Posts Tagged ‘antiaromaticity’

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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Stable “unstable” molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

Sunday, March 5th, 2017

Cyclobutadiene is one of those small iconic molecules, the transience and instability of which was explained theoretically long before it was actually detected in 1965.[1] Given that instability, I was intrigued as to how many crystal structures might have been reported for this ring system, along with the rather more stable congener cyclo-octatetraene. Here is what I found.

The Conquest search query shown (with no disorder, no errors and R < 0.1 also specified). 

There are 23 instances (February 2017 database; see DOI: 10.14469/hpc/2231 for search query) of the supposedly unstable cyclobutadiene motif!

The three clusters deserve explanations. The orange cluster reveals a long C-C bond (rather longer than normal C-C bonds), accompanied by short C=C bonds, as indicated by the valence bond form shown below. Take particular note that the arrow connecting the two forms is NOT a resonance arrow but an equilibrium arrow. The “bond shifting” is not fast but slow, allowing long and short bonds to be measured in a crystal structure.

The rather larger blue cluster exhibits much more equal bonds. These arise from the presence of “push-pull” substituents on the ring which serve to delocalise the unfavourable cyclobutadiene ring and hence decrease the unfavourable anti-aromaticity. A typical example is shown below (EACBUT):

The small red cluster shows a long C=C bond and a short C-C bond! I have commented previously on apparently abnormally long C=C bonds, which in fact all turned out to be errors, and I suspect the same is true here. The bond orders in the indexing in the CSD data base have probably been mis-assigned, as per below for GANBII;

The Conquest search query is shown (with no disorder, no errors and R < 0.1 specified) for the 8-ring, which further specifies a torsion angle about a C-C bond to determine how planar the ring might be.

The “normal” cluster in the top left exhibits long C-C bonds and short C=C bonds. The colour code indicates how planar the ring is (red-blue spectrum = twisted ⇒ planar). The majority of examples are twisted about the C-C bond(s), but there are a few interesting examples that are not, as shown by the blue dots. There are only a few “bond-equalised” examples in the centre; perhaps “push-pull” induced equalisation is more difficult or perhaps few examples have been made?

The members of the red cluster in the bottom right all reveal short “C-C” bonds and long “C=C” bonds. Intriguingly they all also have low values of the torsion about one C-C bond (although not always about all four C-C bonds). A typical example (BAQVUK, DOI: 10.5517/CC4GWWB ) is shown below. These all need careful inspection and possibly reversal of the C-C and C=C indexing.

It was interesting to discover how many crystalline examples of this archetypal “unstable” cyclobutadiene motif have been made, and the means by which some of them at least have been stabilized. In the more abundant cyclo-octatetraene system, I learnt that one has to be cautious about blindly accepting the bond order designations in the database. Perhaps we might learn here that some of these have indeed been re-assigned in the next release of the database.

References

  1. L. Watts, J.D. Fitzpatrick, and R. Pettit, "Cyclobutadiene", Journal of the American Chemical Society, vol. 87, pp. 3253-3254, 1965. https://doi.org/10.1021/ja01092a049

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Stable "unstable" molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

Sunday, March 5th, 2017

Cyclobutadiene is one of those small iconic molecules, the transience and instability of which was explained theoretically long before it was actually detected in 1965.[1] Given that instability, I was intrigued as to how many crystal structures might have been reported for this ring system, along with the rather more stable congener cyclo-octatetraene. Here is what I found.

The Conquest search query shown (with no disorder, no errors and R < 0.1 also specified). 

There are 23 instances (February 2017 database; see DOI: 10.14469/hpc/2231 for search query) of the supposedly unstable cyclobutadiene motif!

The three clusters deserve explanations. The orange cluster reveals a long C-C bond (rather longer than normal C-C bonds), accompanied by short C=C bonds, as indicated by the valence bond form shown below. Take particular note that the arrow connecting the two forms is NOT a resonance arrow but an equilibrium arrow. The “bond shifting” is not fast but slow, allowing long and short bonds to be measured in a crystal structure.

