Posts Tagged ‘10.1021’

Dispersion “bonds”: a new example with an ultra-short H…H distance.

Monday, June 26th, 2017

About 18 months ago, there was much discussion on this blog about a system reported by Bob Pascal and co-workers containing a short H…H contact of ~1.5Å[1]. In this system, the hydrogens were both attached to Si as Si-H…H-Si and compressed together by rings. Now a new report[2] and commented upon by Steve Bachrach, claims a similar distance for hydrogens attached to carbon, i.e. C-H…H-C, but without the ring compression.

This new example is the structure of an C3-symmetric all-meta tBu-triphenylmethane R-H…H-R dimer determined by neutron diffraction (DOI: 10.5517/ccdc.csd.cc1nc1bd) and the close interaction is achieved purely by attractions due to dispersion forces accumulating in the remainder of the molecules. This study also reports a diverse set of computed properties for this new system, but one property reported as part of the previous discussion was not presented, the 1JH-H coupling constant. I have computed it here in the hope that it might be possible to measure by some means, perhaps in the solid state?

The chemical shift of the R3CH proton is measured as a singlet‡ at ~7.35 ppm (in deuterated benzene, Figure S6, SI).† 

The value calculated using B3LYP/Def2-TZVPP (gas phase) is 7.39 and 7.69 ppm (averaged to 7.54 for a rapidly exchanging environment). The 1J coupling is calculated as 4.3 Hz at the B3LYP/Def2-TZVPP level, DOI: 10.14469/hpc/2699. The designation 1J is normally taken as a 1-bond pathway for the coupling. In this example, the designation of the H-H region as a “bond” is the interesting discussion point!

I end by noting here my observation that although the neutron diffraction study of ammonium tetraphenylborate shows the  N-H protons as pointing directly towards the centroid of phenyl groups, the original observation[3] was made that “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system”.  The equivalent thermal motion for the triphenylmethane system here would have the  C-H vectors orbiting around each other in a manner that increases the H-H separation, but which averages out to them pointing directly towards one another?  The calculated normal coordinate analysis of this system is not available from the article SI, so the ease of  C-C-H bending to achieve such motion is difficult to ascertain. Perhaps trying to detect the 1J coupling might illuminate whether this happens?

Postscript. †Prof Schreiner has indicated that that the methine assignment is 5.79 ppm (b below) and not 7.35 as marked with a diamond in the S6 figure caption (a below). This is of course measured in d6-benzene solution and applies to the monomer, not presumably the dimer. The calculated value of 7.54 ppm as reported above applies specifically to the dimer, which suggests a significant shift of ~2ppm upon dimer formation. It would be interesting to verify this prediction via a solid-state measurement.

‡Measuring coupling would require an asymmetric environment to differentiate the two chemical shifts of the interacting hydrogens. Although the C3 symmetry of the crystal structure could provide such an environment, it is observed to be fluxional in solution,  which equalises the two chemical shifts on the NMR time scale. Two non-equivalent protons exhibiting only mutual couplings manifest as an AB-type double doublet of peaks in the NMR spectrum. As the difference in chemical shift between the two nuclei (in units of Hz) approaches in magnitude the value of the coupling constant between them (also in Hz), the AB quartet becomes increasingly second-order in appearance. This means that the intensities of the two outer peaks starts to decrease and the two inner peak intensities increase. When the chemical shift difference between them reaches zero, the intensity of the two outer peaks also becomes zero and the two inner peaks superimpose to become a single peak. This means that the coupling constant cannot be measured from the splitting of the peaks (which has vanished). It does not mean of course that the coupling itself has vanished; it merely no longer manifests in the spectrum.

References

  1. J. Zong, J.T. Mague, and R.A. Pascal, "Exceptional Steric Congestion in an <i>in</i>,<i>in</i>-Bis(hydrosilane)", Journal of the American Chemical Society, vol. 135, pp. 13235-13237, 2013. https://doi.org/10.1021/ja407398w
  2. 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
  3. T. Steiner, and S.A. Mason, "Short N<sup>+</sup>—H...Ph hydrogen bonds in ammonium tetraphenylborate characterized by neutron diffraction", Acta Crystallographica Section B Structural Science, vol. 56, pp. 254-260, 2000. https://doi.org/10.1107/s0108768199012318

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Posted in Interesting chemistry | 3 Comments »

Dispersion "bonds": a new example with an ultra-short H…H distance.

