Proton transfers are amongst the most common of all chemical reactions. They are often thought of as “trivial” and even may not feature in many mechanistic schemes, other than perhaps the notation “PT”. The types with the lowest energy barriers for transfer often involve heteroatoms such as N and O, and the conventional transition state might be supposed to be when the proton is located at about the half way distance between the two heteroatoms. This should be the energy high point between the two positions for the proton. But what if a crystal structure is determined with the proton in exactly this position? Well, the first hypothesis is that using X-rays as the diffracting radiation is unreliable, because protons scatter x-rays very poorly. Then a more arduous neutron diffraction study is sometimes undertaken, which is generally assumed to be more reliable in determining the position of the proton. Just such a study was undertaken for the structure shown below (RAKQOJ)[1], dataDOI: 10.5517/cc57db3 for the 80K determination.
The results obtained for the position of the proton for RAKQOJ were fascinating. They were very dependent on the temperature of the crystal! At room temperatures (using X-rays), the proton was measured as 1.09Å from the oxygen and 1.47Å from the nitrogen (neutral form above). At 20K, the OH distance was 1.309Å and the HN 1.206Å (~ionic form above). Indeed, the very title of this article is First O-H-N Hydrogen Bond with a Centered Proton Obtained by Thermally Induced Proton Migration. The authors give a number of reasons for this behaviour (their ref 17[1] and also[2]), but one they do not mention is thermally induced changes in the dielectric constant of the crystal with temperature, given that in one position for the proton the molecule is ionic and in the other neutral. So I decided to model the system as a function of solvent. In this model, the solvent dielectric is used to approximate the crystal dielectric. My first choice of energy function is to compute geometries using the B3LYP+GD3BJ/Def2=TZVPP/SCRF=solvent method to see what might emerge and as a possible prelude to trying other functionals. FAIR data for these calculations are collected at DOI: 10.14469/hpc/10368.
Solvent | ε | ΔG298 for O…HN | rO…H | rHN | ΔG298 for OH…N | rOH | rH…N | ΔG298 TS (PT) |
rOH | rHN |
---|---|---|---|---|---|---|---|---|---|---|
Water | 78.4 | -2893.387188 -2893.334325♠ |
1.4913 | 1.0827 | -2893.386705 -2893.334333♠ |
1.0364 | 1.5696 | -2893.387668 -2893.336183♠ |
1.1852 | 1.2899 |
Dichloro methane |
8.9 | -2893.385173 | 1.4566 | 1.0945 | -2893.385662 | 1.0309 | 1.5878 | -2893.386022 | 1.2072 | 1.2642 |
Chloroform | 4.7 | -2893.382254 | 1.4227 | 1.1082 | -2893.384514 | 1.0261 | 1.6049 | -2893.384773 | 1.2321 | 1.2388 |
Dibutyl ether | 3.1 | -2893.380813 | 1.3778 | 1.1302 | -2893.383511 | 1.0213 | 1.6235 | -2893.382918 | 1.2667 | 1.2078 |
Toluene | 2.4 | -2893.379752 | 1.3248 | 1.1635 | -2893.382915 | 1.0178 | 1.6385 | -2893.379773 | 1.2851 | 1.1934 |
Gas phase | 0 | n/a | -2893.377949 | 1.0009 | 1.7387 | n/a | ||||
Expt (RT) [1] |
? | n/a | 1.09 | 1.47 | n/a | |||||
Expt (20K) [1] |
? | n/a | 1.309 | 1.206 | n/a |
♠ At 20K
Results:
Conclusions:
These results were obtained with the approximation that minimising the total molecular energy produces a computed geometry that can be compared to the experimental neutron diffraction structures. But can one do better? Obtaining molecular geometries by minimising the computed free energies would be non-trivial. Firstly, minimisation would depend on availability of first derivatives of the energy function with respect to coordinates, in this case ΔG. These are not available for any DFT codes. The result would itself be temperature dependent (as indeed are the experimental results shown above). Furthermore, ΔG is computed from normal vibrational modes and these are only appropriate when the first derivatives of the function are zero, at which point the so-called six rotations and translations of the molecule in free space also have zero energy. So we need vibrations to compute derivatives, but we need derivatives to compute vibrations in this classical approach.
It would be great for example if the approximate model of the potential for a hydrogen transfer used above as based on minimising total energies for derivatives could be checked against a model based on geometries optimised using free energies instead. Such procedures do exist,[3] using molecular dynamics trajectory methods.
This post has DOI: 10.14469/hpc/10382 [4]
In the mid to late 1990s as the Web developed, it was becoming more obvious…
I have written a few times about the so-called "anomeric effect", which relates to stereoelectronic…
The recent release of the DataCite Data Citation corpus, which has the stated aim of…
Following on from my template exploration of the Wilkinson hydrogenation catalyst, I now repeat this…
In the late 1980s, as I recollected here the equipment needed for real time molecular…
On 24th January 1984, the Macintosh computer was released, as all the media are informing…
View Comments
Very insightful article. How about the role of tunneling effect in this particular problem?
Dear Latte,
Tunnelling occurs through a potential energy barrier. If there is no barrier, then no tunnelling can occur. In this case, a free energy barrier.
Just wonder how difficult it was to find the TS, I presumed you first used scans, then calcall and a small stepwise for the actual TS, but are other keywords you can recommend, especially for proton transfer?
Andrew,
Thanks for the comment. To answer your questions
1. I do not recollect any particular difficulties. You can always see the keywords used by going to the results at https://doi.org/10.14469/hpc/10368 to find out.
2. Scans are rarely used for simple proton transfers. I normally place the proton at approximately the mid point. I will then constrain the two X-H lengths using opt(modredundant) to eliminate forces in the rest of the molecule. Normally, calcfc, and recalcfc=5 or so will then do the trick to refine the final position of the proton. Only if that fails is calcall used.
3. The other keyword that is useful is integral=(acc2e=14,grid=superfinegrid,noxctest) The higher than normal integral accuracy ensures that the CPHF section converges quickly, and the extra large quadrature grid ensures even less rotational variance than normal.
Cheers