Tag: metal

Imaging normal vibrational modes of a single molecule of CoTPP: a mystery about the nature of the imaged species.

Previously, I explored (computationally) the normal vibrational modes of Co(II)-tetraphenylporphyrin (CoTPP) as a “flattened” species on copper or gold surfaces for comparison with those recently imaged[cite]10.1038/s41586-019-1059-9[/cite]. The initial intent was to estimate the “flattening” energy. There are six electronic possibilities for this molecule on a metal surface. Respectively positively, or negatively charged and a neutral species, each in either a low or a high-spin electronic state. I reported five of these earlier, finding each had quite high barriers for “flattening” the molecule. For the final 6th possibility, the triplet anion, the SCF (self-consistent-field) had failed to converge, but for which I can now report converged results.^†

charge	Spin Multiplicity	ΔG, Twisted Ph, Hartree	ΔG, “flattened”, Hartree	ΔΔG, kcal/mol
-1	Triplet	-3294.68134 (C₂)	-3294.64745 (C_2v)	21.3
			-3294.616684 (C_2v)	40.6
			-3294.37012 (D_2h)	195.3
	Singlet	-3294.67713 (S₄)	-3294.39418 (D_4h)	175.6
			-3294.39321 (D_2h)	178.2
			-3294.56652 (D₂)	69.4
FAIR data at DOI:10.14469/hpc/5486 FAIR data version of the tables in this and previous post at DOI:10.14469/hpc/5561

I am exploring the so-called “flattened” mode, induced by the voltage applied at the tip of the STM (scanning-tunnelling microscope) probe and which causes the phenyl rings to rotate as per above. This rotation in turn causes the hydrogen atom-pair encircled above to approach each other very closely.^‡ To avoid these repulsions, the molecule buckles into one of two modes. The first causes the phenyl rings to stack up/down/up/down. The second involves an all-up stacking, as shown below. Although these are in fact 4th-order saddle points as isolated molecules, the STM voltage can inject sufficient energy to convert these into apparently stable minima on the metal surface.

The up/down/up/down “flattened” form (below) shows a much more modest planarisation energy than all the other charged/neutral states reported in the previous post, whereas the all-up isomer (which on the face of it looks a far easier proposition to come into close contact with a metal surface) is far higher in free energy.

The caption to Figure 3 in the original article[cite]10.1038/s41586-019-1059-9[/cite] does not explicitly mention the nature of the metal surface on which the vibrations were recorded, but we do get “The intensity in the upper right corner of the 320-cm⁻¹ map is from a neighbouring Cu–CO stretch” which suggests it is in fact a copper surface. Coupled with the other observation that in “contrast to gold, the Kondo resonance of cobalt disappears on Cu(100), suggesting that it acquires nearly a full electron from the metal (see Extended Data Fig. 2),” the model below of a triplet-state anion on the Cu surface seems the most appropriate.

Syn/anti mode, Triplet anion with C2v symmetry

There is one final remark made in the article worth repeating here: “This suggests that the vibronic functions are complex-valued in this state, as expected for Jahn–Teller active degenerate orbitals of the planar porphyrin.²⁶” Orbital degeneracy can only occur if the molecule has e.g. D_4h point group symmetry, whereas the triplet anion stationary-point shown in the figure above has only C_2v symmetry for which no orbital degeneracies (E) are expected. Enforcing D_4h symmetry on Co(II) tetraphenylporphyrin results in eight pairs of H…H contacts of 1.34Å,^‡ which is an impossibly short distance (the shortest known is ~1.5Å). Moreover this geometry has an equally impossible free energy 176 kcal/mol above the relaxed free molecule. Visually from Figure 3, the H…H contact distance looks even shorter (below, circled in red)! A D_2h form (with no E-type orbitals) can also be located.

Singlet, Calculated with D_4h symmetry. Click for vibrations.	Singlet, Calculated with D_2h symmetry. Click for vibrations.
Taken from Figure 3 (Ref 1).

These totally flat species are calculated to be at 13 or 12th-order saddle points, with the eight most negative force constants having vectors which correspond to up/down avoidance motions of the proximate hydrogen pairs encircled above and the remaining being buckling modes of the entire ring.

So to the mystery, being the nature of the “flattened” CoTPP on the copper metal surface, as represented in Figure 3 of the article.[cite]10.1038/s41586-019-1059-9[/cite] Is it truly flat, as implied by the article? If so, the energy of such a species would be beyond the limits of what is normally considered feasible. Moreover, it would represent a species with truly mind-blowing short H…H contacts. Or could it be a saddle-shaped geometry, where the phenyl rings are not lying flat in contact with the metal but interacting via the phenyl para-hydrogens? That geometry has not only a much more reasonable energy above the unflattened free molecule, but also acceptable H…H contacts (~2.0.Å) However, would such a shape correspond to the visualised vibrational modes also shown in Figure 3? I have a feeling that there must be more to this story.

