Posts Tagged ‘energy barrier’

What’s in a name? Carbenes: a reality check.

Sunday, September 11th, 2016

To quote from Wikipedia: in chemistry, a carbene is a molecule containing a neutral carbon atom with a valence of two and two unshared valence electrons. The most ubiquitous type of carbene of recent times is the one shown below as 1, often referred to as a resonance stabilised or persistent carbene. This type is of interest because of its ability to act as a ligand to an astonishingly wide variety of metals, with many of the resulting complexes being important catalysts. The Wiki page on persistent carbenes shows them throughout in form 1 below, thus reinforcing the belief that they have a valence of two and by implication six (2×2 shared + 2 unshared) electrons in the valence shell of carbon. Here I consider whether this name is really appropriate.

carbenes

Let us start by counting the electrons in the 2p atomic orbitals on the ring atoms of 1, forming what we call a π-system. There are six; two from the carbons shown connected by a double bond, C=C and a further four from the two nitrogen lone pairs. Now in benzene, we also have six π-electrons in a ring and this molecule is of course famously aromatic due to the diatropic ring current created by the circulation of these six electrons. Moreover, all the C-C bonds are equal in length, ~1.4Å long (although the reasons for this equality are subtle).

So does 1 behave similarly? A ωB97XD/Def2-TZVPP calculation[1] shows the following calculated structure, in which all the bonds are clearly intermediate between single and double. The N-C(“carbene”) length of 1.357Å in particular is much shorter than a C-N single bond (~1.44AÅ), which tends to suggest that the resonance form 2 is a better representation than 1. This form is also pretty similar to pyrrole, itself a well-known hetero-aromatic species.nhc1

An alternative reality check is crystal structures. There are 42 examples (no errors, no disorder, R < 0.05) in the Cambridge structure database (CSD) and the distribution of C-N bond lengths below is indeed quite similar to the calculation shown above for the unsubstituted parent, with the lhs “hot-spot” almost exactly coincident. The C-C length similarly corresponds.

nhc2

nhc3

Let us try a technique for explicitly counting electrons, the ELF (electron localisation method), which works directly on a function of the electron density to identify the centroids of localized “basins” containing the integrated density. The three surrounding the “carbene” atom sum to 7.54e (with small seepage also into the carbon 1s core; 2.08e). A “normal” carbon on the C=C bond is 7.65e. The localization below turns out to closely resemble resonance structure 2 above.

nhc4

Further in-silico experiments can be carried out with species 3 and 4, in which a carbon atom replaces each of the nitrogens. This reduces the total electron count by two and now this poor molecule has a difficult choice to make. Should it be the π-system that sacrifices these two electrons, or could it be the σ-lone-pair found on the two-coordinate carbon? We will let the quantum mechanical solution decide[2] (with a constraint that the molecule be planar). The electrons arrange themselves to resemble the resonance form 4, choosing to retain the six π-electrons and sacrifice the carbene “unshared pair”. The 2-coordinate carbon as a vinyl cation now does have ~6 valence electrons (ELF indicates 5.23e). nhc5

What about the other choice? By promoting two electrons from HOMO to LUMO one can also calculate 3 (again constrained to planarity)[3] which finally does correspond to the classical description of a carbene.

nhc6

The arrow connecting 3 and 4 in the scheme at the top is NOT in this case an electronic resonance, but a a real equilibrium between two different species separated by an energy barrier. With only four π-electrons in a cycle it is also antiaromatic, and so the two localised alkene bonds avoid any conjugation with each other. This form has a free energy some 5.7 kcal/ml higher than the aromatic form. In fact, the molecule is very keen to avoid all antiaromaticity and hence if the planar constraint is lifted, it will distort with no activation to a non-planar diene (just as cyclo-octatetraene does to a non-planar tetra-ene). And to complete the tale, even though 4 is aromatic, it too distorts without activation to an odd-looking non-planar form with no symmetry[4],[5],[6] (but that is another story).

