Origin of Long-Lived Nuclear Spin States and Coherences in Aliphatic Chains Revealed by Relaxation Theory

Delocalized long-lived states (LLSs) and collective zero-quantum long-lived coherences (LLCs) in aliphatic chains provide a promising route for preserving nuclear spin order with lifetimes that exceed the conventional $T_1$ and $T_2$ relaxation times, respectively. Their extended lifetimes make them attractive for applications including hyperpolarization storage, ligand-observed drug screening based on the loss of longevity upon binding to a target protein, and quantum information processing exploiting the collective properties of many-body spin systems. Although LLSs and LLCs have been observed experimentally in methylene networks, their origin and general structure in chains of arbitrary length have remained unclear. Here we show that these relaxation-protected modes follow directly from Redfield relaxation theory. Specifically, we construct the long-lived subspace, i.e., the zero-eigenvalue subspace of the relaxation superoperator associated with the dominant intra-pair dipole--dipole relaxation mechanism. The long-lived subspace contains $2^N-1$ independent non-trivial operators, which excludes the identity operator, where $N>1$ is the number of $-\mathrm{CH}_2-$ groups in the chain. In achiral molecules, conservation of the global intra-pair permutation parity restricts experimental access to at most $2^N-2$ of these operators, whereas in chiral molecules this parity is not conserved, making up to $2^N-1$ long-lived operators accessible. We further develop a general framework for constructing both LLSs and LLCs in aliphatic chains containing an arbitrary number of $-\mathrm{CH}_2-$ groups in achiral molecules, and illustrate the approach explicitly for chains with $N=2$, 3, and 4 methylene groups.

Source: arXiv:2608.07219v1 - http://arxiv.org/abs/2608.07219v1 PDF: https://arxiv.org/pdf/2608.07219v1 Original Link: http://arxiv.org/abs/2608.07219v1