Activation of C-H and B-H bonds through agostic bonding: an ELF/QTAIM insight

Agostic bonding is of paramount importance in C-H bond activation processes. The reactivity of the σ C-H bond thus activated will depend on the nature of the metallic center, the nature of the ligand involved in the interaction and co-ligands, as well as on geometric parameters. Because of their importance in organometallic chemistry, a qualitative classification of agostic bonding could be very much helpful. Herein we propose descriptors of the agostic character of bonding based on the electron localization function (ELF) and Quantum Theory of Atoms in Molecules (QTAIM) topological analysis. A set of 31 metallic complexes taken, or derived, from the literature was chosen to illustrate our methodology. First, some criteria should prove that an interaction between a metallic center and a σ X-H bond can indeed be described as "agostic" bonding. Then, the contribution of the metallic center in the protonated agostic basin, in the ELF topological description, may be used to evaluate the agostic character of bonding. A σ X-H bond is in agostic interaction with a metal center when the protonated X-H basin is a trisynaptic basin with a metal contribution strictly larger than the numerical uncertainty, i.e. 0.01 e. In addition, it was shown that the weakening of the electron density at the X-Hagostic bond critical point with respect to that of X-Hfree well correlates with the lengthening of the agostic X-H bond distance as well as with the shift of the vibrational frequency associated with the νX-H stretching mode. Furthermore, the use of a normalized parameter that takes into account the total population of the protonated basin, allows the comparison of the agostic character of bonding involved in different complexes.