Posts Tagged ‘Jahn-Teller’

Ammonide: an alkalide formed from ammonia and resembling an electride.

Sunday, December 17th, 2017

Alkalides are anionic alkali compounds containing e.g. sodide (Na–), kalide (K–), rubidide (Rb–) or caeside (Cs–). Around 90 examples can be found in the Cambridge structure database (see DOI: 10.14469/hpc/3453  for the search query and results). So what about the ammonium analogue, ammonide (NH4–)? A quick search of Scifinder drew a blank! So here I take a look at this intriguingly simple little molecule.‡

It can be formed by adding two electrons to the ammonium cation; NH4+ + 2e ↠ NH4–. One might be encouraged to do this since the LUMO (lowest unoccupied molecular orbital, below) of the ammonium cation has A1 symmetry and so can accept two electrons without the penalty of Jahn-Teller distortions. These electrons will apparently expand the valence electron “octet” around the nitrogen from 8 to 10; a hypervalent species then?

So what are the (calculated) properties of NH4–? The energy of the now HOMO (highest occupied molecular orbital) at the ωB97XD/Def2-TZVPPD/solvent=water level is -3.6eV, a respectable electron affinity (the additional electrons are said to be bound). More insight can be obtained from the NBO analysis, which produces localized versions of the molecular orbitals. There are four equivalent NBOs, one of which is shown below.

Each is bonding along one H-N bond, mildly anti-bonding along the other three N-H bonds, but again bonding in the H-H regions! This matches the observations made earlier that when more electrons are pumped into normally valent main group molecules, they will occupy the antibonding levels. This is accompanied by a reduction in the bond orders associated with the central atom. In this case, the N-H bond orders are reduced from 0.79 to 0.602 and the total bond index at the nitrogen is reduced from 3.16 to 2.408. The bond index at hydrogen is at first sight increased from 0.79 to a surprising 1.0003, but this is explained because the H-H bond orders are 0.1328 (three for each H), which brings the H index up to 1.0. The N-H vibration (A1 symmetric) is 3466 cm-1 for NH4+  which is reduced to 2659 for NH4–.†

So it appears that adding two electrons to the ammonium cation induces H-H bonding! More insight can be obtained from an ELF analysis of the electron density basins.

The above shows four attractors (as they are called) centered at the hydrogen nuclei, with 2.053e each (4*2.053 = 8.212e). The remaining ~2e are located in basins (green) centered at two different types of attractors. One is along the axis of each N-H bond and exo to it (0.316e) and the other sits on top of any set of three hydrogens (0.103e), 1.68e in total. The value of the ELF function at the attractor is shown above. You should realize that ELF=1.0 corresponds to perfectly localized electrons (for which the kinetic energy density is zero) and ELF=0.5 would correspond to a free-electron gas. The ELF value of e.g. 0.77 is getting close to an electron gas, and in fact corresponds to what we call an electride.

So, the nitrogen valence shell electron octet is not actually exceeded! The additional two electrons in ammonide sit beyond the nitrogen, in H-H regions. Whether or not it is a viable species for detection remains to be established, but even its computed bonding properties have proved interesting and it deserves to join the alkalide family. 

Postscript

Ammonide exists in a shallow well in the potential energy surface, shown below, with the dissociation to ammonia and hydride anion being exothermic.

The intrinsic reaction coordinate shows one interesting feature at  IRC ~-1.1 which corresponds to repulsion between the hydride and the lone pair of the nitrogen atom resulting in inversion of configuration during the latter stages of the IRC.

‡FAIR data collection; 10.14469/hpc/3455. †Perhaps unsurprisingly, these values are somewhat basis set dependent. Thus a ωB97XD/Def2-QZVPPD/Water calculation gives the following values: bond index at N, 1.998, N-H bond index, 0.4995, H-H bond index 0.1689, H bond index 1.0062, total Rydberg population, 0.2738, ν(A1) 2686 cm-1. The ELF basins are H, 2.039, exo-basins 0.282 and 0.141 (total 1.692). The improved basis set better describes the diffuse regions beyond the N-H bonds.

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Posted in Hypervalency | 2 Comments »

Expanding on the curious connection between the norbornyl cation and small-ring aromatics.