^†These convergence problems were solved by improving the basis set via adding “diffuse” functions, as in (u)ωB97XD/6-311+G(d,p). Convergence to the lowest energy electronic state (³B₂) is achieved using a Huckel initial guess rather than the default Harries, which gives the higher energy ³A₂. ^‡If the crystal structure for these species is flattened without geometry optimisation, the H-H distance is around 0.8Å ^♥This blog has a DOI: 10.14469/hpc/5559.

April 25, 2019

Imaging vibrational normal modes of a single molecule.

The topic of this post originates from a recent article which is attracting much attention.[cite]10.1038/s41586-019-1059-9[/cite] The technique uses confined light to both increase the spatial resolution by around three orders of magnitude and also to amplify the signal from individual molecules to the point it can be recorded. To me, Figure 3 in this article summarises it nicely (caption: visualization of vibrational normal modes). Here I intend to show selected modes as animated and rotatable 3D models with the help of their calculation using density functional theory (a mode of presentation that the confinement of Figure 3 to the pages of a conventional journal article does not enable).

I should start by quoting some pertinent aspects obtained from the article itself. The caption to Figure 3 includes assignments, which I presume were done with the help of Gaussian calculations. Thus in the Methods section, we find … The geometry of a free CoTPP molecule is optimized under tight convergence criteria using Gaussian 09 (ref. 33). The orientationally averaged Raman spectrum and vibrational normal modes are calculated with the geometry of a free molecule … All the calculations mentioned above are performed at the B3LYP/6-31G* level with the effective core potential at the cobalt centre. Armed with this information, I looked at the data included with the article (the data supporting the findings of this study are available within the paper. Experimental source data for Figs. 1–4 are provided with the paper) but did not spot any data specifically relating to those Gaussian 09 calculations; in particular any data that would allow me to animate some vibrational normal modes for display here. No matter, it is easy to re-calculate, although I had to obtain the basic 3D coordinates from the Cambridge crystal data base (e.g. entry IKUDOH, DOI: 10.5517/cc6hj4b) since they were unavailable from the article itself. At this point some decisions about molecular symmetry needed to be made (the symmetry is not mentioned in the article), since it is useful to attach the irreducible representations (IR) of each mode as a label^♥ (lacking in Figure 3). The crystal structure I picked has idealised S₄ symmetry, but it could be higher at D_2d or lower at C₂.

The next issue to be solved is how many electrons to associate with the molecule. Tetraphenylporphyrin has 347 electrons and the free molecule would be expected to be a doublet spin state (with the quartet as an excited state). Were the vibrational modes calculated for this state? Perhaps not since I then found this statement: The physisorbed CoTPP is positively charged on gold, as demonstrated through TERS measurements using CO-terminated tips²⁴ and through the Smoluchowski effect²⁹…. In contrast to gold, the Kondo resonance of cobalt disappears on Cu(100), suggesting that it acquires nearly a full electron from the metal (see Extended Data Fig. 2). So it seems worth calculating both the cation and the anion singlets as well as the neutral doublet. But at this stage we do not know for certain what spin state the Gaussian 09 assignments in Figure 3 were done for, since there is no data associated with the article to tell us, only that they were done for the free molecule (nominally a doublet).

There is one more remark made in the article we need to take into account: After lowering the sample bias to approach the molecule and scanning at close range, the molecule flattens. Its phenyl rings, which in the free molecule assume a dihedral angle of 72°, rotate to become coplanar (see Extended Data Fig. 1b). Evidently, the binding energy of the phenyl groups to copper overcomes the steric hindrance in the planar geometry. So it might be useful to calculate this “flattened” form to see how much steric repulsion energy needs to be overcome by that binding of the phenyl groups to the surface of the metal.

Finally, I decided to not try to replicate exactly the reported calculations (B3LYP/6-31G(d)) since this type of DFT mode does not include any dispersion attraction terms; moreover by today’s standards the basis set is also rather small. So here you have an ωB97Xd/6-311G(d,p) calculation, with tight convergence criteria (integral accuracy 10^-14 and SCF 10^-9; again we do not know what values were used for the article). To ensure that my data is as FAIR as possible, here is its DOI: 10.14469/hpc/5461

charge	Multiplicity	ΔG, Twisted Ph Hartree	ΔG, Co-planar Ph Hartree	ΔΔG, kcal/mol
0	Doublet	-3294.58693	-3294.48867	61.7
0	Quartet	-3294.58777	-3294.51985	42.6
+1	Singlet	-3294.35473	-3294.24973	65.9
+1	Triplet	-3294.40821	-3294.33092	48.5
-1	Singlet	-3294.67713	-3294.56652	69.4

Starting with a singlet cation as a model, the intent is to compare the “free molecule” energy with that of a flattened version where the dihedral angles of the phenyl rings relative to the porphyrin ring are constrained to ~0° rather than ~72°. This emerges as a 4th order saddle point (a stationary point with four negative roots for the force constant matrix). Such a property means that each co-planar phenyl group is independently a transition state for rotation. The calculated geometry overall is far from planar, having S₄ symmetry. The image below in (a) shows how non-planar the molecule still is; (b) an attempt to orient it into the same position as is displayed in Figure 3 of the article.[cite]10.1038/s41586-019-1059-9[/cite]

Singlet cation. Click on the image to get a rotatable model.

