Why does cyanide pretend to be a weak field ligand in [Cr(CN)5]3-?

Chemical reasoning based on ligand-field theory suggests that homoleptic cyano complexes should exhibit low-spin configurations, particularly when the coordination sphere is nearly saturated. Recently, the well-known chromium hexacyano complex anion [Cr(CN)6](4-) was shown to lose cyanide to afford [Cr(CN)5](3-) in the absence of coordinating cations. Furthermore, (NEt 4)3[Cr(CN)5] was found to be in a high-spin (S=2) ground state, which challenges the common notion that cyanide is a strong field ligand and should always enforce low-spin configurations. Using density functional theory coupled to a continuum solvation model, we examined both the instability of the hexacyanochromate(II) anion and the relative energies of the different spin states of the pentacyanochromate(II) anion. By making direct comparisons to the analogous Fe (II) complex, we found that cyanide electronically behaves as a strong-field ligand for both metals because the orbital interaction is energetically more favorable in the low-spin configuration than in the corresponding high-spin configuration. The Coulombic repulsion between the anionic cyanide ligands, however, dominates the overall energetics and ultimately gives preference to the high-spin complex, where the ligand-ligand separation is larger. Our calculations highlight that for a quantitative understanding of spin-state energetic ordering in a transition metal complex, ligand-ligand electrostatic interactions must be taken into account in addition to classical ligand-field arguments based on M-L orbital interaction energies.