The final word should be that the naming of these types of persistent carbene does need a reality check; they should not be called this at all! They are really dipolar species or carbon-ylides as shown in 2. As it happens, a very closely related species in which one sulfur replaces one nitrogen is a very familiar compound, vitamin B1 or thiamine. The only example of a stable deprotonated thiamine derivative is referred to as a carbene[7], perhaps because with an acid catalyst it can dimerise in the manner expected of a real carbene. Significantly however, without acid catalyst this does not happen; a true carbene would not require such a catalyst.

References

  1. H. Rzepa, "NHC wfn", 2016. https://doi.org/10.14469/hpc/1473
  2. H. Rzepa, "butadiene carbene aromatic -192.700746", 2016. https://doi.org/10.14469/hpc/1581
  3. H. Rzepa, "butadiene carbene antiaromatic guess=alter -192.691607", 2016. https://doi.org/10.14469/hpc/1582
  4. H. Rzepa, "C5H4 non-planar, Cs symmetry", 2016. https://doi.org/10.14469/hpc/1583
  5. H. Rzepa, "C5H4 non-planar, C2 symmetry", 2016. https://doi.org/10.14469/hpc/1584
  6. H. Rzepa, "C5H4 non-planar, no symmetry", 2016. https://doi.org/10.14469/hpc/1585
  7. A.J. Arduengo, J.R. Goerlich, and W.J. Marshall, "A Stable Thiazol‐2‐ylidene and Its Dimer", Liebigs Annalen, vol. 1997, pp. 365-374, 1997. https://doi.org/10.1002/jlac.199719970213

Tags:, , , , , , , , , , , , ,
Posted in crystal_structure_mining, General | No Comments »

What's in a name? Carbenes: a reality check.

Sunday, September 11th, 2016

To quote from Wikipedia: in chemistry, a carbene is a molecule containing a neutral carbon atom with a valence of two and two unshared valence electrons. The most ubiquitous type of carbene of recent times is the one shown below as 1, often referred to as a resonance stabilised or persistent carbene. This type is of interest because of its ability to act as a ligand to an astonishingly wide variety of metals, with many of the resulting complexes being important catalysts. The Wiki page on persistent carbenes shows them throughout in form 1 below, thus reinforcing the belief that they have a valence of two and by implication six (2×2 shared + 2 unshared) electrons in the valence shell of carbon. Here I consider whether this name is really appropriate.

carbenes

Let us start by counting the electrons in the 2p atomic orbitals on the ring atoms of 1, forming what we call a π-system. There are six; two from the carbons shown connected by a double bond, C=C and a further four from the two nitrogen lone pairs. Now in benzene, we also have six π-electrons in a ring and this molecule is of course famously aromatic due to the diatropic ring current created by the circulation of these six electrons. Moreover, all the C-C bonds are equal in length, ~1.4Å long (although the reasons for this equality are subtle).

So does 1 behave similarly? A ωB97XD/Def2-TZVPP calculation[1] shows the following calculated structure, in which all the bonds are clearly intermediate between single and double. The N-C(“carbene”) length of 1.357Å in particular is much shorter than a C-N single bond (~1.44AÅ), which tends to suggest that the resonance form 2 is a better representation than 1. This form is also pretty similar to pyrrole, itself a well-known hetero-aromatic species.nhc1

An alternative reality check is crystal structures. There are 42 examples (no errors, no disorder, R < 0.05) in the Cambridge structure database (CSD) and the distribution of C-N bond lengths below is indeed quite similar to the calculation shown above for the unsubstituted parent, with the lhs “hot-spot” almost exactly coincident. The C-C length similarly corresponds.

nhc2

nhc3

Let us try a technique for explicitly counting electrons, the ELF (electron localisation method), which works directly on a function of the electron density to identify the centroids of localized “basins” containing the integrated density. The three surrounding the “carbene” atom sum to 7.54e (with small seepage also into the carbon 1s core; 2.08e). A “normal” carbon on the C=C bond is 7.65e. The localization below turns out to closely resemble resonance structure 2 above.

