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

TL;DR

This paper introduces a diagonalization-free method for spin relaxation calculations that significantly improves computational efficiency, enabling analysis of large spin systems in NMR and related fields.

Contribution

It presents a novel reformulation of spin relaxation theory equations that avoids Hamiltonian diagonalization, facilitating the study of larger systems.

Findings

Enables computation of relaxation superoperators for systems with over 15 spins.

Reduces computational cost by replacing diagonalization with numerical integral evaluation.

Applicable to systems dominated by interactions other than Zeeman, such as quadrupolar resonance.

Abstract

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 Ha-miltonian is dominated by interactions other than Zeeman (e.g. in quadrupolar reson-ance, low-field EPR and Spin Chemistry). When used together with state space re-striction tools, the algorithm reported is capable of computing full relaxation supero-perators for NMR systems with more than 15 spins.