Peter Edwards has just given the 2015 Hofmann lecture here at Imperial on the topic of solvated electrons. An organic chemist knows this species as “e–” and it occurs in ionic compounds known as electrides; chloride = the negative anion of a chlorine atom, hence electride = the negative anion of an electron. It struck me how very odd these molecules are and so I thought I might share here some properties I computed after the lecture for a specific electride known as GAVKIS.[1] If you really want to learn (almost) everything about these strange species, go read the wonderful review by Zurek, Edwards and Hoffmann,[2] including a lesson in the history of chemistry stretching back almost 200 years.
GAVKIS consists of a tricyclic aza-ether ligand or cryptand wrapping a potassium atom in the centre, the overall unit having no charge. The oxygen and nitrogen heteroatoms coordinate to the metal, in the process evicting its single electron. The question that struck me is “where does that electron go?”. You see in all normal molecules that electrons are associated with either one, two (or rarely) three nuclei, to form one-centred monosynaptic basins (lone pairs), two-centre or disynaptic basins (i.e. bonds) and more rarely three-centre bonds. The shared-electron two-centre manifestation was of course famously introduced by Gilbert N. Lewis in 1916 (note the centenary coming up!). Knowing where the electron (pairs) are has enabled the technique popular with organic chemists known as arrow pushing, or the VSEPR analysis of inorganic compounds. But an electride has no nucleus associated with it! So how can one describe its location?
Click for 3D structure of GAVFIS
The crystal structure of GAVFIS shows the potassium to be 8-coordinate. Remember, x-rays are diffracted not by a nucleus but by electrons in the molecule. The highest densities are of course associated with electrons in inner shells centered on nuclei and the much lower densities found in conventional bonds are not normally located by this technique (but see here). So it is no surprise to find that this x-ray analysis[1] did not succeed in answering the question posed above; where is the single electron liberated from the potassium atom? They did look for it, but surmised only that would be found in the “noise level electron density in the spaces between them (molecules)“. For GAVFIS, that empty space is actually dumb-bell shaped, and so perhaps an answer is that the electron occupies the dumb-bell shaped spaces between the ligand-potassium complex.
X-ray analysis was defeated by noise; it is an experimental technique after all. But the noise in a quantum mechanical calculation is much smaller; can this reveal where the evicted electron is? Here is the spin density (unpaired electron) distribution for one molecule of GAVFIS computed using the UωB97XD/6-31++(G) DFT method.[3].[4] It is a stratocumulus-like cloud that enshrouds the molecule (click on the diagram below and you can rotate the function to view it from your own point of interest) but interestingly avoiding the regions along the N….N axis. There are also tiny amounts of (negative) spin density on the ligand atoms. So even when the “empty space” is infinitely large, the shape of the electride anion is nevertheless quite specific, but a holistic function of the shape of the entire molecule rather than its component atoms.‡
Click for 3D
Another way of describing where electrons are is using functions known as molecular orbitals. Below is the SOMO (singly occupied MO) and its shape in this case coincides with that of the spin density.
Click for 3D interaction
The molecular electrostatic potential is rather wackier (red = attractive to protons).
Click for 3D interaction
Odder still is the ELF (electron localisation function) and the identification of the centroids of its basins. These centroids normally coincide with the two-centre basins (bonds) and one-centre basins (lone pairs, inner shell electrons) in normal molecules, both being close to nuclear centres (atoms). For GAVFIS, two unexpected one-centre basins are found close to the two nitrogen atoms in the molecule, each with a population of 0.48 electrons, along with regular one-centre “lone pair” basins pointing inwards to the potassium (2.38 electrons each). The odd-looking pair of locations identified for the electride anion may have little physical reality, except for reminding us that the electride can indeed be in more than one location simultaneously!
I often also use the NCI (non-covalent-interaction) property of the electron density in these blogs. It tells us about regions of non-covalent electron density which represent attractive weak interactions between or within molecules. Here, it again shows us the weak non-covalent density (as the reduced density gradients) wrapping the molecule (green=weakly stabilizing).
Click for 3D interaction
The obvious next question is that if each molecule is surrounded by weak spin density arising from an unpaired electron, would two such species form a dimer in which the spins are paired in an manner analogous to the conventional single bond? The overlap is not going to be fantastic if the spin distribution has the shape shown above, but what the hell. Here is the HOMO of such a species.[5] It appears the shape of the electride is very pliable indeed; they have been squeezed out of the contact region between the two molecules (which form a close contact pair) into wrapping the dimer rather than the monomer! The spin-coupled singlet by the way is about 4.6 kcal/mol more stable in free energy ΔG298 than two isolated monomer doublets, and 5.5 kcal/mol lower than the triplet species[6] which retains two unpaired electrons. A sort of weak molecule-pair bond rather than an atom-pair bond.
Click for 3D interaction
This has hardly started to scratch the surface of the strange properties of electrides. If your appetite has been whetted, go read the article I noted at the beginning.[2]
‡ For normal molecules, a Mulliken or other population analysis reduces the charge and spin density down to an atom-centered distribution. If this is done for GAVFIS, the spin density collapses down to the molecular centroid, in this case the potassium (spin density 1.15). This of course is horribly misleading, and serves to remind us that such atom-centered distributions can sometimes be far from realistic.
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In an earlier post on the Birch reduction of methoxybenzene using sodium in ammonia (with three ammonias solvating one sodium) I had noted two valence bond or electronic isomers of the system, one with spin density on the sodium and one with spin density on the anisole, separated by about 11 kcal/mol in free energy with the latter the more stable.