nhc4

Further in-silico experiments can be carried out with species 3 and 4, in which a carbon atom replaces each of the nitrogens. This reduces the total electron count by two and now this poor molecule has a difficult choice to make. Should it be the π-system that sacrifices these two electrons, or could it be the σ-lone-pair found on the two-coordinate carbon? We will let the quantum mechanical solution decide[2] (with a constraint that the molecule be planar). The electrons arrange themselves to resemble the resonance form 4, choosing to retain the six π-electrons and sacrifice the carbene “unshared pair”. The 2-coordinate carbon as a vinyl cation now does have ~6 valence electrons (ELF indicates 5.23e). nhc5

What about the other choice? By promoting two electrons from HOMO to LUMO one can also calculate 3 (again constrained to planarity)[3] which finally does correspond to the classical description of a carbene.

nhc6

The arrow connecting 3 and 4 in the scheme at the top is NOT in this case an electronic resonance, but a a real equilibrium between two different species separated by an energy barrier. With only four π-electrons in a cycle it is also antiaromatic, and so the two localised alkene bonds avoid any conjugation with each other. This form has a free energy some 5.7 kcal/ml higher than the aromatic form. In fact, the molecule is very keen to avoid all antiaromaticity and hence if the planar constraint is lifted, it will distort with no activation to a non-planar diene (just as cyclo-octatetraene does to a non-planar tetra-ene). And to complete the tale, even though 4 is aromatic, it too distorts without activation to an odd-looking non-planar form with no symmetry[4],[5],[6] (but that is another story).

The final word should be that the naming of these types of persistent carbene does need a reality check; they should not be called this at all! They are really dipolar species or carbon-ylides as shown in 2. As it happens, a very closely related species in which one sulfur replaces one nitrogen is a very familiar compound, vitamin B1 or thiamine. The only example of a stable deprotonated thiamine derivative is referred to as a carbene[7], perhaps because with an acid catalyst it can dimerise in the manner expected of a real carbene. Significantly however, without acid catalyst this does not happen; a true carbene would not require such a catalyst.

References

  1. H. Rzepa, "NHC wfn", 2016. https://doi.org/10.14469/hpc/1473
  2. H. Rzepa, "butadiene carbene aromatic -192.700746", 2016. https://doi.org/10.14469/hpc/1581
  3. H. Rzepa, "butadiene carbene antiaromatic guess=alter -192.691607", 2016. https://doi.org/10.14469/hpc/1582
  4. H. Rzepa, "C5H4 non-planar, Cs symmetry", 2016. https://doi.org/10.14469/hpc/1583
  5. H. Rzepa, "C5H4 non-planar, C2 symmetry", 2016. https://doi.org/10.14469/hpc/1584
  6. H. Rzepa, "C5H4 non-planar, no symmetry", 2016. https://doi.org/10.14469/hpc/1585
  7. A.J. Arduengo, J.R. Goerlich, and W.J. Marshall, "A Stable Thiazol‐2‐ylidene and Its Dimer", Liebigs Annalen, vol. 1997, pp. 365-374, 1997. https://doi.org/10.1002/jlac.199719970213

Tags:, , , , , , , , , , , , ,
Posted in crystal_structure_mining, General | No Comments »

The mechanism of silylether deprotection using a tetra-alkyl ammonium fluoride.

Wednesday, May 25th, 2016

The substitution of a nucleofuge (a good leaving group) by a nucleophile at a carbon centre occurs with inversion of configuration at the carbon, the mechanism being known by the term SN2 (a story I have also told in this post). Such displacement at silicon famously proceeds by a quite different mechanism, which I here quantify with some calculations.

