Short-chain branching in polyethylene, which involves a six-centre transition state, is studied by ab initio quantum mechanics up to the QCISD(T) level. The calculation gives a (low-pressure) activation energy of 73 kJ mol(-1) and a frequency factor of 4.8 x 10(12) s(-1). The frequency factor for this six-centre transition state is expected to be of acceptable accuracy and also applicable to homologous systems, such as short-chain branching to polymer in acrylates. These results overestimate the amount of ethylene short-chain branching observed in experiment, but the discrepancy is within the uncertainties of both experiment and calculation.