Ab initio electronic structure theory provides the practical means to calculate the total electronic energy of moderate-sized molecules. From such data, we can calculate thermochemical properties and, in principle, the complete potential energy surface that governs the motion of the atomic nuclei. Hence, chemical reaction dynamics, rate coefficients, and other observables may be evaluated. However, the computational time required to calculate the total electronic energy increases rapidly with the number of electrons in the molecule, and with the level of ab initio theory employed. We have developed a systematic hierarchy of methods for decomposing a molecule into fragments to obtain a series of approximations to the total electronic energy, at relatively low computational expense. A general computer code has been developed to implement this approach to evaluate molecular energies and energy gradients (and higher derivatives in some cases) and perform geometry optimisation. This approach has recently been applied to the construction of complete PES for polyatomic reactions (for example, H + CH3(CH2)3CH3), opening the possibility for detailed dynamics studies of reaction of large molecules. Further development of the methodology has concentrated on the approximation of the relatively weak long-range interactions between well-separated segments of molecules, in collaboration with Professor Mark Gordon (Iowa State U) and Professor Peter Gill.