The conformational analysis of cyclo-octane

January 31st, 2010

In the previous post, I suggested that inspecting the imaginary modes of planar cyclohexane might be a fruitful and systematic way in which at least parts of the conformational surface of this ring might be probed. Here, the same process is conducted for cyclo-octane. The ring starts with planar D8h symmetry, and at this geometry (B3LYP/6-311G(d,p), DOI: 10042/to-3742) five negative force constants (corresponding to imaginary modes) are calculated. The most negative is non-degenerate, and gives directly the crown conformation of D4d symmetry (DOI: 10042/to-3738). The remaining four modes comprise two degenerate pairs. Following either of the E2u eigenvectors downhill leads to another conformation, D2d (DOI: 10042/to-3741), with a geometry which is noteworthy for exhibiting a pair of unusually close non-bonded H…H contacts (1.908Å). We can debate whether such a close approach of two hydrogens is a bond or not (an AIM analysis appears at the bottom of this post).

D8h, +82.8 kcal/mol
Follow B2u 467i Follow E3g 404i Follow E2u 230i
to D4d +0.8 to Ci 131i (Au), +7.5 to D2d +3.6

B2u

E3g

E2u
Cs 0.0 C2 +1.6 -

Following the remaining E3g mode leads to a stationary point of Ci symmetry (DOI: 10042/to-3743). This is a valley-ridge potential, since this point turns out to be a transition state itself, and following the Au imaginary mode at this point results in another, this time stable conformation, of chiral C2 symmetry (DOI: 10042/to-3744). This has a calculated optical rotation [α]D of 72° (at 589nm in chloroform).

Are these three conformations all there are? Well, a thorough analysis of the conformational space has in fact identified six minima (DOI: 10.1002/(SICI)1096-987X(19980415)19:5<524::AID-JCC5>3.0.CO;2-O), of which the most stable has Cs symmetry (the so-called chair-boat conformation, and the one most frequently found in crystal structures of cyclo-octanes). Where is that one in the above analysis? It arrives by a distortion of the D4d form (DOI: 10042/to-3747) via a transition state of no symmetry (DOI: 10042/to-3752)

Whilst the full potential surface clearly has many more features, following the modes of the planar conformation of cyclo-octane is a simple and rapid way of establishing four of the six limiting stable conformations (the two remaining forms have  D2 and S4 symmetry, see DOI 10.1016/0166-1280(88)80008-3).

AIM analysis of D2d cyclo-octane.

Finally as promised, the AIM analysis of the D2d conformer (above). The ρ(r) value at the interesting H…H critical point is 0.015, which is pretty high in comparison to most normal hydrogen bonds, and would be conventionally taken to indicate attraction. The Laplacian ∇2ρ(r) is +0.05. The “bond” ellipticity ε has a value of 0.29. Single bonds are close to zero, and C=C double bonds are ~0.4, so this is pretty high (see also DOI: 10.1002/anie.200805751).

The two highest C-H stretching vibrations for this conformation are well separated from all the others (ν 3095, 3103 cm-1 for the symmetric A1 and antisymmetric B2 combinations, below for animations). These vibrations serve to both decrease and increase the H…H distances as part of the atomic (harmonic) displacements, and clearly doing so takes more energy than vibrating any of the other C-H bonds. It seems unlikely that the C-H bonds are themselves stronger, so does that mean that the H…H interaction is attractive or is it repulsive? In this context, it is worth noting that the symmetric vibration (both H…H distances decrease/increase at the same time) is lower in wavenumber than the mode which decreases one and increases the other.

A1

B2

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The conformation of cyclohexane

January 28th, 2010

Like benzene, its fully saturated version cyclohexane represents an icon of organic chemistry. By 1890, the structure of planar benzene was pretty much understood, but organic chemistry was still struggling somewhat to fully embrace three rather than two dimensions. A grand-old-man of organic chemistry at the time, Adolf von Baeyer, believed that cyclohexane too was flat, and what he said went. So when a young upstart named Hermann Sachse suggested it was not flat, and furthermore could exist in two forms, which we now call chair and boat, no-one believed him. His was a trigonometric proof, deriving from the tetrahedral angle of 109.47 at carbon, and producing what he termed strainless rings.