Sunday, March 12th, 2017

This is another of those posts that has morphed from an earlier one noting the death of the great chemist George Olah. The discussion about the norbornyl cation concentrated on whether this species existed in a single minimum symmetric energy well (the non-classical Winstein/Olah proposal) or a double minimum well connected by a symmetric transition state (the classical Brown proposal). In a comment on the post, I added other examples in chemistry of single/double minima, mapped here to non-classical/classical structures. I now expand on the examples related to small aromatic or anti-aromatic rings.

Examples of symmetric energy potentials
System Classical with 1 imaginary normal mode Non-classical with 0 imaginary modes
Norbornyl cation TS for [1,2] sigmatropic Minimum, this post
Singlet [6], [10]; 4n+2 annulenes – Minimum with Kekulé vibration
Singlet [4], [8]; 4n annulenes TS for bond shift, 1 imaginary normal mode –
Triplet [4], [8]; 4n annulenes – Minimum, with Kekulé vibration (?)
Semibullvalenes TS for [3,3] sigmatropic Minimum
Strong Hydrogen bonds TS for proton transfer Minimum
SN2 substitutions TS for substitution (C) Minimum (Si)
Jahn-Teller distortions Dynamic Jahn-Teller effects No Jahn-Teller distortions

In the table above, you might notice a (?) associated with the entry for (aromatic) triplet state 4n annulenes. Here I expand the ? by considering triplet cyclobutadiene and triplet cyclo-octatetraene (ωB97XD/Def2-TZVPP, 10.14469/hpc/2241 and 10.14469/hpc/2242 respectively). Each has a normal vibrational mode shown animated below, which oscillates between the two Kekulé representations of the molecule with wavenumbers of 1397 and 1744 cm-1 respectively. These Kekulé modes are both real, which indicates that the symmetric species (D4h and D8h symmetry) is in each case the equilibrium minimum energy position (rCC 1.431 and 1.395Å). For comparison the aromatic singlet state 4n+2 annulene benzene (rCC 1.387Å) has the value 1339 cm-1. Notice that both the triplet state wavenumbers are elevated compared to singlet benzene, because in each case the triplet ring π-bond orders are lower, thus decreasing the natural tendency of the π-system to desymmetrise the ring.[1]

To complete the theme, I will look at singlet cyclobutadiene. According to the table above, the symmetric form should be a transition state (TS) for bond shifting, with one imaginary normal mode. To calculate this mode, one has to use a method that correctly reflects the symmetry, in this case a CASSCF(4,4)/6-311G(d,p) wavefunction (DOI: 10.14469/hpc/2244). The mode (rCC 1.444Å) shown below has a wavenumber of 1477i cm-1; its vectors of course resemble those of the triplet mode, but its force constant is now negative rather than positive!

At first sight any connection between the property of the norbornyl cation at the core of the controversies all those decades ago and aromatic/antiaromatic rings might seem tenuous. But in the end many aspects of chemistry boil down to symmetries and from there to Évariste Galois, who started the ball rolling.

References

  1. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations", Chemical Reviews, vol. 101, pp. 1501-1540, 2001. https://doi.org/10.1021/cr990363l

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Discovering chemical concepts from crystal structure statistics: The Jahn-Teller effect

Saturday, May 30th, 2015

I am on a mission to persuade my colleagues that the statistical analysis of crystal structures is a useful teaching tool.  One colleague asked for a demonstration and suggested exploring the classical Jahn-Teller effect (thanks Milo!). This is a geometrical distortion associated with certain molecular electronic configurations, of which the best example is illustrated by octahedral copper complexes which have a d9 electronic configuration. The eg level shown below is occupied by three electrons and which can therefore distort in one of two ways to eliminate the eg degeneracy by placing the odd electron into either a x2-y2 or a z2 orbital. Here I explore how this effect can be teased out of crystal structures.

JT

The search is set up with Cu specified as precisely 6-coordinate, and X=oxygen. The six X-Cu distances are defined as DIST1-DIST6. The R-factor is specified as < 0.05 (no disorder, no errors). The problem now is how to plot what is in effect a six-dimensional set of data, from which we are exploring whether four of the distances are different from the other two, and whether those four are the longer or the shorter. This requires analysis beyond the capability (as far as I know) of the Conquest program, and so here I will show sets of plots showing just the relationship between any two distances at a time. Of the 15 possible combinations of two distances, only four are shown below.

Some obvious patterns can already be spotted in the 400 or so compounds which satisfy the search criteria.

