Posts Tagged ‘ELF’

An example of an extreme gauche effect: FSSF.

Saturday, September 21st, 2013

The best known example of the gauche effect is 1,2-difluoroethane, which exhibits a relatively small preference of ~0.5 kcal/mol for this conformer over the anti orientation, which is also a minimum. But FSSF, which I discussed in the previous post, beats this hands down! It also, by the way, must surely be the smallest molecule (only four atoms) which could be theoretically resolved into two enantiomers (possibly at say 273K?).‡

FSSF-360FSSF-360g

From this optimised scan[1] of the F-S-S-F torsion angle, you can see two striking differences

  1. Only the gauche form is stable. The anti form is in fact a transition state[2] for enantiomerisation of the two chiral C2-disymmetric gauche forms.
  2. The difference in free energy between the gauche form and the anti is 25.3 kcal/mol, compared with which the 0.5 kcal/mol for 1,2-difluoroethane looks puny indeed.
  3. The effect arises, as with difluoroethane, from overlap of the filled p-lone pair on one sulfur, with the accepting S-F σ* orbital.
    FSSF-NBO

    Click for 3D.

  4. This orbital overlap results in an NBO E(2) interaction energy of 39 kcal/mol. This compares with 5.6 kcal/mol for the equivalent C-H/C-F* term for difluoroethane, and it is of course larger because an S lone pair is a far better donor than a C-H bond. It is also far greater than the anomeric effect, which normally weighs in at about 16 kcal/mol.
  5. There is of course an alternative (and perhaps more unusual) transition state[3] for interconverting the two enantiomers of F-S-S-F which I described previously for F-S-S-Cl as involving a [1,2] migration of F. It however is 23.5 kcal/mol higher in energy than this pure bond rotation. Whereas the [1,2] F migration contracts the S-S bond at the transition state, the bond rotation lengthens it (from 1.922 to 2.142Å).  This arises because the partial double bond character for the S-S bond is destroyed by rotation. The challenge then is whether one can find a 4-atom system where enantiomerisation proceeds by a lower energy continuously-chiral [1,2] migratory pathway rather than just by a simple bond rotation.
  6. An alternative visualisation of the electronic effects resulting in an extreme gauche effect can be seen from the ELF analysis[4] of the lone pair basins;FSSF-ELF
    The two basins ringed in blue (2.25e) are each aligned at an angle of 167° to the axis of the antiperiplanar S-F bond. The knock-on effect of this is that the two lone pairs on each sulfur themselves subtend an unusual angle of 145° at the common sulfur, almost diaxial in fact.

I again marvel at how just four atoms and just two elements, can teach us so much chemistry!

Enhanced by Zemanta

References

  1. H.S. Rzepa, "Gaussian Job Archive for F2S2", 2013. https://doi.org/10.6084/m9.figshare.804328
  2. H.S. Rzepa, "Gaussian Job Archive for F2S2", 2013. https://doi.org/10.6084/m9.figshare.805048
  3. H.S. Rzepa, "Gaussian Job Archive for F2S2", 2013. https://doi.org/10.6084/m9.figshare.802815
  4. H.S. Rzepa, "Gaussian Job Archive for F2S2", 2013. https://doi.org/10.6084/m9.figshare.804332

Tags:,
Posted in Interesting chemistry, reaction mechanism | 2 Comments »

Spotting the unexpected. The trifluoromeric effect in the hydration of the carbonyl group.

Friday, March 9th, 2012

The equilibrium for the hydration of a ketone to form a gem-diol hydrate is known to be highly sensitive to substituents. Consider the two equilibria:

For propanone, it lies almost entirely on the left, whereas for the hexafluoro derivative it is almost entirely on the right. The standard answer to this is that electron-withdrawing substituents destabilize the carbonyl compound more than the hydrate. But could there be more to it than that? Might the converse also be true, that electron-withdrawing substituents stabilise the hydrate more than the carbonyl compound? To answer this last question, consider the anomeric interactions possible in the diol.

  1. There is the standard anomeric effect operating between the two hydroxy groups, whereby a lone pair donor on one oxygen interacts with the C-O acceptor bond of the other oxygen, and vice versa, a total of two stabilising interactions.
  2. But what if the C-CF3 group could also act as an acceptor instead of the C-O? That would give the trifluoromethyl system a total of four anomeric interactions, each of them stabilising, compared to only two for the methyl system.

