The iron complex shown below forms the basis for many catalysts.[1] With iron, the catalytic behaviour very much depends on the spin-state of the molecule, which for the below can be either high (hextet) or medium (quartet) spin, with a possibility also of a low spin (doublet) state. Here I explore whether structural information in crystal structures can reflect such spin states.
We studied this a few years back and the talk I gave on the topic included some of our first statistical explorations of the CSD (Cambridge structure database). Here I update those searches, using the search query (DOI: 10.14469/hpc/2675) shown below. The di-imine ligand contains only 3-coordinate atoms, whilst the iron is 5-coordinate. The angles subtended at the Fe and group X=NM (any non-metal atom) are as defined below.
The resulting scatterplot is shown below and contains a rich variety of phenomena.
Clearly, there is more going on here than can be explained simply by the orientation of X=NM with respect to the Fe-N bond axis. That something is the spin-multiplicity of the molecule. With the Fe complex shown above, this can be one of doublet (one unpaired electron), quartet (three unpaired electrons) or hextet (five unpaired electrons). To gain insight into how this affects the bond lengths, some calculations are needed, using X=Cl, R=H. Here they are done at the TPSSH/Def2-TZVPP level. In fact it is well-known[2] that the energy separations of low/medium/high spin Fe complexes are highly sensitive to the functional, but TPSSH seems to be amongst the best.‡ This shows that the energy ordering of the three states using this particular method is hextet (0.0, DOI: 10.14469/hpc/2676) < quartet (10.5, DOI: 10.14469/hpc/2677) < doublet (13.2 kcal/mol, DOI: 10.14469/hpc/2678), with the bond lengths shown below (for X=Cl).
We might make tentative hypotheses based on these values:
Testing these hypotheses requires knowledge of the spin state of all the entries in any cluster. This information is unfortunately not carried by the CSD, which has relatively little information over and above structural data. Each entry would have to be individually inspected. Indeed the spin state of many of these complexes may not even be known. Nevertheless, it would be great to repeat the graphs shown above as a function of known spin state so that the (again I repeat tentative) hypotheses might be confirmed or refuted.
‡This article evaluates a whole host of functionals against e.g. the spin-state energy separations of the Fe2+ ion. As it happens, TPSSH was not one that was evaluated, but in fact it gives more or less the best match to experiment. Thus Esinglet-Equintet obs = 85.6 kcal/mol, calc 92.4; Etriplet-Equintet obs 56.1, calc 59.5 kcal/mol. A hypothesis therefore is that the TPSSH functional is a reasonable one to go exploring such high-spin species.
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Here are the corresponding plots for Mn and Co, adjacent to Fe. Both seem to show distributions associated with three spin states. For Co, the asymmetry in the Co-N bond lengths appears far greater than for Mn, especially for the putative high-spin state.