SummaryThe determination of the dimerisation constant (KD) for the weak self-association of a compound C in dilute solution according to the equilibrium, 2Cz+C, is described. The method uses chemical shifts measured on a series of solutions of C at different concentrations: the optimum K D is defined by a linear regression best-f& procedure, which simultaneously determines optimum values for 6, and d s o for 6,, the intrinsic chemical shifts for nuclei in the monomer and dimer species. 'The dimerisation of caffeine in D,O is used as a model to demonstrate the working of the method and the quality of results obtained. The most probable value of K D for caffeine at 30.5" is found in the range 5.5-6.0 kg solution.mol-', and the enthalpy and entropy of dimerisation are found to be A H e = -15.1 kJ.mol-l and ASe = -35.3 J."C-'.mol-', respectively. The influence of small errors in 6, on the confidence limits of KD is discussed.Weak complexes are important in molecular biology and in pharmacology €or interpreting biomechanisms and modes of drug action [I]. Methods to date for determining association constants ( K ) of weak molecular complexes as defined in Eqn. 1 and 2 have often been approximate, and there have been many reports of anomalous results[2]. We have recently described a method for estimating KAB values as defined in Eqn. I from complexation-induced displacements of NMR line positions in equimolar solutions of the reactants A and B [3]. We report here an improved version of that method and show how it can be applied to study dimerisation according to Eqn.2. Relative to our earlier method, our present approach shows the following advantages: it is about 20 times faster in calculation time, it uses standard linear least-squares statistical methodology, it can be implemented on a relatively modest programmable desk calculator, and it permits the ready estimation of error limits for complex parameters. Further, it retains our rigorous mathematical treatment of the law of mass action equation; this we feel is important for the estimation of complex parameters which can be validly compared from one complex to another.NMR has often been exploited to determine association constants (KAB) for weak bimolecular complexes forming according to Eqn