Posts Tagged ‘overall free energy’

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

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The SN1 Reaction- revisited

Wednesday, November 11th, 2009

In an earlier post I wrote about the iconic SN1 solvolysis reaction, and presented a model for the transition state involving 13 water molecules. Here, I follow this up with an improved molecule containing 16 water molecules, and how the barrier for this model compares with experiment. This latter is nicely summarized in the following article: Solvolysis of t-butyl chloride in water-rich methanol + water mixtures, which (for pure water) cites the following activation parameters

  • ΔH†283 = 23.0 kcal/mol
  • ΔG†283 = 19.7 kcal/mol
  • ΔS†283 = +11.1 cal/mol/K

But first, a word about how this new transtion state has been obtained. The DFT treatment used is quite standard (B3LYP/6-31G(d) ), and one can indeed locate a transition state using just this approach (this is how the previous model was obtained). One has to work very hard to orient the starting guess for the geometry so that as many hydrogen bonds between the waters themselves, and to the substrate, are created. The previous model took quite a few guesses and attempts! The solvent in such a model is simulated by the explicit water molecules themselves. Of course, the quality of the solvent then depends on how many water molecules are used. A proper solvent field using explicit water molecules is thought to require 100s of water molecules! But a reasonable approximation/compromise may well be 13.

So how can the model be improved? Well, in many ways, some of which include treating the dynamics of the system. But I will stick just to two.

  1. Firstly, we assume that the water molecules are used to form a bridge between the incoming nucleophile (another water) and the leaving group (the chloride). In the previous model, two such bridges were constructed using the 13 water molecules. But in fact, there is still space between two of the methyl groups to construct a third bridge. This takes the total solvent molecules to 16.
  2. Solvent can also be modelled as a continuum, in which a cavity which the substrate occupies is surrounded by a field generated by the continuum solvent. The problem with these cavity approaches in the past has been that it is not easy to optimize the geometry of the molecule contained within the cavity. Because the cavity was constructed by tesselation, the first derivatives of the energy of the molecule within the cavity were not regular, and as a result, geometry optimization (and particularly transition state optimization) would frequently meander and fail to converge. Darrin York and Martin Karplus came to the rescue (some time ago, it has to be said, DOI: 10.1021/jp992097l) by formulating a smoothed out solvation cavity where the first (and second derivatives) are stable and well behaved. This new algorithm has now been implemented in Gaussian09, and it now allows really easy transition state location within a solvent cavity

The result of this optimization is shown below (and can be seen in original form at the following DOI: 10042/to-2894).

Transition state for Sn1 solvolysis of tert-butyl chloride

Transition state for Sn1 solvolysis of tert-butyl chloride. Click for animation.

The model has not changed that much compared to before. The reaction (imaginary) mode still clearly shows formation of the C-O bond and cleavage of the C-Cl bond. Also as before, there is a lot of motion of the methyl groups, as the forming cation induces stereo-electronic alignment with the adjacent C-H bonds (and which explains the large secondary deuterium isotope effects measured for this reaction, kH/kD (298) = 2.39, see DOI: 10.1021/ja01080a004). The hydrogen bonding pattern is also retained (despite the surrounding solvent field!). But what of the predicted activation parameters

  • ΔH†298 = 17.4 kcal/mol
  • ΔG†298 = 18.7 kcal/mol
  • ΔS†298 = -4.4 cal/mol/K

The overall free energy is in great agreement with experiment! But the entropy is the wrong sign!! The calculation is predicting that the transition state is more rigid than the reactant. One can see how this might happen, since the greater ionic character produces very much stronger hydrogen bonds, which strengthen the three solvent bridges. It may be simply that the rigid-rotor-harmonic-oscillator approximation breaks down horribly for the entropy in this calculation. But it is encouraging that the activation barrier is reproducing experiment, which suggests the model cannot be completely wrong!

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