Posts Tagged ‘similar energy’

The roles of water in the hydrolysis of an acetal.

Wednesday, November 18th, 2015

In the previous post, I pondered how a substituent (X below) might act to slow down the hydrolysis of an acetal. Here I extend that by probing the role of water molecules in the mechanism of acetal hydrolysis.

acetal1

Water molecules can participate in three ways:

  1. One water acts as a nucleophile to replace one of the oxygen atoms of the acetal
  2. n waters in total participate in a proton transfer relay, in which a proton from the acid used to protonate one oxygen in the acetal is counterbalanced by another removed by a cooperating water.
  3. m waters serve as a stabilizer via hydrogen bonding. 
  4. Water can also be modelled as a continuum dielectric solvent.

My previous model included just one explicit water molecule (n=1) participating in 1 and 2 above (but not via 3) + the continuum model 4; the objective then being to study variation in X. I noted that the resulting barriers to reaction were too high for a facile thermal reaction; the model had to be incomplete. Here the objective is to probe the consequences of various deployments of up to four water molecules in this mechanism (X=R=H) to see if the model can be improved.

n m ΔE, kcal/mol ΔG‡ DataDOI
1 0 38.4 38.2 [1]
2 0 36.5 34.1 [2],[3],[3]
3 0 32.1 30.4 [4],[5][6]
4 0 28.1 29.9 [7],[8],[5]
3 1 29.8 29.5 [9],[8],[10]
2 2 30.5 31.3 [11],[8],[12]
1 3 26.9 29.7 [13],[8],[14]

The energies shown above generally show that water molecules are almost as happy when participating in a (cyclic) proton relay as when (passively) solvating the acid. This is probably in part at least because a cyclic proton transfer relay cross-polarises adjacent waters, increasing their own hydrogen bond strengths. Nevertheless, with four water molecules, the possible arrangements in the table above are all in fact quite similar in energy, suggesting that the actual system is a complex dynamic one involving many states of similar energy. A proper molecular-dynamics based sampling of these and other states is probably needed to construct the most realistic model. The extended four-water model results in a lowering of the predicted barrier by ~9-10 kcal/mol to become a more reasonable value for a thermal reaction, perhaps appropriate for catalysis by a relatively weak acid such as acetic. The improvement in part may be because the linear requirement for an Sn2 displacement is more easily accommodated by the larger rings created by using more water molecules.

Click for 3D

Click for 3D

An intrinsic reaction coordinate (IRC) is also instructive, shown as the gradient normal along the IRC. The features are as follows:

  1. IRC ~8, the water molecules are reorganising themselves ready for the proton relay
  2. IRC 2, a dip in the gradient norm reveal a hidden intermediate corresponding to the first proton transfer to the oxygen of the acetal.
  3. IRC 0 is of course the transition state
  4. IRC -2 corresponds to a dip for the second proton transfer
  5. IRC -3 to -4 the third and fourth proton transfers occur, showing that they are sequential rather than synchronous.

3+0G

3+0a

This examples shows how modelling using transition state theory can yield reasonably realistic answers, but also that the next step in computational modelling, reaction dynamics, is probably needed to properly explore the statistical aspects of mechanism.

References

  1. H.S. Rzepa, "C 6 H 14 O 5", 2015. https://doi.org/10.14469/ch/191581
  2. H.S. Rzepa, and H.S. Rzepa, "C 6 H 16 O 6", 2015. https://doi.org/10.14469/ch/191599
  3. H.S. Rzepa, "C6H16O6", 2015. https://doi.org/10.14469/ch/191600
  4. H.S. Rzepa, "C 6 H 18 O 7", 2015. https://doi.org/10.14469/ch/191601
  5. https://doi.org/
  6. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191606
  7. H.S. Rzepa, and H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191607
  8. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191604
  9. H.S. Rzepa, "C6H20O8", 2015. https://doi.org/10.14469/ch/191610
  10. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191603
  11. H.S. Rzepa, "C6H20O8", 2015. https://doi.org/10.14469/ch/191605
  12. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191609
  13. H.S. Rzepa, "C6H20O8", 2015. https://doi.org/10.14469/ch/191621

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How many water molecules does it take to ionise HCl?