The rather larger blue cluster exhibits much more equal bonds. These arise from the presence of “push-pull” substituents on the ring which serve to delocalise the unfavourable cyclobutadiene ring and hence decrease the unfavourable anti-aromaticity. A typical example is shown below (EACBUT):

The small red cluster shows a long C=C bond and a short C-C bond! I have commented previously on apparently abnormally long C=C bonds, which in fact all turned out to be errors, and I suspect the same is true here. The bond orders in the indexing in the CSD data base have probably been mis-assigned, as per below for GANBII;

The Conquest search query is shown (with no disorder, no errors and R < 0.1 specified) for the 8-ring, which further specifies a torsion angle about a C-C bond to determine how planar the ring might be.

The “normal” cluster in the top left exhibits long C-C bonds and short C=C bonds. The colour code indicates how planar the ring is (red-blue spectrum = twisted ⇒ planar). The majority of examples are twisted about the C-C bond(s), but there are a few interesting examples that are not, as shown by the blue dots. There are only a few “bond-equalised” examples in the centre; perhaps “push-pull” induced equalisation is more difficult or perhaps few examples have been made?

The members of the red cluster in the bottom right all reveal short “C-C” bonds and long “C=C” bonds. Intriguingly they all also have low values of the torsion about one C-C bond (although not always about all four C-C bonds). A typical example (BAQVUK, DOI: 10.5517/CC4GWWB ) is shown below. These all need careful inspection and possibly reversal of the C-C and C=C indexing.

It was interesting to discover how many crystalline examples of this archetypal “unstable” cyclobutadiene motif have been made, and the means by which some of them at least have been stabilized. In the more abundant cyclo-octatetraene system, I learnt that one has to be cautious about blindly accepting the bond order designations in the database. Perhaps we might learn here that some of these have indeed been re-assigned in the next release of the database.

References

  1. L. Watts, J.D. Fitzpatrick, and R. Pettit, "Cyclobutadiene", Journal of the American Chemical Society, vol. 87, pp. 3253-3254, 1965. https://doi.org/10.1021/ja01092a049

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The mechanism of the Birch reduction. Sequel to benzene reduction.

Wednesday, December 5th, 2012

I noted briefly in discussing why Birch reduction of benzene gives 1,4-cyclohexadiene (diagram below) that the geometry of the end-stage pentadienyl anion was distorted in the presence of the sodium cation to favour this product. This distortion actually has some pedagogic value, and so I elaborate this here.

The starting point is now the molecular orbitals of benzene, and in particular the lowest unoccupied set (LUMO), which is doubly degenerate (in energy).

First of the pair of degenerate lowest unoccupied MOs of benzene. Click for 3D.

Second of the pair of degenerate lowest unoccupied MOs of benzene. Click for 3D.

An (overall) two-electron reduction of benzene (followed by protonation) can formally at least place the two electrons into either of these orbitals. Doing so would lower the energy of the occupied orbital, and hence induce a geometric distortion as illustrated below. In effect, the outcome is an (antiaromatic) di-anion with either two short and four long bonds, or the alternative of four shorter and two long bonds. The proximate presence of a solvated sodium cation now clearly breaks this degeneracy; the coordination preference of Na+ (and a proton) favours the former over the latter, and the outcome is as shown in the previous post.

The orbitals of benzene are frequently included in undergraduate teaching, but here we have a direct use for the LUMO pair in explaining the outcome of the reduction of benzene by electrons. It also links into what happens when anti-aromaticity is avoided (when a  4n π-electron system distorts to avoid it).

Postscript:  The computed structure of benzene di-anion is shown below. It is 19.5 kcal/mol lower than the alternative valence bond isomer.

Stable form. Click for 3D.


Less stable form. Click for 3D.

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Less is more: the dyotropic rearrangement of ethane

Saturday, June 11th, 2011

In a time when large (molecules) are considered beautiful (or the corollary that beauty must be big), it is good to reflect that small molecules may teach us something as well. Take ethane. Is there anything left which has not been said about it already? Well, consider the reaction below, in which two hydrogen atoms mutually hop from one carbon to the other.

The dyotropic reaction of ethane.

This is a class of reaction known as pericyclic, in which a cyclical movement of electrons occurs in concerted fashion. Such reactions are frequently the topic of both lecture courses and book chapters. There, one is taught to count the total number of these electrons and (in some ways of teaching the subject), to apply the rules of aromaticity to the transition state describing the pericyclic reaction. I have previously described how (for themal, closed shell molecules), a 4n+2 electron count leads to aromaticity and a 4n count to antiaromaticity. In that discussion, I told of how antiaromatic molecules often go to great lengths to avoid it, and how for example cyclopropenium anion distorts to achieve this objective. Well, the above reaction, known formally as a dyotropic pericyclic rearrangement, leads to an electron count of 4, and hence belongs to our 4n rule (n=1). It must proceed through an antiaromatic transition state. Which in turn must be avoided if it possibly can.