The free energy ΔG is 65.9 kcal/mol higher than the twisted form, which means that according to the model proposed, the binding energy of the phenyl groups to copper must recover at least this much energy. If we consider a cationic porphyrin interacting with an anionic metal surface as an ion-pair, then this is perhaps feasible. It is difficult however to see how more than two of the phenyl rings can simultaneously interact with a flat metal surface.

Next, the triplet state of the cation, again a 4th-order saddle point with a rotational barrier of ΔG^‡48.5 kcal/mol; the triplet being 33.6 kcal/mol lower than the singlet using this functional (singlet-triplet separations can be quite sensitive to the DFT functional used).

Triplet cation. Click on the image to get a rotatable model.

Next, the neutral doublet, another 4th-order saddle point and below it the quartet state, which this time is just a 2nd-order saddle point (an interesting observation in itself).

Finally, the “flattened” singlet anion, which also emerges as a 4th-order saddle point (~~the triplet state has SCF convergence issues which I am still grappling with~~).

To inspect the vibrational modes of any of these species, click on the appropriate image to open a JSmol display. Then right-click in the molecule window, navigate to the 3rd menu down from the top (Model – 48/226), where the frames/vibrations are ordered in sets of 25. Open the appropriate set and select the vibration you want from the list of wavenumbers shown. The preselected normal mode is the one identified in Figure 3 as 388 cm^-1, the symmetric N-Co stretch (I note the figure 3 caption refers to them as vibrational frequencies; they are of course vibrational wavenumbers!). You can also inspect the four modes shown as negative numbers (correctly as imaginary numbers) to see how the phenyl groups rotate. If you want to analyze the vibrational modes using other tools (the free Avogadro program is a good one), then download the appropriate log or checkpoint file from the FAIR data archives at 10.14469/hpc/5461.

I conclude by noting that the aspect of this article which I presume reports the Gaussian normal vibrational mode calculations (Figure 3, caption Bottom, assigned vibrational normal modes), has been a challenging one to analyse.^† Neither the charge state nor the spin state of these calculations is clearly indicated in the article (unless I missed it somewhere). The barriers to flattening out the molecule by twisting all four phenyl groups are unreported in the article, but emerge as substantial from the calculations here. The various species I calculated (summarised in the table and figures above) are all predicted to be non-planar. In the absence of provided coordinates with the article, the visual appearances (bottom row, Figure 3) are the only information available. These certainly appear flat and rather different from my projections shown above or below.

All of which amounts to a plea for more data and especially FAIR data to be submitted, providing information such as the charge and spin states used for the calculations, along with a full listing of all the normal mode vectors and wavenumbers. The article is only a letter at this stage; perhaps this information will appear in due course!

^†As noted above I have not attempted a direct replication, not least because there is no reported data to which any replication could be compared. ^♥The IRs of each vibrational mode are displayed along with the wavenumber when the 3D JSmol display is shown with a right-mouse-click.

April 18, 2019

Hypervalent hydrogen?
I discussed the molecule the molecule CH₃F^2- a while back. It was a very rare computed example of a system where the added two electrons populate the higher valence shells known as Rydberg orbitals as an alternative to populating the C-F antibonding σ-orbital to produce CH₃^– and F^–. The net result was the creation of a weak C-F “hyperbond”, in which the C-F region has an inner conventional bond, with an outer “sheath” encircling the first bond. But this system very easily dissociates to CH₃^– and F^– and is hardly a viable candidate for experimental detection. In an effort to “tune” this effect to see if a better candidate for such detection might be found, I tried CMe₃F^2-. Here is its story.

