Posts Tagged ‘aromaticity’

Dispersion-induced triplet aromatisation?

Thursday, January 3rd, 2019

There is emerging interest in cyclic conjugated molecules that happen to have triplet spin states and which might be expected to follow a 4n rule for aromaticity.[1] The simplest such system would be the triplet state of cyclobutadiene, for which a non or anti-aromatic singlet state is always found to be lower in energy. Here I explore some crystal structures containing this motif for possible insights.

My search query is shown below, and the search is constrained so that the four substituents are Si, C or H.


The results show three clusters. The top left and bottom right have one long bond length ~1.6Å and the other much shorter at ~1.35Å (Δr ~0.25Å) The central region contains two examples, 2 where the difference between the two lengths is rather smaller and 1 where they are equal.

The first example 1[2] is in fact the di-anion of cyclobutadiene and as a 6π aromatic, one indeed expects the C-C bonds to be equal in length. The second 2 is tetra t-butylcyclobutadiene as reported in 1983.[3] At room temperature the two C-C bond lengths are 1.464 and 1.483Å, at -30°C, 1.466 and 1.492Å and at -150°C 1.441 and 1.526Å (Δr 0.085Å). These results led to the conclusion that this species was not intrinsically square but rectangular, as expected of singlet cyclobutadiene. The equalisation was attributed to equal populations of two disordered rectangular orientations averaging to an approximately square shape at higher temperatures.

But why is the behaviour of this particular cyclobutadiene different from the others in the plot above? Perhaps the answer lies these in the results of the Schreiner group[4], in which the dispersion attractions of substituents such as t-butyl can have substantial and often unexpected effects on the structures of molecules. So it is reasonable to pose the question; could the room temperature bond length differences of 2 be smaller compared with the other more extreme examples as a result of dispersion effects?

Here I have computed the singlet geometry of tetra t-butylcyclobutadiene at the B3LYP+D3BJ/Def2-TZVPP level (i.e. using the D3BJ dispersion correction, FAIR data DOI: 10.14469/hpc/4924). Δr for this singlet state is 0.264Å, larger than apparently from the crystal structure, but in agreement with the other crystal results as seen above.

The origins of the measured structure of 2 must be in the barrier to the automerisation of the singlet state. For normal cyclobutadienes, this must be relatively high since the transition state is presumably anti-aromatic. High enough that the averaging of the two rectangular structures is slow enough that it manifests as two different bond lengths. But in 2, as the temperature of the crystal increases, the bonds become more equal, suggesting a lower barrier to the equalisation than the other examples. This is also supported by the apparent identification of a triplet square state for the tetra-TMS analogue of tetra-tert-butyl cyclobutadiene derivative [5] which again suggests that dispersion might favour a square form over the rectangular one.

To finish, I show the crystal structure search for the 8-ring homologue of cyclobutadiene, plotted for the two adjacent C-C lengths and (in colour) the dihedral angle associated with the three atoms involved and the fourth along the ring. Cluster 1 represents various boat-shaped derivatives with very different C-C bond lengths. Cluster 2 are all ionic, and as per above represent a planar 10π-electron ring. Cluster 3 are mostly “tethered” molecules in which additional rings enforce planarity. 

COT

Unfortunately, none of these derivatives include tert-butyl or TMS derivatives in adjacent positions around the central ring. Perhaps octa(t-Bu)cyclo-octatetraene or its TMS analogue would be interesting molecules to try to synthesize!