  • The largest clustering occurs at ~1.95Å, with two clusters each of fewer hits at ~2.5Å. The Wikipedia page notes that for Cu(OH2)6 the Jahn-Teller distortion favours four short bonds at ~1.95Å and two long ones at ~2.38Å, which agrees approximately with the positions and sizes of the centroids of these clusters.†
  • Plots 1 and 2 show very little along the diagonals, where the two plotted distances have the same value. This probably means that one of the distances relates to an equatorial ligand and the other to an axial ligand.
  • Plots 3 and 4 show a strong diagonal trend, and so these distances both relate to either axial or equatorial, but not one of each.
  • All four plots show a hot spot at ~1.95Å, which hints that the Jahn-Teller distortion is four short bonds/two long.
  • Plot 4 also shows a green spot at ~2.5Å which is a tantalising suggestion of examples of four long bonds/two short.‡
  1. CuO-12
  2. CuO-34
  3. CuO-56
  4. CuO-13

Clearly this analysis can be followed up by a visual inspection of individual molecules in each cluster (as well as the outliers which appear to follow no pattern!), together with a more bespoke analysis of the six distances. Unfortunately, the spin state of the complexes cannot be quickly checked (are they all doublets?) since the database does not record these.  But the basic search described above takes only a few minutes to do, and it is surprising at how quickly the Jahn-Teller effect can be statistically tested with real experimental data obtained for ~400 molecules. Of course, here I have only explored X=O but this can easily be extended to X=N or X=Cl, to other metals or to alternative coordination numbers such as e.g. 4 where the Jahn-Teller effect can also in principle operate.

‡ One genuine example of this type, also called compressed octahedral coordination, was reported for the species CuFAsF6 and CsCuAlF6[1]

† The measured geometry of Cu(H2O)6 may in fact manifest with six equal Cu-O bond lengths due to the dynamic Jahn-Teller effect, because the kinetic barrier separating one Jahn-Teller distorted form and another (equivalent) isomer is small and hence averaged atom positions are measured which mask the effect. Thus the Jahn-Teller effects shown in the plots above may be under-estimated because of this dynamic masking. Reducing the temperature of the sample at which data was collected would reduce this dynamic effect. Indeed, Cu(D2O)6 collected at 93K shows a very clear Jahn-Teller distortion[2] with four long bonds ranging from 1.97-1.99Å and two long bonds 2.37-2.39Å.[3] Another example measured at 89K with dimethyl formamide replacing water and coordinated via oxygen[4] shows four short (1.97-1.98Å) and two long (2.315Å) bonds. This latter example is also noteworthy because this analysis is as yet unpublished in a journal, but the data itself has a DOI via which it can be acquired. A nice example of modern research data management!

References

  1. Z. Mazej, I. Arčon, P. Benkič, A. Kodre, and A. Tressaud, "Compressed Octahedral Coordination in Chain Compounds Containing Divalent Copper: Structure and Magnetic Properties of CuFAsF<sub>6</sub> and CsCuAlF<sub>6</sub>", Chemistry – A European Journal, vol. 10, pp. 5052-5058, 2004. https://doi.org/10.1002/chem.200400397
  2. W. Zhang, L. Chen, R. Xiong, T. Nakamura, and S.D. Huang, "New Ferroelectrics Based on Divalent Metal Ion Alum", Journal of the American Chemical Society, vol. 131, pp. 12544-12545, 2009. https://doi.org/10.1021/ja905399x
  3. Zhang, Wen., Chen, Li-Zhuang., Xiong, Ren-Gen., Nakamura, T.., and Huang, S.D.., "CCDC 755150: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctbspl
  4. M.M. Olmstead, D.S. Marlin, and P.K. Mascharak, "CCDC 1053817: Experimental Crystal Structure Determination", 2015. https://doi.org/10.5517/cc14cl36

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Following one’s nose: a quadruple bond to carbon. Surely I must be joking!

Thursday, December 16th, 2010

Do you fancy a story going from simplicity to complexity, if not absurdity, in three easy steps? Read on! The following problem appears in one of our (past) examination questions in introductory organic chemistry. From relatively mundane beginnings, one can rapidly find oneself in very unexpected territory.

How would one make 3-nitrobenzonitrile?

