Predicting 1H NMR relaxation in Gd3+-aqua using molecular dynamics simulations

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker-Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole-dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.

Effect of Nanoconfinement on NMR Relaxation of Heptane in Kerogen from Molecular Simulations and Measurements

Kerogen-rich shale reservoirs will play a key role during the energy transition, yet the effects of nanoconfinement on the NMR relaxation of hydrocarbons in kerogen are poorly understood. We use atomistic MD simulations to investigate the effects of nanoconfinement on the ¹H NMR relaxation times T₁ and T₂ of heptane in kerogen. In the case of T₁, we discover the important role of confinement in reducing T₁ by ∼3 orders of magnitude from that of bulk heptane, in agreement with measurements of heptane dissolved in kerogen from the Kimmeridge Shale, without any models or free parameters. In the case of T₂, we discover that confinement breaks spatial isotropy and gives rise to residual dipolar coupling which reduces T₂ by ∼5 orders of magnitude from the value for bulk heptane. We use the simulated T₂ to calibrate the surface relaxivity and thence predict the pore-size distribution of the organic nanopores in kerogen, without additional experimental data.

NMR Relaxivities of Paramagnetic, Ultra-High Spin Heterometallic Clusters within Polyoxometalate Matrix as a Function of Solvent and Metal Ion

Selectivity and image contrast are always challenging in magnetic resonance imaging (MRI), which are - inter alia - addressed by contrast agents. These compounds still need to be improved, and their relaxation properties, i. e., their paramagnetic relaxation enhancement (PRE), needs to be understood. The main goal is to improve specificity and relaxivities, especially at the high magnetic fields currently exploited not only in material science but also in the medical environment. Longitudinal and transverse relaxivities, r₁ and r₂ , which correspond to the longitudinal and transverse relaxation rates R₁ and R_2, normalized to the concentration of the paramagnetic moieties, need to be considered because both contribute to the image contrast. ¹ H-relaxivities r₁ and r₂ of high-spin heterometallic clusters were studied containing lanthanide and transition-metal ions within a polyoxometalate matrix. A wide range of magnetic fields from 0.5 T/20 MHz to 33 T/1.4 GHz was applied. The questions addressed here concern the rotational and diffusion correlation times which determine the relaxivities and are affected by the solvent's viscosity. Moreover, the variation of the lanthanide and transition-metal ions of the clusters provided insights into the sensitivity of PRE with respect to the electron spin properties of the paramagnetic centers as well as cooperative effects between lanthanides and transition metal ions.