Posts Tagged ‘Interesting chemistry’

« Older Entries
Newer Entries »

Reactions in supramolecular cavities – trapping a cyclobutadiene: ! or ?

Sunday, August 8th, 2010

Cavities promote reactions, and they can also trap the products of reactions. Such (supramolecular) chemistry is used to provide models for how enzymes work, but it also allows un-natural reactions to be undertaken. A famous example is the preparation of P4 (see blog post here), an otherwise highly reactive species which, when trapped in the cavity is now sufficiently protected from the ravages of oxygen for its X-ray structure to be determined. A colleague recently alerted me to a just-published article by Legrand, van der Lee and Barboiu (DOI: 10.1126/science.1188002) who report the use of cavities to trap and stabilize the notoriously (self)reactive 1,3-dimethylcyclobutadiene (3/4 in the scheme below). Again sequestration by the host allowed an x-ray determination of  the captured species!

Scheme for production of 1,3-dimethylcyclobutadiene 3 and CO2.

The colleague tells me he has himself already penned an article on the topic and submitted this to a conventional journal. However, their rules decree that whilst it is being refereed, I could not discuss the article here, or indeed even name its author. Assuming his article is published, I will indeed reveal his identity, so that he gets the credit he deserves! Meanwhile, I will concentrate in this blog purely on two other aspects of this reaction which caught my own eye after he brought the article to my attention.

The reaction involves imobilising a precursor 1 in a crystalline calixarene network as shown above, and then in situ photolysis to form the Dewar lactone 2. Further photolysis then results in extrusion of carbon dioxide and the formation of 1,3-dimethyl cyclobutadiene 3 and CO2, both still trapped in the host crystals. Thus imobilised, here they both apparently remain (at 175K) for long enough for their X-ray structure to be determined. What attracted me to this chemistry was the potential of this reaction as a nice example of a Diels Alder reaction occuring in a cavity. The first example of such catalysis was reported by Endo, Koike, Sawaki, Hayashida, Masuda, and Aoyama (DOI: 10.1021/ja964198s) and I have used this in my lectures for many years. This latter example however illustrates the promotion of a cycloaddition, which inside a cavity is accelerated by a factor of ~105, rather than of the reverse cycloelimination. I explain this to students by invoking entropy. Normally, when two molecules react together, there is an entropic penalty, which can add 8 or more kcal/mol to the free energy of activation of a bimolecular reaction in the absence of the cavity.

Structure of entrapped 1,3-dimethylcyclobutadiene, obtained from the CIF file provided via DOI: 10.1126/science.1188002

By a strange coincidence, my name is also on a recently published article (DOI: 10.1021/ol9024259) with other colleagues on the use of (Lewis) acid catalysts to accelerate a type of reaction known as the Prins. This involves the addition of an alkene to a carbonyl group. Now as it happens, the reaction in the scheme above showing 4 → 2 happens to combine these features; it is both a Diels-Alder cycloaddition and also involves an alkene adding to a carbonyl compound! It is therefore noteworthy that the claimed reaction 1 → 2 → 3 + CO2 is done in the presence of a strong acid catalyst, the guanidinium cation 5, which is itself part of the structure of the calixarene-based host. It is represented as X in the scheme above, and can also be identified in the above 3D model via the light blue atoms.

There are however crucial differences between these two earlier examples I quoted and the reaction of 2 → 3; the latter is in fact a cycloelimination and not a (cyclo)addition. In other words, according to literature precedent, the guanidinium cation-based cavity should act to accelerate the reverse cycloaddition 4 → 2 rather than the forward cycloelimination. Since the isomerisation 3 → 4 is thought to be fast, the question arises: how rapid is the reverse reaction 4 → 2? In particular, is it slow enough to allow X-ray diffraction data to be collected for 3/4 over the necessary period of 24 hours or more? Legrand, van der Lee and Barboiu do not address this point in their article. Nor is there discussion there of how the cavity and the acid catalyst might influence the position of the equilbrium 2 → 3 + CO2.

This is where calculations can help. At the B3LYP/6-311G(d,p) level four different models were selected.

  1. Model A is a simple gas phase calculation for the singlet state, which reveals the free energy barrier for 4 → 2 is already quite modest for a Diels-Alder reaction (more typical values are ~22 kcal/mol), due no doubt to the instability/reactivity of the cyclobutadiene. However, at 175K, that would still be quite sufficient to prevent the reverse reaction from occurring to any extent over the period of X-ray data collection.
  2. Model B adds a condensed phase (water) to the model. This serves in part to simulate the condensed crystal environment (which is pretty ionic being a tetra ion-pair). The barrier drops to 12.1 kcal/mol.
  3. Adding one guanidinium cation to both these models (C and D) which simulate the Prins conditions, drops the barrier to 8.3 kcal/mol (model 4).
  4. You can inspect details of any of the calculations by clicking on the digital repository entry (shown as dr in the table), where full data is available.

None of these models includes the entropic effects of full constraint in a cavity (which I estimated above as capable of reducing the free energy barrier for reaction by ~8 or more kcal/mol). If this correction is applied to model D, it would reduce the barrier to ~0 kcal/mol! The calculations also reveal that the reverse reaction 4 → 2 is exothermic, and this exothermicity is enhanced by the acid catalyst 5. It would be further enhanced by reducing the entropy of reaction by pre-organizing the reactants in the cavity. The tendency must therefore be for 3/4 to revert to 2 on purely thermodyamic grounds, and only the presence of a significant kinetic barrier would allow them to exist as separate species. This barrier, as one might infer from the calculations shown in the table below, may not be a large one. Even a barrier of 8 kcal/mol might require cooling to significantly lower than 175K to render the reaction slow on a ~24 hour timescale.