References

  1. A. Kostenko, B. Tumanskii, Y. Kobayashi, M. Nakamoto, A. Sekiguchi, and Y. Apeloig, "Spectroscopic Observation of the Triplet Diradical State of a Cyclobutadiene", Angewandte Chemie International Edition, vol. 56, pp. 10183-10187, 2017. https://doi.org/10.1002/anie.201705228
  2. T. Matsuo, T. Mizue, and A. Sekiguchi, "Synthesis and Molecular Structure of a Dilithium Salt of the <i>cis</i>-Diphenylcyclobutadiene Dianion", Chemistry Letters, vol. 29, pp. 896-897, 2000. https://doi.org/10.1246/cl.2000.896
  3. H. Irngartinger, and M. Nixdorf, "Bonding Electron Density Distribution in Tetra‐<i>tert</i>‐butylcyclobutadiene— A Molecule with an Obviously Non‐Square Four‐Membered ring", Angewandte Chemie International Edition in English, vol. 22, pp. 403-404, 1983. https://doi.org/10.1002/anie.198304031
  4. S. Rösel, H. Quanz, C. Logemann, J. Becker, E. Mossou, L. Cañadillas-Delgado, E. Caldeweyher, S. Grimme, and P.R. Schreiner, "London Dispersion Enables the Shortest Intermolecular Hydrocarbon H···H Contact", Journal of the American Chemical Society, vol. 139, pp. 7428-7431, 2017. https://doi.org/10.1021/jacs.7b01879

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Expanding on the curious connection between the norbornyl cation and small-ring aromatics.

Sunday, March 12th, 2017

This is another of those posts that has morphed from an earlier one noting the death of the great chemist George Olah. The discussion about the norbornyl cation concentrated on whether this species existed in a single minimum symmetric energy well (the non-classical Winstein/Olah proposal) or a double minimum well connected by a symmetric transition state (the classical Brown proposal). In a comment on the post, I added other examples in chemistry of single/double minima, mapped here to non-classical/classical structures. I now expand on the examples related to small aromatic or anti-aromatic rings.

Examples of symmetric energy potentials
System Classical with 1 imaginary normal mode Non-classical with 0 imaginary modes
Norbornyl cation TS for [1,2] sigmatropic Minimum, this post
Singlet [6], [10]; 4n+2 annulenes – Minimum with Kekulé vibration
Singlet [4], [8]; 4n annulenes TS for bond shift, 1 imaginary normal mode –
Triplet [4], [8]; 4n annulenes – Minimum, with Kekulé vibration (?)
Semibullvalenes TS for [3,3] sigmatropic Minimum
Strong Hydrogen bonds TS for proton transfer Minimum
SN2 substitutions TS for substitution (C) Minimum (Si)
Jahn-Teller distortions Dynamic Jahn-Teller effects No Jahn-Teller distortions

In the table above, you might notice a (?) associated with the entry for (aromatic) triplet state 4n annulenes. Here I expand the ? by considering triplet cyclobutadiene and triplet cyclo-octatetraene (ωB97XD/Def2-TZVPP, 10.14469/hpc/2241 and 10.14469/hpc/2242 respectively). Each has a normal vibrational mode shown animated below, which oscillates between the two Kekulé representations of the molecule with wavenumbers of 1397 and 1744 cm-1 respectively. These Kekulé modes are both real, which indicates that the symmetric species (D4h and D8h symmetry) is in each case the equilibrium minimum energy position (rCC 1.431 and 1.395Å). For comparison the aromatic singlet state 4n+2 annulene benzene (rCC 1.387Å) has the value 1339 cm-1. Notice that both the triplet state wavenumbers are elevated compared to singlet benzene, because in each case the triplet ring π-bond orders are lower, thus decreasing the natural tendency of the π-system to desymmetrise the ring.[1]

To complete the theme, I will look at singlet cyclobutadiene. According to the table above, the symmetric form should be a transition state (TS) for bond shifting, with one imaginary normal mode. To calculate this mode, one has to use a method that correctly reflects the symmetry, in this case a CASSCF(4,4)/6-311G(d,p) wavefunction (DOI: 10.14469/hpc/2244). The mode (rCC 1.444Å) shown below has a wavenumber of 1477i cm-1; its vectors of course resemble those of the triplet mode, but its force constant is now negative rather than positive!

At first sight any connection between the property of the norbornyl cation at the core of the controversies all those decades ago and aromatic/antiaromatic rings might seem tenuous. But in the end many aspects of chemistry boil down to symmetries and from there to Évariste Galois, who started the ball rolling.

References

  1. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations", Chemical Reviews, vol. 101, pp. 1501-1540, 2001. https://doi.org/10.1021/cr990363l

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Ammonium tetraphenylborate and the mystery of its π-facial hydrogen bonding.