Monday, June 26th, 2017

About 18 months ago, there was much discussion on this blog about a system reported by Bob Pascal and co-workers containing a short H…H contact of ~1.5Å[1]. In this system, the hydrogens were both attached to Si as Si-H…H-Si and compressed together by rings. Now a new report[2] and commented upon by Steve Bachrach, claims a similar distance for hydrogens attached to carbon, i.e. C-H…H-C, but without the ring compression.

This new example is the structure of an C3-symmetric all-meta tBu-triphenylmethane R-H…H-R dimer determined by neutron diffraction (DOI: 10.5517/ccdc.csd.cc1nc1bd) and the close interaction is achieved purely by attractions due to dispersion forces accumulating in the remainder of the molecules. This study also reports a diverse set of computed properties for this new system, but one property reported as part of the previous discussion was not presented, the 1JH-H coupling constant. I have computed it here in the hope that it might be possible to measure by some means, perhaps in the solid state?

The chemical shift of the R3CH proton is measured as a singlet‡ at ~7.35 ppm (in deuterated benzene, Figure S6, SI).† 

The value calculated using B3LYP/Def2-TZVPP (gas phase) is 7.39 and 7.69 ppm (averaged to 7.54 for a rapidly exchanging environment). The 1J coupling is calculated as 4.3 Hz at the B3LYP/Def2-TZVPP level, DOI: 10.14469/hpc/2699. The designation 1J is normally taken as a 1-bond pathway for the coupling. In this example, the designation of the H-H region as a “bond” is the interesting discussion point!

I end by noting here my observation that although the neutron diffraction study of ammonium tetraphenylborate shows the  N-H protons as pointing directly towards the centroid of phenyl groups, the original observation[3] was made that “even at 20 K the ammonium ion performs large amplitude motions which allow the N-H vectors to sample the entire face of the aromatic system”.  The equivalent thermal motion for the triphenylmethane system here would have the  C-H vectors orbiting around each other in a manner that increases the H-H separation, but which averages out to them pointing directly towards one another?  The calculated normal coordinate analysis of this system is not available from the article SI, so the ease of  C-C-H bending to achieve such motion is difficult to ascertain. Perhaps trying to detect the 1J coupling might illuminate whether this happens?

Postscript. †Prof Schreiner has indicated that that the methine assignment is 5.79 ppm (b below) and not 7.35 as marked with a diamond in the S6 figure caption (a below). This is of course measured in d6-benzene solution and applies to the monomer, not presumably the dimer. The calculated value of 7.54 ppm as reported above applies specifically to the dimer, which suggests a significant shift of ~2ppm upon dimer formation. It would be interesting to verify this prediction via a solid-state measurement.

‡Measuring coupling would require an asymmetric environment to differentiate the two chemical shifts of the interacting hydrogens. Although the C3 symmetry of the crystal structure could provide such an environment, it is observed to be fluxional in solution,  which equalises the two chemical shifts on the NMR time scale. Two non-equivalent protons exhibiting only mutual couplings manifest as an AB-type double doublet of peaks in the NMR spectrum. As the difference in chemical shift between the two nuclei (in units of Hz) approaches in magnitude the value of the coupling constant between them (also in Hz), the AB quartet becomes increasingly second-order in appearance. This means that the intensities of the two outer peaks starts to decrease and the two inner peak intensities increase. When the chemical shift difference between them reaches zero, the intensity of the two outer peaks also becomes zero and the two inner peaks superimpose to become a single peak. This means that the coupling constant cannot be measured from the splitting of the peaks (which has vanished). It does not mean of course that the coupling itself has vanished; it merely no longer manifests in the spectrum.

References

  1. J. Zong, J.T. Mague, and R.A. Pascal, "Exceptional Steric Congestion in an <i>in</i>,<i>in</i>-Bis(hydrosilane)", Journal of the American Chemical Society, vol. 135, pp. 13235-13237, 2013. https://doi.org/10.1021/ja407398w
  2. 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
  3. T. Steiner, and S.A. Mason, "Short N<sup>+</sup>—H...Ph hydrogen bonds in ammonium tetraphenylborate characterized by neutron diffraction", Acta Crystallographica Section B Structural Science, vol. 56, pp. 254-260, 2000. https://doi.org/10.1107/s0108768199012318

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Posted in Interesting chemistry | 3 Comments »

The "hydrogen bond"; its early history.