Model ΔG‡4 → 2
kcal/mol		 ΔGreac 4 → 2 Singlet-triplet
separation
A. Gas phase,X=none dr ts 16.8 dr -3.5dr +5.7 dr
B. Continuum solvent (water),X=none dr ts 12.1dr -6.0 dr +7.7 dr
C. Gas phase,X=guanidinium+ dr ts 6.1 dr -19.5dr +2.1dr
D. Continuum solvent (water),X=guanidinium+ dr ts 8.3 dr -10.1 dr +7.7 dr

So I end my own speculations here on the nature of the reaction reported by Legrand, van der Lee and Barboiu by asking: are the products they claim (1,3-dimethylcyclobutadiene and carbon dioxide) capable of existing as separate species for long enough inside their cavity, even at 175K, to allow for the collection of X-ray data for a structure determination?

I tend to think probably not (? rather than !). But do decide for yourselves.

Archived as http://www.webcitation.org/5rpkn2Z5S on 08/08/2010. See also this post.

Tags:, , , , , , , , , , , , , , , , , ,
Posted in Interesting chemistry | 8 Comments »

Bio-renewable green polymers: Stereoinduction in poly(lactic acid)

Saturday, July 24th, 2010

Lactide is a small molecule made from lactic acid, which is itself available in large quantities by harvesting plants rather than drilling for oil. Lactide can be turned into polymers with remarkable properties, which in turn degrade down easily back to lactic acid. A perfect bio-renewable material!

Lactide

The starting point for ring opening polymerisation is racemic lactide, or rac-LA. This is an equal mixture of the R,R and S,S enantiomers, and it is now treated with a catalyst based on a metal M. If M=Mg, there is a rather remarkable stereochemical outcome for the resulting polymer. The catalyst selects alternating enantiomers for the assembly, resulting in a chain (R,R),(S,S),(R,R),(S,S), etc, the name for which is a heterotactic polymer. It could instead have created a blend of equal proportions of (R,R),(R,R),(R,R) and (S,S),(S,S),(S,S) which is an isotactic polymer. Needless to say, these two polymers have quite different properties, and it very much matters which is formed. Without such a catalyst, a random atactic polymer is created rather than a stereoregular arrangement.

Poly (lactic acid)

The question is how does the catalyst manage to assemble the polymer with such stereoinduction? The origins of this depend on a detailed understanding of the mechanism of the reaction, and in 2005 we suggested one which offered an explanation for the stereospecificity (see E. L. Marshall, V. C. Gibson, and H. S. Rzepa, DOI: 10.1021/ja043819b and an interactive storyboard).

Mechanism for stereoregular polymerisation

The key features of this rational were:

  1. Two possible transition states may control the reaction, TS1 and TS2. Which one depends on which is the higher in energy.
  2. The smallest model for this process involves loading two molecules of lactide onto the catalyst. The first has already been ring opened, and will control the stereochemistry of the second, which is the one suffering the ring opening bond formations/breakings shown above (the first is lurking in the group R).
  3. This leads to four different possibilities, (R,R)-(R,R)*, (S,S)-(S,S)*, (R,R)-(S,S)*, and (S,S)-(R,R)* (where the * denotes the reacting lactide, as in the diagram above). These are all diastereomers, and hence will be different in energy. If one of the first two is the lowest, then isotactic polymer will result; if the latter two then a heterotactic polymer.

Back in 2004, we had constructed a model based on B3LYP and of necessity a mixed basis set, being 6-311G(3d) on the Mg, 6-31G on the lactide and only STO-3G on the catalyst. This was done because the complete system was actually rather large. Even so, a transition state calculation would regularly take at least 10 days to find using the fastest computers available to us at that time. Using this procedure, we found that the rate limiting kinetic step  was in fact TS2 for all four possibilities noted above. Of these, the (R,R)-(S,S) transition state turned out to represent the lowest energy pathway, thus confirming the observed heterotacticity for this particular catalyst.

Well, times have moved on:

  1. Six years later, computers are around 20 times faster! We can now afford to improve the basis set to 6-31G(d,p) on all the atoms, including the catalyst (the Mg stays at 6-311G(3d) however; improving it to 6-311G(3d,2f) makes little difference).
  2. We can now include the solvent (thf) as a continuum field.
  3. In the last five years the B3LYP functional has been shown to underestimate the energies of globular molecules. A modern functional such as ωB97XD, which includes dispersion energy corrections, should be expected to do much better.

It is the purpose of this blog to report an update to the modelling. Quoting relative free energies (including the solvation correction), the results come out as;

  1. (R,R)-(S,S) 0.0 kcal/mol for the TS1 geometry (see DOI: 10042/to-4950)
  2. (S,S)-(S,S) 1.8 for the TS2 geometry
  3. (S,S)-(R,R) 5.5 for the TS1 geometry
  4. (R,R)-(R,R) 9.1 for the TS1 geometry.

Well, there are surprises! Using the gas phase B3LYP model the key transition state was TS2; now its TS1 (for in fact three of the four possible transition states). The bottom line (almost) is that the same stereoisomer as before comes out the winner! The take home lesson is that in six years of progress, modelling can now encompass solvent and dispersion corrections. Many mechanisms with > ~100 atoms investigated in the past without inclusion of these effects could probably do with a re-investigation, especially if the transition states are “globular” in nature. Any by now you are probably wondering what the transition state looks like. Well, here it is (and see it in all its glory by clicking on the diagram below).

