Computational Modeling and Least-Squares Fittingof EPR Spectra

In EPR (electron paramagnetic resonance) spectroscopy, computer simulation and least-squares fitting are essential in extracting quantitative structural and dynamic parameters from experimental spectra.Without numerical methods, this extraction would be restricted to simple systems. This chapter summarizes simulation and fitting methods that have been proposed in the literature and implemented in software. It includes an extensive, though not complete, list of references. Emphasis is placed on methods currently implemented in the software package EasySpin [1], which covers EPR simulations in the following regimes: (i) rigidlimit continuous-wave (cw) EPR spectra for arbitrary spin systems, for both powders and single crystals, at various levels of theory including eigenfields, matrix diagonalization, and perturbation theory; (ii) dynamic EPR spectra of tumbling spin centers with one electron spin and several nuclei, implementing stochastic Liouville equation (SLE) solvers and perturbative approaches; (iii) EPR spectra in the fast-motion limit, using either a Breit–Rabi solver or perturbation theory; (iv) dynamic EPR spectra due to chemical exchange in solution, implementing a direct Liouville-space method; (v) solid-state ENDOR (electron nuclear double resonance) spectra based on eithermatrix diagonalization or perturbation theory; and (vi) pulse EPR spectra for general pulse sequences using the Hilbert-space density matrix formalism in the high-field limit. All these simulation regimes are reviewed in the following. Similarly to many other programs, EasySpin also provides a range of leastsquaresfitting algorithms, among themLevenberg–Marquardt (LM),Nelder–Mead simplex, genetic algorithms, particle-swarm optimization, as well as simple Monte Carlo and grid searches. These algorithms, as well as the objective function choice, multicomponent fitting, and error analysis, are discussed below. This chapter is not intended to be a complete review of all theory underlying EPR simulation methods, which would be utterly impossible. Instead, it summarizes theoretical and algorithmic aspects that are implemented in or are relevant to EasySpin. Applicability and limitations of methods are discussed as well. The