Saturday, December 31st, 2016

My holiday reading has been Derek Lowe’s excellent Chemistry Book setting out 250 milestones in chemistry, organised by year. An entry for 1920 entitled hydrogen bonding seemed worth exploring in more detail here.

As with many historical concepts, it can often take a few years to coalesce into something we would readily recognise today, and hydrogen bonds are no exception. Wikipedia is another source of the history and it cites a 1912 article as the origin of the term in relation to the solvation of amines[1] but also notes that the better known setting of water occurs later in 1920.[2] Here I try to capture the essence of the concept with a few diagrams taken from these two articles.

 Firstly “The state of amines in aqueous solution“[1] which is mostly concerned with the measurement of ionization constants of primary, secondary and tertiary amines. It boils down to the below:

and the connection to ionization is laid out as:

Since in 1912, Lewis’ electron pair theory of the covalent bond had not yet emerged, the authors use the terms “strong union” and “weak union”, and of course it is the “weak union” that we now know of as the hydrogen bond. Some other comments about this seminal diagram:

  1. The article contains the very explicit and modern term stereochemical, which is used in a manner that suggests it was already common.‡ But there is only a hint at most that the nitrogen atoms might be tetrahedral, or that the “weak union” between (what we now think of as the lone pair on) the nitrogen and the hydrogen of the water is directional.
  2. The second weak union between the tetramethyl ammonium (which we now describe as a cation) and the hydroxide (now described as an anion; both terms are however implied by the description strong electrolyte) is probably not what we would now call a hydrogen bond, more an intimate ion-pair.

The second article in 1920 on water itself[2] is post-Lewis, but perhaps applied in a manner which we would not entirely agree with nowadays. Thus dinitrogen, N≡N is shown as below with just a single connecting bond.

Then we get the interaction between ammonia and water,† analogous to the example shown above:

and for water itself:♠

which in each case shows the central hydrogen having what we now call a valence shell of four electrons,♣ and hence more equivalent to the “strong unions” above. This shows that in 1920 chemists were rapidly adopting Lewis’ representations, but not always entirely successfully.

On balance, I think the 1912 article sets out the modern concept of a hydrogen bond representing a weak union to a hydrogen rather better than the Latimer and Rodebush attempt (at least diagrammatically).

‡Stereochemical notation is discussed in this post, and it dates from the 1930s.

†The modern take is explored here, in which the equilibrium set up between a “weak union” between ammonia and water (the weak electrolyte) and an isomeric “strong union” which represents ionization into an ammonium hydroxide ion-pair (the strong electrolyte) is favoured for the former by ΔG ~6 kcal/mol.

♠The equilibrium between a “weak union” of two water molecules and the fully ionized strong union of hydronium hydroxide favours the former by ΔG ~23 kcal/mol.

♣ This 1920 representation does imply symmetry for the hydrogen, being ~equally disposed between the two oxygens. We now know that such symmetric hydrogen bonding is not unusual (see this post for how to fine-tune a hydrogen bond into this situation) but rather than requiring four electrons as implied in the diagram above, it is now better described as a three-centre-two-electron bond instead.

References

  1. T.S. Moore, and T.F. Winmill, "CLXXVII.—The state of amines in aqueous solution", J. Chem. Soc., Trans., vol. 101, pp. 1635-1676, 1912. https://doi.org/10.1039/ct9120101635
  2. W.M. Latimer, and W.H. Rodebush, "POLARITY AND IONIZATION FROM THE STANDPOINT OF THE LEWIS THEORY OF VALENCE.", Journal of the American Chemical Society, vol. 42, pp. 1419-1433, 1920. https://doi.org/10.1021/ja01452a015

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Posted in Historical | 2 Comments »

The “hydrogen bond”; its early history.

Saturday, December 31st, 2016

My holiday reading has been Derek Lowe’s excellent Chemistry Book setting out 250 milestones in chemistry, organised by year. An entry for 1920 entitled hydrogen bonding seemed worth exploring in more detail here.

