  Traditional theories of the NMR autocorrelation function for intramolecular
dipole pairs assume single-exponential decay, yet the calculated
autocorrelation of realistic systems display 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
autocorrelation using simple, physical models within a rigorous statistical
mechanical development that encompasses both rotational 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 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 Pad{\'e}-Laplace transform of the simulated autocorrelation agree
with the eigenvalues predicted by the theory.
