Extended molecular eigenmodes treatment of dipole–dipole NMR relaxation in real fluids

Abstract

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, we describe the relative diffusion of the spin dipoles by means of a Fokker–Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker–Planck equation for the diffusion propagator, we estimate dipole–dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)–aqua and Gd(III)–DO3A–butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen–Purcell–Pound, the Solomon–Bloembergen–Morgan, and the Hwang–Freed models. Our implementation is general and publicly available for application to a broad range of systems.