Notes on Direct Simulation Methods for Electron Paramagnetic Resonance Spectra

Direct simulation methods of Electron Paramagnetic Resonance (EPR) spectra are an alternative to standard eigenfunction-based approaches. Both methods can be employed to find numerical solutions of the Stochastic Liouville Equation (SLE) in order to compute spectral lineshapes. It can be shown rigorously that the domain of validity of eigenfunction expansion solutions of the SLE covers only a limited range of parameter space. Although the computed spectrum in the linear response regime may appear ‘reasonable’, the eigenvectors and eigenvalues of the matrix representation of the spectral resolvent are only approximately correct. This is a serious issue for the accurate representation of time domain experiments, where the eigenvalues and eigenvectors must be known precisely. With the advent of time-domain experiments at high fields on fluid systems, the breakdown of standard eigenfunction expansions is more acute. It is clear that a more accurate method of spectral simulation is needed to address these issues. Direct simulation of the spectra from a time series of molecular orientations does not suffer from the defects of eigenfunction expansion methods and may be usefully combined with state of the art molecular dynamics simulations both in the linear response regime and in the non-linear response regime.