This potential example of a molecule on the edge of chaos was suggested to me by a student (thanks Stephen!), originating from an inorganic tutorial. It represents a class of Mo-complex ligated by two dithiocarbamate ligands and two aryl nitrene ligands (Ar-N:).
I focus on two specific examples[1], where R=R’ = H or Me, with crystal structures available for both. The reason for its appearance in a tutorial is that it provides a nice example of electron counting. Relocated to a tutorial on organic chemistry, it might also provide an interesting challenge for drawing a Lewis structure. So before we deal with the edge of chaos, let me start with the electron counting/Lewis structure. I have set out three possibilities for these above.
We can now apply the reality check of inspecting the crystal structure.
What happens with R=Me? The two angles are now 167 and 175°, a mere 8° different. The system appears to have “flipped” from 6+4 bonding heading to 5+5 bonding, all because of an apparently innocuous change on the two aryl groups.
With this sort of behaviour, one has to ask if it might in fact be a crystallographic artefact. One way of checking this is to calculate the geometries of the two molecules, at the ωB97XD/Def2-TZVPD level in this instance. Any errors are at least systematic, and not subject to crystallographic effects. For R=H,[2] the two angles subtended at N are 175.1 and 146.6, a difference of 28.5°, in good agreement with the crystallographic value of 30°. For R=Me, the values are 169 and 152°, a difference of 17°. It is certainly less than for R=H, but a bit more than is apparently measured (8°).
On balance, I think we probably can assign these two Mo complexes to the category of molecules on the edge of chaos, where the mere replacement of an o-H by an o-Me can have a big change on the angles at N.
In an earlier post, I discussed a phenomenon known as the "anomeric effect" exhibited by…
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…
View Comments
Here is another example of bimodal bond angles (thanks Mark!), from doi: 10.1002/anie.201100816
The unique feature here is that at each Ru centre, one equatorial nitroso ligand is clearly bent (124°) and one axial is perfectly linear. This is replicated with a calculation (ωB97XD/Def2-SVPD), which gives one nitroso bent with angle 126.9° and the other linear (doi: 10.6084/m9.figshare.810402).
If Ru2+ is [Kr].4d6, it receives six electrons from respectively the two-electron donors axial Cl-: (obs. Cl-Ru distance 2.349Å), ether O: and bent O=N: (obs. N-Ru distance 1.915Å), requiring six more electrons to achieve an 18-electron configuration. To explain why the second nitroso group is linear, I suggest a four-electron ON=Ru bond (obs. N-Ru distance 1.727å) rather than ON-Ru, which leaves just two electrons from one of the two asymmetrically bridging chlorines (obs. Cl-Ru distances 2.392Å and a longer 2.812Å) to make up the 18. So, rather than each Ru receiving four electrons in total (two each) from the two bridging chlorines, which would require both nitroso groups to be bent as two electron donors, the molecule decides to linearise one of the NO groups instead as a four-electron donor and to downgrade one of the bridging chlorines as a donor by lengthening its bond length to the Ru.
Certainly, a further interesting example not only of bimodal angle behaviour, but of associated bimodal bond length behaviour!
Mark (in an email) has raised the possibility of a counting scheme for the nitroso complex above that starts from Ru(IV); [Kr].4d4. If one follows the (formal) covalencies outlined above, one must get to a 16-electron valence shell for Ru. The two electrons ionised from the Ru must end up on the ligands somewhere, but not in the covalent bonds to Ru. One might think this should then be reflected in the calculated partial atomic charge on Ru.
In this regard, an interesting new charge scheme has been proposed in 2012 (CM5: doi: 10.1021/ct200866d) which has been parametrised by "fitting to reference values of the gas-phase dipole moments of 614 molecular structures". This enables, in an empirical manner, a direct correlation between partial atomic charges and the measurable property of a dipole moment.
When the CM5 analysis is applied to the complex above (doi: 10.6084/m9.figshare.810445), the Ru = +0.77. The older Hirshfeld charge is +0.15. On the face of it, this probably does not provide any overwhelming evidence for Ru(IV) involvement. But of course charge schemes are only one way of partitioning electrons! (I wonder for example if the CM5 scheme is equally successful at predicting quadrupole moments in molecules?)
The Ru(II)/Ru(IV) debate (along with others, i.e. Pd(II)/Pd(IV), Cu(I)/Cu(III) etc) can be juxtaposed with the Hg(IV) story at doi: 10.1002/anie.200703710). It may be that many of these systems exhibit multi-reference character in their wavefunctions, which makes any single-reference analysis of the charge distribution only a very approximate estimation (I should note that multi-reference character further degrades the concept of integer formal charges, and one is forced to accept non-integer formal charges as inevitable. Which rather destroys their conceptual simplicity).