Friday, March 10th, 2017

A few years back, I did a post about the Pirkle reagent[1] and the unusual π-facial hydrogen bonding structure[2] it exhibits. For the Pirkle reagent, this bonding manifests as a close contact between the acidic OH hydrogen and the edge of a phenyl ring; the hydrogen bond is off-centre from the middle of the aryl ring. Here I update the topic, with a new search of the CSD (Cambridge structure database), but this time looking at the positional preference of that bond and whether it is on or off-centre. 

The search (February 2017 database, DOI:10.14469/hpc/2233) is shown above, QA = N, O, F, Cl and other constraints are R < 0.01, no errors, no disorder. Two distances are plotted, one (DIST1) is from the H to the ring centroid and the second (DIST2) from the H to an edge carbon atom. The colour code relates to ANG1, the angle subtended at the centroid. A value of 90° would indicate the H is orthogonal to the plane of the aromatic ring.

You can see from the above that the yellow dots correspond to ~90° and that by and large the H…centroid distances are shorter than the H…C distances. 

The above is another representation of this search, again showing that the preferred angle is 90°, although there is a fair bit of scatter. The extreme outliers may be crystallographic errors, but one point caught my eye and is circled in red above; ammonium tetrafluoroborate (3D model DOI: 10.5517/CC4V6TZ). This has a very short distance from the H to the centroid (2.07Å), shorter than the Pirkle reagent that we looked at all those years back. The authors[3] note that “The N-H…Ph distances, H…M 2.067Å … are exceptionally short (M = aromatic midpoint)” but also that “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system.” This implies that such bonds are largely agnostic about whether they bind to the centroid of the ring or to its edge and that the most probable position might arise simply because of crystal packing. An interesting variation on this molecule is a crystal that includes a further 5NH3 in addition to ammonium tetraphenylborate (3D model DOI: 10.5517/cc7bly2). Here an ammonia intervenes between the ammonium cation and a phenyl ring, resulting in a binding of the ammonia with two NHs closer to the edge of the ring and one NH interacting in parallel mode.

Time therefore for a calculation, using B3LYP+GD3BJ/Def2-TZVPP, the functional being chosen because the dispersion contribution is not built in, but uses what is currently thought to be the best representation of these attractions. The issue now is what molecular unit to use? This is an ionic structure and so a periodic boundary model is most appropriate, but given its size I reduced this to two models comprising smaller discrete fragments.

  1. A unit just comprising the simple ion pair. This leaves two of the four N-H bonds devoid of hydrogen bonding (DOI:10.14469/hpc/2234). The optimisation adopts a pose where two NH groups are directed towards a carbon atom rather than the ring centroid. How much of this is due to the smallness of this model?
  2. A unit comprising a double ion pair, which allows one ammonium group to participate with all four NH groups across four phenyl rings and exhibiting six NH interactions in total with six rings (DOI: 10.14469/hpc/2235). The NH hydrogen vectors all interact with ring carbons rather than the ring centroid.

This brief computational exploration has covered only one method (the B3LYP DFT procedure), albeit with what is thought to be a good dispersion attraction term added and a reasonable basis set. It does seem to show that hydrogen bonds interacting with the centroid of a phenyl ring are not the preferred mode, which is instead an interaction with the edge of the ring. The quote above, “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system” suggests that whilst the average position might be the centroid, a true hydrogen bond to the centroid might be rarer than thought. Although most of the crystallographic examples located in the searches above deem to show a preference for the ring centroid, this might be more apparent than real. 