Trialkylsilyl is often used to protect OH groups, and as shown in the diagram above is specifically used to enforce the enol form of a ketone by replacing the OH with OTMS. The TMS can then be removed when required by utilising nucleophilic addition of e.g. fluoride anion from tetra-alkyl ammonium fluoride to form a 5-coordinate silicon intermediate, followed by collapse of this intermediate with expulsion of the oxygen to form an enolate anion. Before starting the calculations, I searched the crystal structure database for examples of R3SIF(OR), as in the search query below.

There were 55 instances of such species, and show below are their geometric characteristics. In all cases, the two electronegative substituents occupy the axial positions of a trigonal bipyramidal geometry. This of course is the orientation adopted by the two electronegative substituents in the SN2 mechanism for carbon, but with silicon this carbon "transition state" can be replaced by a stable (and as we see often crystalline) intermediate!

Turning to calculations (ωB97XD/6-31+G(d)/SCRF=thf), one can locate three transition states for the silicon process (there is only one for the SN2 reaction with carbon).

  1. TS1 represents attack of fluoride anion along the axial position of the forming 5-coordinate silicon.[1],[2] The oxygen in this instance occupies an equatorial position, and this close proximity between the incoming F(-) and the about to depart OR groups represents a retention of configuration at the Si. Note that the reaction is endo-energic. (c.f. [3]).


  2. The next step, TS2[4],[5]  is to move the F ligand to an equatorial position and the OR group from equatorial to its own axial position so that it can depart in the manner the F adopted to arrive. This requires what is called a Berry pseudorotation, an essentially isoenergic process.



    You might note a "hidden intermediate" at IRC ~-7 (the "bump" in the energy profile). This is caused by re-organisation of the ion-pair geometry, with the tetra-alkyl ammonium cation moving its orientation.
  3. TS3[6],[7] now eliminates the –OR group to complete the deprotection.


The free energies are summarised below. Key points include:

  1. The overall free energy of deprotection is appropriately exo-energic.
  2. The highest energy barrier is actually for pseudo-rotation! This suggests that tuning the deprotection with alternative alkyl or aryl groups on the silicon may be a matter of controlling the Berry pseudorotation process.
  3. TS1-3 proceed with the attacking and leaving groups in close proximity (the angle between an axial and an equatorial group is ~90° of course, whereas for a di-axial relationship (the inversion of the SN2 mechanism) it is instead 180°. This close proximity of nucleophile and nucleofuge minimises the required reorganisation of the ammonium counter-ion in the ion-pairs, and possibly also the dipole moments induced by the reactions, the changes of which for the three reactions are shown below:


  4. The 5-coordinate intermediate where both F and O are axial is in fact significantly lower in energy (a cooperative effect) than when only one of them is axial, which matches the orientations identified above in the 55 crystal structures. For a substitution to occur, the cooperative strengthening of the Si-O and Si-F bonds must be removed; hence the retention of configuration.
System Relative free energy DataDOI
Reactants 0.0 [8]
TS1 7.9 [1]
Int F(ax), O(eq) 5.1 [9]
TS2 10.2 (9.2)* [4]
Int F(eq), O(ax) 5.1 [10]
TS3 5.2 [6]
Products -4.0 [11]
Int F,O(ax) -2.5 [12]

*A lower energy orientation of the ion-pair has subsequently been found.[13]

This analysis shows just how different the carbon and the silicon substitution reactions are and how it is the pseudorotation interconverting two 5-coordinate intermediates that appears to be a key step. But questions remain unanswered. What is the energy of the pseudorotation interconverting an intermediate with ax/eq electronegative groups to one with di-axial electronegative groups? Are there transition states starting from the diaxial intermediate and resulting in elimination, and if so what are their relative energies? I leave answers to a follow up post. 