As with many historical concepts, it can often take a few years to coalesce into something we would readily recognise today, and hydrogen bonds are no exception. Wikipedia is another source of the history and it cites a 1912 article as the origin of the term in relation to the solvation of amines[1] but also notes that the better known setting of water occurs later in 1920.[2] Here I try to capture the essence of the concept with a few diagrams taken from these two articles.

 Firstly “The state of amines in aqueous solution“[1] which is mostly concerned with the measurement of ionization constants of primary, secondary and tertiary amines. It boils down to the below:

and the connection to ionization is laid out as:

Since in 1912, Lewis’ electron pair theory of the covalent bond had not yet emerged, the authors use the terms “strong union” and “weak union”, and of course it is the “weak union” that we now know of as the hydrogen bond. Some other comments about this seminal diagram:

  1. The article contains the very explicit and modern term stereochemical, which is used in a manner that suggests it was already common.‡ But there is only a hint at most that the nitrogen atoms might be tetrahedral, or that the “weak union” between (what we now think of as the lone pair on) the nitrogen and the hydrogen of the water is directional.
  2. The second weak union between the tetramethyl ammonium (which we now describe as a cation) and the hydroxide (now described as an anion; both terms are however implied by the description strong electrolyte) is probably not what we would now call a hydrogen bond, more an intimate ion-pair.

The second article in 1920 on water itself[2] is post-Lewis, but perhaps applied in a manner which we would not entirely agree with nowadays. Thus dinitrogen, N≡N is shown as below with just a single connecting bond.

Then we get the interaction between ammonia and water,† analogous to the example shown above:

and for water itself:♠

which in each case shows the central hydrogen having what we now call a valence shell of four electrons,♣ and hence more equivalent to the “strong unions” above. This shows that in 1920 chemists were rapidly adopting Lewis’ representations, but not always entirely successfully.

On balance, I think the 1912 article sets out the modern concept of a hydrogen bond representing a weak union to a hydrogen rather better than the Latimer and Rodebush attempt (at least diagrammatically).

‡Stereochemical notation is discussed in this post, and it dates from the 1930s.

†The modern take is explored here, in which the equilibrium set up between a “weak union” between ammonia and water (the weak electrolyte) and an isomeric “strong union” which represents ionization into an ammonium hydroxide ion-pair (the strong electrolyte) is favoured for the former by ΔG ~6 kcal/mol.

♠The equilibrium between a “weak union” of two water molecules and the fully ionized strong union of hydronium hydroxide favours the former by ΔG ~23 kcal/mol.

♣ This 1920 representation does imply symmetry for the hydrogen, being ~equally disposed between the two oxygens. We now know that such symmetric hydrogen bonding is not unusual (see this post for how to fine-tune a hydrogen bond into this situation) but rather than requiring four electrons as implied in the diagram above, it is now better described as a three-centre-two-electron bond instead.

References

  1. T.S. Moore, and T.F. Winmill, "CLXXVII.—The state of amines in aqueous solution", J. Chem. Soc., Trans., vol. 101, pp. 1635-1676, 1912. https://doi.org/10.1039/ct9120101635
  2. W.M. Latimer, and W.H. Rodebush, "POLARITY AND IONIZATION FROM THE STANDPOINT OF THE LEWIS THEORY OF VALENCE.", Journal of the American Chemical Society, vol. 42, pp. 1419-1433, 1920. https://doi.org/10.1021/ja01452a015

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Posted in Historical | 2 Comments »

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

Wednesday, June 22nd, 2016

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

aromatic-pi-query

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

aromatic-pi-HN-140

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

390

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

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

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

aromatic-pi-OH-140

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

 

References

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

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Posted in Chemical IT, crystal_structure_mining | 3 Comments »

The solvation of ion pairs.

Thursday, November 6th, 2014

Solvolytic mechanisms are amongst the oldest studied, but reproducing their characteristics using computational methods has been a challenging business. This post was inspired by reading Steve Bachrach’s post, itself alluding to this aspect in the title “Computationally handling ion pairs”. It references this recent article on the topic[1] in which the point is made that reproducing the features of both contact and solvent-separated ion pairs needs a model comprising discrete solvent molecules (in this case four dichloromethane units) along with a continuum model.

