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Blisteringly bent (quadruple) bonds

Saturday, January 23rd, 2010

So ingrained is the habit to think of a bond as a simple straight line connecting two atoms, that we rarely ask ourselves if they are bent, and if so, by how much (and indeed, does it matter?). Well Hursthouse, Malik, and Sales, as long ago as 1978, asked just such a question about the unlikeliest of bonds, a quadruple Cr-Cr bond, found in the compound di-μ-trimethylsilylmethyl-bis-[(tri-methylphosphine) (trimethylsilylmethyI)chromium(II) (DOI: 10.1039/dt9780001314). They arrived at this conclusion by looking very carefully at how the overlaps with the Cr d-orbitals might be achieved.

A system with a bent Cr-Cr quadruple bond. Click for 3D

One would indeed instinctively think that whilst the relatively weak single bond (about which rotation is easily possible) might be bendable, it seems less intuitive to imagine that something as apparently strong as a quadruple bond could be so. What might the measurable consequences be? Well, Girolami et al 16 years later (DOI: 10.1021/om00017a023) pointed out that such compounds exhibit restricted rotation about the Cr-CH2 bonds in the system, with quite significant barriers. This, it was felt, was due to an agostic CH…Cr interaction,  which might in turn have induced bending of the Cr-Cr bond itself. There the story sort of peters out; no-one else has discussed bent quadruple bonds, or indeed exactly how bent they actually are.

Well, another 16 years has passed, and now we have a rather better set of tools with which to answer such questions, yes you guessed (if you have read my earlier posts), AIM and ELF. Lets start with AIM, shown below (B3LYP/6-311G(d) calculation, for a somewhat reduced model compared to the real system).

AIM analysis. Click for 3D

The bond critical point labelled 1 is the Cr-Cr interaction. It has a ρ(r) of 0.142, really very modest for a purportedly quadruple bond. The ∇2ρ(r) is +0.39, which is the wrong sign for a simple covalent bond, and indeed matches the criteria for the (homonuclear) charge shift category popularized by Shaik and Hibberty. Point 2 is the Cr-CH2(si) bond (of calculated length 2.157Å), ρ(r) 0.078 and with an ellipticity ε of 0.34. This latter value compares to e.g. a value of 0.0 expected for a single (rotatable) bond and ~0.4 for a double bond, and seems to match very well with the observation of restricted rotation about this bond. So far, so good! Surprising however is the absence of any BCP in the region marked with a ?, given that the Cr-C length in this region is 2.257Å (only slightly longer than than that for point 2 and surely a good candidate for some sort of Cr-C bond!). There is no sign of any bending of the Cr-Cr bond in this type of analysis (i.e. point 1 lies along the Cr-Cr axis), or indeed of any evidence for α CH…Cr agostic bonding.

Time then for ELF (below). Well, in one regard, a similar picture to the earlier AIM is obtained. Points 1 and 2 sort of match, and again, no point is found in the region marked with a ?. However, there the similarities end.

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ELF basin centroids for Cr-Cr system. Click for 3D

Thus, point 1 (the apparent quadruple bond) integrates to only 1.04 electrons! But wait for it, it lies well off the straight line connecting the two chromium atoms. Wow! So the bond really is bent! And, because it is contains only 1.04 electrons, that might explain why it can bend so easily! Well, if the Cr-Cr bond does not contain the electrons, where have they gone? The mystery is solved when point 2 is inspected (there are of course two of them, the molecule having C2 symmetry). These each correspond to 1.92 electrons. The ELF analysis furthermore tells us that point 2 is actually trisynaptic, covering both chromium atoms and the carbon. We have found 4.88 electrons associated with the Cr-Cr bond after all (and this is not bad, since one rarely finds the full quota directly in such regions using ELF). To indicate this, point 2 above is actually shown connected to three atoms.

So to summarise, our Cr-Cr quadruple bond in the ELF analysis occupies three different synaptic basins, arranged in a triangle around the C-Cr axis (as shown below), and with the straight line between the Cr-Cr not entertaining any basin. That certainly is bent!

View showing the three synaptic basins comprising the Cr-Cr bond

ELF of course gives only one interpretation of the bonding; there are others. But this interpretation certainly seems to give an interesting and unusual insight into this remarkable (and largely ignored) phenomenon.

