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We propose three basis screening methods for state space restriction in Liouville space simulations of large densely coupled spin systems encountered in electron paramagnetic resonance (EPR) spectroscopy and spin chemistry. The methods are based on conservation law analysis, symmetry factorization, and the analysis of state space connectivity graphs. A reduction in matrix dimensions by several orders of magnitude is demonstrated for common EPR and spin chemistry systems.

A numerical procedure is presented for mapping the vicinity of the null-space of the spin relaxation superoperator. The states populating this space, i.e. those with near-zero eigenvalues, of which the two-spin singlet is a well-studied example, are long-lived compared to the conventional T(1) and T(2) spin-relaxation times. The analysis of larger spin systems described herein reveals the presence of a significant number of other slowly relaxing states. A study of coupling topologies for n-spin systems (4≤n≤8) suggests the symmetry requirements for maximising the number of long-lived states.

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