The system is a methylated glucose with a triflate in the anomeric position, and the reaction is the ionisation of the triflate to form an oxenium cation and a triflate anion, this occurring in dichloromethane as solvent. The resulting ion pair can only be modelled if around four explicit solvent molecules are included in the model. The normal wisdom is that explicit hydrogen bonds are not replicated by a continuum solvent model. But relatively non-polar molecules such as dichloromethane are not normally thought of as strong hydrogen bond donors or acceptors. I thought I would take the geometries of the initial covalently bound triflate and the solvent-separated species as reported [1] and subject both to a non-covalent-interaction analysis (NCI). This analyses the electron density in the molecule, and converts a property of the second derivatives of that density into a colour-code surface. Here, blue emerges mostly for hydrogen bonds, whereas weaker interactions such as dispersion attraction emerge as green. The first such diagram relates to covalently bound triflate.
R

You can see from this that most of the NCI features are coded green; it is a typical dispersion map. Next, the solvent-separated ion-pair. There is a lot more (pale) blue. This indicates that explicit (albeit weak; strong H-bonds emerge as dark blue) hydrogen bond interactions are indeed set up. This in turn might explain why a simple continuum model does not properly account for this species.

SSIP

Because these are rather globular molecules, with the NCI features distributed internally, it is important that one views these interactively and not simply from one perspective in a static diagram. So do take the opportunity to click on the two images above to load such rotatable views. And then you can explore for yourself exactly where those blue regions occur, and whether you would have classified them as hydrogen bonds without the benefit of the NCI visualisation helping you! The lesson is that a zwitterionic molecule strongly polarises and hence strengthens any weak hydrogen bonds present, meaning they can no longer be dismissed.

References

  1. T. Hosoya, T. Takano, P. Kosma, and T. Rosenau, "Theoretical Foundation for the Presence of Oxacarbenium Ions in Chemical Glycoside Synthesis", The Journal of Organic Chemistry, vol. 79, pp. 7889-7894, 2014. https://doi.org/10.1021/jo501012s

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How to predict the regioselectivity of epoxide ring opening.

Sunday, April 28th, 2013

I recently got an email from a student asking about the best way of rationalising epoxide ring opening using some form of molecule orbitals. This reminded me of the famous experiment involving propene epoxide.[1]

propenoxide

In the presence of 0.3% NaOH, propene epoxide reacts with ethanol at the unsubstituted carbon (~82% compared with 56% in pure water, with retention of configuration at the other carbon) but in 1.3% H2SO4, the predominant product involves attack of ethanol at the more substituted carbon (presumably with inversion of configuration at that carbon). There are many ways of modelling this, but here I choose a simple one; inspecting the energy of the lowest unoccupied orbital (the one that will interact with the lone pair orbital on the incoming nucleophile). The issue is what kind of orbital that should be? The best to choose in this sort of situation is a localized orbital, an NBO in fact.

NaOH H2SO4
Energy

Energy 0.353 au
Energy

Energy -0.004 au

 
Energy

Energy 0.347 au

  
Energy

Energy -0.061 au

In NaOH solutions (where protonation of the epoxide oxygen is suppressed), the lowest energy unoccupied NBO is the O-C  σ* orbital involving the unsubstituted carbon, but where the oxygen is protonated, it now becomes the O-C σ* orbital involving the substituted carbon.

One can also teach a simpler heuristic, namely that protonation of the epoxide encourages the early formation of a carbocation, and that the most substituted such cation is the most stable. In the absence of protonation, some (small) contribution from an incipient alkoxy anion favours the alkoxide formed on the more stable carbon.

References

  1. H.C. Chitwood, and B.T. Freure, "The Reaction of Propylene Oxide with Alcohols", Journal of the American Chemical Society, vol. 68, pp. 680-683, 1946. https://doi.org/10.1021/ja01208a047

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Secrets of a university tutor: (curly) arrow pushing

Thursday, October 28th, 2010

Curly arrows are something most students of chemistry meet fairly early on. They rapidly become hard-wired into the chemists brain. They are also uncontroversial! Or are they? Consider the following very simple scheme.

