Schematic representation of the interrelations of molecular motions, field-cycling NMR relaxometry experiments and theoretical model concepts. Dipolar couplings between two dipoles with the vector operators I=γIħI⃑ and S=γSħS⃑ depend on the inter-dipole vector r⃑. If I and S are identical, one speaks of ‘like’ spins. The cones symbolize precession about the external flux density B⃑0. r⃑ can be expressed in spherical coordinates r(t), ϕ(t), ϑ(t) fluctuating as a consequence of molecular dynamics. For dipolar couplings, the autocorrelation function (τ) is formed on the basis of the functions F{r(t), φ(t), ϑ(t)} [see eqn (1.10)]. Note that the functions F depend on the absolute time t whereas the autocorrelation function varies with the time interval τ. The spectral densities (ωk) are Fourier transforms of (τ) for the angular frequencies ωk. They determine the spin–lattice relaxation rate as a linear combination for all allowed angular transition frequencies ωk in the spin system under consideration. Predictions based on a theoretical model can be compared with experimental field-cycling NMR relaxometry data. The other way round, dispersion features of the spectral density deduced from experimental data can be taken as conditions to be fulfilled by dynamic models in question.