Determination of the NMR monomer shift and dimerization constant in a self-associating system by direct application of the least-squares method

Abstract

The monomer shift and dimerization constant of a self-associating system have been determined directly by applying the least-squares method to the NMR experimental data. Equations have been obtained in which two analytic methods can be applied. In the first method, a value of the dimerization constant is assumed and by linear regression the error sum of squares (ESS) is calculated. The minimum ESS is located by a five-point searching algorithm. In the second method, non-linear regression analysis of the model equation with the least-squares method results in a single equation of unknown K. A conventional root finding method is then applied from which the values of monomer shift and dimerization constant are determined. The numerical procedures proposed in this paper have been illustrated with an example using previously published experimental NMR data. Results of calculations are discussed.