Multiple Bonds Between Metal Atoms / 03-Chromium Compounds

Chromium Compounds 65

Cotton

3.4Concluding Remarks

The number of isolated dichromium compounds is large, probably several hundred. Counting only those for which there are crystal structures, there are at least 110. Many of the earliest carboxylates, of course, have never been structurally characterized and have not been discussed here individually. Another entity not discussed here is the gaseous Cr2 molecule, in which the Cr–Cr distance is about 1.68 Å. The entire range of Cr–Cr distances in isolable compounds, from c. 1.83 Å to c. 2.7 Å, occurs within a common paddlewheel arrangement of ligands. The problem posed by this is how best to formulate the interactions between the chromium atoms and explain why they vary so much. It has been established, empirically, that axial ligation is the most important factor influencing Cr–Cr bond lengths.

While all CrII–CrII interactions can, presumably, be regarded as having μ, / and β components, these are not distinctly separated as in analogous MoII–MoII compounds. The strengths of these interactions, like all others, must vary inversely with Cr–Cr distance. At distances <2.00 Å it seems reasonable to assign μ2/4β2 quadruple bonds. At much longer distances it is clear that the β bonding becomes so weak that population of a state based on a triplet ββ* configuration is easily detected and quantified, as discussed in Section 3.1.2. Over the entire range of Cr–Cr distances all of the orbital overlaps, μμ, // and ββ will vary continuously. It is possible that at the longest distances, the covalence in the Cr–Cr interactions might be negligible and the interaction regarded as mere antiferromagnetic coupling. However, there are no criteria, either experimental or theoretical, for drawing any line of demarcation, and probably none exists.

The failure of Hartree-Foch calculations to provide a useful description of the bonding in Cr24+ compounds was referred to in Section 3.1.3. The source of the difficulty lies in the severe problem of electron correlation, a matter that was addressed in an instructive way by M. B. Hall.69 Clearly, calculations without any allowance for configuration interaction70,71 give hopelessly erroneous results. The idea of distinct LCAO-MOs, each occupied by an electron pair, is too simple an approximation, although it serves well for Mo24+ compounds. Even efforts to salvage it by adding heavy corrections for configuration interaction72-77 are of doubtful value. Neither generalized valence bond calculations nor DFT have given anything like satisfactory results either. The only calculations that have given any theoretical inkling that a bare Cr2(O2CR)4 molecule could have a Cr–Cr distance below 2.00 Å were done by a complete- active-space, self-consistent-field (CASSCF) method applied to Cr2(O2CH)4.118 A measurement of the photoelectron spectrum119 of Cr2[(p-tol)NC(H)N(p-tol)]4 showed that the nominal μ, / and β orbitals, together with some ligand-based orbitals, are all bunched together in a range of 0.81 eV.

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