Scope¶
Current capabilities¶
NMRDfromMD is currently designed for the prediction and analysis of \(^{1} \text{H}\) nuclear magnetic relaxation dispersion (NMRD) profiles from molecular dynamics trajectories. The current implementation focuses on relaxation mechanisms that can be described from time-dependent fluctuations of molecular properties extracted directly from MD trajectories, from both isotropic and anisotropic molecular systems [44, 45]. For protons, these fluctuations are typically dominated by dipole–dipole interactions. \(^{1} \text{H}\) relaxation can be calculated from the autocorrelation functions of interatomic vectors extracted from MD trajectories, followed by spectral densities calculations [5, 46].
Future extensions¶
The dominant relaxation mechanisms depend strongly on the nuclear species and chemical environment. Therefore, extending the framework to nuclei other than \(^{1} \text{H}\), such as \(^{13}\mathrm{C}\), \(^{15}\mathrm{N}\), and \(^{19}\mathrm{F}\), requires the implementation of additional relaxation mechanisms that may become important for specific chemical environments. For example, \(^{13}\mathrm{C}\) relaxation in protonated carbons is often governed by heteronuclear (\(^{13}\mathrm{C}\) - \(^{1}\mathrm{H}\)) dipole–dipole interactions, whereas carbonyl and quaternary carbons may require the inclusion of chemical shift anisotropy (CSA), which arises from the orientation dependence of the chemical shielding tensor and its modulation by molecular rotational dynamics [47]. Likewise, relaxation of \(^{15}\mathrm{N}\) nuclei generally requires a combined treatment of dipolar and CSA mechanisms [48].
Although these mechanisms are not currently implemented, extending NMRDfromMD to support multi-nuclear relaxation analysis represents a natural direction for future development.
Out-of-scope relaxation mechanisms¶
While NMRDfromMD is designed to describe relaxation processes that can be related to molecular motions extracted from classical MD trajectories, some relaxation mechanisms require additional physical information not typically available from standard classical MD simulations. The following sections describe relaxation processes that are currently outside the scope of NMRDfromMD and would require significant theoretical and methodological extensions.
Quadrupolar relaxation¶
Nuclei with spin quantum numbers \(I \geq 1\), such as \(^{2} \text{H}\) and \(^{14} \text{N}\), often experience relaxation dominated by quadrupolar interactions. Quadrupolar relaxation originates from fluctuations of the electric field gradient (EFG) tensor at the nucleus [49, 50, 51]. Therefore, predicting quadrupolar relaxation from MD trajectories requires the calculation of the time-dependent EFG tensor along the trajectory, followed by the evaluation of its autocorrelation function and corresponding spectral densities. The EFG can be obtained using quantum-mechanical calculations or suitable molecular models, for example classical force fields combined with an appropriate description of electronic response, such as Sternheimer antishielding corrections [52]. These developments introduce additional methodological requirements and are therefore outside the current scope of NMRDfromMD.
Paramagnetic relaxation¶
In the presence of paramagnetic centers containing unpaired electrons, such as transition-metal ions or stable radicals, additional relaxation mechanisms arise from electron–nuclear magnetic interactions. These mechanisms depend not only on molecular dynamics but also on electron spin dynamics and its coupling to surrounding nuclei [53]. Classical MD simulations can describe structural fluctuations and electron–nucleus distance distributions, but they do not typically provide the electronic properties required for quantitative predictions of paramagnetic relaxation, such as electron spin relaxation times, hyperfine coupling parameters, or magnetic susceptibility tensors. These quantities can be obtained from quantum-mechanical calculations or dedicated spin dynamics approaches [54]. Supporting paramagnetic relaxation would therefore require additional theoretical developments beyond the current MD-based relaxation framework.