OPTESIM, a versatile toolbox for numerical simulation of electron spin echo envelope modulation (ESEEM) that features hybrid optimization and statistical assessment of parameters

Electron spin echo envelope modulation (ESEEM) is a technique of pulsed-electron paramagnetic resonance (EPR) spectroscopy. The analyis of ESEEM data to extract information about the nuclear and electronic structure of a disordered (powder) paramagnetic system requires accurate and efficient numerical simulations. A single coupled nucleus of known nuclear g value (g_N) and spin I = 1 can have up to eight adjustable parameters in the nuclear part of the spin Hamiltonian. We have developed OPTESIM, an ESEEM simulation toolbox, for automated numerical simulation of powder two- and three-pulse one-dimensional ESEEM for arbitrary number (N) and type (I, g_N) of coupled nuclei, and arbitrary mutual orientations of the hyperfine tensor principal axis systems for N > 1. OPTESIM is based in the Matlab environment, and includes the following features: (1) a fast algorithm for translation of the spin Hamiltonian into simulated ESEEM, (2) different optimization methods that can be hybridized to achieve an efficient coarse-to-fine grained search of the parameter space and convergence to a global minimum, (3) statistical analysis of the simulation parameters, which allows the identification of simultaneous confidence regions at specific confidence levels. OPTESIM also includes a geometry-preserving spherical averaging algorithm as default for N > 1, and global optimization over multiple experimental conditions, such as the dephasing time (τ) for three-pulse ESEEM, and external magnetic field values. Application examples for simulation of ¹⁴N coupling (N = 1, N = 2) in biological and chemical model paramagnets are included. Automated, optimized simulations by using OPTESIM lead to a convergence on dramatically shorter time scales, relative to manual simulations.