Multiscale modelling of nuclear magnetisation dynamics: spin relaxation, polarisation transfer and chemical exchange in ¹²⁹Xe@cryptophane(<i>aq</i>) structures

Computational nuclear magnetic resonance (NMR) spectroscopy of supramolecular Xe@cryptophane(<i>aq</i>) complexes requires a multiscale approach due to the interplay of molecular dynamics, spin relaxation, chemical exchange, and solvent effects. The flexible cryptophane cage consists of approximately 150 atoms, including 50 protons, and the encapsulated xenon atom undergoes significant dynamics. Furthermore, the biosensing applications of this structure occur in aqueous, non-deuterated solvents. Consequently, fluctuations in internuclear dipole-dipole (DD) couplings lead to spin relaxation and polarisation transfer between nuclei, with Xe exchange between the solvent and the cage playing a pivotal role. Here, we introduce a novel molecular dynamics (MD)-based approach to simulate DD-driven magnetisation dynamics, incorporating intermolecular relaxation and cross-relaxation effects that are often overlooked in traditional MD-DD modelling. We compute the ¹²⁹Xe and ¹H relaxation times for Xe(<i>aq</i>) and two water-soluble Xe@cryptophane(<i>aq</i>) systems and examine the spin polarisation-induced nuclear Overhauser effect (SPINOE) between hyperpolarised xenon and the surrounding protons, obtaining results in good agreement with the available experimental data. Using a two-site exchange model and first-principles computed Xe chemical shifts, we assess the impact of xenon exchange on observable relaxation and polarisation transfer and simulate the ¹²⁹Xe NMR spectrum, accounting for both chemical exchange and DD relaxation. This work bridges the gap between fully quantum-mechanical spin dynamics simulations and traditional MD-DD approaches and presents the first comprehensive SPINOE modelling and relaxation analysis in xenon biosensor systems.