Quantitative assessment of the carbocation/carbene character of the gold-carbene bond

The geometric perturbation of the cyclopropyl ring in [LAu(S)](n+) (S = cyclopropyl(methoxy) carbene) complexes has been recently proposed as an indirect experimental probe of the [LAu](n+) electron-donating power, but experimental data are available only for a phosphine ligand [Brooner et al., Chem. Commun., 2014, 50, 2420, L = P(t-Bu)(2)(o-biphenyl)]. We broaden the study through DFT geometry optimization of a large number of systems, including anionic, neutral and cationic ligands. We combine these results with the accurate calculation, through charge displacement analysis, of the Dewar-Chatt-Duncanson components of the Au-carbene bond. The results demonstrate a linear correlation between the distortion of the cyclopropyl ring (Delta d) and the Au -> C pi back-donation, which enables us to confidently estimate back-donation from a simple geometry optimization or, when available, from experimental data such as X-ray crystal structures. Consequently, Delta d can be reliably used to quantitatively determine the position of each system in the continuum between the carbocationic and carbene extremes and the percentage of back-donation that S is able to accept (P-back). In particular, P-back results to be vanishing with cationic ligands, between 18 and 27% with neutral phosphines and carbenes and around 50% with anionic ligands. Finally, we study the effect of the heteroatom on the substrate, showing that the absolute value of the back-donation is enhanced by around 25% when the methoxy is substituted by a methyl group. Despite this, since the absence of the heteroatom also enhances the maximum capacity of the carbene to accept back-donation, the position of the systems in the continuum moves only slightly toward the carbene end.