So time for a calculation (B3LYP/6-311G(d,p) as it happens). A symmetric geometry is imposed (D2h symmetry), and this allows us to probe whether the geometry will really distort to avoid this symmetric (and hence antiaromatic) transition state.

First imaginary vibrational mode for dyotropic reaction of ethane. Click for 3D.

A vibrational analysis of this geometry reveals a negative force constant corresponding to the desired motion of the two hydrogen atoms (ν 1936i cm-1, click on above for animation). But all is not what it seems; a second force constant is also negative (ν 425i cm-1). This is our distortion, in which both carbons pyramidalize, much in the manner observed previously for the cyclopropenium anion.

Distortive tendency for the dyotropic rearrangement. Click for 3D.

One might notice other oddities. For example, the dyotropic reaction does not (formally) involve the central C-C bond. Yet in the stationary point above, it has the distinctly odd value of 1.824Å. Here we see another type of distorsion taking place. In order to avoid the 4n electron count, some additional electrons are starting to be “borrowed” from the supposedly passive C-C bond. Indeed, following this second vibrational mode to see where it leads us gives us another stationary point looking as below, in which the central C-C bond has expanded further to 2.12Å. Those desired electrons have been well and truly borrowed, and we are now dealing with six of them, not four (and as it happens a quite different reaction).

Developed distortion of the symmetric geometry.

So, ethane taught us a lot in the end. In trying to persuade it to undergo a dyotropic rearrangement, we found it came across the undesired antiaromaticity in the transition state. A nice simple example of a pericyclic selection rule in action. Of course, one could make things more complicated, but I leave that to another day.

Advanced bit: Above, I ponder whether the formal arrow pushing mechanism, which shows two arrows (= 4 electrons) might have been subverted into six electrons (=4n+2 electrons) to avoid the (formal) transition state anti-aromaticity. One (of many) methods which can tell us more or less where the electrons are and how many of them there are is ELF (electron localization function) partitioning. This is shown below for the D2h-symmetric geometry.

ELF analysis. Click for 3D.

 

The yellow spheres are the transposing hydrogen atoms, each carrying 1.44 electrons, in what is termed a trisynaptic ELF basin (we also know this as a three-centre-not-quite-2-electron bond). The red spheres are additional basins each carrying a further 0.74 electrons. The total number of electrons in these six (cyclically arranged) basins is 5.84. Notice in fact that in this scheme, there is no central C…C basin! Its electrons have indeed been well and truly scavenged to avoid overall anti-aromaticity (a sort of molecular democracy). Note there is no easy way of illustrating this process using arrow pushing!

Postscript: Silicon is nowadays considered an often extreme opposite of carbon in many of its properties. Disilane is no exception. Its dyotropic rearrangement (D2h symmetry) is also a second order saddle point, having two negative force constants. The first of these is, like ethane, the dyotropic proper. But the second has a different mode for distorsion. This in fact corresponds to a disproportionation into SiH4 and SiH2.

2n -ve forc constant for dyotropic rearrangement of disilane. Click for 3D

The ELF analysis of the electrons is also different from ethane, revealing 3.67e in two three-centre Si-H-Si regions, and an Si-Si region with 2.2e. Digermane is very similar, showing carbon to be the outlier, not silicon.

ELF analysis for Si2H6.

One can play this game with Titanium as well (Ti2H6), a group four transition element. This shows an entirely new behaviour. The dyotropic mode force constant is no longer negative, but positive, ν 1146 cm-1. The ELF basins reveal 1.85e for the three-centre bond, and 0.47 for the Ti-Ti region (an explanation can be found in the differing nodal behaviour of the molecular orbitals, but that analysis is for another post).

 

ELF analysis for Ti2H6. Click for vibration.

This postscript ends with one more system, which finally reveals a true dyotropic transition state: ethene! The two three-centre basins have 1.36e each, whilst the C-C region has 4.45e distributed interestingly enough into two basins. We have seen earlier ~6 and ~4 cyclic electron systems, this one finally is approaching ~2e.

 

ELF analysis for ethene. Click for vibration.

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