014. https://doi.org/10.1002/anie.201407165
  2. J. Hurmalainen, M.A. Land, K.N. Robertson, C.J. Roberts, I.S. Morgan, H.M. Tuononen, and J.A.C. Clyburne, "Comment on “Crystallographic Snapshot of an Arrested Intermediate in the Biomimetic Activation of CO<sub>2</sub>”", Angewandte Chemie International Edition, vol. 54, pp. 7484-7487, 2015. https://doi.org/10.1002/anie.201411654
  3. J. Almond-Thynne, A.J.P. White, A. Polyzos, H.S. Rzepa, P.J. Parsons, and A.G.M. Barrett, "Synthesis and Reactions of Benzannulated Spiroaminals: Tetrahydrospirobiquinolines", ACS Omega, vol. 2, pp. 3241-3249, 2017. https://doi.org/10.1021/acsomega.7b00482
  4. S.L. Ackermann, D.J. Wolstenholme, C. Frazee, G. Deslongchamps, S.H.M. Riley, A. Decken, and G.S. McGrady, "Corrigendum: Crystallographic Snapshot of an Arrested Intermediate in the Biomimetic Activation of CO<sub>2</sub>", Angewandte Chemie International Edition, vol. 54, pp. 7470-7470, 2015. https://doi.org/10.1002/anie.201504197

Tags: , , , , , , , ,
Posted in Chemical IT, crystal_structure_mining | No Comments »

A form of life that can stably store genetic information using a six-letter, three-base-pair alphabet?

December 2nd, 2017

For around 16 years, Floyd Romesberg’s group has been exploring un-natural alternatives (UBPs) to the Watson-Crick base pairs (C-G and A-T) that form part of the genetic code in DNA. Recently they have had remarkable success with one such base pair, called X and Y (for the press) and dNaMTP and d5SICSTP (in scholarly articles).[1],[2] This extends the genetic coding from the standard 20 amino acids to the possibility of up to 172 amino acids. Already, organisms engineered to contain X-Y pairs in their DNA have been shown to express entirely new (and un-natural) proteins.

There is also some measure of controversy. Why? Well, you might spot why with the structures of the bases as shown below.

I first note that d5SICS only has one exemplar in the Cambridge structural database (CSD), with the deoxyribose ring replaced by something quite different. The dNaM sub-structure is rather more abundant (360), although none have a deoxyribose ring attached. So we cannot really tell how these molecules might interact when adjacent (they are after all described as a base pair). But it is unlikely to be via hydrogen bonds, since d5SICS has only C-H groups, and dNaM has no acidic hydrogens either. Hence this base pair is described as being hydrophobic! I might suggest that some small molecule analogues of the two systems above are rapidly made and their crystal structures determined so that we might have at least some data about their interactions (or absence thereof).

If you were set the task of designing some un-natural base pairs to splice into DNA, I doubt you would start with the premise of dropping the complementary base pairing induced by two or three pairs of hydrogen bonds. Of course the integrity of the double helix is retained because of the C-G/A-T base pairs accompanying the hydrophobic d5SICS-dNaM ones. The controversy is about exactly how many such hydrophobic base pairs can in fact be included before the DNA structure becomes unstable to life. 

When I first came across attempts to engineer new forms of DNA (and possibly life), it was directed at replacing the pentose sugar by a hexose,[3] a project that ultimately failed because the resulting DNA was too flexible. Now we have the enthralling prospect of the discovery of many new alternatives to the standard base pairs, with biochemical consequences I cannot even begin to imagine! 

References

  1. A.W. Feldman, M.P. Ledbetter, Y. Zhang, and F.E. Romesberg, "Reply to Hettinger: Hydrophobic unnatural base pairs and the expansion of the genetic alphabet", Proceedings of the National Academy of Sciences, vol. 114, 2017. https://doi.org/10.1073/pnas.1708259114
  2. D.A. Malyshev, K. Dhami, H.T. Quach, T. Lavergne, P. Ordoukhanian, A. Torkamani, and F.E. Romesberg, "Efficient and sequence-independent replication of DNA containing a third base pair establishes a functional six-letter genetic alphabet", Proceedings of the National Academy of Sciences, vol. 109, pp. 12005-12010, 2012. https://doi.org/10.1073/pnas.1205176109
  3. M. Egli, P.S. Pallan, R. Pattanayek, C.J. Wilds, P. Lubini, G. Minasov, M. Dobler, C.J. Leumann, and A. Eschenmoser, "Crystal Structure of Homo-DNA and Nature's Choice of Pentose over Hexose in the Genetic System", Journal of the American Chemical Society, vol. 128, pp. 10847-10856, 2006. https://doi.org/10.1021/ja062548x

Tags: , , , , , , , , , , ,
Posted in Interesting chemistry | 3 Comments »

Octet expansion and hypervalence in dimethylidyne-λ6-sulfane.