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Chemical intimacy: Ion pairs in carbocations

Monday, January 11th, 2010

The scheme below illustrates one of the iconic reactions in organic chemistry. It is a modern representation of Meerwein’s famous experiment from which he inferred a carbocation intermediate, deduced from studying the rate of enantiomerization of isobornyl chloride when treated with the Lewis acid SnCl4.

The isomerisation of iso-bornyl chloride

Meerwein himself suggested (in effect, since he lacked the modern terminology used here) that the reaction proceeded via a hydride shift 3, which was acting as the mirror in reflecting 1 onto 1‘. A few years later, isotopic labelling studies demonstrated that another pathway occurs, at more or less the same rate. This alternative proceeds via a series of [1,2] carbon shifts, with the mirror now being 8 rather than 3. I have documented the story in detail in an article that will shortly appear in the J. Chemical Education (DOI: 10.1021/ed800058c). There, calculations reveal that the two transition states, 3 and 8 (which the experiments above suggest should be almost equal in energy) in fact differed by ~8 kcal/mol in favour of the latter for a gas-phase model which does not include the counterion. These calculations were done at a level (B3LYP/cc-pVQZ) which indicates that 8 kcal/mol represents a real discrepancy not so much in the calculation as in the model used for that calculation. I suggested that perhaps the discrepancy might be due to tunneling effects in the hydride transfer reaction, accelerating that pathway compared to methyl transfer.

What was missing from that particular model was the counter-ion, which is supposed to form an intimate ion-pair with the carbocation in moderately polar solvents. How much does the presence of such an object perturb the transition states?  To find out, we need calculate such systems (which by definition have very large dipole moments) with inclusion of solvation corrections. Now that new algorithms for computing transition states with solvation have made this a routine calculation, I can report an update to these results. This was done at the B3LYP/cc-pVTZ (aug-cc-pVTZ-pp for the Sn) level, using dichloromethane as a continuum solvent. Without the SnCl5 counterion, 3 and 8 differ by 5.4 kcal/mol in free energy (this difference now includes all the solvation free energy terms), and in the presence of the counter-ion this remains unchanged at 5.4 kcal/mol (see DOIs 10042/to-3668 and 10042/to-3667 without SnCl5 and 10042/to-3670 and 10042/to-3665 with). The free energy of activation with SnCl5 (see DOI: 10042/to-3695 for starting material) is 16.6 kcal/mol (for the [2,6] H shift) and 11.2 kcal/mol (for the  [1,2] Me shift), which indicates a facile room temperature reaction (as indeed is the case).

TS H-transfer. Click for animation

TS 1,2 Methyl shift. Click for animation

What are the implications for this result?

  1. Modelling an (intimate) ion-pair is different from that of covalent compounds in one respect. Whereas the geometry at covalent atoms is very well established and largely predictable, ion-pairs are potentially much more flexible. In other words, it is nowhere near as obvious where to place the counter-ion. In the above diagrams, the SnCl5 is located at a reasonable position, but there are other positions where it could be. Although what is shown is an energy optimized structure, a full search of all the possible positions that the SnCl5 could adopt has not been undertaken, and the possibility must remain that another pose of the ion might be lower in energy, for either of the two transition states. Indeed, if it turns out there are many positions for the ion of very similar in energy, then the entropy of the system would have to be corrected for these microstates.
  2. Nevertheless, one can draw insight from the two structures shown above (click to animate the transition mode). The counter-ion for the hydride transfer does approach the transferring hydrogen quite closely, and does appear to establish a H-bond between two hydrogens and one chlorine. This would stabilize that structure relative to the methyl shift transition state, where such hydrogen bonds do not appear to form. In this case  however, these interactions do not change the relative stabilties.
  3. These ion-pairs do have very large dipole moments (~23D for 3, ~27D for 8), which suggests that the result might in fact be sensitive to the nature of the solvent (and presumably the counter-ion itself).

Many reactions do take place in which intimate ion-pairs are formed (including a fair number of catalytic systems involving metals). We cannot generalise from the result above, but it may well be that the perturbation induced by such counter-ion may play significant roles in deciding selectivities. I would venture to suggest that increasingly modelling such as reported here will play a significant role in establishing mechanisms accounting for the selectivity of catalytic reactions.

