Molecular dynamics simulations of $^1$H NMR relaxation in Gd$^{3+}$--aqua

Atomistic molecular dynamics simulations are used to investigate $^1$H NMR $T_1$ relaxation of water from paramagnetic Gd$^{3+}$ ions in solution at 25$^{\circ}$C. Simulations of the $T_1$ relaxivity dispersion function $r_1$ computed from the Gd$^{3+}$--$^1$H dipole--dipole autocorrelation function agree within $\simeq 5$\% of measurements above $f_0 \gtrsim $ 5 MHz, without any adjustable parameters in the interpretation of the simulations. The agreement between simulated and measured $r_1$ above $f_0 \gtrsim $ 5 MHz (i.e. $B_0 \gtrsim $ 0.1 T) shows potential for predicting $r_1$ in chelated Gd$^{3+}$ contrast-agents used for clinical MRI, without any adjustable parameters or models. Below $f_0 \lesssim $ 5 MHz the simulation overestimates $r_1$ compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The most strongly bound water molecule to the Gd$^{3+}$ complex evinces an autocorrelation function consistent with the mono-exponential decay used in the Solomon-Bloembergen-Morgan (SBM) inner-sphere model.