The calculation^‡ is at the ωB97XD/Def2-TZVPPD/SCRF=water level (water is here used as an approximate model for a condensed environment, helping to bind the two added electrons).
1. An NBO (Natural Bond orbital) analysis reveals a total Rydberg orbital population of 1.186e and the following bond indices; F 0.853, C 3.977, C(methyl) 4.051, H(*3) 1.332. The latter corresponds to the three methyl hydrogens aligned antiperiplanar to the C-F bond.
2. To put this value into context, the hydrogen in the FHF^– anion has an NBO H bond index of 0.724, and the bridging hydrogens in diborane only have a value of 0.988. Even the hexa-coordinate hydride system [Co₆H(CO)₁₅]^– discussed in an earlier blog has an H bond index of just 0.86. Actually, coordination of six or even higher for hydrogen is no longer rare; some 28 crystal structures of the type HM₆ (M=metal) are known (it would be useful to find out if any of the other 27 such structures might have a hydrogen bond index >1).
3. Next, the ELF analysis (Electron localisation function), analysed firstly using the excellent MultiWFN program.[cite]10.1002/jcc.22885[/cite]
  
  This reveals an attractor basin integrating to 1.663e and located along the axis of the F-C bond and extended into the region of the three antiperiplanar methyl hydrogens. The C-F bond itself only supports a basin of 0.729e, typical of the fairly ionic C-F bond. The covalent C-Me bonds are also pretty normal, as are the other hydrogens.
4. I also show ELF analysis using the alternative TopMod program[cite]10.1016/S0097-8485(99)00039-X[/cite]; the numerical values on this diagram are the calculated bond lengths in Å. The basin integrations are very similar to those obtained using MultiWFN.
  
  The Wiberg bond orders of the three H…H regions shown connected by dashed lines above are 0.154, which contributes to the bond index of >1 at these three hydrogens.
5. The predicted ¹H chemical shift of these three “hypervalent” hydrogens is +3.0 ppm, whilst the other six methyl hydrogens are at -0.87ppm.
So changing CH₃F^2- to CMe₃F^2- has dramatically changed the bonding picture that emerges, rather than a fine-tuning. The C-F is no longer a “hyperbond”, although the Rydberg occupancy of 1.186e remains unusually large. Most of the additional electrons have fled the torus surrounding the C-F bond and relocated to the exo-region of that bond where they now influence the three antiperiplanar methyl hydrogens. A two-electron-three-centre interaction if you like, but with the electron basin occupying a tetrahedral vertex rather than the triatom centroid.

I end with a challenge. Is it possible to find “real” molecules containing hydrogen where the formal bond index for at least one hydrogen exceeds 1.0 significantly, thus making it hypervalent?

^‡The calculations are all collected at FAIR doi; 10.14469/hpc/3372.
January 13, 2018
How does carbon dioxide coordinate to a metal?
Mention carbon dioxide (CO₂) to most chemists and its properties as a metal ligand are not the first aspect that springs to mind. Here thought I might take a look at how it might act as such.

There are up to five binding modes with one metal that one might envisage:
1. Bonded interaction with the metal via just one oxygen atom,
2. Bonded interaction via just the central carbon atom,
3. Bonded interaction via the π-face of one C=O double bond,
4. A weaker non-bonded interaction via carbon, or
5. via oxygen.
Search queries of the Cambridge structure database (CSD) for these five modes are illustrated below (dataDOI: 10.14469/hpc/2524), with the constraints being applied to how many bonds (of unspecified type) each atom carries, along with no disorder and no errors. Thus query 1 is constrained by 1-coordination on one oxygen, and two on the carbon and other oxygen.
1. This query yields four hits: 10.5517/ccvcdq9, 10.5517/cc12nq6n, 10.5517/cc12nq5m, 10.5517/cc12nq4l. The angle subtended at the central carbon of the CO₂ ranges from 172-176°, a very modest bending of the linear CO₂. There are no examples where the metal is bonded to both oxygens.
2. The next category involves the metal binding just to the central carbon. Two examples are known, differentiated from O-coordination by a more acute angle at the central carbon of 121-132°.
3. The π-coordinated type requires a slightly more complex search query, shown below. The π-complex is defined as adding one coordination to each of one oxygen and the carbon.
  
  This reveals 16 examples:
  
  The sine of the angle subtended at the centroid of one C-O bond shows that for most of the examples, the metal is close to perpendicular to this bond. The angle subtended at the central carbon ranges from 128-138, rather larger than the examples where the metal is bound just to the carbon. I have picked these two for illustration. The first (dataDOI: 10.5517/cc86r17) contains both CO₂ and CO coordinated to the metal.This one (dataDOI: 10.1021/ic101652e) contains a short metal-centroid distance of 1.78Å (as also does 10.5517/ccz34kr).
  
  There are two examples where BOTH π-CO bonds are coordinated to a metal; 10.5517/ccqlv7c and 10.5517/ccqlv8d (Ni-centroid distance 1.9Å) but these are intriguing because the two π-complexes are co-planar and not orthogonal.
4. The final two cases are defined in the CSD database by having not so much bonds between metal and either C or O, as close intermolecular contacts typical of e.g. hydrogen bonds. This one (dataDOI: 10.5517/cc12nq9r) is to Fe, with a metal-C distance of 2.87Å which is significantly shorter than the anticipated sum of the van der Waals radii of the two atoms. The next (dataDOI: 10.5517/cc12npn2) has a close approach of Co to O of 2.23Å. The angles subtended at the carbon range from 174-180°. There are no convincing examples of close non-bonded approaches of the metal to both oxygen atoms simultaneously.
It is striking that the searches (as defined above) reveal relatively few examples. This might simply be a result of how the compounds are indexed in the CSD, reflected in the coordination constraints applied in the searches. Nevertheless, we see three quite different types of ligand-metal coordination in which bonds can be said to form and a more diffuse spectrum of weaker interactions to carbon dioxide. As a metal ligand, it is certainly interesting! Several deserve their wavefunctions looked at and I might report back on this aspect.
May 6, 2017
Silyl cations?