References

  1. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate F axial TS", 2016. https://doi.org/10.14469/hpc/554
  2. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate F axial TS IRC", 2016. https://doi.org/10.14469/hpc/564
  3. L. Wozniak, M. Cypryk, J. Chojnowski, and G. Lanneau, "Optically active silyl esters of phosphorus. II. Stereochemistry of reactions with nucleophiles", Tetrahedron, vol. 45, pp. 4403-4414, 1989. https://doi.org/10.1016/s0040-4020(01)89077-3
  4. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate Berry pseudorotation TS", 2016. https://doi.org/10.14469/hpc/551
  5. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate Berry pseudorotation TS IRC", 2016. https://doi.org/10.14469/hpc/553
  6. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) TS", 2016. https://doi.org/10.14469/hpc/539
  7. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) TS IRC", 2016. https://doi.org/10.14469/hpc/552
  8. H. Rzepa, "enol + Me4N(+).F(-) Reactant", 2016. https://doi.org/10.14469/hpc/565
  9. H. Rzepa, "enol + Me4N(+).F(-) 5-coordinate intermediate F axial", 2016. https://doi.org/10.14469/hpc/555
  10. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate", 2016. https://doi.org/10.14469/hpc/540
  11. H. Rzepa, "enol + Me4N(+).F(-) Product", 2016. https://doi.org/10.14469/hpc/563
  12. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate F/O axial", 2016. https://doi.org/10.14469/hpc/550
  13. H. Rzepa, "5-coordinate intermediate Berry pseudorotation TS2 New conf?", 2016. https://doi.org/10.14469/hpc/577

Tags:, , , , , , , , , , , , , , ,
Posted in reaction mechanism | No Comments »

Thalidomide. The role of water in the mechanism of its aqueous racemisation.

Saturday, November 10th, 2012

Thalidomide is a chiral molecule, which was sold in the 1960s as a sedative in its (S,R)-racemic form. The tragedy was that the (S)-isomer was tetragenic, and only the (R) enantiomer acts as a sedative. What was not appreciated at the time is that interconversion of the (S)- and (R) forms takes place quite quickly in aqueous media. Nowadays, quantum modelling can provide good in-silico estimates of the (free) energy barriers for such processes, which in this case is a simple keto-enol tautomerism. In a recently published article[1], just such a simulation is reported. By involving two explicit water molecules in the transition state, an (~enthalpic) barrier of 27.7 kcal/mol was obtained. The simulation was conducted just with two water molecules acting as solvent, and without any additional continuum solvation applied. So I thought I would re-evaluate this result by computing it at the ωB97XD/6-311G(d,p)/SCRF=water level (a triple-ζ basis set rather than the double-ζ used before[1]), and employing a dispersion-corrected DFT method rather than B3LYP.

Keto-enol tautomerisation occupies a unique position in the history of mechanistic chemistry[2]. In 1889, Beckmann got the whole field rolling by proposing an inferred enol intermediate (which he did not observe) to explain the isomerism of menthone to iso-menthone in conc. sulfuric acid. In modelling the enolisation of thalidomide, I have used both implicit and explicit solvents acting in a self-consistent manner. This approach is not yet much adopted in the wider literature[3]. I have deployed it extensively in this blog as an encouragement to others (selected examples are listed at the bottom of this post). It is worth noting at the outset that the transition state reported previously[1] has a computed dipole moment of ~10D. My experience[3] suggests that any geometry with a dipole moment of this magnitude (or greater) is likely to relax when placed into a continuum field, and this relaxation becomes an important perturbation of both the computed geometry of the transition state and the intrinsic reaction coordinate profile computed from that starting point.

