Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Abstract

The same experimental data can often be equally well described by multiple mathematically equivalent kinetic schemes. In the present work, we investigate several model-fitting algorithms and their ability to distinguish between mechanisms and derive the correct kinetic parameters for several different reaction classes involving consecutive reactions. We have conducted numerical experiments using synthetic experimental data for six classes of consecutive reactions involving different combinations of first- and second-order processes. The synthetic data mimic time-dependent absorption data as would be obtained from spectroscopic investigations of chemical kinetic processes. The connections between mathematically equivalent solutions are investigated, and analytical expressions describing these connections are derived. Ten optimization algorithms based on nonlinear least squares methods are compared in terms of their computational cost and frequency of convergence to global solutions. Performance is discussed, and a preferred method is recommended. A response surface visualization technique of projecting five-dimensional data onto the three-dimensional search space of the minimal function values is developed.