One teaches how to disconnect each group, identifying that both are meta-directing towards electrophiles, and hence asking what an appropriate electrophile might be? The “correct” answer is a nitronium cation (nitric + sulfuric acids) acting upon m-directing benzonitrile. But (sacrilege), why not a “cyonium” cation (CN+) on m-directing nitrobenzene? Well, as a tutor one would normally swat it away on the grounds it has never been previously observed (or that cyanide is always seen as an anion, not a cation). But then one (or a student) asks, why not? How about generating it from e.g. TfOCN. TfO– is a jolly good leaving group, one of the best. Well, this precursor truly appears never to have been made (or even calculated!). By now (if encountered in a tutorial), most chemistry students would be rather bemused. So the process of following one’s nose (more accurately, my nose) continues in the peace and quiet of a blog, where a rather different readership might be bemused (or inflamed).

A Quadruple CN bond?

One might start the same place a student would. How would one represent this diatomic with bonds? How about the above? It has the merit that both atoms are associated with a (shared) octet of electrons, in the form of a quadruple bond. I did show this (briefly) to a colleague, but they recoiled in horror, although it has to be said they were slightly at a loss to actually explain their horror.

Well, time for calculations. How about CCSD/aug-cc-pVTZ (DOI: 10042/to-6261) or B3LYP/aug-cc-pVTZ (DOI: 10042/to-6255). The latter allows a so-called Wiberg bond index to be computed (a reasonably accepted index). This comes out at 3.55, well on the way to being quadruple. An NBO analysis (NBO 5.9) identifies FOUR NBO orbitals with an occupancy of ~2.0, all designated BD (rather than e.g. Lp). What are these NBOs like? (as it turns out, they are almost identical to the MOs for this molecule).

Orbital 7. Click for 3D

Orbital 6 (π)

Orbital 5 (π)

Orbital 4. Click for 3D

Orbital 3. Click for 3D

Orbitals 5 & 6 are standard π orbitals with no mystery (and 8 & 9, not shown, are the matching π* pair). Orbital 3 results from the overlap of two 2s AOs (but note the curious little toroid at the carbon end). Orbitals 4 and 7 (the LUMO) are the interesting ones. Nominally, the result of overlapping two 2px AOs to give what should be a bonding and antibonding pair, they both appear to be bonding in the C-N region! Perhaps the quadruple bond is not looking quite so unlikely after all (comprising ~double occupancy of orbitals  3-6)!

What about those stalwarts I often use in these blogs, QTAIM and ELF? The former  (using the CCSD natural orbitals) has a ρ(r) of 0.346 and a ∇2ρ(r) of +2.01 at the bond-critical point (BCP). The former is certainly a high value, although no calibration exists to compare it to a quadruple bond. The Laplacian has a positive value at this point, possibly an indication of a charge-shift bond (see this and this blog, although more likely due to the adjacency of the bond critical point to the core shell of the carbon atom). ELF (also using natural orbitals) declares the presence of TWO disynaptic basins, with integrations of 5.39e and 2.44 (totalling 7.83e). The basins will each take the form of a torus (see DOI: 10.1021/ct100470g). Hm, perhaps, on reflection, this paragraph might not be entirely suitable for an introductory tutorial to organic chemistry. The density of mumbo-jumbo is rather high!

So starting from a simple retrosynthetic analysis of a simple aromatic molecule, in which the less obvious route is at least considered, one derives a “new” reagent, the cyonium cation CN+. In a effort to analyse its bonding, one concludes that a quadruple bond needs to be taken at least seriously. I would note as a warning that these diatomic species can be really tricky to pin down, and the iso-electronc C2 is a good example of that. But C2 has all sorts of issues, some of which are avoided with CN+. So the last word is hardly written, but not a bad outcome, I venture to suggest, of following one’s nose in a tutorial.

I have appended to this post a 3D exploration of the ELF function, showing the two torus basins referred to above.

 

ELF function for CN+. Click for 3D

Henry Rzepa, URL:http://www.ch.imperial.ac.uk/rzepa/blog/?p=3065. Accessed: 2011-06-04. (Archived by WebCite® at http://www.webcitation.org/5zBSjBjhM)

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Posted in Hypervalency, Interesting chemistry | 19 Comments »

Following one's nose: a quadruple bond to carbon. Surely I must be joking!

Thursday, December 16th, 2010

Do you fancy a story going from simplicity to complexity, if not absurdity, in three easy steps? Read on! The following problem appears in one of our (past) examination questions in introductory organic chemistry. From relatively mundane beginnings, one can rapidly find oneself in very unexpected territory.