Whilst the chair form of cyclohexane now delights all generations of chemistry students, the boat is rather more mysterious. Perhaps due to Sachse, it is still often referred to as a higher energy form of the chair (Barton, in the 1956 review that effectively won him the Nobel prize, clearly states that the boat is one of only two conformations free of angle strain, DOI: 10.1039/QR9561000044). Over the last 30 years or so, and especially with the advent of molecular modelling programs, the complexity of the conformations of cyclohexane has become realised. A nice recent illustration of that complexity is by Jonathan Goodman using commercial software. Here a slightly different take on that is presented.

The starting point is the flat Baeyer model for cyclohexane. Like benzene, it has D6h symmetry. When subjected to a full force constant analysis using a modern program (in this instance Gaussian 09), this geometry is revealed (DOI: 10042/to-3708) to have three negative force constants, which in simple terms means it has three distortions which will reduce its energy. The eigenvectors of these force constants are shown below, and each set of vectors acts to reduce the symmetry of the species. Such symmetry-reduction is a well known aspect of group theory, and its analysis in the Lie symmetry groups is used in many areas of physics and mathematics, but it is a less used in chemistry.

348i cm-1 (B2g) 244i (E2u) 244i (E2u)

D6h to C2h for cyclohexane

D6h to C2h for cyclohexane. Click for animation.

D6h to D2

D6h to D2. Click for animation.

D6h to C2v

D6h to C2v. Click for animation.

The first of these symmetry-reducing vibrations (the B2g mode) converts the geometry immediately to the chair conformation of cyclohexane. So in some ways, this use of symmetry is a modern equivalent of the trigonometry used by Sachse to prove his point.

The next two modes are degenerate in energy, and the first of these reduces the symmetry to D2. The result is what we now call the twist-boat. It is interesting, because the D2 group is one of the (relatively few) chiral groups, and the twist-boat exhibits disymmetric symmetry. In other words, following the vibrational eigenvectors in one direction leads to one enantiomer of the twist boat, and in the other direction to the other enantiomer. So (in theory only), one might actually be able to produce chiral cyclohexane (the experiment and resolution would have to be done at very low temperatures!). It is also interesting that theory nowadays could quite reliably calculate the optical rotation of this species (and its circular dichroism spectrum), so we certainly would know what to look out for.

The second component of the degenerate E imaginary mode leads directly to a species of C2v symmetry, which we recognize as Sachse’s second possible form of cyclohexane. The symmetry-reductions of D6h to C2h, D2 and C2v all have paths on the grand diagram of the 32 crystallographic point groups and their sub groups, and is an interesting application of group theory to a mainstream topic in organic chemistry.

But the story is not quite complete yet. The C2v boat is not the final outcome of the last distortion! It too is a transition state, connecting again the two D2 forms. So the path from D6h to C2v is NOT a minimum energy reaction path, but a rather different type of path known as a valley-ridge inflection path. An example of such a surface can be seen for the dimerisation of cyclopentadiene (DOI: 10.1021/ja016622h) and effectively it connects one transition state to a second transition state, without involving any intermediates on the pathway. At some stage, the dynamics of the system takes over, and the symmetry breaks without the system ever actually reaching the second transition structure. This final aspect of the potential energy surface of cyclohexane was not discussed by Jonathan Goodman in his own article on the topic.

So symmetry-breaking is the topic of this blog, and its connection to physics and mathematics. And, I might add that the same approach can be taken for looking at the conformations of cyclobutane, pentane, heptane and octane. But that will be left for another post.