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Contriving aromaticity from S≡C Triple bonds

Friday, January 1st, 2010

In the previous post, the molecule F3S-C≡SF3 was found to exhibit a valence bond isomerism, one of the S-C bonds being single, the other triple, and with a large barrier (~31 kcal/mol, ν 284i cm-1) to interconversion of the two valence-bond forms. So an interesting extension of this phenomenon is shown below:

A cyclic form of the SCS Motif. Click for 3D

If the same type of valence bond isomerism were to occur, we would now have three C≡S triple bonds swapping places with three CS single bonds, a sort of super version of the notation normally shown for benzene itself. If the barrier to this swapping is finite, then the interconversion shown above would be a proper equilibrium (the top arrows), but if there is no barrier, then the interconversion would be a proper resonance (the bottom double-headed arrow). Another way of posing the question is whether the so-called Kekulé vibrational mode (which in effect represents the motions implied above) has a negative force constant or a positive one respectively for the two sets of arrows shown.

A B3LYP/cc-pVTZ calculation (DOI: 10042/to-3646) reveals that the optimized geometry exhibits six equal SC bonds, all 1.616Å long. Typically, a single SC bond is around 1.82Å, a double 1.65Å and a triple is about 1.5Å at the same level of theory, so this C=S bond is clearly at least a double one. A NICS(0) calculation at the centroid has the value of -14.6 ppm, which indicates aromaticity. We conclude the appropriate arrow above is the bottom resonance one, rather than the top equilibrium one. This is confirmed by finding that the Kekulé vibrational mode has a strongly positive force constant (ν 1083 cm-1, animated in 3D model above), which contrasts with the negative value (ν 284i cm-1) found for bond shifting in F3S-C≡SF3 itself. Again, comparison indicates that a C≡S triple bond has a frequency of around 1400 cm-1 and a double around 1200 cm-1 (the degenerate C=S non–Kekulé vibrational mode for this system is indeed calculated at around 1225 cm-1). So to summarise; a single F3S-C≡SF3 unit reveals very strong bond alternation, and negative force constant (transition state) for interconversion of the two bond forms, but a cyclic form reveals the opposite behaviour, with no alternation and instead strong aromaticity.

In part this difference in behaviour must be due to the constraints on the geometry of the cyclic form. F3S-C≡SF3 interconverts via a highly twisted geometry with C2 symmetry, and this twisting is not exactly possible if you create a cyclic equivalent. In part it is also due to the aromatic stabilisation energies. In the resonance above, you should be able to count a total of 12 electrons involved! Nominally, if you try to apply the 4n+2 aromaticity rule, it does not fit, until you realise that in fact you must be dealing with two sets of 6 electrons. The system in fact is a classic double-aromatic, in which six electrons circulate in the plane of the molecule (the σ-set) and six above and below (the π-set; the MOs for the molecule confirm exactly this interpretation). Notice how this itself contrasts with a similarly aromatic system, the atom swapping in three nitrosonium cations, where the Kekulé mode force constant was strongly negative.

ELF Analysis for F6S3C3. Click for 3D

To complete the analysis, the ELF basins (above) reveal the six SC regions to each contain 2.7 electrons, together with three carbon carbene monosynaptic basins. For comparison, a system with a high degree of SC triple character (HCS+) has around 3.8 in the SC region. Perhaps a better model is TfOSCH (for which the carbon also has a carbene lone pair), which has 2.6e in the CS region. The carbene lone “pair” for the present molecule integrates to 2.6e each, which totals to a nice octet of electrons around each carbon and to around 7 for each S, confirming that whilst the S is hypervalent, its valence octet is not expanded!). This ELF picture does rather tend to confirm the original resonance structure representation shown at the top.

All that is needed is is for someone to make this molecule to confirm its properties. Perhaps by trimerising F2SC, itself formed by cheletropic elimination? It is worth noting that the iso-electronic P/N (e.g. of S/C) analogues are very well known.

Phosphonitrilic compounds

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Ménage à deux: Non-classical SC bonds.

