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Traditional theories of the NMR autocorrelation function for intramoleculardipole pairs assume single-exponential decay, yet the calculatedautocorrelation of realistic systems display a rich, multi-exponential behaviorresulting in anomalous NMR relaxation dispersion (i.e., frequency dependence).We develop an approach to model and interpret the multi-exponentialautocorrelation using simple, physical models within a rigorous statisticalmechanical development that encompasses both rotational and translationaldiffusion in the same framework. We recast the problem of evaluating theautocorrelation in terms of averaging over a diffusion propagator whoseevolution is described by a Fokker-Planck equation. The time-independent partadmits an eigenfunction expansion, allowing us to write the propagator as a sumover modes. Each mode has a spatial part that depends on the specifiedeigenfunction, and a temporal part that depends on the corresponding eigenvalue(i.e., correlation time) with a simple, exponential decay. The spatial part isa probability distribution of the dipole-pair, analogous to the stationarystates of a quantum harmonic oscillator. Drawing inspiration from the idea ofinherent structures in liquids, we interpret each of the spatial contributionsas a specific molecular mode. These modes can be used to model and predict NMRdipole-dipole relaxation dispersion of fluids by incorporating phenomena on themolecular level. We validate our statistical mechanical description of thedistribution in molecular modes with molecular dynamics simulations interpretedwithout any relaxation models or adjustable parameters: the most importantpoles in the Pad{\'e}-Laplace transform of the simulated autocorrelation agreewith the eigenvalues predicted by the theory.

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