The (re)computed geometry of the aqueous transition state for enolisation of thalidomide is shown below, and for which the entropy-corrected ΔG†298 is 31.0 kcal/mol (the barrier for the prototypical enolisation of propanone is computed as 34.4 kcal/mol). The value in the literature[1] is given as 27.7 kcal/mol for the zero-point-energy corrected total energy barrier, but this value notably does NOT include any entropic corrections. The measured literature value for ΔG†298 is reported as 24.3 kcal/mol at pH 8, a value which probably also includes contributions from both the pure water catalysed route and those from hydroxide anion catalysis (see below). At this point, I should remind that the free energy of activation for a bi- or termolecular reaction in solution must be obtained by correcting the value obtained for a standard state of 1 atmosphere (the state used for the value quoted above). According to Alvarez-Idaboy and co-workers[4], this amounts to a total correction of -4.5 kcal/mol for a bimolecular reaction, and -8.73 kcal/mol for a termolecular reaction. Where one of the components of a termolecular reaction is also the solvent, these corrections probably need to be themselves reduced. But this does achieve a reduction in the computed value of 31.0 kcal/mol to something quite close to the experimental value! 

Aqueous transition state for enolisation of thalidomide. Click for 3D.

Next, I want to consider the base-catalysed enolisation pathway. As with the reaction of dichlorobuteneone with tolyl-thiolate about which I wrote in another post, the authors of the thalidomide study[1] modelled this route by introducing a solvated hydroxide anion, “OH–·H2O” into the structure without any accompanying counter-ion. In other words, their total system has an overall negative charge. I argued before, and I argue again here, that there is no real need to have to do this. Why not for example introduce NaOH•H2O instead? One might argue that the cationic counter-ion so introduced cannot be properly modelled, but the combination of explicit first-sphere water molecules coupled with a continuum model actually handles these counter-ions reasonably well. So may I introduce you to my version of the base-catalysed reaction, involving a contact-ion-pair:

Base-catalysed (NaOH) enolisation of thalidomide. Click for 3D.

This has ΔG†298 4.7 kcal/mol, much lower than the neutral water catalysed reaction. This value is of course for a standard state for [Na+OH–] (1 atm). At pH 8, [OH–] is at least six orders of magnitude less, which may rationalise why the experimental rate is so much slower than this barrier might imply. The IRC corresponds to proton transfer.

I would like to end by noting that many mechanisms which would otherwise involve the development of charge-separation may well borrow a protic solvent molecule in the manner shown here to reduce the degree of charge-separation needed.  Further examples of this are listed below.

  1. Oxime formation from hydroxylamine and ketone. Part 2: Elimination.
  2. Oxime formation from hydroxylamine and ketone: a (computational) reality check on stage one of the mechanism.
  3. Transition state models for Baldwin dig(onal) ring closures.
  4. Transition state models for Baldwin’s rules of ring closure.
  5. The mechanism (in 4D) of the reaction between thionyl chloride and a carboxylic acid.
  6. Mechanism of the diazomethane alkylation of a carboxylic acid.
  7. The mechanism of the Baeyer-Villiger rearrangement.
  8. Stereoselectivities of Proline-Catalyzed Asymmetric Intermolecular Aldol Reactions.
  9. Secrets of a university tutor: tetrahedral intermediates.

References

  1. C. Tian, P. Xiu, Y. Meng, W. Zhao, Z. Wang, and R. Zhou, "Enantiomerization Mechanism of Thalidomide and the Role of Water and Hydroxide Ions", Chemistry – A European Journal, vol. 18, pp. 14305-14313, 2012. https://doi.org/10.1002/chem.201202651
  2. E. Beckmann, "Untersuchungen in der Campherreihe", Justus Liebigs Annalen der Chemie, vol. 250, pp. 322-375, 1889. https://doi.org/10.1002/jlac.18892500306
  3. J. Kong, P.V.R. Schleyer, and H.S. Rzepa, "Successful Computational Modeling of Isobornyl Chloride Ion-Pair Mechanisms", The Journal of Organic Chemistry, vol. 75, pp. 5164-5169, 2010. https://doi.org/10.1021/jo100920e
  4. J.R. Alvarez-Idaboy, L. Reyes, and J. Cruz, "A New Specific Mechanism for the Acid Catalysis of the Addition Step in the Baeyer−Villiger Rearrangement", Organic Letters, vol. 8, pp. 1763-1765, 2006. https://doi.org/10.1021/ol060261z

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