Curly arrow pushing

It represents protonation of an alkene by an acid. Two products are of course possible, leading to either a tertiary carbocation as shown in (a), or a primary one (not shown). Either involves two arrows, but how to illustrate this (important) difference in the outcome using the arrows. Most textbooks show (a). The lhs arrow starts at the middle of the bond, and ends at the atom of hydrogen. This unfortunately leads to an ambiguity. It does not define which carbon is involved in forming the new C-H bond.

In recognition of this problem an article has recently appeared (DOI: 10.1021/ed086p1389) which attempts to improve model (a) by using what they call bouncing arrows, as in (b). The arrow starts at the mid point of the C=C bond, but then bounces to one end, before heading off to again to end at the H atom. The idea is that the direction of bounce informs which of the two possible bonds will be formed. Leaving aside the (non-trivial) issue of how to persuade e.g. ChemDraw to produce a bouncing arrow, I note that an alternative system has been in use where I teach for many years; (c).

  1. This starts by addressing the problem of which bond to form by immediately drawing a dotted line where you want the bond to go.
  2. The arrow starts as before, at the mid point of a bond, but this time it ends at the mid-point of the dotted line. If nothing else, Chemdraw has no problem with this notation!
  3. Are there any other advantages? Consider (d). The green dots indicate the results of a QTAIM analysis, revealing bond-critical points (BCP) in either the reactants or the products. The first arrow both starts and ends at such a BCP. The second arrow starts at a BCP, and ends at a lone pair (these are not revealed using QTAIM. If instead, ELF synaptic basin centroids were to be used, then all arrows would start or end at such a basin). This therefore gives (c)/(d) some quantum mechanical reality.
  4. Another advantage is that one can formulate check-sumrules. By this I mean extra rules that can be used to check you have gotten things correct. Take a look at the red dots, one on the oxygen, another on the bromine. The metaphor is that these can be regarded as hinges, about which the bond swivels, the course of the swivel following that of the trajectory of the arrow.
    1. For heterolytic (electron pair) arrow pushing in which none of the centres involved changes its valency, the red dots must be located on alternating atoms.
    2. For heterolytic (electron pair) arrow pushing in which a valency change does occur (e.g. formation of a carbene), two red dots must be on adjacent atoms.
    3. In general, no more than one arrow either starts, or ends, at a bond. This used to be thought of as a fairly hard rule, but in fact its not difficult to come up with reactions which break it. For example, this one, where as many as three arrows either start or end at a given bond. And, as a challenge, can you break the rule by formulating arrow pushing for the (concerted) reaction between an alkyne and a per-acid (avoiding the anti-aromatic oxirene, the ring opening of which may conflate with the peroxidation).
    4. One can interrupt the concerted flow of arrows to form intermediates along the way. One famous example of such interruption is aromatic electrophilic substitution, which can however be persuaded to move all of its arrows more or less synchronously.
  5. The metaphor now is one of doors opening and closing, rather than bouncing arrows.

There must be thousands of tutors around the world, teaching tens of thousands of students the arcane art of arrow pushing. If anyone has yet another schema for doing so, I would be delighted to hear from them.

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Conformational analysis of biphenyls: an upside-down view

Friday, April 2nd, 2010

One of the (not a few) pleasures of working in a university is the occasional opportunity that arises to give a new lecture course to students. New is not quite the correct word, since the topic I have acquired is Conformational analysis. The original course at Imperial College was delivered by Derek Barton himself about 50 years ago (for articles written by him on the topic, see DOI 10.1126/science.169.3945.539 or the original 10.1039/QR9561000044), and so I have had an opportunity to see how the topic has evolved since then, and perhaps apply some quantitative quantum mechanical interpretations unavailable to Barton himself.

The example I have chosen to focus on here is biphenyl (a derivative of which also happens to be the first structure shown by Barton in his 1970 Science article noted above), but modified with iso-electronic B/N substitution for carbon for a particular reason.

biphenylFour hydrogen atoms are highlighted in the above drawings by virtue of how close they might approach each-other, and what impact this will have on the conformation of each species. Such close approaches are normally defined with reference to the so-called van der Waals radius of the element concerned. For hydrogen, this radius is either 1.2Å (if the contact is to another hydrogen) or 1.1Å (if its to any other element, see DOI: 10.1021/jp8111556). An interpretation of this value is that the van der Waals attraction due to to dispersion or long range correlation effects reaches a maximum for two non-bonded hydrogen atoms at ~2.4Å. Significantly, a slightly closer approach than this value might still be mildly attractive, but it would be generally agreed that any distance less than ~2.1Å now represents a genuine repulsion between the hydrogens (see also this post). This represents a somewhat more quantitative judgement on what used to be called steric interactions.