Wednesday, December 30th, 2009

A previous post posed the question; during the transformation of one molecule to another, what is the maximum number of electron pairs that can simultaneously move either to or from any one atom-pair bond as part of the reaction? A rather artificial example (atom-swapping between three nitrosonium cations) was used to illustrate the concept, in which three electron pairs would all move from a triple bond to a region not previously containing any electrons to form new triple bonds and destroy the old. Here is a slightly more realistic example of the phenomenon, illustrated by the (narcisistic) reaction below of a bis(sulfur trifluoride) carbene. Close relatives of this molecule are actually known, with either one SF3 of the units replaced by a CF3 group or a SF5 replacing the SF3 (DOI: 10.1021/ja00290a038 ).

F3SCSF3 and the nature of its S-C bonds

The two C-S bonds in this molecule are not the same (and similarly for the CF3 analogue), one being long (single), the other short (assumed triple), and the angle subtended at the central carbon is around 150° (B3LYP/cc-pVTZ calculation, DOI: 10042/to-3643). The transition state for interconverting one form to the other would presumably correspond to the concerted movement of two pairs of electrons from one CS region to the other as shown above, not so much a Ménage à trois, as a Ménage à deux! The transition state itself (DOI: 10042/to-3644) has C2 symmetry, with a calculated free energy barrier of 31 kcal/mol and ν 284i cm-1 for the bond shifting process.

Transition state for bond equalisation

Transition state for bond equalisation. Click for animation

The molecule above does have a further point of interest; one of the sulfur atoms (the triply bonded one) is approximately tetrahedral in coordination, whilst the other has a “T-shape”. An inorganic chemist would describe one sulfur as tetravalent (oxidation state IV), the other as hexavalent (oxidation state VI) and the equilibrium between them a dismutation of the two oxidation states. Does this have any reality? The ELF method has been mentioned a number of times in these posts, and it is applied here to seek an answer. The ELF basin centroids are shown below.

The ELF function, as isosurfaces contoured at various thresholds

ELF basins for F3SCSF3. Click for 3D

The integrations are as follows: 14 = 2.24 (a single C-S bond), 30=1.66 (an incipient carbene forming, as implied above), 13+15+16 = 4.34 (a reasonably persuasive triple bond, comprising, unusually, three separated basins). The fluorines 2, 3 and 6 all exhibit bonding basins to the S (respectively 2.17, 2.17 and 2.09), but fluorines 1,5 and 4 do not! Sulfur 8 additionally has a lone pair, 29=2.31, but sulfur 9 does not. One aspect of this analysis is the nature of the triple bond between S9-C7. Because the three basins are separate, does that mean that the bond cannot rotate about its axis?

AIM Analysis of F3SCSF3

An alternative AIM analysis is shown above. Now, the CS triple bond is reduced to a single bond critical point (BCP), labelled 10. AIM allows a property known as bond ellipticity to be computed at that BCP. Typically, single and triple bonds have ellipticities close to zero, whilst double bonds have a value of around 0.4 to 0.5. That for point 10 is 0.18, which seems to support the ELF analysis above. Pretty unsual bonding it would have to be agreed!

ELF centroids for transition state for dismutation.

But what of the original question posed at the start in the diagram; do two pairs of electrons move away together from one triple bond to form another. A further ELF analysis at the transition state for this process reveals that in effect the two pairs do different things. One localizes onto the carbon, to form a proper carbene, the other becomes a sulfur lone pair. So the valence dismutation involves three pairs of electrons, not two as shown at the start, with each pair doing its own thing.

Six-electron model for valence isomerism in F3SCSF3

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Clar islands in a π Cloud

Wednesday, December 9th, 2009

Clar islands are found not so much in an ocean, but in a type of molecule known as polycyclic aromatic hydrocarbons (PAH). One member of this class, graphene, is attracting a lot of attention recently as a potential material for use in computer chips. Clar coined the term in 1972 to explain the properties of PAHs, and the background is covered in a recent article by Fowler and co-workers (DOI: 10.1039/b604769f). The concept is illustrated by the following hydrocarbon:

