Geometries of proton transfers: modelled utilizing whole power or free power?

Proton transfers are amongst the commonest of all chemical reactions. They’re usually regarded as “trivial” and even might not characteristic in lots of mechanistic schemes, apart from maybe the notation “PT”. The kinds with the bottom power limitations for switch usually contain heteroatoms resembling N and O, and the standard transition state is likely to be speculated to be when the proton is positioned at in regards to the half means distance between the 2 heteroatoms. This needs to be the power excessive level between the 2 positions for the proton. However what if a crystal construction is decided with the proton in precisely this place? Effectively, the primary speculation is that utilizing X-rays because the diffracting radiation is unreliable, as a result of protons scatter x-rays very poorly. Then a extra arduous neutron diffraction examine is typically undertaken, which is usually assumed to be extra dependable in figuring out the place of the proton. Simply such a examine was undertaken for the construction proven under (RAKQOJ)[1], dataDOI: 10.5517/cc57db3 for the 80K willpower. The substituents had been chosen to attempt to maximise the symmetry of the O…H…N motif by way of pKa tuning (for one more tuning try, see this weblog). The extra normal panorama this molecule suits into[2] is proven under:

The outcomes obtained for the place of the proton for RAKQOJ have been fascinating. They have been very depending on the temperature of the crystal! At room temperatures (utilizing X-rays), the proton was measured as 1.09Å from the oxygen and 1.47Å from the nitrogen (impartial type above). At 20K, the OH distance was 1.309Å and the HN 1.206Å (~ionic type above). Certainly, the very title of this text is First O-H-N Hydrogen Bond with a Centered Proton Obtained by Thermally Induced Proton Migration. The authors give quite a lot of causes for this behaviour (their ref 17[1] and likewise[2]), however one they don’t point out is thermally induced modifications within the dielectric fixed of the crystal with temperature, provided that in a single place for the proton the molecule is ionic and within the different impartial. So I made a decision to mannequin the system as a perform of solvent. On this mannequin, the solvent dielectric is used to approximate the crystal dielectric. My first selection of power perform is to compute geometries utilizing the B3LYP+GD3BJ/Def2=TZVPP/SCRF=solvent technique to see what may emerge and as a potential prelude to making an attempt different functionals. FAIR knowledge for these calculations are collected at DOI: 10.14469/hpc/10368.

^♠ At 20K

Outcomes:

1. The geometries for every mannequin are obtained by minimising the whole power of the system as a perform of the 3N-6 geometric variables (coordinates). 
2. The geometries present that for all solvents, TWO minima within the whole power are obtained, one for the ionic and one for the impartial type. That is referred to as a double-well power potential. Even a non-polar solvent resembling toluene produces a solvation power of ~3.1 kcal/mol in comparison with the gasoline section, which is ample to induce a double-well potential.
3. With out solvent (gasoline section), solely the impartial geometry is obtained. 
4. In probably the most polar solvent water, the double properly potential seems to be like this:
   
   The ionic properly is about 0.4 kcal/mol decrease in whole power (and ~0.3 kcal/mol in free power, see desk above) than the impartial type, with a barrier connecting impartial to ionic just one.0 kcal/mol. A transition state + intrinsic response coordinate (IRC) could be simply positioned on this whole power potential, confirming the double-well type.
5. When free energies ΔG are computed, which embody thermal results resembling entropy and zero-point power, the transition state emerges as 0.3 kcal/mol lower than the whole power of the ionic type (purple entries, Desk). In impact, the free power potential floor is INVERTED in comparison with the whole power floor and the “transition state” turns into the bottom level on the power floor. So this level is a minimal within the free power however a most within the whole power, the results of including thermal results to the whole power.
6. In dichloromethane, the free power of the impartial type is now decrease by 0.3 kcal/mol than the ionic type. The OH bond is beginning to get shorter and the NH one longer. The transition state is now 0.22 kcal/mol decrease than the impartial type. With chloroform, the OH and HN bonds have develop into ~equal in size, the proton is symmetrically disposed.
7. By the point dibutyl ether as solvent is reached, the transition state is now not decrease in ΔG than the impartial type, transferring on to being 2.0 kcal/mol larger for toluene. In order the solvent polarity decreases, we see a change within the potential from a single properly in ΔG, by which the proton is centred, to a really uneven properly by which the proton is hooked up to the oxygen.
   
8. Can we match the noticed neutron diffraction outcomes to the calculations? Because the temperature decreases, the neutron diffraction exhibits the beginning of proton switch from oxygen to nitrogen to type an ionic species. The calculations present that this may be modelled by a rise within the efficient dielectric fixed of the  medium. The computed “transition state” for proton switch someplace between dibutyl ether and toluene (as a dielectric media) emerges as roughly the very best mannequin for the construction of this species. At this dielectric, the calculated ΔG is now not fairly the bottom free power level within the potential. This is likely to be because of the many approximations used on this mannequin resembling minimisation of whole power, the partition perform technique used to calculate entropy, the character of the DFT practical, the continuum solvation mannequin, the premise set, and so on. 

Conclusions:

These outcomes have been obtained with the approximation that minimising the whole molecular power produces a computed geometry that may be in comparison with the experimental neutron diffraction constructions. However can one do higher? Acquiring molecular geometries by minimising the computed free energies could be non-trivial. Firstly, minimisation would rely upon availability of first derivatives of the power perform with respect to coordinates, on this case ΔG. These should not obtainable for any DFT codes. The outcome would itself be temperature dependent (as certainly are the experimental outcomes proven above). Moreover, ΔG is computed from regular vibrational modes and these are solely acceptable when the primary derivatives of the perform are zero, at which level the so-called six rotations and translations of the molecule in free house even have zero power. So we’d like vibrations to compute derivatives, however we’d like derivatives to compute vibrations on this classical strategy.

It will be nice for instance if the approximate mannequin of the potential for a hydrogen switch used above as primarily based on minimising whole energies for derivatives may very well be checked towards a mannequin primarily based on geometries optimised utilizing free energies as an alternative. Such procedures do exist,[3] utilizing molecular dynamics trajectory strategies.

This submit has DOI: 10.14469/hpc/10382 [4]