It is not only the non-classical norbornyl cation that has proved controversial in the past. A colleague mentioned at lunch (thanks Paul!) that tri-coordinate group 14 cations such as R₃Si⁺ have also had an interesting history.[cite]10.1021/ja990389u[/cite] Here I take a brief look at some of these systems.

Their initial characterisations, as with the carbon analogues, was by ²⁹Si NMR. The first (of around 25) crystal structures appeared in 1994 (below) and they continue to fascinate to this day. I decided to focus on searching the Cambridge structure database (CSD), using the search query shown below (NM = non-metal). For a planar system the three angles subtended at the Si would of course total to 360°.

The first such structure, published in 1994[cite]10.1021/om00018a041[/cite] is shown in 2D representation below

However, the three angles subtended at the Si are 113, 115 and 114°. Could it be that these types of cation are not planar but pyramidal (a ωB97XD/Def2-TZVPP calculation of SiH₃⁺ certainly gives it as planar). Below is a plot of the three angles:

Ringed in red are two systems where all three angles are ~120° (the ones with red dots). The blue circle contains examples where all three angles are <110°. So I took a closer look at the first of these published[cite]10.1021/om00018a041[/cite] and known by the code HAGCIB10 (angles of 113, 115 and 114°). The Si appears to be connected to a toluene present in the crystals via an Si-C bond (blue arrow). If correct, that would account for the angles around Si being <120° and indeed closer to tetrahedral, but it would also mean that the species was actually an arenium cation, otherwise known as a “Wheland intermediate”. That extra bond means that it is not a tri-coordinate silicon, but a four-coordinate silicon and that perhaps the indexing in the CSD needs correcting (as was done here).

Looking further, quite a few of the 25 examples contain so-called “N-heterocyclic carbene” ligands, as below (DOI for 3D model: 10.5517/CC12FWM0[cite]10.1002/chem.201403083[/cite]).

Again one might question the location of the formal +ve charge. Perhaps it might instead reside on the nitrogen as per below, in which case we again do not have a true tri-coordinate silicon cation for systems with such ligands.

This cannot be the whole story, although I would note that Si=C bonds can contain pyramidalised Si. The bonding clearly needs more investigation!

Very probably each of the 25 examples identified by this search as a silylium or silyl cation has its own story to tell. But in unravelling these stories, one should always perhaps take the 2D representations shown in both the CSD and the original publications with a pinch of salt until other possibly better representations such as the one above are excluded.

March 23, 2017
Pyrophoric metals + the mechanism of thermal decomposition of magnesium oxalate.

A pyrophoric metal is one that burns spontaneously in oxygen; I came across this phenomenon as a teenager doing experiments at home. Pyrophoric iron for example is prepared by heating anhydrous iron (II) oxalate in a sealed test tube (i.e. to 600° or higher). When the tube is broken open and the contents released, a shower of sparks forms. Not all metals do this; early group metals such as calcium undergo a different reaction releasing carbon monoxide and forming calcium carbonate and not the metal itself. Here as a prelude to the pyrophoric reaction proper, I take a look at this alternative mechanism using calculations.

There are ~60 crystal structures of metal oxalates, of which several are naturally occurring minerals (Fe, humboldtine[cite]10.1007/s00269-008-0241-7[/cite], Ca, Weddellite[cite]10.1107/S0365110X65002219[/cite], Li[cite] 10.1107/S0365110X64002079[/cite], Na[cite]10.1021/ja01650a007[/cite], K[cite]10.5517/cc6fzcy[/cite], Cs[cite]10.5517/cc6fzf0[/cite]. The natural geometry of the oxalate di-anion is planar (torsion 0 or 180°) but a small number are twisted such as the caesium oxalate.

The kinetics of pyrolysis of a number of metal oxalates were studied some years ago (Ca[cite]10.1021/j100861a029[/cite], Li[cite]10.1039/j19710003043[/cite]) indicating barriers ranging from 53-68 kcal/mol. One proposed mechanism is as shown in this article.[cite]10.1021/j100861a029[/cite]

It was surmised from the kinetic analysis that the k₁ activation step (rotation about the C-C bond from planar to twisted) was ~12 ± 20 kcal/mol, whilst steps k₂ or k₃ had the much higher activation energy noted above. A search (of Scifinder) for quantum mechanical “reality checks” of this mechanism revealed a blank and so I apply such a check here using Mg as the metal.