How would one make 3-nitrobenzonitrile?

One teaches how to disconnect each group, identifying that both are meta-directing towards electrophiles, and hence asking what an appropriate electrophile might be? The “correct” answer is a nitronium cation (nitric + sulfuric acids) acting upon m-directing benzonitrile. But (sacrilege), why not a “cyonium” cation (CN+) on m-directing nitrobenzene? Well, as a tutor one would normally swat it away on the grounds it has never been previously observed (or that cyanide is always seen as an anion, not a cation). But then one (or a student) asks, why not? How about generating it from e.g. TfOCN. TfO– is a jolly good leaving group, one of the best. Well, this precursor truly appears never to have been made (or even calculated!). By now (if encountered in a tutorial), most chemistry students would be rather bemused. So the process of following one’s nose (more accurately, my nose) continues in the peace and quiet of a blog, where a rather different readership might be bemused (or inflamed).

A Quadruple CN bond?

One might start the same place a student would. How would one represent this diatomic with bonds? How about the above? It has the merit that both atoms are associated with a (shared) octet of electrons, in the form of a quadruple bond. I did show this (briefly) to a colleague, but they recoiled in horror, although it has to be said they were slightly at a loss to actually explain their horror.

Well, time for calculations. How about CCSD/aug-cc-pVTZ (DOI: 10042/to-6261) or B3LYP/aug-cc-pVTZ (DOI: 10042/to-6255). The latter allows a so-called Wiberg bond index to be computed (a reasonably accepted index). This comes out at 3.55, well on the way to being quadruple. An NBO analysis (NBO 5.9) identifies FOUR NBO orbitals with an occupancy of ~2.0, all designated BD (rather than e.g. Lp). What are these NBOs like? (as it turns out, they are almost identical to the MOs for this molecule).

Orbital 7. Click for 3D

Orbital 6 (π)

Orbital 5 (π)

Orbital 4. Click for 3D

Orbital 3. Click for 3D

Orbitals 5 & 6 are standard π orbitals with no mystery (and 8 & 9, not shown, are the matching π* pair). Orbital 3 results from the overlap of two 2s AOs (but note the curious little toroid at the carbon end). Orbitals 4 and 7 (the LUMO) are the interesting ones. Nominally, the result of overlapping two 2px AOs to give what should be a bonding and antibonding pair, they both appear to be bonding in the C-N region! Perhaps the quadruple bond is not looking quite so unlikely after all (comprising ~double occupancy of orbitals  3-6)!

What about those stalwarts I often use in these blogs, QTAIM and ELF? The former  (using the CCSD natural orbitals) has a ρ(r) of 0.346 and a ∇2ρ(r) of +2.01 at the bond-critical point (BCP). The former is certainly a high value, although no calibration exists to compare it to a quadruple bond. The Laplacian has a positive value at this point, possibly an indication of a charge-shift bond (see this and this blog, although more likely due to the adjacency of the bond critical point to the core shell of the carbon atom). ELF (also using natural orbitals) declares the presence of TWO disynaptic basins, with integrations of 5.39e and 2.44 (totalling 7.83e). The basins will each take the form of a torus (see DOI: 10.1021/ct100470g). Hm, perhaps, on reflection, this paragraph might not be entirely suitable for an introductory tutorial to organic chemistry. The density of mumbo-jumbo is rather high!

So starting from a simple retrosynthetic analysis of a simple aromatic molecule, in which the less obvious route is at least considered, one derives a “new” reagent, the cyonium cation CN+. In a effort to analyse its bonding, one concludes that a quadruple bond needs to be taken at least seriously. I would note as a warning that these diatomic species can be really tricky to pin down, and the iso-electronc C2 is a good example of that. But C2 has all sorts of issues, some of which are avoided with CN+. So the last word is hardly written, but not a bad outcome, I venture to suggest, of following one’s nose in a tutorial.

I have appended to this post a 3D exploration of the ELF function, showing the two torus basins referred to above.

 

ELF function for CN+. Click for 3D

Henry Rzepa, URL:http://www.ch.imperial.ac.uk/rzepa/blog/?p=3065. Accessed: 2011-06-04. (Archived by WebCite® at http://www.webcitation.org/5zBSjBjhM)

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Posted in Hypervalency, Interesting chemistry | 15 Comments »