Clar islands in a polybenzenoid hydrocarbon

Clar islands in a polybenzenoid hydrocarbon

The Clar islands are shown in red, and represent in effect the resonance form of this species which maximises the number of aromatic electronic sextets possible to achieve via a cyclohexatriene resonance form. It encapsulates the concept that maximum stabilization is achieved when the π-electrons in the molecule cluster together (or localize) in cyclic groups of six (rather than eg other allowed values as predicted by the 4n+2 rule of aromaticity). As a historical note, although Clar popularized the concept in the 1970s, the (C) representation had in fact been introduced almost one hundred years earlier, by Henry Armstrong (DOI: 10.1039/PL8900600095). Many demonstrations that Clar islands are reasonably based in quantum mechanical reality have been made; a very graphical and convincing one is that by Fowler and coworkers in the reference noted above, using the calculated magnetic response property known as π current densities (although this shows that the six outer islands tend merge into a single continuous outer periphery).

Current density maps showing Clar islands (taken from DOI: 10.1039/b604769f
Current density maps showing Clar islands for the molecule above (taken from DOI: 10.1039/b604769f)

Previous posts on this blog have mentioned the application of another computed quantum mechanical property known as ELF, the electron localization function introduced by Becke and Edgecombe in 1990 (DOI: 10.1063/1.458517 ) and subsequently adapted for use with DFT-based wavefunctions. ELF is normally applied to help analyze the bonding in a molecule; the value of the function is normalized to lie between 1.0 (a simple interpretation is that this is the value associated with a perfectly localized electron pair) and 0.0. ELF has no association with magnetic response (the latter being an excitation phenomenon), but since the Clar islands can also be considered a localizing property of the π electrons, it is tempting to ask whether the ELF function can also reveal their characteristics (this question was first posed in DOI: 10.1039/b810147g).

The ELF function, as isosurfaces contoured at various thresholds

The ELF function, as isosurfaces contoured at various thresholds. Click for 3D

The diagram above shows the ELF function computed for the π-electrons of the molecule above (B3LYP/6-31G(d), as isosurfaces contoured at various values. At the value of 1.0, no features are discernible, but at 0.95 features which resemble basins associated with each atom centre have appeared, in the region of the 2p-valence atomic orbital on each carbon atom we regard as contributing the π-electron to the system. As the ELF threshold is reduced, these objects start to merge into what are called valence basins associated with bonds in the molecule. The outer periphery is the first to start coalescing. By a value of 0.75 (click on the diagram above to see a 3D model) the basins have merged to form seven clear-cut rings which happen to coincide exactly with the Clar islands. This feature persists down to a threshold of 0.55. Below this value, the seven individual basins merge into a single basin contiguous across the top (and bottom) surfaces of the molecule. One can also conceptualize the journey in the other direction. At low ELF values, the function is continuous, but as the threshold increases, it starts to bifurcate into separated basins. The first clear-cut bifurcation is indeed into the Clar islands, and this persists across a relatively wide range of ELF values, which suggests it is a significant feature. What is somewhat surprising is the close apparent correspondence of this way of analysing the electronic properties of the π electrons with their magnetic response computed via current densities. But association with aromaticity has previously been made (DOI: 10.1063/1.1635799). Thus Santos and co-workers have shown that the value of the ELF function at the point where it bifurcates from a ring into discrete valence or atomic basins can be related to other metrics of aromaticity. Here, that value is around 0.75 for the Clar basins, which is also within the range of values that Santos et al associate with prominent aromaticity (benzene itself has a value around  0.95).

A C114 PAH

A C114 PAH

The ELF function for the 114-carbon unit shown above again reveals prominent Clar islands, the inner heptet being very similar to the picture painted using current densities.

Clar islands in the ELF function for a C114 carbon PAH

Clar islands in the ELF function for a C114 carbon PAH

The final example involves diboranyl isophlorin (DOI: 10.1002/chem.200700046), a 20 π-electron antiaromatic system. Such systems are particularly prone to forming locally aromatic Clar islands as an alternative to global antiaromaticity (DOI: 10.1039/b810147g).

A Diborinyl system.

A Diboranyl isophlorin.