Garnering evidence, firstly we compute (ωB97XD/6-311G(d,p) ) the free energy difference for the two equilibria above. These turn out to be +3.3 kcal/mol for the top equilibrium, and -9.0 kcal/mol for the bottom, which agrees with the assertions made earlier. The computed geometry looks as below.

Geometry of hydrate. Click for 3D.

We must now go hunting for anomeric interactions, and this is done using an NBO analysis. We look for large interactions between a donor (a lone pair on either oxygen) and an acceptor (which is conventionally the C-O anti-bonding NBO, but can now also be the C-CF3 anti-bonding NBO). Indeed exactly four large interactions are found, in pairs of E(2) = 17.5 and 9.8 kcal/mol. The former is common to both the systems above, but the latter is larger for the trifluoromethyl substituted equilibrium than the methyl system (for which E(2) is 6.2 kcal/mol), and therefore constitutes additional stabilisation by the electron-withdrawing groups of the diol.

Each oxygen has two lone pair NBO orbitals. The initial hypothesis is surely that it uses one of these to align with a C-O anti bonding acceptor, and the other to align with the C-CF3 anti bonding acceptor. The first of these is shown below.

The interaction between an O(Lp) and a O-C BD* orbital. Click for 3D.

  1. The colour code is that the two phases of the oxygen lone pair (Lp) are shown as purple/orange.
  2. These are superimposed upon the C-O anti bonding NBO (referred to as BD* in the output), which has the colours red and blue.
  3. I advise you now to click on the graphic above to load the 3D model and the orbital surfaces. You should spot the node along the C-O bond with a blue-red boundary.
  4. You will also spot that the orange phase of the Lp overlapping with the red phase of the C-O BD*. This is defined as a positive (stabilizing) overlap.
  5. Likewise the purple phase of the Lp overlaps with the blue phase of the C-O BD*. In other words orange=red, and purple=blue. I have made orange and red, and purple and blue deliberately different so that the origins of each NBO can be spotted.
  6. This combination therefore has good overlap, and this gives rise to the large E(2) interaction energy of 17.5 kcal/mol.
Now for the interaction with the C-CF3 BD*, the one with E(2) = 9.8 kcal/mol.

The interaction between an O(Lp) and a C-CF3 BD* orbital. Click for 3D.

  1. You can see the blue-red node along the C-CF3 bond quite clearly.
  2. But hang on, the O Lp orbital is the same as before! It is overlapping with BOTH the C-O and the C-CF3 BD* orbitals.

The other O Lp is shown below (viewed along the axis of the C-CF3 bond). Note how an equal proportion of the orange phase and the other purple phase of the O Lp overlap equally with the blue phase of the C-CF3 bond. In other words, one cancels the other.

The interaction between the other O(Lp) and a C-CF3 BD* orbital. Click for 3D.

So we have found that just one (of the two lone pairs) on each oxygen overlaps with both the C-O and the C-CF3 anti bonding NBOs, the latter giving a stabilisation not present when the group is instead C-CH3. We can attribute this to the far greater acceptor properties of the C-CF3 BD* because of the electronegative character of the fluorines.

This is an anomeric effect with a difference. The CF3 group is not normally associated with inducing such an effect (just as the CN group is not, see this post or this post where an alkene acts the donor instead of a lone pair). Also unusual (more accurately, I have not encountered it before) is the (apparent) use of the SAME donor lone pair to induce TWO quite different anomeric interactions. Before getting too excited by this unexpected effect, it it is worth taking a look at another technique for analysing lone pairs. The ELF (electron localisation function) can provide the centroid of what is referred to as a monosynaptic basin (a lone pair in other words).

EKF function, showing O Lone pairs (in yellow). Click for 3D.

You can see in yellow the oxygen lone pairs. Note how one of them aligns with the C-O bond, and the other with the C-CF3 bond. Unfortunately, the ELF method does not allow the strength of the interaction to be quantified, which is why the NBO analysis is preferred.

So we can conclude that not only might electron-withdrawing substituents destabilize the carbonyl compound more than the hydrate, but they certainly also stabilise the hydrate more than the carbonyl compound.