(R,R)-(S,S) Transition state for stereoregular lactide polymerisation. Click for animation

And if you are also wondering how one might proceed to analyse the origins of the stereoinduction, the NCI interaction surfaces (as described in this post) are shown below. Note how the extensive degree of green interaction surface is associated with the globular nature referred to above.

Non-covalent interaction (NCI) surfaces for the (R,R)-(S,S) transition state. Click for 3D

Tags:, , , , , , , , , , , , , , , , ,
Posted in General, Interesting chemistry | 3 Comments »

The weirdest bond of all? Laplacian isosurfaces for [1.1.1]Propellane.

Wednesday, July 21st, 2010

In this post, I will take a look at what must be the most extraordinary small molecule ever made (especially given that it is merely a hydrocarbon). Its peculiarity is the region indicated by the dashed line below. Is it a bond? If so, what kind, given that it would exist sandwiched between two inverted carbon atoms?

1.1.1 Propellane

One (of the many) methods which can be used to characterize bonds is the QTAIM procedure. This identifies the coordinates of stationary points in the electron density ρ(r) (at which point ∇ρ(r) = 0) and characterises them by the properties of the density Hessian at this point. At the coordinate of a so-called bond critical point or BCP, the density Hessian has two negative eigenvalues and one positive one. The sum, or trace of the eigenvalues of the density Hessian at this point, denoted as ∇2ρ(r), provides in this model a characteristic indicator of the type of bond, according to the following qualitative partitions:

  1. ρ(r) > 0, ∇2ρ(r) < 0; covalent
  2. ρ(r) ~0, ∇2ρ(r) > 0; ionic
  3. ρ(r) > 0, ∇2ρ(r) > 0; charge shift

The third category of bond was first characterised by Shaik, Hiberty and co. using valence-bond theory1 and they went on to propose [1.1.1] propellane (above, along with F2) as an exemplar of this type.2 Matching the conclusions drawn from VB theory was the value of the Laplacian. As defined above, for the central C-C bond, both ρ(r) and  ∇2ρ(r) have been calculated to be positive, supporting the identification of this interaction as having charge-shift character.3

The Laplacian represents one of those properties where quantum mechanics meets experiment, in that its value (and that of ρ(r) itself) can be measured by (accurate) X-ray techniques.4 This was recently accomplished for propellane,5 with the same conclusion that the Laplacian in the central C-C region has the significantly positive value of +0.42 au. The electron density ρ(r) at this point was measured as 0.194 au. Calculations5 at the B3LYP/6-311G(d,p) level report ρ(r) as ~0.19 and ∇2ρ(r) as +0.08 au. Whilst the former is in good agreement with experiment, the latter is calculated as rather smaller than expected. This was originally interpreted as indicating that the “the experimental bond path has a stronger curvature [in ρ(r)] than the theoretical” although more recent thoughts are that both experimental and theoretical uncertainty may account for the discrepancy.5,6 An experiment worth repeating?

A hitherto largely unexplored aspect of characterising a bond using the Laplacian is whether the value at the bond critical point is fully representative of the bond as a whole. The Laplacian is related to two components of the electronic energy by the Virial theorem;

2G(r) + V(r) = ∇2ρ(r)/4; H(r) = V(r) + G(r)

where G(r) is the kinetic energy density, V(r) is the potential energy density and H(r) the energy density. Charge-shift bonds exhibit a large value of the (repulsive) kinetic energy density, a consequence of which is that ∇2ρ(r) is more likely to be positive rather than negative. The relationships above hold not just for the specific coordinate of a bond critical point, but for all space. Accordingly, another way therefore of representing the Laplacian ∇2ρ(r) is to plot the function as an isosurface, including both the negative surface (for which |V(r)| > 2G(r)) and the positive surface [for which |V(r)| < 2G(r)].

Such an analysis is the purpose of this post, using wavefunctions evaluated at the CCSD/aug-cc-pvtz level (see DOI: 10042/to-5012). The values of ρ(r) and ∇2ρ(r) at the bcp for the central bond are 0.188 and +0.095 au, which compares well with previous calculations. The values for the wing C-C bonds are 0.242 and -0.491 respectively (and were measured5 as 0.26 and -0.48). Laplacian isosurfaces corresponding to ± 0.49 (the value at the wing C-C bcp), ± 0.47 and ± 0.2 (which reveals prominent regions of +ve values for the Laplacian) can be seen in the figures below (and can be obtained as rotatable images by clicking).


Laplacian isosurface contoured at ± 0.49

 –

Laplacian isosurface contoured at ± 0.47. Red = -ve, blue= +ve.

Laplacian isosurface contoured at ± 0.20

A significant feature is the isosurface at -0.47, which corresponds to the lowest contiguous Laplacian isovalued pathway connecting the two terminal carbon atoms (and which coincidentally is similar in magnitude to that reported5 as measured for these two atoms). Three such bent pathways of course connect the two carbon atoms. The energy density H(r) shows a minimum value of -0.21 au along any of these pathways. It is significantly less negative (-0.13) for the direct pathway taken along the axis of the C-C bond.