November 28th, 2017

I started this story by looking at octet expansion and hypervalence in non-polar hypercoordinate species such as S(-CH3)6, then moved on to S(=CH2)3. Finally now its the turn of S(≡CH)2.‡

As the triple bonds imply, this seems to represent twelve shared valence electrons surround the sulfur, six from S itself and three from each carbon. The octet is clearly expanded from eight to twelve. But is all as it seems?

The linear form reveals the following localized orbitals. Six NBOs are localized to the S-C regions, of which four are bonding, two σ and two π. The remaining four electrons are in two non-bonding lone pairs, with a mild anti-bonding S-C component. So the bond order comes out as ~four, not six! This corresponds to the story told in the earlier blogs that the electrons in excess of the octet tend to occupy either non or antibonding orbitals.

In fact the full NBO analysis gives a value of 4.0920 for the S bond index and little Rydberg character; S: [core]3S(1.02)3p(3.61)3d(0.13).

Next, the ELF analysis, based not on orbitals but the derived electron densities. Each S-C region shows an ELF circular attractor integrating to 5.44e (or 10.88e for the S valence region). So the ELF reflects not only the density arising from bonding orbitals, but the non-bonding ones as well! 

Take a look at the ELF basin for the two hydrogen atoms; at 2.42e each this shell is ALSO expanded from the normal 2! Apart from the normal C-H localised NBO orbital, one can also see small C-H bonding contributions from the four NBOs labelled B above as well. So ELF analysis of the shared electrons in this species seems to show octet expansion for S and similar shell expansion for H. But we now know that simply taking the ELF basin population and dividing by two to get the bond or valence index can be misleading. The ELF analysis includes non or even anti-bonding density contributions and so it cannot be used to infer hyperbonding (hypervalence).

I must now confess to withholding some vital information from you. The linear HC≡S≡CH molecule is not a minimum, having four computed negative force constants, the normal mode of one of which is animated  below. 

The true minimum has C2 symmetry as follows and it corresponds to that mysterious structure shown at the top and hitherto not mentioned. This form is 14.6 kcal/mol lower in free energy than the linear variety. 

The ELF analysis confirms this species as bis(carbene), with two “lone pairs” on S. All the octet expansion has vanished; of the ~six electrons hitherto located in each C-S region, four have morphed into lone pairs, leaving only ~two in the S-C regions. The sulfur is now allocated 7.44e, a  “normal” octet.

At this point, I remind that the great G. N. Lewis himself, the original coiner of the eight electron valence rule, pondered whether acetylene might have a related bis(carbene) form. It is nice to come up with an example of this more than 100 years after his original suggestion.

‡FAIR Data DOI for the collection: 10.14469/hpc/3333

Tags: , , , , , , ,
Posted in Historical, Hypervalency | 3 Comments »

Hypervalence and octet-expansion in trimethylene-λ6-sulfane and related species.

November 27th, 2017

Previously: “Non-polar” species such as SeMe6, SMe6, ClMe3, ClMe5 all revealed interesting properties for the Se-C, S-C or Cl-C “single” bonds. The latter two examples in particular hinted at internal structures for these single bonds, as manifested by two ELF basins for some of the bonds. Here I take a look at the related molecule where a formal double bond between carbon and the central sulfur atom replacing the single-bond might also hint at octet expansions and hypervalence.

Starting with X=Y=Z=CH2,‡ the calculated (ωB97Xd/Def2-TZVPP) geometry has an interesting chiral D3-symmetric form. The density based ELF-basin centroids are shown below, with each formal C=S π-double bond represented by two ELF basins above and below the C-S axis and with each pair of ELF basins being twisted by 48° with respect to the other two pairs. The total valence shell count around the S is 10.98e and the octet is “expanded” (by ~3e).