Tags:, , , , , ,
Posted in Interesting chemistry | 2 Comments »

Hexavalent carbon revisited (and undecavalent boron thrown in).

Sunday, June 26th, 2011

A little while ago, I speculated (blogs are good for that sort of thing) about hexavalent carbon, and noted how one often needs to make (retrospectively) obvious connections between two different areas of chemistry. That post has attracted a number of comments in the two years its been up, along the lines: what about carboranes? So here I have decided to explore that portal into boron chemistry. The starting point is the reported crystal structure of a molecule containing a CH12B11– anion (DOI: 10.1021/ja00201a073). This differs from the molecule I previously reported in having not so much 5C-C + 1C-H bonds around a single carbon, but instead 5B-C + 1C-H bonds. The basic cluster is much in fashion (as B12Cl122-) for its properties as a non-coordinating counterion.

The CH12B11 (-) anion. AIM analysis. Click for 3D.

Above is the QTAIM topological analysis of the electron density (B3LYP/6-311G(d,p) calculation) which reveals all 11 borons and the single carbon atom as being surrounded by six bond critical points. ELF tells us how many electrons populate the synaptic basins.

The CH12B11 (-) anion ELF basins. Click for 3D.

This clearly reveals that the bonding to the carbon and all the boron atoms is non-Lewis, i.e. that of the six bonds to each of the non-hydrogens, five are not of the Lewis two-electron pair type. The carbon for example is surrounded by five C-B basins, each of 1.02e, with its valence shell occupied by ~7.2e in total. The boron involved in each of the C-B bonds also has five bonds, with basins corresponding to 1.01, 2*0.95 and 2*0.73e. The boron directly opposite the carbon has five basins corresponding to five B-B two-centre bonds of 0.6e each, and a further five basins of 0.3e corresponding to 3-centre BBB bonds (shown as yellow spheres above). Arguably, that particular boron atom has eleven bonds to it!

This molecule reveals quite clearly how sterile the debate is about whether carbon can be hypervalent. If the Lewis definition of a bond as an electron pair is removed, then hypervalency exceeding four can easily be obtained. What is certainly sacrosanct is the valence shell octet for carbon (and boron).

Finally, I throw B12H122- in. This has the wonderful icosahedral symmetry, and as you might expect, each boron is defined by five two-centre B-B bonds (~0.66e) and five three-centre BBB bonds (~0.24e), as well as a conventional two-electron B-H bond. Each boron is undecavalent! Not seen that particular valency before!!

Tags:,
Posted in Hypervalency | 1 Comment »

Quintuple bonds: part 2

Saturday, February 20th, 2010

In the previous post, I ruminated about how chemists set themselves targets. Thus, having settled on describing regions between two (and sometimes three) atoms as bonds, they added a property of that bond called its order. The race was then on to find molecules which exhibit the highest order between any particular pair of atoms. The record is thus far five (six has been mooted but its a little less certain) for the molecule below

A molecule with a Quintuple-bond

There are many ways of describing the electronic behaviour in that region called a bond, one being the ELF (Electron localization function) technique, which certainly sounds as if it is describing a bond! The ELF function for the molecule above however was distinctly odd, and this was attributed to the Cr-Cr bond being not so much a covalent bond, but another (much less recognized type) known as a charge-shift bond. In particular, two of the ELF basin centroids did not occupy the central region between the two atoms, but had in effect fled that region, and in the process had also each split into two. Other ELF basins did not much look like bonds, but retained much of their core-electron (i.e. non bonding) character. The issue now becomes whether the ELF method is sensible, or simply an artefact. In other words, it needs calibrating against other (homonuclear) molecules which might exhibit charge-shift behaviour.

Three such molecules are in fact the halogens, F2, Cl2, Br2 as discussed by Shaik, Hiberty and co (DOI: 10.1002/chem.200500265). So lets take a look at what an ELF analysis shows for these, and how it compares with the chromium quintuple bond.