References

  1. H.S. Rzepa, M.L. Webb, A.M.Z. Slawin, and D.J. Williams, "? Facial hydrogen bonding in the chiral resolving agent (S)-2,2,2-trifluoro-1-(9-anthryl)ethanol and its racemic modification", Journal of the Chemical Society, Chemical Communications, pp. 765, 1991. https://doi.org/10.1039/c39910000765
  2. H.S. Rzepa, M.H. Smith, and M.L. Webb, "A crystallographic AM1 and PM3 SCF-MO investigation of strong OH ⋯π-alkene and alkyne hydrogen bonding interactions", J. Chem. Soc., Perkin Trans. 2, pp. 703-707, 1994. https://doi.org/10.1039/p29940000703
  3. T. Steiner, and S.A. Mason, "Short N<sup>+</sup>—H...Ph hydrogen bonds in ammonium tetraphenylborate characterized by neutron diffraction", Acta Crystallographica Section B Structural Science, vol. 56, pp. 254-260, 2000. https://doi.org/10.1107/s0108768199012318

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How does an OH or NH group approach an aromatic ring to hydrogen bond with its π-face?

Wednesday, June 22nd, 2016

I previously used data mining of crystal structures to explore the directing influence of substituents on aromatic and heteroatomatic rings. Here I explore, quite literally, a different angle to the hydrogen bonding interactions between a benzene ring and OH or NH groups.

aromatic-pi-query

I start by defining a benzene ring with a centroid. The distance is from that centroid to the H atom of an OH or NH group and the angle is C-centroid-H. To limit the search to approach of the OH or NH group more or less orthogonal to the ring, the absolute value of the torsion between the centroid-H vector and the ring C-C vector is constrained to lie between 70-100° (the other constraints being no disorder, no errors, T < 140K and R < 0.05).[1]

aromatic-pi-HN-140

The above shows the results for NH groups interacting with the aromatic ring. The maximum distance 2.8Å is more or less the van der Waals contact distance between a hydrogen and a carbon and as you can see the contacts "funnel down" to the centroid at < 2.1Å. The shortest distance[2] is for ammonium tetraphenylborate, which you can view in e.g. spacefill mode here[3]

390

The other interesting close contact derives from a protonated pyridine[4], which can in turn be viewed here.[5] The main message from the distribution shown above is that as the distances between the HN and the centroid get shorter, the "trajectory" of approach remains orthogonal to the ring (the angle defined above remains ~90°) and heads towards the centroid of the π-cloud. The hotspot itself (red, ~2.6Å) also lies along this trajectory.

Recollect that when I used such hydrogen bonding to see if crystal structures discriminate between the ortho or meta positions of a ring carrying an electron donating substituent, it was the distance from a HO to the carbon that was measured as the discriminator. So it's a faint surprise to find that with HN, and without the necessary perturbation of an electron donating substituent, the intrinsic preference seems to be for the ring centroid and not any specific carbon atom of the ring.

So how about the OH group? There are in fact rather fewer examples, and so the statistics are a bit less clear-cut. But there is a tantalising suggestion that this time, the trajectory is not ~90° but rather less, implying that the destination is no longer the centroid of the π-cloud but one of the carbon atoms of the ring itself. For those who like to "read between the lines" and spot things that are absent rather than present, you may have asked yourself why I did not use NH probes in my earlier post. Well, it appears that the NH group is less effective at e.g. o/p discrimination than is an OH group.

aromatic-pi-OH-140

I can only speculate as to the origins (real or not) of the difference in behaviour between OH and NH groups towards a phenyl π-face. Perhaps it is simply bias in the CSD database? Or might there be electronic origins? Time to end with that phrase "watch this space".

 

References

  1. H. Rzepa, "How does an OH or NH group approach an aromatic ring to hydrogen bond with its π-face?", 2016. https://doi.org/10.14469/hpc/673
  2. T. Steiner, and S.A. Mason, "Short N<sup>+</sup>—H...Ph hydrogen bonds in ammonium tetraphenylborate characterized by neutron diffraction", Acta Crystallographica Section B Structural Science, vol. 56, pp. 254-260, 2000. https://doi.org/10.1107/s0108768199012318
  3. Steiner, T.., and Mason, S.A.., "CCDC 144361: Experimental Crystal Structure Determination", 2000. https://doi.org/10.5517/cc4v6tz
  4. O. Danylyuk, B. Leśniewska, K. Suwinska, N. Matoussi, and A.W. Coleman, "Structural Diversity in the Crystalline Complexes of <i>para</i>-Sulfonato-calix[4]arene with Bipyridinium Derivatives", Crystal Growth & Design, vol. 10, pp. 4542-4549, 2010. https://doi.org/10.1021/cg100831c
  5. Danylyuk, O.., Lesniewska, B.., Suwinska, K.., Matoussi, N.., and Coleman, A.W.., "CCDC 819118: Experimental Crystal Structure Determination", 2011. https://doi.org/10.5517/ccwhc5w

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A new way of exploring the directing influence of (electron donating) substituents on benzene.