The ELF function is shown for both the neutral diboranyl system and its (supposedly more aromatic) dication. Here a mystery forms. No Clar islands are seen, and instead it is the periphery that bifurcates, at ELF thresholds of 0.5 for the neutral and 0.7 for the dication. The latter value clearly is that of an aromatic species, but the former is somewhat in no-man’s land, but certainly less aromatic that the dication. One for further study I fancy!

ELF Function for diboranyl molecules (red=neutral, green=dication). Click for 3D

ELF Function for diboranyl molecules (red=neutral, green=dication). Click for 3D

Does the ELF function have any possible advantage over the use of current density methods for analysing aromaticity? Well, the latter is normally applied to flat systems with planes of symmetry defining the π-system, and with respect to which an applied magnetic field is oriented. How to orient this magnetic field is not so obvious for prominently non-planar or helical molecules. Since the ELF function does not depend on the orientation of an applied magnetic field, it may be a useful adjunct for studying the properties of π-electrons in non-planar systems.

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The nature of the C≡S triple bond: part 3.

Sunday, December 6th, 2009

In the previous two posts, a strategy for tuning the nature of the CS bond in the molecule HO-S≡C-H was developed, based largely on the lone pair of electrons identified on the carbon atom. By replacing the HO group by one with greater σ-electron withdrawing propensity, the stereo-electronic effect between the O-S bond and the carbon lone pair was enhanced, and in the process, the SC bond was strengthened. It is time to do a control experiment in the other direction. Now, the HO-S group is replaced by a H2B-S group. The B-S bond, boron being very much less electronegative than oxygen, should be a very poor σ-acceptor. In addition, whereas oxygen was a π-electron donor (acting to strengthen the S=C region), boron is a π-acceptor, and will also act in the opposite direction. So now, this group should serve to weaken the S-C bond.

The H2BSCH molecule. Click for 3D.
The H2BSCH molecule. Click for 3D.

At the B3LYP/cc-pVTZ level (DOI: 10042/to-3189), the S-C bond now emerges as 1.834Å compared to 1.544Å for the HO-substituted version and the S-C stretch is reduced to 803 cm-1. The NBO interaction term between LP(1)C2 and BD*(1) S1-B3 is indeed quite small (6.9 kcal/mol). The basin integration for point 10 increases to 2.22e, whilst point 9 decreases to 1.90e, and 8 is again up at 2.11. The SC bond is now merely a single bond!

So what have we proved? Well, we find that our hypothesis works in both directions, to either strengthen or weaken the CS region. Indeed, variation of the S-substituent (HO, OTf, BH2) has quite a dramatic effect on the nature of the CS bond, evolving it all the way from a single bond at one extreme to one with significantly triple character at the other.

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The nature of the C≡S Triple bond: Part 2

Saturday, December 5th, 2009

In my first post on this theme, an ELF (Electron localization function) analysis of the bonding in the molecule HO-S≡C-H (DOI: 10.1002/anie.200903969) was presented. This analysis identified a lone pair of electrons localized on the carbon (integrating in fact to almost exactly 2.0) in addition to electrons in the CC region. This picture seems to indicate that the triple bond splits into two well defined regions of electron density (synaptic basins). In a comment to this post, I also pointed out that an NBO analysis showed a large interaction energy between the carbon lone pair and the S-O σ* orbital, characteristic of anomeric effects (in eg sugars). This latter observation gives us a handle on possibly tweaking the effect. Thus if the S-O σ* orbital can be made a better electron acceptor, then its interaction with the lone pair could be enhanced.

Accordingly, the analysis has been repeated for H-C≡S-OTf (OTf = triflate = trifluoromethane sulfonate), since the triflate would be expected to increase significantly the electron accepting properties of the S-O bond.

ELF analysis for H-C≡S-OTf

ELF analysis for H-C≡S-OTf. Click for 3D model

One dramatic change has indeed occurred. Previously, a well-defined ELF disynaptic basin had been identified in the S-O region, with an integration of 1.12e. If the OH group is replaced by OTf, this disynaptic basin can no longer be located. The electrons have instead moved into sulfur lone pairs, and the S-CF3 bond, which is an expected consequence of the greater electronegativity of the triflate group. Point 15 (the S=C region) integrates to 2.56e (compared with 2.36 for the OH analogue), and the carbon lone pair decreases from 2.01 to 1.86e.