The carbonyl extrusion step (ωB97XD/Def2-TZVPPD/SCRF=water, DOI: 10.14469/hpc/2320) was studied with a water solvent field applied in an effort to mimic the solid state crystal structure of the species as a better representation of the ionic lattice than a pure vacuum calculation.An IRC (intrinsic reaction coordinate, DOI: 10.14469/hpc/2324) reveals the start-point geometry still has a very small negative force constant (-38 cm^-1, DOI: 10.14469/hpc/2321) which now corresponds to a small rotation about the C-C bond to give a C₂-symmetric conformation:

But the barrier for this process is tiny and nothing like the ~12 ± 20 kcal/mol inferred from the kinetic analysis. Perhaps most of the incentive to pack into a totally planar geometry comes from the interactions in the ionic lattice. The calculated free energy barrier (ΔG₂₉₈^‡ 54.7 kcal/mol, ΔG₇₅₅^‡ 55.1 kcal/mol) is within the reported measured range.

The mechanism for production of pyrophoric metal itself is likely to be far more complex, involving (inter alia) electron transfer from oxygen to metal. If I find anything I will report back here.

March 19, 2017
Molecules of the year? Pnictogen chains and 16 coordinate Cs.

I am completing my survey of the vote for molecule of the year candidates, which this year seems focused on chemical records of one type or another.

The first article[cite]10.1002/chem.201601916[/cite] reports striving towards creating a molecule covering a complete column of the period table. In this case, group 7, containing N, P, As, Sb, Bi and Mc. Only the first four of these were incorporated, although the prospects of extending this to five seem good (and to six extremely unlikely). The structure of this pnictogen chain is referenced here: DOI: 10.5517/CCDC.CSD.CC1LHPJ9 and I have demurred from a calculation.

The second article[cite]10.1021/jacs.6b02590[/cite] relates to what might be called hypercoordination, and the achievement of what is felt is a maximum value of 16 to a single metal. I thought I might approach this one by searching the Cambridge structure database (CSD) by specifying any metal with a coordination number 16 as the search query. However, I was foiled in this query because the search software (Conquest) allows a maximum value of only 15! So instead I list the total number of hits retrieved for coordination numbers of 10-15: 25224, 4753, 8856, 2492, 839, 348 respectively.

These totals have to be taken with some caution; the coordination number of what may often be very weak interactions may be often determined by human chemical perception rather than hard and fast rules. Nevertheless, the assignment of 348 molecules to having a coordination number of 15 is still a remarkably high number. If I can persuade CCDC to allow searches with 16, who knows what other candidates might emerge to rival this one, DOI: CCDC.CSD.CC1KFCQ2

The final candidate[cite]10.1039/C6SC01726F[/cite] is the only one where no measured coordinates are reported, with the title “Preparation of an ion with the highest calculated proton affinity: ortho-diethynylbenzene dianion”. There high level theoretical and computational modelling is reported to which I cannot add anything useful.

The common theme emerging of my review is that most of the candidates have crystal structures to which I have been able to occasionally add some computed quantum mechanical properties to try to tease out some other aspects of their character. It is also nice to be able to cite a persistent identifier (DOI) that leads directly to the 3D coordinates for the structures. My first ever post to this blog in 2008 addressed one solution on how such immediacy might be achieved and it is nice to see this now as a mainstream aspect of chemical publishing.

December 19, 2016
Molecule of the year? “CrN123”, a molecule with three different types of Cr-N bond.

Here is a third candidate for the C&EN “molecule of the year” vote. This one was shortlisted because it is the first example of a metal-nitrogen complex exhibiting single, double and triple bonds from different nitrogens to the same metal[cite]10.1039/c5sc04608d[/cite] (XUZLUB has a 3D display available at DOI: 10.5517/CC1JYY6M). Since no calculation of its molecular properties was reported, I annotate some here.

Firstly, the ¹⁴N spectra were recorded, and so it is of interest to see if the chemical shifts reported can be replicated using calculation (ωB97XD/Def2-TZVPP/SCRF=thf). The method selected is not in the least “optimised” for this nucleus; it is often the case that various permutations of functional and basis set must be probed for the best combination for any particular nucleus. Another limitation of the calculation is that it has been done without the (rather large) counterion in place; a full model should certainly include this. The shifts below are referenced with respect to the internal N≡N signal reported at 310 ppm. The calculations have DOI: 10.14469/hpc/1980 (N₂) and 10.14469/hpc/1983 (CrN123).