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Posted in General, Interesting chemistry | 7 Comments »

Blisteringly bent (quadruple) bonds

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.

none

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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Semantic Blogs

January 17th, 2010

A Semantic blog is one in which the system at least in part understands about (some of the) concepts and topics that are in the content. The idea is that this content can be more intelligently (is that the correct word?) and importantly, automatically searched, harvested, and connected to the same or similar concepts found elsewhere in other blogs and the Web as whole. I am writing this blog using Firefox, having added a Firefox extension called Zemanta. As I write, the system offers suggestions for similar themes elsewhere that I could choose to link to the blog (and obviously the more one writes, or the more specific the terms one uses, the more sensible the suggestions become. At this precise moment, it is still offering fairly generic suggestions, one of which I have just chosen to add). My purpose in this particular post is to explore how the very process of writing a blog might be affected by such a product. I am also inferring (but cannot add detail at the moment) that all the (semantic) connections or links to other materials will be expressed in this blog using some form of formal declaration, such as e.g. RDFa.

Thus this blog has a WordPress plugin called wp-RDFa as part of its library. This gathers meta-data in two forms, FOAF and Dublin-Core, and expresses it using the RDFa formalism. This is really just a standard way of letting any software that might visit the blog know that this meta-data is available for harvesting. FOAF is something we discussed a year or so back; it is a formal way of expressing information about yourself in RDF (see an ACS talk on the topic), and in particular indicating what you are interested in (as a chemist in my case), who you collaborate with, where you visit (information of course that you do wish to make public, you do not have to include any private details). Nowadays, a variety of social networking tools have become semantically enabled. This blog is, a flavour of Wikis (SemediaWiki, and its potential as a format for science journals), Second Life and many others. At the moment, there is little apparent added value emerging from such enrichment (I have just noted another two Zemanta articles flagged, which I will add at this instant) and certainly little in chemistry.

But what could one aspire to? For example, Steve Bachrach on his blog routinely adds InChI identifiers and keys to uniquely identify all molecules mentioned on his site. Just imagine a situation where one is describing a molecule in one’s own blog, and e.g. Zemanta instantly flags up any other article out there which has tagged the same molecule. That article and your blog can now be semantically identified as talking about the same system. A harvester could collect the information about this molecule, and create a superset of information about it (hey, we chemists already have such a system, it is called Chemical Abstracts! But of course its not quite the same, and I had better reserve a comparison with CAS for another post), which in turn enriches resources such as Zemanta. Its a sort of positive feed-back loop!

Well, the Semantic Web has been a long time coming (see DOI: http://dx.doi.org/10.1021/ci000406v or 10.1087/095315101750240421 which were both written in 2001), and since it has not yet changed the Web, some tend to write it off as a lost cause. Perhaps the semantification of blogs will make a difference?

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Chemical intimacy: Ion pairs in carbocations

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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How long will a blog last? ArchivePress

January 9th, 2010

After around 40 posts here, I decided to take a look at the whole effort and ask some questions. For example

  1. Should (scientific) blogs be used to report new science, or merely opinion on existing science (see this blog also)?
  2. If the former, should they be abstracted in the manner of regular articles (e.g. by CAS etc).
  3. Unlike e.g. a journal, a blog is often (and certainly in this case) the effort of an individual. Journals on the other hand can last for centuries (see for example this link to the ToC of the world’s oldest scientific journal that has been in continuous publication for 355 years!). So how long should/can a blog last?
  4. The last question leads on to whether blogs should be archived or curated in a larger sense?

The last question leads directly to projects such as ArchivePress which has just started up a few months ago. I will quote two of their objectives

  • Methodology and guidance for the effective capture and management of blog posts.
  • Scripts/plugins to enable WordPress to be used as a blog aggregator and archiving engine.

Of course, this will have to be a fairly generic solution, and certainly one aspect of my blog presents another challenge, namely how to preserve the molecules mentioned here (many of the posts include 3D coordinates lurking under the images). But one step at a time!

I will post on another solution to the preservation issues, which should enter the public domain in a month or so. Meanwhile, let’s see what the ArchivePress project can offer!

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Contriving aromaticity from S≡C Triple bonds

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.

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 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

Posted in Hypervalency, Interesting chemistry | 1 Comment »

Clar islands in a π Cloud

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.

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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