ELF analysis for F2

ELF analysis for Cl2

ELF analysis for Br2

At the B3LYP/6-311G(d) level, the ELF function shows the (valence) electrons located in two regions. Firstly, what we might call the lone pairs are located in a torus surrounding each halogen atom (i.e. the molecule must be axially symmetric). The remaining electrons are in basins with centroids along the axis of each bond. The Br2 centroid is a single conventional disynaptic basin, with an integration of 0.77 electrons. With Cl2 however, something odd happens (and the effect was described in DOI: 10.1002/chem.200500265 ); the disynaptic basin splits into a close pair, each integrating to 0.33 electrons, and looking as if the two parts want to run away from one another. This was interpreted as indicating that the purely covalent description of the halogen bond is in fact repulsive and not attractive! The effect is enhanced for F2, with two very much split basins, each integrating to 0.08 electrons. This serves to remind us of how odd a bond the F-F one truly is (and how easily it is homolyzed)!

Now that we have our calibration, does it match to the Cr-Cr quintuple bond? Very much so! Again, the valence basins show very low integrations (compared to the nominal bond order), and again they appear to have split and run away from each other. Most of the valence electrons in that species prefer instead to masquerade as core-electrons. So we can conclude that by the ELF criterion, the Cr-Cr bond is not quintuple, and not covalent but charge shifted. Of course, this does seem at odds with the Cr-Cr internuclear distance, which is indeed very short! This shortening probably arises from electrostatic attractions in the charge-shifted valence bond forms. It simply goes to show that what the nuclei get up to and what the electrons do may not be one and the same thing!

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

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.

Tags:, , , , , , , , , ,
Posted in Interesting chemistry | 1 Comment »

Uncompressed Monovalent Helium

Saturday, October 3rd, 2009

Quite a few threads have developed in this series of posts, and following each leads in rather different directions. In this previous post the comment was made that coordinating a carbon dication to the face of a cyclopentadienyl anion resulted in a monocation which had a remarkably high proton affinity. So it is a simple progression to ask whether these systems may in turn harbour a large affinity for binding not so much a H+ as the next homologue He2+?

Inventing the Helium bond

Inventing the Helium bond

This possibility is explored with the series X=Be, B, C (tetramethyl substituted, resulting in neutral, +1 and +2 systems overall). The first two emerge as stable in terms of having all positive force constants for C4v symmetry; the last emerges as a transition state and is not discussed further. The specific system X=B has a B-He bond length of 1.317Å/B3LYP/6-311G(d,p), 1.305Å/B3LYP/Def2-QZVPP and 1.290Å/double-hybrid RI-B2GP-B2PLYP/TZVPP, which does seem as if it might be typical of a single bond between these two elements. The ρ(r)B-He AIM value (B3LYP/6-311G(d,p) is 0.069 au, and νB-He of 713 cm-1 (727 for Def2-QZVPP basis) makes it about one third the strength of a C-H bond. The disynaptic basin for the B-He region integrates to 1.99 electrons, whilst the four B-C basins correspond to 1.22 electrons each.

X Charge ρ(r) X-He C-B ELF
integration		 νX-He, cm-1 Repository
Be 0 0.031 1.10 484 10042/to-2443
B 1 0.069 1.22 713 10042/to-2444

10042/to-2446

10042/to-2453
C 2 0.026 – 136 10042/to-2445
AIM for X=B-He

AIM for X=B-He. Click for 3D
B-He vibrational stretching mode

B-He stretching mode. Click to vibrate

We can conclude that for X=B, this species exhibits not only a pentavalent boron atom, but a monovalent helium atom. The latter bond may indeed be amongst the strongest ever proposed for this element in a ground state, and indeed perhaps is even viable as a solid crystalline compound rather than merely existing in the gas phase. The Cambridge crystal database contains no entries for He or Ne, not even as an encapsulated clathrate (although crystal structures of such complexes for Kr and Ar are known). Theoretical studies of the rare gases in endohedral fullerene-like cages (DOI: 10.1002/chem.200801399) predict that under these compressed circumstances e.g. two helium atoms can approach each other to 1.265Å or less (see also DOI: 10.1002/chem.200700467) but these close approaches were not considered to be chemical bonds as we think of them. Perhaps Merino, Frenking, Krapp and co’s search for the chemistry of helium (they had found it earlier in the gas phase excited states of their molecules, DOI: 10.1021/ja00254a005) might be realised for the ground state of the system described here.

Tags:, , , , , , , , , ,
Posted in Hypervalency, Interesting chemistry | 1 Comment »