Estimation of second order rate constants using chemometric methods with kinetic constraints

Several methods are described for determining rate constants for second order reactions of the form U + V --> W using chemometrics and hard modelling to analyse UV absorption spectroscopic data, where all species absorb with comparable concentrations and extinctions. An interesting feature of this type of reaction is that the number of steps in the reaction is less than the number of absorbing species, resulting in a rank-deficient response matrix. This can cause problems when using some of the methods described in the literature. The approaches discussed in the paper depend, in part, on what knowledge is available about the system, including the spectra of the reactants and product, the initial concentrations and the exact kinetics. Sometimes some of this information may not be available or may be hard to estimate. Five groups of methods are discussed, namely use of multiple linear regression to obtain concentration profiles and fit kinetics information, rank augmentation using multiple batch runs, difference spectra based approaches, mixed spectral approaches which treat the reaction as two independent pseudospecies, and principal components regression. Two datasets are simulated, one where the spectra are quite different and the other where the spectrum of one reactant and the product share a high degree of overlap. Three sources of error are considered, namely sampling error, instrumental noise and errors in initial concentrations. The relative merits of each method are discussed.