Nucleus N-Cr N=Cr N≡Cr

N(obs,thf), ppm 214 560 963

N(calc,thf), ppm 213;223 558 1093

The match is reasonable for three nitrogens; less so for the Cr≡N variety (DOI: 10.14469/hpc/1982) but no doubt could be improved by playing with the method as noted above and probably also correcting for spin-orbit coupling perturbations of the N nucleus by the Cr nucleus. The ¹⁴N shifts of quite a number of other intermediates in the synthesis of this molecule are reported and having a method to hand which can be used to check if the structural assignment matches that calculated for it is always useful.

Next, I have a look at the nature of the Cr-N bonds themselves. The observed lengths are Cr-N: 1.863 (1.862) 1.881 (1.873); Cr=N 1.736 (1.714); Cr≡N 1.556 (1.518)Å. Calculated values in parentheses. To put this into context, I show CSD (Cambridge structure database) searches (search query DOI:10.14469/hpc/1981) for the three types of CrN bond. Firstly the triple bond (65 examples) which reveals the most probable value of ~1.54Å. This matches fairly well with the above values.

Next, Cr=N (50 examples) with a most probable value of 1.65Å. The value reported for CrN123 (1.736Å) is quite a bit longer for this bond. Again a caveat; the searches specified the bond type exactly, and this does then depend very much on how each entry in the CSD was indexed, by humans perceiving the structure and assigning the bond type on the basis of their expert chemical knowledge. It is quite likely that these integer assignments are at best informed estimates and at worst poor guesses.

Finally, Cr-N (1398 examples) with the most probable value of 2.07Å which is a fair bit longer than the two values for CrN123. There are relatively few examples in the region of 1.87Å, which is where the CrN123 values come.

If one repeats this search, but limiting the N atom to carrying two carbons as well as a bond to Cr (as in NPrⁱ₂) one gets the surprise of a bimodal (perhaps even trimodal) distribution, with an additional cluster at lengths of 1.82Å, in closer agreement with CrN123. Again I remind of the caveat that “single” bonds are often assigned by human curators on the basis of perceived chemistry. It would nevertheless be interesting to tunnel down to the possible explanation of this bimodal feature.

These comparisons suggest that in CrN123, the three types of bond are not isolated but may be interacting electronically in a complex manner to increase the bond order of the nominal Cr-NR₂ “single” bonds (Cr=N(+)R₂) whilst decreasing that of the nominal Cr=N “double” bond.

Try try to quantify the bond properties a bit more, I tried the ELF basin population technique. ELF (electron localization function) is one method of partitioning the electron density in the molecule into well defined regions or basins (which we call bonds). The results (DOI: 10.14469/hpc/1984) came out Cr-N 4.05 and 4.01e, each comprising two basins which is often typical of a bond with significant π character. The integration for a single bond is of course 2.0. The Cr=N bond was 5.07e in two basins and that for the Cr≡N 3.26e (far removed from ~6.0 in a triple bond). The valence shell total is 16.4e. These values could be said to be “challenging”, perhaps hinting that the bonding and electron density distribution in this molecule is not quite what it seems. Certainly worth a more detailed look with other methods of bond partitioning.

Well, with M123 synthesized, are there any prospects of a M1234 complex being discovered? (quadruple bonds to N HAVE been suggested!).

December 16, 2016
The largest C-C-C angle?
I am now inverting the previous question by asking what is the largest angle subtended at a chain of three connected 4-coordinate carbon atoms? Let’s see if further interesting chemistry can be unearthed.

Specifying only angles > 130°, the following distribution is obtained.
- Note the maximum at ~138°. This is typical of that found in spiro-cyclopropanes, although I have not checked if other kinds of compound can also sustain this angle.
- There appear to be a few examples at 180° but these appear to be simple errors in the crystal coordinates.
- The first real example occurs at 166°[cite]10.1039/C3DT32335H[/cite] and contains an almost hemispherical carbon atom, doi: 10.5517/CCZBB2P [cite]10.5517/CCZBB2P[/cite]
- A second example is a sprung spiro-cyclopropane [cite]10.1021/ja00186a058[/cite] in which the large angle is maintained without the help of a metal.
- This latter example suggests that a structural modification as shown below might take the angle to almost 180° (calc. ωB97XD/Def2-TZVPP = 177.2°[cite]10.14469/hpc/1861[/cite]).
It is remarkable how much the standard angle subtended at four-coordinate carbon (109.47°) can be opened. It makes one wonder whether something approaching 180° is achievable, and what the properties of such a molecule might be.
November 1, 2016
A wider look at π-complex metal-alkene (and alkyne) compounds.

Previously, I looked at the historic origins of the so-called π-complex theory of metal-alkene complexes. Here I follow this up with some data mining of the crystal structure database for such structures.