Friday, April 17th, 2015

The knowledge that substituents on a benzene ring direct an electrophile engaged in a ring substitution reaction according to whether they withdraw or donate electrons is very old.[1] Introductory organic chemistry tells us that electron donating substituents promote the ortho and para positions over the meta. Here I try to recover some of this information by searching crystal structures.

I conducted the following search:
xray

  1. Any electron donating group as a ring substituent, defined by any of the elements N, O, F, S, Cl, Br.
  2. A distance from the H of an OH fragment (as a hydrogen bonder to the aryl ring) to the ortho position relative to the electron donating group.
  3. A similar distance to the meta position.
  4. The |torsion angle| between the aryl plane and the C…H axis to be constrained to 90° ± 20.
  5. Restricting the H…C contact distance to the van der Waals sum of the radii -0.3Å (to capture only the stronger interactions)
  6. The usual crystallographic requirements of R < 0.1, no disorder, no errors and normalised H positions.

The result of such a search is seen below. The red line indicates those hits where the distance from the H to the ortho and meta positions is equal. In the top left triangle, the distance to ortho is shorter than to meta (and the converse in the bottom right triangle). You can see that both the red hot-spot and indeed the majority of the structures conform to ortho direction (of π-facial ) hydrogen bonding.

benzene-xrayHere is a little calculation, optimising the position that HBr adopts with respect to bromobenzene. You can see that the distance discrimination towards ortho is ~ 0.17Å, a very similar value to the “hot-spot” in the diagram above.

benzene-HBr

This little search of course has hardly scratched the surface of what could be done. Changing eg the OH acceptor to other electronegative groups. Restricting the wide span of N, O, F, S, Cl, Br. Probing rings bearing two substituents. What of the minority of points in the bottom right triangle; are they true exceptions or does each have extenuating circumstances? Why do many points actually lie on the diagonal? Can one correlate the distances with the substituent? Is there a difference between intra and intermolecular H-bonds? What of electron withdrawing groups?

The above search took perhaps 20 minutes to define and optimise, and it gives a good statistical overview of this age-old effect. It is something every new student of organic chemistry can try for themselves! If you run an introductory course in organic aromatic chemistry, or indeed a laboratory, try to see what your students come up with!

References

  1. H.E. Armstrong, "XXVIII.—An explanation of the laws which govern substitution in the case of benzenoid compounds", J. Chem. Soc., Trans., vol. 51, pp. 258-268, 1887. https://doi.org/10.1039/ct8875100258

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The oldest reaction mechanism: updated!

Tuesday, September 14th, 2010

Unravelling reaction mechanisms is thought to be a 20th century phenomenon, coincident more or less with the development of electronic theories of chemistry. Hence electronic arrow pushing as a term. But here I argue that the true origin of this immensely powerful technique in chemistry goes back to the 19th century. In 1890, Henry Armstrong proposed what amounts to close to the modern mechanism for the process we now know as aromatic electrophilic substitution [1]. Beyond doubt, he invented what is now known as the Wheland Intermediate (about 50 years before Wheland wrote about it, and hence I argue here it should really be called the Armstrong/Wheland intermediate). This is illustrated (in modern style) along the top row of the diagram.

The mechanism of aromatic electrophilic substitution

In 1887, Armstrong had tabulated the well known ortho/meta/para directing properties of substituents already on the ring towards this reaction[2]. He even offered an explanation, which is not entirely wrong, given that in 1890, the electron had not yet been discovered! That did not stop Armstrong, who invented an entity he called the affinity for the purpose of developing his theories (in this theory, benzene had an inner circle of six affinities, which had a tendency to resist disruption). Armstrong’s description of the properties of the affinity matches that of the (yet to be discovered) electron very closely! But that is enough of history. The mechanism shown above emerged in its present representation (and naming) during the heyday of physical organic chemistry between 1926 – 1940, and of course is an absolute staple of all text books on organic chemistry. But, sacrilege, is it correct? Could what is referred to as an intermediate instead be a transition state? (shown in the bottom pathway of the scheme).