Saturday, February 14th, 2015

According to Guggemos, Slavicek and Kresin, about 5-6![1]. This is one of those simple ideas, which is probably quite tough to do experimentally. It involved blasting water vapour through a pinhole, adding HCl and measuring the dipole-moment induced deflection by an electric field. They found “evidence for a noticeable rise in the dipole moment occurring at n≈5–6“.

Modelling the structures takes little time. So here are some ωB97XD/6-311++G(2d,2p) gas phase models. I state at the outset that these are not dynamic-stochastic models, averaged over many conformations, but a static picture of individual poses. As usual, click on individual images to obtain an interactive 3D model (Java required).‡

n=1.[2] Dipole moment 3.7D

hcl+1h2o

n=2.[3] Dipole moment 2.4D. Note how the O…H bond becomes shorter.

hcl+2h2o

n=3.[4] Dipole moment 2.5D. Note how the key O..H bond is contracting rapidly, as are the other H-bond interactions. This is the cyclic polarisation effect, where each bond influences the others. We are starting to approach the formation of H3O+ and Cl–!

hcl+3h2o

n=4.[5] Dipole moment 2.3 D, We have two ways to add the next water molecule, firstly to try to stabilise the H3O+. Nope.

hcl+4h2o

n=4,[5] Dipole moment 1.1 D. Better by solvating the Cl–! The proton originally attached to the Cl is now starting its transfer to the water to form that hydronium cation, but the dipole moment is not yet large.

hcl+4h2o1

n=5.[6] Dipole moment 4.7D. The ionisation is almost complete and the dipole moment is on the increase.

5

n=6.[7] The dipole moment is up to 8.2D and the three H-O bonds of the hydronium cation are almost all equal in length.

6

A cautionary observation though. The isomer below for n=6[8] is lower in energy by ΔG -1.2 kcal/mol, and its dipole moment is only 2.5D! The charges (summed onto heavy atoms) show the chloride to have -0.88 and the hydronium cation +0.88, so it is a true ion-pair, despite its dipole moment.

6a

So these calculations do indeed appear to confirm that 5-6 water molecules are required to ionise HCl. But it does raise the interesting issue that even for n=6, there are poses for the assembly which have low dipole moments. Clearly of course the observed dipole moment is a dynamic average over many conformations of similar energy but the prediction that some of these may have low dipole moments should be noted.

‡ If you right-click in the 3D model area, you can bring down a list of vibrational modes for each complex from the first item of the pop-up menu that appears (labelled model). You might wish to e.g. explore how the H-Cl stretch vibration changes as the ionisation increases.

References

  1. N. Guggemos, P. Slavíček, and V.V. Kresin, "Electric Dipole Moments of Nanosolvated Acid Molecules in Water Clusters", Physical Review Letters, vol. 114, 2015. https://doi.org/10.1103/physrevlett.114.043401
  2. H.S. Rzepa, "H 3 Cl 1 O 1", 2015. https://doi.org/10.14469/ch/189758
  3. H.S. Rzepa, "H 5 Cl 1 O 2", 2015. https://doi.org/10.14469/ch/189760
  4. H.S. Rzepa, "H 7 Cl 1 O 3", 2015. https://doi.org/10.14469/ch/189759
  5. H.S. Rzepa, "H 9 Cl 1 O 4", 2015. https://doi.org/10.14469/ch/189763
  6. H.S. Rzepa, "H 11 Cl 1 O 5", 2015. https://doi.org/10.14469/ch/189756
  7. H.S. Rzepa, "H 13 Cl 1 O 6", 2015. https://doi.org/10.14469/ch/189761
  8. H.S. Rzepa, "H 13 Cl 1 O 6", 2015. https://doi.org/10.14469/ch/189764

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Dial a molecule: Can new reactions be designed by computer?

