NONLINEAR-LEAST-SQUARES ANALYSIS OF SLOW-MOTION EPR-SPECTRA IN ONE AND 2 DIMENSIONS USING A MODIFIED LEVENBERG-MARQUARDT ALGORITHM

The application of the ''model trust region'' modification of the Leve nberg-Marquardt minimization algorithm to the analysis of one-dimensio nal CW EPR and multidimensional Fourier-transform (FT) EPR spectra esp ecially in the slow-motion regime is described. The dynamic parameters describing the slow motion are obtained from least-squares fitting of model calculations based on the stochastic Liouville equation (SLE) t o experimental spectra, The trust-region approach is inherently more e fficient than the standard Levenberg-Marquardt algorithm, and the effi ciency of the procedure may be further increased by a separation-of-va riables method in which a subset of fitting parameters is independentl y minimized at each iteration, thus reducing the number of parameters to be fitted by nonlinear least squares. A particularly useful applica tion of this method occurs in the fitting of multicomponent spectra, f or which it is possible to obtain the relative population of each comp onent by the separation-of-variables method. These advantages, combine d with recent improvements in the computational methods used to solve the SLE, have led to an order-of-magnitude reduction in computing time , and have made it possible to carry out interactive, real-time fittin g on a laboratory workstation with a graphical interface, Examples of fits to experimental data will be given, including multicomponent CW E PR spectra as well as two- and three-dimensional FT EPR spectra, Empha sis is placed on the analytic information available from the partial d erivatives utilized in the algorithm, and how it may be used to estima te the condition and uniqueness of the fit, as well as to estimate con fidence limits for the parameters in certain cases. (C) 1996 Academic Press, Inc.