Consider instead the following, in which X is replaced by an acetic acid motif;

Transition state alternative to the Wheland

The two steps, a bond formation between the benzene and E, and the proton abstraction from the benzene by X, are now synchronized into a single step, and the intermediate is now transformed into a transition state. Time to put this theory to the test. X is going to be made trifluoroacetate (R=CF3) and we are going to test it with E= NO+ and F+ (yes, trifluoroacetyl hypofluorite is a known chemical, and it really does fluorinate1 aromatic compounds at -78C). Firstly, E= NO+. A B3LYP/6-311G(d,p) calculation[3]  run in a solvent simulated as dichloromethane, reveals the mid point to indeed be a transition state and NOT an intermediate![4].

Wheland as a transition state. Click image for animation

There is one crucial aspect to this transition state that Armstrong himself made a point of. In the Wheland intermediate proper, the aromaticity of the benzene ring must be disrupted. As a transition state, it need not be (at least not completely). Thus the two bonds labeled as a have calculated lengths of ~1.415Å, only slightly longer than the aromatic length, and certainly not single bonds as implied by the Wheland intermediate! Notice also the significant motion by the hydrogen, which implies the reaction would be subject to a kinetic isotope effect (this would normally be interpreted in terms of the second stage of the stepwise reaction shown along the top a being rate limiting, but this result shows this need not be so). Thus, if the structure is favourable, this veritable old mechanism can be redesigned to give a new, 21st century look to a 19th century staple! By the way, the free energy of activation for this reaction is calculated as ~22 kcal/mol, a perfectly viable thermal reaction. No doubt, by suitable design of the group X, this might be reduced.

Now on to E=F+[5]. This looks a little different. F+ is now a much more voracious electrophile than the nitrosonium cation, and it therefore jumps ahead of the second mechanistic step, with no motion of the hydrogen being involved at this stage (one might also imagine making X a better base to swing things the other way).

Transition state E=F+ leading to Wheland Intermediate. Click for  3D model.

Genuine Wheland intermediate for E=F+ Click for 3D model

Now a full blown Armstrong/Wheland intermediate does indeed form (10042/to-5174); an intimate ion pair if you will, even in the relatively non polar dichloromethane as modelled solvent. The structure  (shown above) is rather unexpected.  This reaction has ΔG† of ~5 kcal/mol,  which is significantly lower than for the E=NO+ system.

Chemistry is full of surprises, and it is always a wonder how a slightly different take on even the oldest of reactions can reveal something new.

Reference.

<

p>1. Umemoto, T.; Mukono, T.. 1-Acylamido-2-fluoro-4-acylbenzenes. Jpn. Kokai Tokkyo Koho  (1986), Patent number JP61246156.

References

  1. "Proceedings of the Chemical Society, Vol. 6, No. 85", Proceedings of the Chemical Society (London), vol. 6, pp. 95, 1890. https://doi.org/10.1039/pl8900600095
  2. H.E. Armstrong, "XXVIII.—An explanation of the laws which govern substitution in the case of benzenoid compounds", J. Chem. Soc., Trans., vol. 51, pp. 258-268, 1887. https://doi.org/10.1039/ct8875100258
  3. "C 8 H 6 F 3 N 1 O 3", 2010. http://doi.org/10042/to-5172
  4. S.R. Gwaltney, S.V. Rosokha, M. Head-Gordon, and J.K. Kochi, "Charge-Transfer Mechanism for Electrophilic Aromatic Nitration and Nitrosation via the Convergence of (ab Initio) Molecular-Orbital and Marcus−Hush Theories with Experiments", Journal of the American Chemical Society, vol. 125, pp. 3273-3283, 2003. https://doi.org/10.1021/ja021152s

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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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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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