One of the most powerful experimental techniques for probing the nature of the transition state (TS) is the measurement of a kinetic isotope effect (KIE). The magnitude and direction of a KIE contains information about the mechanistic events in a chemical reaction, reflecting differences in bonding between the reactants and the TS. However, the interpretation of a KIE as a measure of TS structure requires a sound theoretical framework. Previously, qualitative theories have allowed qualitative conclusions to be drawn, but the development of QM techniques for the study of organic reaction mechanisms now poses questions regarding whether meaningful quantitative information can be obtained from KIEs. Many workers have hitherto assumed an optimistic stance on this question, but a recent important paper has cast a ray of cold, bright light upon the issue. It concludes that the current portfolio of conventional QM methods is not capable of reproducing the range of KIEs measured experimentally for isotopic substitution at six positions in a prototypical SN2 reaction of cyanide anion with chloroethane in DMSO. This fact is an awkward reality that sits uneasily alongside the ambition of computational chemistry to provide reliable models for the rationalisation of known chemical behaviour and the prediction of unknown behaviour.The aim of this project is to investigate ways to overcome this gap between theory and experiment concerning KIEs for simple organic reactions in solution, and thereby to bring an important part of physical organic chemistry into the 21st century. Furthermore, we wish to perform a critical update on some of the received wisdom concerning the meaning of KIEs observed in prototypical organic reactions that has accumulated over the past 40 or 50 years, largely on the basis of over-simplified theoretical models and unjustified assumptions.The key development we will introduce is ensemble averaging of force constants or frequencies for collections of structures in the region of the reactant state and of the transition state which provide representative samples of many different solvent configurations. These ensembles of snapshots will be generated from molecular dynamics simulations, and the force constants will be computed by combined quantum/classical methods for reacting species and specifically solvating molecules with the frozen environment of the surrounding solvent.It is necessary first to bring together a number of methodological developments into a suite of computational codes for practical application. This is a non-trivial exercise since the applications proposed are novel, and significant tweaking will be required to achieve optimal performance for the types of molecular systems and chemical problems to be addressed. Second, it makes sense to begin the applications work by considering isotope effects for molecules at equilibrium since the recommended protocol for ensemble-averaged vibrational frequencies has been developed for this case. Third, all four KIE applications involve aliphatic nucleophilic substitution, with which the PI has experience but which still present significant challenges for mechanistic interpretation that are timely to address now.