Transition-state energy and position along the reaction coordinate in an extended activation strain model

We investigate polladium-induced activation of the C-H, C-C, C-F, and C-Cl bonds in methane, ethane, cyclopropone, fluoromethane, and chloromethane, using relativistic density functional theory (DFT) at ZORA-BLYP/TZ2P Our purpose is to arrive at a qualitative understanding, based on accurate calculations, of the trends in activation barriers and transition state (TS) geometries (e.g. early or late along the reaction coordinate) in terms of the reactants' properties. To this end, we extend the activation strain model (in which the activation energy Delta E-not equal is decomposed into the activation strain Delta E-strain(not equal) of the reactants and the stabilizing TS interaction Delta E-int(not equal) between the reactants) from a single-point analysis of the TS to an analysis along the reaction coordinate xi, that is, Delta E(xi)=Delta E-strain(xi)+Delta E-int(xi). This extension enables us to understand qualitatively, trends in the position of the TS along xi and, therefore, the values of the activation strain Delta E-strain(not equal)=Delta Estrain(xi(TS)) and TS interaction Delta E-int(not equal) = Delta E-int(xi(TS)) and trends there-in. An interesting insight that emerges is that the much higher barrier of metal-mediated C-C versus C-H activation originates from steric shielding of the C-C bond in ethane by C-H bonds. Thus, before a favorable stabilizing interaction with the C-C bond can occur, the C-H bonds must be bent away, which causes the metal-substrate interaction Delta E-int(xi) in C-C activation to lag behind. Such steric shielding is not present in the metal-mediated activation of the C-H bond, which is always accessible from the hydrogen side. Other phenomena that are addressed are anion assistance, competition between direct oxidative insertion (Oxln) versus the alternative S(N)2 pathway, and the effect of ring strain.