The orbital-based NBO approach indicates little utilisation of higher (Rydberg) atomic orbital shells (S: [core]3S(1.13)3p(3.35)3d(0.11)4p(0.02); C: [core]2S(1.15)2p(3.77)3p(0.01)3d(0.01) ). Each S-C bond has a Wiberg bond order of 1.36 (significantly less than a double bond), and the central S has an overall bond index of 4.102. There is a real mis-match between the orbital partitioning (2*1.36 = 2.72e) and the ELF partitioning (2*1.83 = 3.66e) into the S-C bonds. The former indicates that ~two of the twelve valence electrons are entering into anti-bonding orbitals to reduce the total bond index from a possible six to just four, but that they still contribute to the electron-density based ELF disynaptic C-S basins. To cast light on this behaviour, successively one to three of the CH2 groups can be replaced by O.

For each “S=O” bond, we find the ELF basin population more or less halves and electrons instead populate the non-bonding O “lone pairs”. The S-C ELF populations in contrast remain approximately constant. These species therefore have “double” S=C bonds but just “single” S-O bonds. The Rydberg population increases slightly; S: [core]3S(1.06)3p(2.95)3d(0.16)4p(0.02)) and the S bond index is 4.18 for one oxygen and S: [core]3S(0.99)3p(2.67)3d(0.19)4p(0.02) and S bond index 4.16 for two oxygens.

Sulfur trioxide (below) seems best represented by S-O rather than S=O bonds. The Rydberg population is S: [core]3S(0.91)3p(2.41)3d(0.21)4p(0.03) and the S bond index is 4.32.

Just for good measure sulfur trisulfide S(S)3 shows rather lower lone pair population because of course it is less electronegative than oxygen, and hence has a slightly greater S-S ELF basin population. Rydberg, S: [core]3S(1.43)3p(3.73)3d(0.21)4p(0.03) and central S bond index 4.04.

It seems molecules where the electrons in a valence shell exceed the “octet” are only too happy to let the excess electrons leak out into adjacent electronegative atoms as lone pairs, where they are no longer classified as  “shared”. Trimethylene-λ6-sulfane does not have this option and the excess electrons remain in the region of the valence shell, but here they do not contribute to augmenting the bond index at the central atom.  In this specific interpretation, the octet is exceeded, but hypervalence is not induced. It is a slippery concept; one where general agreement about its properties may indeed be difficult to achieve!

‡The FAIR data DOI collection for this post is 10.14469/hpc/3316.

Tags: , , , , , , , , ,
Posted in Hypervalency | No Comments »

Hypervalence and octet-expansion in sulfur hexafluoride.

November 20th, 2017

Following on from discussing octet expansion in species such as SeMe6, ClMe3 and ClMe5, I felt impelled to return to SF6, often used as an icon for hypervalence.

With this molecule we have twelve electrons to partition, six from sulfur and one each from six fluorines (the other six electrons on each F are presumed to form three sets of lone pairs). Recollect the two ways of dealing with them:

  1. To place them in pairs firstly into bonding MOs formed from using a 3s/3p valence atomic orbital basis on the S and a 2s/2p AO basis on F and to place any remaining electron pairs into antibonding orbitals constructed from the same basis. This would tend to reduce individual S-F bond orders.
  2. To place four pairs into bonding MOs and the remaining two pairs into MOs constructed using higher or Rydberg valence shells on S. This would tend to increase S-F bond orders by forming hyperbonds.

I will start with (delocalized) molecular orbitals (FAIR data DOI: 10.14469/hpc/3283). The HOMO (highest occupied MO) and the next 16 are in fact various variations of orbitals which can be regarded as fluorine lone pairs. The first of interest to us is the A1g-symmetric HOMO-17, which certainly looks as if it is antibonding along the six F-S bonds. But the heavy delocalization of the MOs makes it really difficult to comment on bonding/antibonding character.

So next, the more localized NBO orbitals (FAIR Data DOI: 10.14469/hpc/3284), which tends to “collect” the wavefunction into localized regions of bonds and lone pairs. There are twelve equivalent F lone pairs of the following type:

Next the remaining six F lone pairs, which are oriented axially along the S-F bonds. They have distinct S-F anti-bonding character.

Finally six S-F bonding pairs (“acorn” orbitals). But note that whilst they are bonding along one S-F bond, they are mildly antibonding along the opposing S-F bond. 