Energy density H(r) @-0.21

Energy density H(r) @-0.13

ELF isosurface @0.7

A useful comparison with this result is the ELF isosurface. This too is computed at the correlated CCSD/aug-cc-pVTZ using a new procedure recently described by Silvi.7 Contoured at an isosurface of +0.7, the ELF function is continuous between the two terminal atoms, much in the manner of Laplacian. Significantly, the ELF function at the bcp appears at the very much lower threshold value of 0.54, and forms a basin with a tiny integration for the electrons (0.1e). Since both methods provide a measure of the Pauli repulsions via the excess kinetic energy, the similarity of the Laplacian to the ELF function is probably not coincidental.

The issue then is whether a bond must be defined by the characteristics of the electron density distribution along the axis connecting that bond, or whether other, non-least-distance pathways can also be considered as being part of the bond.8 The former criterion defines a pathway involving a positive Laplacian (+0.095) and would be interpreted as indicating charge shift character for that bond. The latter involves three (longer) pathways for which the Laplacian is strongly -ve, and which would therefore per se imply more conventional covalent character for the interaction. Considered as a linear (straight) bond, it has charge shifted character; considered as three “banana” bonds, it may be covalent. Weird!

  1. Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C., “Charge-Shift Bonding – A Class of Electron-Pair Bonds That
    Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach,” Chem. Eur. J., 2005,
    11, 6358-6371, DOI: 10.1002/chem.200500265 and references cited therein.
  2. W. Wu, J. Gu, J. Song, S. Shaik, and P. C. Hiberty, “The Inverted Bond in [1.1.1]Propellane is a Charge-Shift Bond,” Angew. Chem. Int. Ed., 2008,
    DOI: 10.1002/anie.200804965; 10.1002/cphc.200900633
  3. S. Shaik, D. Danovich, W. Wu & P. C. Hiberty, “Charge-shift bonding and its manifestations in chemistry”, Nature Chem, 2009, 1, 443-3439. DOI: 10.1038/nchem.327
  4. P. Coppens, “Charge Densities Come of Age”, Angew. Chemie Int. Ed., 2005, 44, 6810-6811. DOI: 10.1002/anie.200501734
  5. M. Messerschmidt, S. Scheins, L. Grubert, M. Pätzel, G. Szeimies, C. Paulmann, P. Luger. “Electron Density and Bonding at Inverted Carbon Atoms: An Experimental Study of a [1.1.1]Propellane Derivative, Angew. Chemie Int. Ed., 2005, 44, 3925-3928. DOI: 10.1002/anie.200500169
  6. L. Zhang, W. Wu, P. C. Hiberty, S. Shaik, “Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types”, Chem. Euro. J., 2009, 15, 2979-2989. DOI: 10.1002/chem.200802134
  7. F. Feixas , E. Matito, M. Duran, M. Solà and B. Silvi, submitted for publication. See also this abstract.
  8. See for example the work of R. F. Nalewajski

Rzepa, Henry S. The weirdest bond of all? Laplacian isosurfaces for [1.1.1]Propellane. 2010-07-21. URL:http://www.ch.ic.ac.uk/rzepa/blog/?p=2251. Accessed: 2010-07-21. (Archived by WebCite® at http://www.webcitation.org/5rOFp6EuM)

Tags:, , , , , , , , , ,
Posted in Hypervalency, Interesting chemistry | 4 Comments »

Non-covalent interactions (NCI): revisiting Pirkle

Thursday, July 15th, 2010

NCI (non-covalent interactions) is the name of a fascinating new technique for identifying exactly these. Published recently by Johnson, Keinan, Mori-Snchez, Contreras-Garca, Cohen and Yang, it came to my attention at a conference to celebrate the 20th birthday of ELF when Julia Contreras-Garcia talked about the procedure. It is one of those methods which may seem as if it merely teases out the obvious about a molecule, but it is surprising how difficult seeing the obvious can be sometimes. I have blogged about this previously, in discussing the so-called Pirkle reagent. On that occasion, I used the QTAIM technique to identify so-called critical points in the electron density. NCI goes one stage further in identifying surfaces of interaction rather than just single points, the idea being that this focuses attention on regions in molecules which are primarily responsible for binding, stereoselection and other aspects of molecular selectivity.

The Pirkle reagent

The Pirkle reagent

So I was intrigued as to whether the NCI method might find something that my analysis using the QTAIM procedure might have missed. The required program is available for download. I will not go into the theory behind the program, but like AIM, it uses the properties of the electron density via a combination of the first and second derivatives to concentrate on the non-bonded or weakly interacting regions of a molecule.

NCI interactions in the Pirkle reagent

The results of the analysis (using the SCF option in the program, and a B3LYP/6-31G calculation) are displayed using VMD, and I cannot pull my usual trick of displaying the surface within the page of a blog via Jmol (although it seems Jmol with some effort could probably be persuaded to also render the information). So the above cannot be rotated. I have therefore circled one (there are others) interesting region in red. This encloses two surfaces. I should explain the colour coding adopted by the program. Red would be a repulsive interaction, and blue attractive. Weak interactions are shown in green. In the diagram above, these include the π-π stacking and various hydrogen bonds. But concentrating on the two surfaces inside the red circle, one occurs between the two hydrogens shown below. It catches the eye because there is a blue-tinge to the colour coding! This might mean it is a bit stronger than just “weak”.

A Weak interaction in the Pirkle reagent

The NCI method I do not think is meant to provide a definitive answer to the question; is that interaction real/strong? It serves, as I noted earlier, to spike interest. Here, it does that, since this particular interaction had indeed never previously been identified for attention (the obvious had been missed!). Highlighting such potential regions of a molecule and perhaps then helping in the design of experiments to test if the interactions are real is what the NCI program is meant to do (IMHO)!

