A theoretical study has been carried out on four σ-bond metathesis reactions mediated by the electron-poor lutetium metal centre. The four processes include hydrogen exchange, X2Lu-H + D2 → X2Lu-D + HD (1), and hydrogenolysis X2Lu-CH3 + H2 → Cl2Lu-H + CH4 (2), in which a H—H bond is activated, as well as methane exchange, X2Lu-CH3 + CH4 → X2Lu-CH3 + CH4 (3), and methylation, Cl2Lu-H + CH4 → X2Lu-CH3 + H2 (4), in which a C—H bond is activated. The [Formula: see text] fragment employed in a number of experimental studies was modelled by Cl2Lu and all calculations were based on approximate Density Functional Theory (DFT). The study combined methods from quantum mechanics and statistical mechanics to obtain enthalpies and entropies of activation as well as transition state structures. All four processes were found to have an ordered four-centre transition state with negative entropies of activation given by ΔS≠ = −109(1), −124(2), −131 (3), and −134(4) J mol−1 K−1 at T = 298.15 K. The Gibb's free energies of activation, ΔG≠(= ΔH≠ − TΔS≠) were calculated as ΔG≠ = 81.6 (1), 126.0 (2), 136.7 (3), and 130.6 (4) kJ mol−1 at T = 298.15 K. The calculated trends in ΔG≠ are consistent with the observed order of reactivity for σ-bond metathesis reactions between R—H and M—R′ bonds: R = R′ = H >> R = H, R′ = CH3 > R = R′ = CH3. The decrease in the reaction rate is related to the different abilities of the 1s hydrogen orbital and the [Formula: see text] methyl orbital to stabilize the four-centre transition state. Thus, the spherical 1s hydrogen orbital is better able to overlap fully with orbitals on adjacent centres than the directional [Formula: see text] orbital. As a consequence, the electronic barrier is seen to increase from the hydrogen exchange reaction towards the hydrogenolysis and methane exchange processes as one or two hydrogens, respectively, are replaced by methyl groups in the four-centre transition state. Keywords: Density Functional Theory, C—H activation, metathesis, hydrogenolysis, H—H activation.