The Rydberg occupancy is S:[core]3S(0.98)3p(2.13)3d(0.24)4p(0.03)4f(0.01) and F: [core]2S(1.91)2p(5.51)3d(0.01), which gives a total  Rydberg occupancy of 0.35177e.  Adding up these effects, the NBO analysis tells us that the individual S-F bond orders are 0.7213. Six times this gives the Wiberg bond index at sulfur:  4.3276. This is close to the value of 4 expected from utilising an atomic orbital basis of one 2s and three 2p AOs on sulfur. One can think of this in another way.

  1. Start with a valence shell of twelve electrons to form six two-electron S-F bonds. The sulfur would have a bond index of six. Then promote either two electrons into fully antibonding orbitals (5-1=4) or four into non-bonding orbitals (F lone pairs) or possibly intermediate solutions, thus reducing the sulfur bond index by ~two bonds to give a bond index of four. Since the antibonding orbitals in this case are not fully antibonding, the bond index emerges a bit higher at 4.3276, a value also augmented by 0.35177/2 = 0.175885 due to Rydberg occupancy.
  2. One might usefully then ask if a bond index for sulfur of ≥ 4 can be usefully described as “hypervalent sulfur“? As usual in bonding theory, we need a reference state for non-hypervalent sulfur. If this is taken as two valencies, with a bond index of two, then this molecule is definitely hypervalent. If you assume that you can only construct the equivalent of four two-electron bonds using just a 3s1/3p3 atomic orbital basis, then it is merely mildly hypervalent; the four two-electron bonds are then distributed of course across six S-F regions, or 0.667 bonds per S-F region. The value of 0.7213 actually calculated is exalted by contributions in part from Rydberg orbitals. 

What about the octet? 6*0.7213*2 = 8.66e, a mildly expanded octet. I am now going to use the ELF method as an alternative counting procedure. This is based not on orbitals but on the electron density (a more direct experimental observable than orbitals). Six disynaptic basins are located totalling 6.5e. The remainder of the electrons populate the F lone pairs shown below as four distinct monosynaptic basins per F. This is an artefact of the resolution of the cube of ELF values and how the basin centroids are located. These are in fact circular and not point ELF attractors, forming a circular ELF torus around each fluorine.

So, ELF suggests that the sulfur “octet” is not exceeded and in this form of analysis the compound is merely hypercoordinate. In contrast the orbital-based approach indicates mild hypervalency in which the total bond index at S modestly exceeds 4. If you regard the normal valency of sulfur to be two, this is clearly hypervalent. But no substantial octet-expansion beyond the modest Rydberg type is needed to rationalise this species and certainly not up to twelve!

Tags: , , , ,
Posted in Hypervalency | 7 Comments »

PIDapalooza 2018: the open festival for persistent identifiers.

November 14th, 2017

PIDapalooza is a new forum concerned with discussing all things persistent, hence PID. You might wonder what possible interest a chemist might have in such an apparently arcane subject, but think of it in terms of how to find the proverbial needle in a haystack in a time when needles might look all very similar. Even needles need descriptions, they are not all alike and PIDs are a way of providing high quality information (metadata) about a digital object.  

The topics for discussion along with descriptions are now available at https://pidapalooza18.sched.com/list/descriptions/ and yes, before you ask, the event has its own PID (DOI: 10.5438/11.0002). Check out the speakers at https://pidapalooza18.sched.com/directory/speakers. I will be telling some stories from chemistry, and who knows, even some of the posts on this blog might feature. And if you do not brush up on the topic, no doubt your librarian, your funding body and your publisher will be telling you about it soon!

Tags: , , , , , , ,
Posted in Chemical IT | No Comments »

VSEPR Theory: Octet-busting or not with trimethyl chlorine, ClMe3.

November 12th, 2017

A few years back, I took a look at the valence-shell electron pair repulsion approach to the geometry of chlorine trifluoride, ClF3 using so-called ELF basins to locate centroids for both the covalent F-Cl bond electrons and the chlorine lone-pair electrons. Whereas the original VSEPR theory talks about five “electron pairs” totalling an octet-busting ten electrons surrounding chlorine, the electron density-based ELF approach located only ~6.8e surrounding the central chlorine and no “octet-busting”. The remaining electrons occupied fluorine lone pairs rather than the shared Cl-F regions. Here I take a look at ClMe3, as induced by the analysis of SeMe6.