Tags:, ,
Posted in Interesting chemistry | 3 Comments »

Tunable bonds looked at in a different way

Sunday, July 11th, 2010

The title of this post merges those of the two previous ones. The tunable C-Cl bond brought about in the molecule tris(amino)chloromethane by anomeric effects will be probed using the Laplacian of the electronic density.

Laplacian @0.67 for tris(amino)choromethane. Click for 3D

The figure above shows the Laplacian for a conformation of tris(amino)chloromethane with one of the nitrogen lone pairs antiperiplanar to the C-Cl bond, and the other two lone pairs antiperiplanar to C-N bonds. The features visible at an isosurface of ± 0.67 include

  1. (a) The Laplacian here has a value of -0.67 (= red isosurface), which indicates an accumulation of (covalent) shared density along the C-N bond (underneath this surface, you can see the blue sphere representing depletions from the nitrogen atomic region). This bond has the lone pair antiperiplanar to a C-N bond.
  2. (b) Contrast this with the C-N bond which is antiperiplanar to the C-Cl bond. A greater volume of the covalent C-N region is bounded by this isosurface. More of the N lone pair on this atom is donating into the C-N, as more conventionally represented below.
  3. Notice how the red isosurface associated with the N lone pair and the region associated with the C-N bond are in fact contiguous, and not separated basins!

    Anomeric donation

  4. (c) represents the lone pairs on the chlorine, which have been augmented by the donation from the nitrogen. Notice how they come out as a torus rather than the conventional double dot representations!
  5. Notice the absence of any features along the C-Cl bond! This would be typical of a fully or even partially ionic bond, but it also illustrates that with a property such as the Laplacian, one does not get a complete picture by inspecting at just one isosurface value.

The next isosurface chosen is 0.3. At this lower value, more depletions (blue = electrophilic regions) are seen and a tiny feature now appears along the C-Cl bond, which is the covalent accumulation of that bond, a feature that grows @ 0.2. This nicely illustrates the variable covalency/ionicity of the C-Cl bond. Notice also how the lhs is all red (anionic) and the rhs is mostly blue (cationic), showing the formation of in effect an ion pair.

tris(amino)chloroethane @ 0.3

tris(amino)chloroethane @ 0.2

There are many other features which can be explored in these Laplacian maps, but I leave those for the reader to indulge in. Just click on any of the diagrams above,and start your exploration.

Tags:, , ,
Posted in Interesting chemistry | No Comments »

Looking at bonds in a different way: the Laplacian.

Tuesday, July 6th, 2010

The Cheshire cat in Alice’s Adventures in Wonderland comes and goes at will, and engages Alice with baffling philosophical points. Chemical bonds are a bit like that too. In the previous post, we saw how (some) bonds can be tuned to be strong or weak simply by how a lone pair of electrons elsewhere in the molecule is oriented with respect to the bond. Here I explore another way of looking at bonds. To start, we must introduce a quantity known as ∇2ρ(r), henceforth termed the Laplacian of the electron density ρ(r).

Firstly, a recipe: obtain a description of the electron density distribution in the molecule; we will call this the wavefunction (and programs such as Gaussian can write this out in something called a wavefunction file, or .wfn). In a cube of space enclosing the molecule, at each point obtain the second derivatives of ρ(r) with respect to the x, the y and the z coordinate of the point, and populate a (3,3) matrix with the values. Diagonalize the matrix, and add the three eigenvalues of the matrix at that point together to get ∇2ρ(r). Repeat this procedure at regular intervals for all the other points in the cube of space (typically ~200 points in each of the three directions). You will end up with a cube of (in this case 8 million) Laplacian values for the molecule.

Typically (in atomic units), any one value may range from ~-1.0 to ~+1.0, but more meaningful insight is obtained by a (local-virial theorem) expression which relates the Laplacian to a sum of the potential and kinetic energy densities (see. eg here for more detail). A negative Laplacian is dominated by a lowering of the (negative) potential energy at that point in space, whereas a positive Laplacian arises by a domination of the (positive) excess kinetic energy. Measured at the ~mid-point of a (homonuclear) bond, the former indicates an attractive covalent bond, whereas the latter will indicate either an ionic bond or a third type known as charge-shift in which the covalent term (in the valence-bond description of the bond) is repulsive rather than attractive (the actual bond binding energy arises from resonance terms between the covalent and ionic structures). A -ve Laplacian is describing local accumulations or concentrations of (bonding) electron energy densities, whereas a +ve value is describing local depletions. The former can also be used to identify a Lewis base or nucleophilic region, and the latter a Lewis acid or electrophilic region.

Now that we have a cube of points describing the Laplacian for the molecule, we can look at the surface defined by any particular (positive or negative) value of the function to see what insight, if any, can be obtained. Time for some pictures.

Ethane. Laplacian isosurface +/- 0.3 Click for 3D

The above is ethane, contoured at a Laplacian isosurface value of either -0.3 (red surface) or +0.3 (blue surface). Interpreted simply, all seven bonds in this molecule coincide with the red components, which can be taken as typical covalent interactions. The blue spheres represent the valence atomic orbital regions, which have been depleted at the expense of the bond. Nicely intuitive thus far. Let us contour the Laplacian at a rather lower value of +/- 0.2.