No doubt two such electronic states are also possible with electrides, and their relative stability will certainly be a function of the character and number of ligands, and of course the metal.
The paper by Hoffmann reminds me of this old paper by Victor Luana et. al. on the presence of NNA in alkali metal crystals under high pressure. It seems that the authors of the new paper were not aware of this older contribution.
http://scitation.aip.org/content/aip/journal/jcp/119/12/10.1063/1.1600433
It is often the case that different communities come across the same phenomenon, and name them differently. I only realised recently for example that the term chemists use in NMR spectra, "chemical shifts" is named entirely differently by the physics community that also analyses such spectra!
Three years ago, I posted here a blog on Birch reduction of anisole. There I described a pre-complex of Na.3NH3 with anisole where I noted a Mulliken analysis as placing the spin density on the Na, but that another lower energy complex could be located where the spin density transferred to the anisole. I had not then picked up on the observation that a Mulliken analysis of electrides does indeed put the spin density on the metal, but that such an atom-centered decomposition might be quite misleading. I have now added a comment to that post clearly identifying the "pre-complex" as in fact a sodium electride.
Its not just new authors that fail to pick up on old pre-existing results in the literature, its also blog authors who fail to pick up on their own older posts!
Whilst I am on the topic of what might be out there in the literature, in the Birch mechanism we have two species each in energy minima but with different electronic distributions or states. There must presumably be a transition state representing the energy high point for the electron transfer? Has anyone located such transition states or might they indeed simply be conical intersection in the energy manifolds?
I agree that different communities are not aware of the works done in their neighboring community. However, I should mention something here. I several times have heard criticisms about AIM and one of the most frequent ones is that AIM suggests presence of \"non-physical\" entities such as NNAs. I wonder why free electrons, loosely bonded to molecules, i.e., NNAs, are called non-physical. In particular when an old idea can go to JACS with a new name.
Sorry for sounding too grumpy in this comment.
There is a lot more to Hoffmann's article than just the concept of interstitial quasi-atoms, and of course the name of the game is not just discovering a new concept but exploiting it.
I was at the 50th birthday bash of the Cambridge structure database last week, where I encountered 2-3 crystallographers mulling over Bijvoet's 1951 use of anomalous dispersion to settle the absolute configuration of tartaric acid. Of course, they said, physicists knew about anomalous dispersion decades earlier, and yet they never get any credit for it! But on its own it is not useful and Bijvoet managed to do something really useful with it! To my mind, its Kirkwood working around the same time as Bijvoet, but using an entirely different technique to achieve the same result that gets perhaps less credit than he deserves.
Re non-physical manifestations of Bader's QTAIM, the one I have heard most often is the non-physical "bond critical point" manifested in cis-but-2-ene between two hydrogen atoms. It is non-physical in a chemical sense, since the chemistry community does not find the concept of such a bond between two hydrogen atoms useful in being exploitable for them. A physicist, who is less worried about bonds, and perhaps more interested in the electron density itself, would find it entirely physical. It is in many ways a cultural thing, depending on whether the community finds it a useful concept for its own purposes.
Regarding the meaning of (3,-1) CPs (BCP or LCP) there is a general misunderstanding that is caused by Bader's terminology. As far as I know, (3,-1) CPs are not chemical bonds for a simple reason. These CPs appear/disappear upon molecular vibrations; see for example DOI:10.1002/chem.201402177
This was not unknown to Bader either. He several times repeated that so-called "bond paths" are not chemical bonds. Finally, he wrote this paper to clarify the situation: 10.1021/jp906341r
Bader however has shown that (3, -1) CPs in electron density have a mirror image in Virial field. This can be interpreted as a local stabilization to prevent a "more severe increase" in energy of a molecule. (It may sounds weird but it is not. This is very similar to the concept of aromatic TS for concerted reactions. Nevertheless, formation of a (3,-1)CP in a strained molecule is not necessarily synonym to formation of a chemical bond. Besides, in his terminology a "bonded atomic pair" are those that are connected by a CP. This terminology is misleading but he realized that quite late. An alternative way for calling atoms, which are connected by CPs, is the term "neighboring atoms" see: DOI: 10.1002/chem.201402177.
Similarly, one can call bond critical points, line critical point (LCP) in analogy with ring and cage critical points. These are some suggestions that does not harm the main body of theory but make them less troublesome.
Thanks for that interesting insight. I am happy with the term line critical point to replace bond critical point. Of course in the vast number of cases, a LCP point will also describe a bond.
It\'s my honour to hear that you liked it :)
I am sure replacing BCP with LCP or "bonded/nonbonded atoms" with "neighboring/non-neighboring atoms" will reduce the confusion regarding AIM. Most of critiques of AIM are just discussing about terminology. Very recently, I myself made the same mistake, did not explain terminology of my work and got a very nice paper nicely rejected! :D
Cina,
A valuable insight from your identification of NNAs using AIM2000 was that the density is near the threshold for cutoff. One way of exploring that is to change the characteristics of the metal. ROGDAS is a lithium electride, similar to GAVKIS, but with rather smaller ligands. Some of the analogous surfaces obtained for the Li system are shown below:
NCI
MEP:
SOMO (red) superimposed upon Spin density (blue):
SOMO on its own:
The archive is doi: 10.5281/zenodo.19966.
I would be interested if AIM2000 shows NNAs for this system as well.