The difference between ClF3 and ClMe3 is that octet-excess electrons (two in this case) in the former can relocate into fluorine lone pairs by occupying in effect anti-bonding orbitals and hence end up not contributing to the central atom valence shell.‡ With ClMe3 the methyl groups cannot apparently sustain such lone pairs, at least not distinct from the Cl-C bond region. So might we get an octet-busting example with this molecule? A ClMe3 calculation (ωb97xd/6-311++g(d,p)) reveals a molecule with all real vibrational modes (i.e. a minimum, FAIR data DOI: 10.14469/hpc/3241) and ELF (FAIR data DOI 10.14469/hpc/3242)† basins as shown below:

Density-derived approach: Two of the C-Cl bonds each exhibit two ELF basins; one disynaptic basin (0.94e) and one monosynaptic basin (0.20e) closer to the chlorine. The former pair integrate to 1.88e, density which largely arises from carbon (natural charge -0.84) and which contribute to a total integration for these carbons of 7.17e. The latter pair contributes to a total chlorine integration of 7.19e. The angle subtended at chlorine for the two 2.68e “lone pair” basins is 141°. Thus an inner, octet-compliant, valence-shell for chlorine is revealed, plus an expanded-octet outer one into which the two additional electrons go. The latter contribute to forming an octet-compliant carbon valence shell, but may be considered as not contributing to the valence shell of the other atom of the pair, the chlorine. An endo lone-pair rather than the more usual exo lone-pair if you will. These results reveal that the molecular feature we know as a (single) “bond” may in fact have more complex inner structures or zones, something we do not normally consider bonds as having. In this model, these zones are not invariably considered as shared between both the atoms comprising the bond.

Orbital-derived approach: NBO analysis (FAIR data DOI: 10.14469/hpc/3241) reveals the chlorine electronic configuration as [core]3S(1.83)3p(4.67)4S(0.01)3d(0.03)5p(0.02,) showing very little population of the Rydberg shells (4s, 3d, 5p) occurs (0.13e in total). This method of partitioning the electrons allocates a chlorine Wiberg bond index of 2.00 and the methyl carbon bond index of  3.83. If the regular valence of Cl is taken as 1, then the central chlorine can be regarded as non-Rydberg hypervalent (the electrons in the 0.94e basins are taken as contributing to the chlorine bond index).

The carbon-halogen bond internal structures simplify for Br (DOI: 10.14469/hpc/3248, 10.14469/hpc/3250) and I (DOI: 10.14469/hpc/3249, 10.14469/hpc/3247); for each only a single ELF basin is located and the NBO Br and I bond indices are respectively 2.10 and 2.1. This is not due to incursion of  Rydberg hypervalence (Br: [core]4S(1.83)4p(4.46)5S(0.02)4d(0.03)6p( 0.01); I: [core]5S(1.82)5p(4.29)6S(0.02)5d(0.02)6p(0.01) ) but of a merging of the carbon and halogen valence basin such that the ELF contributions to each cannot be deconvoluted. In each case the NBO bond indices of ~2 suggest hypervalency for the halogen.

What have we learnt?  That the shared electron (covalent) bond can have complex internal features, such as two discrete basins for the apparently shared electrons. How one partitions these electrons can influence the value one obtains for the total shared electron count and hence whether the octet is retained or expanded for main group elements such as the halogens. And finally, that hypervalence and hyper-coordination are related in the orbital model at least. Thus along the series MenI (n= coordination number 1,3,5,7), the values of the Wiberg bond index at the halogen progress as 1.0, 2.1, 3.1 (DOI: 10.14469/hpc/3236) and 4.01 (DOI: 10.14469/hpc/3238), or one extra atom bond index per electron pair.  Given this, it seems useful to retain the distinction between the terms hypervalence and hyper-coordination, but also recognize that we still may have much to learn about the former.

‡See the previous post on SeMe6 for a more detailed discussion.

† The FAIR Data accompanying this blog post is organised in a new way here. All the calculations are collected together with an over-arching DOI: 10.14469/hpc/3252 associated with this post, with individual entries accessible directly using the DOIs given above. The post itself has a  DOI: 10.14469/hpc/3255 and the two identifiers are associated with each-other via their respective metadata.  A set of standards (https://jats.nlm.nih.gov) with implementation guidelines for e.g. repositories, authors and publishers-editors  are expected in the future to establish infra-structures for cross-linking narratives/stories with the data on which they are based.

Tags: , , , , , , , , , ,
Posted in Chemical IT, Hypervalency | 5 Comments »

« Older Entries
Newer Entries »