Ethane, Laplacian isosurface +/- 0.2 Click for 3D

New blue features have appeared which correspond to +ve Laplacian values. Close inspection reveals them to coincide with what we might describe as the anti-bonding regions of each bond (eight in all). They have been named σ-holes.  Indeed, one might reasonably expect a depletion from just those regions in favour of the bonding regions (one might also regard it an electrophilic region, susceptible to eg nucleophilic attack). Well, we could explore both lower and higher values of the Laplacian (for example, a value of either -0.511 or -0.869 happens to have special significance for the C-C or C-H bonds of ethane) but to keep this blog short, I will move on to (and conclude with) benzene, another iconic molecule.

Benzene. Laplacian isosurface +/- 0.3 Click for 3D

Benzene. Laplacian isosurface +/- 0.2 Click for 3D

Again, the +/- 0.3 isosurface has the expected red bonds, and at the lower value, further blue regions (it is tempting, but we really should not call them anti-bonds!) materialize. Look at the central region of the ring, where depletion seems to have happened.

I close with a musing. Firstly, it is noteworthy that the Laplacian can actually be measured, it is not merely a theoretical concept (although the experiments are in fact pretty difficult, and need very specialised apparatus) but a real observable. Secondly, (at certain values) the Laplacians do seem to recover the simple picture of covalent bonding. The issue really is how far to push the analogy and whether in fact it results in any significant additional insight compared to more conventional ways of representing bonds. At least the pictures are pretty!

Postscript: One can use  a sub-set of electrons to calculate the Laplacian.  Shown below is benzene calculated for just the σ and π-electrons.

Benzene, σ-manifold

Benzene. π-manifold

Notice how the σ set does not differ much from the total set, but the π-set shows accumulation above and below the plane, at the expense of depletion in the plane (one must be aware that integration of the  Laplacian over all space should yield the value of zero). This explains the unusual features of the total set at the  0.2 theshold above.

Tags:, , , , , , ,
Posted in Interesting chemistry | 10 Comments »

Tunable bonds

Saturday, July 3rd, 2010

Car transmissions come in two types, ones with fixed ratio gears, and ones which are continuously variable. When it comes to chemical bonds, we tend to think of them as being very much of the first type. Bonds come in fixed ratios; single, aromatic, double, triple, etc. OK, they do vary, but the variations are assumed as small perturbations on the basic form. Take for example the molecule shown below. The bonds as shown are all clearly single (the wedge and hashed bond are merely stereochemical notations). No-one would really think of drawing this molecule in any other way, and this idea of the transferability of bonds between molecules (all double bonds react in specific ways which are different from single bonds, and they also have characteristic spectroscopic properties, etc) is what allows molecules to be classified.

A Highly tunable molecule

With this molecule however, there really is an elephant in the room; the three electron lone pairs associated with each nitrogen atom (not shown above, but most chemists are trained to recognize their implicit presence). Where are they? Well, each lone pair will tend to orient itself such that it is aligned with an adjacent σ-bond. It has two such bonds to choose from, an adjacent C-N bond or a C-Cl bond. One might now envisage the following permuations; all three N lone pairs gang-up on the C-Cl bond, or perhaps only two do, or only one, or none. What happens in each of these scenarios? The table below shows these permutations calculated using B3LYP/6-31G(d).

app lone pairs
to C-Cl		 Relative free
energy, kcal/mol		 C-Cl bond
length, Å		 ν C-Cl, cm-1
3 0.0 2.542 158
2 4.2 2.099 221
1 7.3 1.937 352
0 14.4 1.869 441

3 app lone pairs. Click for animation

2 app lone pairs. Click for animation

1 app lone pairs. Click for animation

0 app lone pairs. Click for animation

The C-Cl bond length changes from a normal single bond length (1.87Å) when none of the nitrogen lone pairs are antiperiplanar to the C-Cl bond, to a very abnormal 2.54Å when all three are, and the C-Cl stretching mode decreases in wavenumber from 441 to 158 cm-1. There is lots of other fun to be had inspecting the geometries and vibrations, but  I will leave that for you to explore rather than discuss it here. Click on the thumbnails above to start.

This effect does have a name, sugar chemists call it the anomeric effect. But this one is supercharged! It would be quite reasonable to say that at some stage, the C-Cl single bond turns from being covalent to being ionic (and indeed, repeating the calculation using an applied solvent field certainly accelerates this process). Whilst this might be a contrived example and hence an extreme example, it does serve to remind us that on occasion, molecules may come with continuously variable transmissions rather than with fixed ratio gears!

And a postscript. I mentioned the nitrogen lone pairs ganging up on the C-Cl bond. How might one go even one step further? A standard trick to enhance the donating power of a nitrogen lone pair is to replace the NH2 group with a hydrazine group, H2N-NH. The lone pair derived from the second nitrogen buttresses the first. This too has a name, it is called the α-effect.

An anomeric effect on steroids

For this example (see digital repository), the C-Cl bond length lengthens even further to 2.90Å, which interestingly, is the same value as for the SN1 transition state!

Tags:, , , , ,
Posted in Interesting chemistry | 3 Comments »

The mysteries of stereoinduction.

Thursday, July 1st, 2010

Stereo-induction is, lets face it, a subtle phenomenon. The ratio of two stereoisomers formed in a reaction can be detected very accurately by experiment, and when converted to a free energy difference using ΔG = -RT Ln K, this can amount to quite a small value (between 0.5 – 1.5 kcal/mol). Can modelling reproduce effects originating from such small energy differences? Well one system that has been argued about now for several decades is shown below as 1.