With the scene set, let me introduce the results of a calculation (wB97XD/6-31G(d,p), a DFT method selected because it treats the long range correlation effects with a specific correction)

Conformational analysis of biphenyl 1

One can see here minima at ~45, 135, 225 and 315° for 1 (see DOI 10042/to-4853). Due to symmetry, the first and last are identical as are 2nd and 3rd, and the 1st and 2nd minima are in fact enantiomers of each other (the symmetry is D2, which is chiral). Two different transition states connect these minima, one with angles of 0/180 and the other slightly lower energy at 90/270°.

The non-bonded H…H distance are as follows: 1.95Å@0°, 2.39Å@45° and 3.54Å@90°. We may conclude that the first of these is repulsive, the second attractive and the third non interacting. Counterbalancing this effect is of course resonance due to π-π-overlaps across the central bond, which decreases to zero as the angle moves to 90°. The conformational minimum @45° is such because of the maximal H…H dispersion attraction and the still significant π-π-overlap. This brief analysis suggests however that these two effects are finely balanced, and so the next question is whether one might be able to perturb the system to distort the balance. The perturbation chosen is to replace one or two pairs of carbon atoms with the iso-electronic combination B+N.

The first perturbation is to replace the central rotating bond by a B-N combination 2 (DOI: 10042/to-4854).

Rotation about the B-N bond in 2

For this species, the H…H distances are 2.02Å@0°, 2.36Å@45° and 3.61Å@90°, the only significant difference with 1 emerging as the 0° conformation being around 1 kcal/mol lower relative to the other two. It is tempting to attribute this to the longer H…H separation for this rotamer in 2 due to the B-N bond being longer (1.562Å) than the C-C bond it replaced (1.496Å)

The next perturbation is to relocate the N/B pair as in 3 (DOI: 10042/to-4855). If one imagines that this will be a minor perturbation, take a look at the profile below.

Rotation about central C-C bond in 3.

The world has been turned upside down. What were transition states @0° and @180° are now minima and the reason is easy to find. The central C-C bond is now only 1.400Å long, having acquired substantial double bond character, and being accordingly very much more difficult to twist (the barrier being ~30 kcal/mol). The π-π-overlap has won out completely, and in the process has forced the H…H distance down to a presumably repulsive 1.918Å. The penalty for this is that the overall energy of 3 is some 22.8 kcal/mol higher than 2.

Added in proof (as the expression goes): If the above profile is conducted with full geometry optimization in a solvent field (water), which helps stabilise charge separations, the profile changes to the below. The solvation reduces the barrier to rotation considerably, the energy maxima now reveal a proper stationary point (rather than the cusp), the minima are very slightly non-planar, but the basic inversion of the potential energy surface compared to 1 or 2 is still observed.

Rotation about the C-C bond for 3, with solvation correction

The final perturbation is 4 (DOI: 10042/to-4856) with the following rotational profile. Another surprise:

Rotation about the central C-C bond in 4.

The H…H distances are 1.930Å@0°, 1.789/2.275Å@180°. The difference from 1 is that the hydrogens now have opposite polarity for the N-H (which is positive) and the B-H (which is negative). At the rotation angle of 0°, two H(+)…(-)H style dihydrogen bonds (see also this post) are established (these are presumed to be very attractive); at an angle of 180°, the H(+)…(+)H and H(-)…(-)H interactions are presumed to be very repulsive. The difference between the two is ~18 kcal/mol.

We have learnt that conformational analysis for molecules such as these is a fight between π-π-overlaps, which themselves can have unexpected outcomes, weak van der Waals dispersion interactions between “neutral” non-bonded hydrogen atoms, and strong electrostatic attractions and repulsions between “ionic” hydrogens. Now perhaps the reason for the choice of the wB97XD DFT method can be seen; it is capable (at least in theory) of balancing these forces properly.

So the world of conformational analysis can be turned upside down, and analysing what happens from this topsy-turvy viewpoint can teach a lot!

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