Alkene-metal "π-complexes" have what might be called a representational problem; they do not happily fit into the standard Lewis model of using lines connecting atoms to represent electron pairs. Structure 1 was the original representation used by Dewar intending the meaning of partial back donation from a filled metal orbital to the empty π* of the alkene. At the other extreme these compounds can be called metallacyclopropanes (2) in which only single bonds feature (these can be thought of as representing full back bonding from metal to alkene and full forward bonding from alkene to metal). Representations 3 and 4 are a more fuzzy blend of these, implying some sort of partial bond order for the metal-carbon bonds. Taken together, they imply that the formal bond order of the C-C bond might vary between single to double. Structures 1 and 2 in particular imply that there might be two distinct ways in arranging the bonding and that π-complexes and metallacyclopropanes might therefore be distinct valence-bond isomers, each potentially capable of separate existence.

Why do these representations matter? Well, I am going to mine the crystal structure database for these species to try to see if there is any evidence for a bimodal distribution in the C-C lengths, perhaps indicating evidence of the isomerism suggested above. Such a structural database is indexed against atom-pair connectivity in the first instance and then bond type; one can specify the following types of bond connecting any two atoms: single, double, triple, quadruple, polymeric, delocalised, pi and any. It is not entirely obvious which if any of these types apply to structure 1 (it is not possible to draw a bond ending at the mid-point of another bond using the Conquest structure editor); the dashed lines in structures 3 and 4 could be classed as delocalised, pi, or most generally any. The search query can be constructed thus, where the two carbons carry R which can be either H or C and all four C-R bonds are specified as acyclic (to try to avoid complications by excluding compounds such as cyclic metallacenes). Because representation 1 cannot be constructed in the editor, I am going to specify that each carbon carries four bonds of any type in the first instance. The torsion specified is defined as R-C-C-M and the full queries can be found deposited here.[cite]10.14469/hpc/642[/cite]

If the metallacyclopropane representation 2 is defined with explicit single bonds, one gets only 22 hits (no errors, no disorder, R < 0.1). The distribution of C-C bond lengths is shown below. Already one sees a representational problem emerging. A true metallacyclopropane might be expected to show a C-C single bond length, say > ~1.5Å. But only one or two of these examples actually have this value, the most probable value being ~1.4Å.

Using representation 3, one gets 1861 hits, but as before one sees a maximum at ~1.4Å with a tail reaching to both single and double bond values for the C-C distance.^‡

If the C-C bond is also specified as "any", the hits increase to 3948, but the bond length distribution is still very similar, with no sign of any bimodal distribution.

Such a distribution is however found if the torsions between the R-C bond vector and the C-M bond vector are plotted (for all types of bond). A large number of the complexes have a torsion <90°, which suggests that in fact the substituent R is probably interacting with the metal (even though this would lead to formal cyclicity, specifying R-C as acyclic does not detect this interaction). Could this be masking a bimodal distribution in the C-C lengths?

If the previous search is repeated, but this time specifying that all four torsions must lie in the range 90-180° (the range expected for a "classical" alkene-metal complex and selecting only the top right hand side cluster in the plot above) the reduced value of 1051 hits are obtained, but the monomodal distribution remains.

For this last set, here is a plot of the two C-metal bond length, with colour indicating the C-C bond length, indicating the two C-metal bonds are clearly linearly correlated.

One final variation; the atom on either C can only be H or a 4-coordinate (sp³) carbon; 645 hits. Again, a monomodal distribution centered at 1.4Å.

So this foray through metal alkene complexes suggests that there is a continuum between the formal metallacyclopropane with a C-C single bond and the only slightly perturbed alkene-metal complex with a C=C double bond. Whilst this would not prevent any one of these compounds existing as two distinctly different valence-bond isomers, it makes it very unlikely. I had noted in an earlier post that for molecules of the type RX≡XR (X=Si, Ge, Sn, Pb) that there was indeed a clear bimodal distribution of the X-X lengths evident in the crystal structures (for a relatively small sample number). The structures 1-4 shown at the start of this post are all simply just variations in a continuum and not distinct isomers.

POSTSCRIPT: I noted above the bimodel distribution in compounds involving formal triple bonds. So I repeated the search above for π-complex metal-alkyne complexes. Specifying an acyclic C-R bond, and any for the CC bond type, one gets the following.

There is now a tantalizing suggestion of two clusters, one at 1.3 and another at 1.4Å. The torsional distribution shows that the latter distance appears to be associated with much smaller torsions, whereas the top right cluster is associated with shorter lengths.

If the torsions are restricted to the range 90-180, then the histogram looses the smaller cluster, and perhaps gains a second cluster at 1.22Å? As I said, all quite tantalizing!

^‡The tail in all the histograms extends into the 1.1-1.3Å region, which seems unreasonable for a carbon where four bonds are specified. This region probably represents errors in the crystallographic analysis or reporting. But who knows, perhaps some very unusual compounds are lurking there!

June 13, 2016

Nucleus	N-Cr	N=Cr	N≡Cr
N(obs,thf), ppm	214	560	963
N(calc,thf), ppm	213;223	558	1093