Norbornene systems

Way back in 1992, we thought that the explanation for attack by an electrophile on the alkene from the syn face was electrostatic (although it did depend on the nature of the electropile; thus we concluded that attack by Hg(OH)2 was electrostatic, but by BH3 was orbital controlled). Recently, a different explanation has emerged, relating to how the fundamental normal vibrational modes of the molecule interact with the transition normal mode for the reaction. A new example of this, relating to reaction of the isomeric 2 with a peracid has recently been discussed on Steve Bachrach’s blog. Here, the peroxide of the peracid is thought to act as an electrophile (although one must bear in mind that it does bear two electron lone pairs!). The conclusion was pretty clear cut; the experimental preference for syn (92%) over the anti isomer (8%, ΔΔG = 1.4 kcal/mol) was NOT due to electrostatic effects, but due to distorsional asymmetry in the vibrational mode that couples/forms the transition state mode.

I could not resist revisiting this system. As in 1992, a molecular electrostatic potential was calculated for 2. The method used was wB97XD/aug-cc-pvdz, and if you want the archive of this calculation to evaluate it yourself, see here).

MEP for 2. Click on diagram for 3D.

A very clear electrostatic bias for syn attack emerges (orange = attractive to a proton=electrophile). This electrostatic picture is not directly related to any distortional asymmetry, although of course both could arise from the same electronic factors. They may indeed be different manifestations of the same underlying nature of the wavefunction. But I would claim here that to make the clear statement that electrostatic effects are NOT responsible for the discrimination in this reaction is perhaps too simplistic (electrostatic potentials were not reported in the original article). The control experiment is 3, which is known to be far less selective. The calculated electrostatic potential likewise shows much less discrimination.

The norbornene with a four-membered ring

Is there another take on 2? Well, how about an NBO (natural bond order) analysis? The interaction energy between the filled C1-C2 orbital and the antibonding C15-C16 π* bond is 3.24. This could be regarded as pushing electrons into the anti-periplanar syn face of the alkene. The corresponding C2-C9/C15-C16 interaction resulting in an anti-preference is less at 2.55 kcal/mol. This effect arises because the C1-C2 bond (localised as an NBO) is a better donor (E=-17.8eV) than C2-C9 (E=-18.1eV). Because C2 is common to both, it must be the difference between C1 and C9 (i.e. the hybridization of each). Perhaps it’s an orbital effect after all?

Norbornene electrostatic potential

I would conclude by saying that it can be ferociously difficult to identify the fundamental origins of stereo-induction. But I leave the argument in the hands of the reader now. What do you think?

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

Chemistry with a super-twist: A molecular trefoil knot, part 2.

Tuesday, June 1st, 2010

A conjugated, (apparently) aromatic molecular trefoil might be expected to have some unusual, if not extreme properties. Here some of these are explored.

  1. The first is the vibrational spectrum. With 144 atoms for this molecule, it has 426 vibrational modes, but one is highlighted below. This is the mode that moves the atoms in accord with the Kekulé resonance. If real, this mode resists such alternation. The mode has a value of ~ 1310 cm-1 for benzene, although this is accepted as being lower than expected due to the phenomenon of π-distortivity (DOI: 10.1039/b911817a and also this post). The mode shown below has the value of 1650 cm-1, which is a good deal higher than for benzene. The significant coupling of the CH wagging motions with the C-C/C-N stretching (Duschinsky coupling) makes the interpretation more complex (it also occurs for benzene itself), but the Kekulé mode (there are in fact several) is surprisingly large for so many π-electrons. Perhaps the large degree of writhe noted in the previous post might have something to do with it?

    Molecular trefoil: the Kekulé mode for bond alternation. Click for animation.

  2. The NICS (nucleus independent chemical shift) at the centroid of the trefoil is -16.4 ppm. This is clearly an aromatic value, and confirms our inference that the system is a 4n+2 aromatic molecule. In this example, the aromaticity is not only three-dimensional, but helical as well. The predicted 1H NMR spectrum (below) shows three regions. The upfield region (~ -5 ppm) corresponds to protons pointing directly inwards to the centre, whilst the lowfield region (~ 8ppm) corresponds to protons at the outside edge.

    Predicted 1H NMR spectrum

  3. Shown below is the calculated electronic circular dichroism (ECD) spectrum. It shows a large Cotton effect due to the chiral nature of the trefoil. The electronic transitions extend beyond ~1500nm, approaching the near infra-red. The phase of the Cotton effect at ~600nm calculated for the chiral isomer shown in the 3D model above would certainly suffice to assign the absolute configuration of the system should the experimental spectrum be measurable.

    Calculated Electronic circular dichroism spectrum for the base trefoil.

    The spectrum above shows maximum absorption at ~600nm, which means optical rotation at the sodium D-line (589 nm) cannot be measured (light has to get through to measure its rotation). However, the region of 880nm (the highest value available on commercial spectrometers) is reasonably transparent for such measurement. Calculations may not be much help, since the linear CPHF equations appear unstable. Thus [α]880 shows an enormous dependence on the precise DFT method chosen to compute it (~ +8763°@CAM-B3LYP but the very different -59898°@B3LYP).

Henry Rzepa. Chemistry with a super-twist: A molecular trefoil knot, part 2.. . 2010-06-02. URL:http://www.ch.ic.ac.uk/rzepa/blog/?p=2084. Accessed: 2010-06-02. (Archived by WebCite® at http://www.webcitation.org/5qC4NiFsM)

 

Tags:, , , ,
Posted in Interesting chemistry | 3 Comments »

Chemistry with a super-twist: A molecular trefoil knot, part 1.