Taken as a whole, these changes suggest that the CS bond has gotten stronger, resulting from transfer of electron density from the non-bonding carbon lone pair, to the CS bond itself. Indeed, its length is now 1.492Å, a significant shrinkage compared to 1.544Å for the OH parent (B3LYP/cc-pVTZ). Likewise, the C-S vibrational stretch of 1381 cm-1 for the OTf derivative is an increase over 1215 cm-1 for the OH system and 1304 cm-1 for diatomic CS itself (B3LYP/cc-pVTZ).

These results suggest that the ELF procedure, combined with the insight from the NBO analysis, can be used as a tool to rationally design a variation to the original molecule which does appear to enhance the triple bond character of the CS region, and to fulfil further the ambition of the original article by Schreiner and co-workers. As a triflate, it may even be susceptible to a simple preparation from the alcohol parent! Anyone up for it?

It is also worth noting that the above system is headed off towards HC≡S+, the thioacylium cation (although crystal structures of the acylium ion are known, none have been reported for the thioacylium ion). Both N≡N and C≡O contract their bond lengths when protonated, so it should be no great surprise to find that CS does so as well (1.476Å, ν 1543 cm-1).

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The nature of the C≡S triple bond

Tuesday, December 1st, 2009

Steve Bachrach has just blogged on a recent article (DOI: 10.1002/anie.200903969) claiming the isolation of a compound with a C≡S triple bond;

A compound with a CS triple bond

A compound with a C≡S triple bond

Steve notes that Schreiner and co claim a “structure with a rather strong CS double bond or a weak triple bond”. With this size of molecule, the proverbial kitchen sink can be thrown at the analysis of the bonding. But one technique that was NOT applied is ELF (see the earlier post using ELF to analyze the bonding in MgPh2). So here is such an analysis, computed for the CCSD/cc-pVTZ wavefunction at the geometry reported in the publication (see also DOI: 10042/to-2980). The (centroids of the) synaptic basins are the small purple spheres.

ELF analysis of the bonding in HOCCH. Click for 3D

ELF analysis of the bonding in HOS≡CH. Click for 3D

The key (disynaptic) basin is labelled 10, and it integrates to 2.36 electrons, rather far from the 6 electrons which might be expected for a triple bond! Its centroid is also significantly off-centre from the S-C bond. Basin 11 integrates to 2.01 electrons; it resembles a lone pair on the carbon, although the ELF analysis actually labels it a S-C disynaptic basin. It approximately maps to the HOMO orbital. Monosynaptic basin 9 encompases the two formal lone pairs on the sulfur, and it integrates to 3.59e (quite often, what we regard as separate, rabbit-ear, lone pairs on an atom manifest only as a single monosynaptic basin). Completing the analysis are two further monosynaptic basins 6 and 7, which represent lone pairs on the oxygen (2.45e each) and the disynaptic basin 8 (1.1e).

Bonding, much like the Humpty-Dumpty meaning, is very much what you want it to be! But in this case, one has to ask whether the description of the bonding in the C≡S region really is best described as a weak triple bond, or even a strong double bond, or whether the nominal six electrons of the triple bond split into two regions, one clearly bonding, the other more non-bonding.

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Multi-centre bonding in the Grignard Reagent

Tuesday, December 1st, 2009

The Grignard reaction is encountered early on in most chemistry courses, and most labs include the preparation of this reagent, typically by the following reaction:

2PhBr + 2Mg → 2PhMgBr ↔ MgBr2 + Ph2Mg

The reagent itself exists as part of an equilibrium, named after Schlenk, in which a significant concentration of a dialkyl or diarylmagnesium species is formed. The topic of this blog entry is to analyse the structure and bonding in this latter species.

First, the structure is shown below (for 2,6-diethylphenyl magnesium). This reveals a dimeric structure with a four membered ring core, comprising two  Mg atoms  connected by two bridging  aryl groups.

