NMR relaxation - Various measurements of magnetization decay are timescale sensitive. We illustrate how this works in the following video: —In each of six panels, we have a random bond motion (green vector, left), resulting in reorientation of magnetization for one nucleus (blue vectors, left panels), or 20 nuclei (blue vectors, right panels). —The magnetization of each nucleus rotates around the z-axis at the Larmor frequency, but also is re-oriented by a random field in the xy-plane (red vector). This is shown in the lab frame (middle of each of 6 panels) and in the rotating frame (right of each 6 panels). —In the top panels, motion is faster than the Larmor rotation, in the middle panels, motion is approximately the same rate as Larmor rotation, and in the bottom panels, motion is slower.
Characterizing rate of motion - When the rate of motion matches the Larmor frequency, reorientation becomes faster (see middle panels). The net effect is shown in the right panels, where 20 spins end up moving randomly in different directions, so that the total magnetization decays (the mean vector direction shown in red, which decays towards zero in the middle panel on the right). Then, relaxation experiments provide information both on amplitude of motion and timescale of motion (timescale dependence illustrated here).
Detector analysis - Entanglement of amplitude and timescale information makes data analysis is non-trivial. We have developed detector analysis as a means of analyzing both experimental data without introducing bias, and for combining that data with simulation for better interpretation of the results.
Separating motion - As an example, we take motion of a lipid in MD simulation. We separate motion into H–C bond libration. Within the two chains, we separate motion into re-orientation of the moment of inertia (MOI), motion parallel to the MOI, and motion perpendicular to the MOI. Each motion is illustrated in the video. Within the head group, motion is separated into internal and overall motion. The trajectory is shown where the time axis accelerates, to highlight both fast and slow motions.
Correlation functions for relaxation - Relaxation in NMR, as illustrated in the previous video, is determined mathematically from a time-correlation function. By separating motional types in simulation, we can calculate contributions to the correlation function from each. The product of these yields the correlation function describing the total motion.
Tensors and motion - Each motion acts on the residual H–C dipolar interaction tensor from all faster motions. These tensors are plotted on top of their respective bonds for each of the motions. The action of the bond motion on this tensor yields the resulting correlation function for that motion (lower right, where the plots correspond to the H–C bonds highlighted in yellow). The product of the individual correlation functions yields the total motion's correlation function (approximately).
Detector analysis- Results for each motion from MD may be analyzed with detector analysis, and so can the product of all motions.
Simulation to Experiment - The total motion may be compared to experiment, to verify the simulation quality. Then, one may see how each individual motion contributions to the overall dynamics of the system, as illustrated below.