Monday, May 31st, 2010

Something important happened in chemistry for the first time about 100 years ago. A molecule was built (nowadays we would say synthesized) specifically for the purpose of investigating a theory. It was cyclo-octatetraene or (CH)8, and it was made by Willstätter and Waser to try to find out if benzene, (CH)6, was an aromatic one-off or whether it might be a member of a series, envisaged as (CH)n. Of course, a hell of a surprise was in store for Willstätter and Waser! Prior to this synthesis, (CH)8 had never existed; nature had not gotten there first. In that sense, chemistry became much like mathematics had before it; it was OK to make molecules because they might be interesting, and for the purpose of  investigating possible patterns in nature. So it is in this spirit that I suggest an interesting molecule here. It is a molecular trefoil, constructed by joining 15 pyrrole units together into a ring with appropriate linkers and in effect tying a knot in that ring. A trefoil knot to be specific.

A molecular trefoil knot, shown with a Mg at the centre. Click to view in 3D

Why might such a molecule be interesting? These are ten reasons:

  1. It would make an interesting ligand for a metal
  2. It has lots of interesting groves and dimples for transition states to nest in
  3. It would be an extended porphyrin (a pentadecaphyrin to be precise). Nature likes to make molecules out of tetraphyrins (chlorophyll, haemoglobin, etc), and so we are pushing beyond nature’s own boundaries. Both a penta and a hexadecaphyrin have already been made (DOI 10.1002/chem.200701909, 10.1021/ja005588o).
  4. The trefoil knot is a most interesting object in a branch of mathematics called knot theory, and it is also related to another fascinating object, the Möbius band.
  5. The pyrrole units in such a molecule are conjugated via the π-system, and the molecule above is potentially fully conjugated across its entire length. This could make it aromatic, and hence it is interesting for the same reason that Willstätter found cyclo-octatetraene so.
  6. The system above, if carefully counted, would have 74 π-electrons in cyclic conjugation. This would make it a 4n+2 aromatic (n=18), just like benzene, but not at all like (CH)8 (which as Willstätter and Waser found, is not aromatic).
  7. It seems highly twisted. Indeed the title of this post is super-twisted. But is it really? We learn from topology that twist is not the only property that cyclic bands or strips can have. They can also exhibit writhe. So is it writhed as well as twisted?
  8. Aromatic molecules have one rather mysterious behaviour. The ring bonds in in such systems resemble neither double nor single bonds, but aromatic bonds, and in this they have a length intermediate between the single and the double, and this applies to all of the bonds. The origins of this delocalization continue to provoke controversy (see this post). Thus it is thought that only (planar) carbon rings with around 26 or less π-electrons can exhibit such equal lengths (boron rings can apparently go much further, see 10.1039/B911817A). More than that, and distortion sets in which makes the lengths alternate. The molecule above has 74 π-electrons. What will its bonds do, and is what they do related to the twist (or the writhe) of the system?
  9. The trefoil is chiral. It cannot be superimposed upon its mirror image. But how chiral (whatever that means)?
  10. The system has many design handles, including the number of pyrrole (or thiophene) units, the number of  N-H  vs =N motifs, and the scope for templating using a metal cation (Mg in the example above).

So what might be the properties of our trefoil knot? I am going to list only two here.

  1. A theorem emerged from mathematics in the 1970s known as the White, Cãlugãreanu, Fuller Theorem. It defines the topological properties of bands in terms of a quantity known as the linking number (Lk). The theorem states that: Lk = Tw + Wr, where Lk is an integer, being the sum of two properties Tw (the total twist of the band) and Wr (the total writhe of the band). This theory was recently extended to the analysis of twisted conjugated molecular rings (DOI: 10.1021/ja710438j), for which Lk adopts integer values (in units of π). Thus a conjugated Möbius π-cycle has a value Lk = 1π (specifically when describing the band formed by the π-electrons). Most of this value is composed of twist rather than writhe. What of our molecule? Well, it has Lk =6π, and this comprises Tw = ~ -0.8π and Wr ~ +6.8π (yes the two can be either positive or negative, and do not have to be the same sign). The surprise is that it is (overall) hardly twisted! The knot is composed almost entirely of writhe. So much for the title of this post!
  2. What about the bond lengths? The best way of analyzing these (see DOI: 10.1021/ol703129z) is to compare pairs of so-called meso-bonds, being the coupler unit connecting any two pyrrole rings. Around the cycle, all the C-C meso-pairs are ~1.4Å and the C-N pairs are both ~1.34Å. That characteristic of benzene, in having all its (C-C) bonds equal, seems true here as well (at least at the B3LYP/6-311G(d,p) level, see e.g.10042/to-2109. There are reasons for thinking that in fact the B3LYP method does predict this behaviour more or less realistically). By the way, a molecule with a π-linking number of  six is indeed classified by the same selection rule as benzene, ie  4n+2 (odd numbers of  Lk are governed by a 4n rule instead).

It is tempting to conclude that perhaps the extended conjugation of this molecule (shown by the bond length equality) is somehow connected to the dominance of writhe over twist in this trefoil.

I will follow this post up with another relating to the predicted chiro-optical properties. For now, I leave its synthesis to be contemplated by a present day Willstätter or Waser.

Webcite archive:. Chemistry with a super-twist: A molecular trefoil knot, part 1. . 2010-06-01. URL:http://www.ch.ic.ac.uk/rzepa/blog/?p=2046. Accessed: 2010-06-01. (Archived by WebCite® at http://www.webcitation.org/5qA81X8qW)

Tags:, , , ,
Posted in Interesting chemistry | 9 Comments »

« Older Entries
Newer Entries »