The crystal structure of a di-aryl magnesium. Click to view 3D

The crystal structure of a di-aryl magnesium. Click to view 3D

The question to be addressed here is the nature of the aryl groups. Put simply, it seems as if their bridging role means that one of the six carbons involved in the benzene ring has become sp3 hybridized. This would in turn mean that the cyclic conjugation of the benzene ring is interrupted, and a species akin to the Wheland intermediate is formed in which the aromaticity of two of the benzene rings is no longer sustained. This situation could be depicted thus;

A Simple bonding representation in Ph2Mg dimer

A Simple bonding representation in Ph2Mg dimer

Is this really the best way of depicting the bonding in this species? A more subtle analysis of the bonding can be achieved using a technique known as ELF (involving analysis of the electron localization function). This reveals bonds as so-called synaptic basins, which come in two varieties; disynaptic basins corresponding to two-centre bonds, and trisynaptic basins which reveal three-centre bonds (there is also a monosynaptic basin which corresponds to electron lone pairs). Such an ELF analysis (based on a B3LYP/6-311G(d,p) computed wavefunction for Ph2Mg dimer) is shown below;

ELF analysis of the bonding in Ph2Mg dimer

ELF analysis of the bonding in Ph2Mg dimer. Click for 3D model

The small purple dots represent synaptic basins. Several of these are circled. The  ones circled in orange are conventional disynaptic forms, and the basins can be integrated to to 2.48 electrons each. The red basin however is clearly revealed as a trisynaptic form (covering both metal centres and the carbon) and integrating to  2.7 electrons. The  three basins surrounding each Mg atom integrate to 7.91 electrons, which reveal the metal to have a conventional octet of electrons in its valence shell. The bonding in the central region could therefore be described as comprising two three-centre-three-electron bonds. The key aspect of this is that the two bridging phenyl groups do not break their aromaticity, ie all four phenyl/aryl groups largely retain their aromaticity! Thus the disynaptic basins for  the normal non-bridging phenyl group and  circled in green integrates to 2.6 electrons and the blue to 2.8 (an ideal aromatic bond would of course integrate to 3.0 electrons), whereas the equivalent basins for the bridging phenyl (brown and purple, 2.5 and  2.8) are virtually the same.

It is interesting how a veritable mainstay of most taught chemistry courses, the Grignard reagent,  can have such subtle aspects of the bonding surrounding both the metal atom and the aromatic groups, and how rarely this bonding is actually dissected in most text books.

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The Fine-tuned principle in chemistry

Sunday, November 29th, 2009

The  so-called  Fine tuned model of the universe asserts that any small change in several of the dimensionless fundamental physical constants would make the universe radically different (and hence one in which life as we know it could not exist). I suggest here that there may be molecules which epitomize the same principle in chemistry. Consider for example dimethyl formamide. The NMR spectra of this molecule reveal that at room temperature, the two methyl groups are inequivalent, indicating that the rate constant for rotation about the C-N bond has a very particular range of values at the temperatures at which most living organisms exist on our planet.

Dimethyl formamide

Dimethyl formamide

The half-restricted room-temperature rotation about the C-N bond arises from exactly the right amount of resonance contribution from the ionic form shown on the right, and this in turn depends on the relative energies of the nitrogen pair and the π system of the carbonyl group having the correct relationship. It is probably also true that the environment that this grouping finds itself in will alter the contribution (i.e. stabilize the ionic form over the neutral one).   A little less contribution and the C-N bond would rotate much more easily, a little more and it would be much more rigid. Since this peptide bond is an essential and repeated feature of the structure of most biological proteins and enzymes, one might speculate that if that bond could rotate more easily, most enzymes would be much floppier than they are, and may not be easily induced to fold in a repeatable manner into the conformations that enable all the metabolic processes and make them the efficient catalysts they are. If the bond rotated less easily, it might be that the same enzymes would end up being too rigid, and this may prevent them from flexing sufficiently to allow key metabolites to enter or leave the active site.

Nowadays, the flexing of proteins is commonly studied using techniques of molecular dynamics,  the driving forces for which are specified using molecule mechanics force fields. Here, the rotation about the C-N bond is defined by simple mechanical force constants or torsional barriers. I ask here how sensitive the dynamics of protein folding and catalysis are to the C-N rotational barrier? Is this truly a fine-tuned molecule, or might it be that the existence of life as we know it has a wide tolerance to the strength of the C-N bond?

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