Saturday, March 13th, 2010

One future vision for chemistry over the next 20 years or so is the concept of having machines into which one dials a molecule, and as if by magic, the required specimen is ejected some time later. This is in some ways an extrapolation of the existing peptide and nucleotide synthesizer technologies and sciences. A pretty significant extrapolation, suitable no doubt for a grand future challenge in chemistry (although the concept of tumbling a defined collection of atoms in a computer model and seeing what interesting molecules emerge, dubbed with some sense of humour as mindless chemistry, is already being done; see DOI: 10.1021/jp057107z).

A possible carbene transfer reagent

Well, let us return to present day reality (I know it was a little unfair to capture your attention with such a grand title!). Consider the sequence above. Sulfenes are known simple elaborations of sulfur trioxide, with one oxygen replaced by a CH2 group. They can exist as isomeric rings, known as sultines (and which are of similar energy to the sulfenes, see DOI: 10.1016/j.theochem.2007.10.035). Few people have speculated upon what might be done with this small collection of atoms. It struck me (I am unaware it has struck anyone else, but I am happy to be corrected) that it might be useful as a reagent for delivering a carbene. The precedent is that oxaziridines (in which the SO unit is replaced by e.g. NR) can be used to transfer either oxygen or NR to alkenes, and dioxiranes (in which the SO unit is replaced by an oxygen) are very useful reagents for oxygen transfer to an alkene. In the example of the sultine, loss instead of carbene (CH2) would result in the thermodynamically stable sulfur dioxide. Also apparent is that the sultine is asymmetric (chiral) and so perhaps there is also a prospect of delivering that carbene asymmetrically (a reaction normally done with the help of metal catalysts). As shown above, the carbene is also nucleophilic, rather than electrophilic, which may also be useful in some contexts.

Enter the computer, which will be used to see if these simple ideas can be turned into the design of a new reaction. Firstly, the assertion that the reaction producing cyclopropane and sulfur dioxide is exothermic is easily tested (B3LYP/cc-pVTZ); it comes out as exothermic in free energy by -26.6 kcal/mol (some of which of course is due to entropy). Next, the transition state for the delivery.

Transition state for carbene transfer from sulfine

This emerges (DOI: 10042/to-4476) with a free energy barrier of 37.4 kcal/mol relative to the sultine. Rather too high a barrier to constitute a useful synthetic reaction! But there is something interesting to be learnt from this transition state. Whilst the product is clearly cyclopropane and sulfur dioxide, the reactant is not the sultine but appears to be another species, labelled above as the 1,3 dipole (DOI: 10042/to-4487), a species which is 13 kcal/mol higher in free energy than the sultine itself (but does it have to be formed first, or is it merely on the reaction path?). There are other noteworthy aspects of the transition state. The carbene cycloaddition is a 4n electron process, with an apparent antarafacial component, this mapping onto inversion at the carbene centre. The bond formation at the alkene is very asynchronous, and the SO2 unit clearly does appear to act as a chiral auxilliary. Also these aspects would have to be factored into the eventual design.

We now enter an optimization stage of the process, in which we try to reduce the activation barrier in order to produce a viable reaction. Replacing CH2 by CF2 however increases the barrier to 42.5 kcal/mol, whilst substituting Se for S induces a barrier of 40.6 kcal/mol. More variation of the various substituents (including the alkene) will be needed to see if such a reaction could actually be carried out, but this is relatively routine process, not attempted here (perhaps not entirely routine; thus predicting what might happen is easy compared to analyzing what does not happen, see DOI: 10.1002/anie.200801206). So, there is certainly no claim here that a new reaction has been designed. Rather a tentative hint at the kind of processes that might be involved, eventually, in dialing a molecule.

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