THEORY OF 2-DIMENSIONAL FOURIER-TRANSFORM ELECTRON-SPIN-RESONANCE FORORDERED AND VISCOUS FLUIDS

A comprehensive theory for interpreting two-dimensional Fourier transf orm (2D-FT) electron spin resonance (ESR) experiments that is based on the stochastic Liouville equation is presented. It encompasses the fu ll range of motional rates from fast through very slow motions, and it also provides for microscopic as well as macroscopic molecular orderi ng. In these-respects it is as sophisticated in its treatment of molec ular dynamics as the theory currently employed for analyzing cw ESR sp ectra. The general properties of the pulse propagator superoperator, w hich describes the microwave pulses in Liouville space, are analyzed i n terms of the coherence transfer pathways appropriate for COSY (corre lation spectroscopy), SECSY (spin-echo correlation spectroscopy),and 2 D-ELDOR (electron-electron double resonance) sequences wherein either the free-induction decay (FID) or echo decay is sampled. Important dis tinctions are made among the sources,of inhomogeneous broadening, whic h include (a) incomplete spectral averaging in the slow-motional regim e, (b) unresolved superhyperfine structure and related sources, and (c ) microscopic molecular ordering but macroscopic disorder (MOMD). The differing effects these sources of inhomogeneous broadening have on th e two mirror image coherence pathways observed in the dual quadrature 2D experiments, as well as on the auto vs crosspeaks of 2D-ELDOR, is d escribed. The theory is applied to simulate experiments of nitroxide s pin labels in complex fluids such as membrane vesicles, where the MOMD model applies and these distinctions are particularly relevant, in or der to extract dynamic and ordering parameters. The recovery of homoge neous linewidths from FID-based COSY experiments on complex fluids wit h significant inhomogeneous broadening is also described. The theory i s applied to the ultraslow motional regime, and a simple method is dev eloped to determine rotational rates from the broadening of the autope aks of the 2D-ELDOR spectra as a function of the mixing time, which is due to the development of ''motional crosspeaks.'' The application of this method to recent experiments with nitroxide probes illustrates t hat rotational correlation times as slow as milliseconds may be measur ed. It is shown how 2D-ELDOR can be useful to distinguish between the cases of very slow motional (SM) rates with little or no ordering and of very high ordering (HO) but substantial motional rates even though the cw ESR spectra are virtually the same. The effects of motion and o f microscopic ordering on the nuclear modulation patterns in 2D-FT-ESR are compared, and it is suggested that these effects could be utilize d to further distinguish between SM and HO cases. Key aspects of the c hallenging computational problems are. discussed, and algorithms are d escribed which lead to significant reductions in computation time as n eeded to permit nonlinear least-squares fitting of the theory to exper iments.