Applying quantum-chemical methods to the reactions of larger molecules, such as in free-radical polymerisation, poses a major challenge. Not only do accurate methods require significant computer power, the computational cost of a method scales exponentially with the size of the molecule. To address this problem, we have designed a reliable low-cost methodology for studying radical reactions that involves the use of an ab initio version of the ONIOM method, the design of small model reactions, capable of mimicking the kinetic behaviour of their larger counterparts, and additional cost-saving measures such as our new efficient algorithm (called Energy-Directed Tree Search) for exploring the conformational space of larger molecules. We have demonstrated that our computational methodology delivers chemical accuracy for radical polymerisation kinetics, radical thermochemistry in general, and the prediction of one- and two-electron redox potentials of a range of biologically active species. We have also combined ab initio calculations with kinetic modelling techniques, so as to produce the first ab initiosimulation of an entire polymerisation process from first principles. In a proof-of-principle study, we modelled initialisation in RAFT polymerisation, demonstrating excellent agreement between theory and experiment.