Diagonalization-free implementation of spin relaxation theory for large spin systems

The Liouville space spin relaxation theory equations are reformulated in such a way as to avoid the computationally expensive Hamiltonian diagonalization step, replacing it by numerical evaluation of the integrals in the generalized cumulant expansion. The resulting algorithm is particularly useful in the cases where the static part of the Hamiltonian is dominated by interactions other than Zeeman (e.g. in quadrupolar resonance, low-field EPR and Spin Chemistry). When used together with state space restriction tools, the algorithm reported is capable of computing full relaxation superoperators for NMR systems with more than 15 spins.

Static Hamiltonian diagonalization is avoided in Bloch-Redfield-Wangsness theory, leading to a more numerically efficient algorithm that is useful in large-scale simulations.101Research Highlights► Bloch-Redfield-Wangsness relaxation theory is reformulated in a way that avoids matrix diagonalization. ► It is shown that the integral in the master equation can be more efficiently evaluated by a numerical quadrature. ► The resulting approach can generate full relaxation superoperators for bigger spin systems than was previously possible.