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Abstract Nuclear magnetic resonance relaxometry represents a powerful tool for extracting dynamic information. Yet, obtaining links to molecular motion is challenging for many ions that relax through the quadrupolar mechanism, which is mediated by electric field gradient fluctuations and lacks a detailed microscopic description. For sodium ions in aqueous electrolytes, we combine ab initio calculations to account for electron cloud effects with classical molecular dynamics to sample long-time fluctuations, and obtain relaxation rates in good agreement with experiments over broad concentration and temperature ranges. We demonstrate that quadrupolar nuclear relaxation is sensitive to subpicosecond dynamics not captured by previous models based on water reorientation or cluster rotation. While ions affect the overall water retardation, experimental trends are mainly explained by dynamics in the first two solvation shells of sodium, which contain mostly water. This work thus paves the way to the quantitative understanding of quadrupolar relaxation in electrolyte and bioelectrolyte systems. 

Phosphates and polyphosphates play ubiquitous roles in biology as integral structural components of cell membranes and bone, or as vehicles of energy storage via adenosine triphosphate and phosphocreatine. The solution phase space of phosphate species appears more complex than previously known. We present nuclear magnetic resonance (NMR) and cryogenic transmission electron microscopy (cryo-TEM) experiments that suggest phosphate species including orthophosphates, pyrophosphates, and adenosine phosphates associate into dynamic assemblies in dilute solutions that are spectroscopically “dark.” Cryo-TEM provides visual evidence of the formation of spherical assemblies tens of nanometers in size, while NMR indicates that a majority population of phosphates remain as unassociated ions in exchange with spectroscopically invisible assemblies. The formation of these assemblies is reversibly and entropically driven by the partial dehydration of phosphate groups, as verified by diffusion-ordered spectroscopy (DOSY), indicating a thermodynamic state of assembly held together by multivalent interactions between the phosphates. Molecular dynamics simulations further corroborate that orthophosphates readily cluster in aqueous solutions. This study presents the surprising discovery that phosphate-containing molecules, ubiquitously present in the biological milieu, can readily form dynamic assemblies under a wide range of commonly used solution conditions, highlighting a hitherto unreported property of phosphate’s native state in biological solutions. 

Nuclear spin relaxation mechanisms are often difficult to isolate and identify, especially in molecules with internal flexibility. Here we combine experimental work with computation in order to determine the major mechanisms responsible for 31 P spin–lattice and singlet order (SO) relaxation in pyrophosphate, a physiologically relevant molecule. Using field-shuttling relaxation measurements (from 2 μT to 9.4 T) and rates calculated from molecular dynamics (MD) trajectories, we identified chemical shift anisotropy (CSA) and spin–rotation as the major mechanisms, with minor contributions from intra- and intermolecular coupling. The significant spin–rotation interaction is a consequence of the relatively rapid rotation of the –PO 3 2− entities around the bridging P–O bonds, and is treated by a combination of MD simulations and quantum chemistry calculations. Spin–lattice relaxation was predicted well without adjustable parameters, and for SO relaxation one parameter was extracted from the comparison between experiment and computation (a correlation coefficient between the rotational motion of the groups). 

Nuclear spin singlet states are often found to allow long-lived storage of nuclear magnetization, which can form the basis of novel applications in spectroscopy, imaging, and in studies of dynamic processes. Precisely how long such polarization remains intact, and which factors affect its lifetime is often difficult to determine and predict. We present a combined experimental/computational study to demonstrate that molecular dynamics simulations and ab initio calculations can be used to fully account for the experimentally observed proton singlet lifetimes in ethyl-d 5 -propyl-d 7 -maleate in deuterated chloroform as solvent. The correspondence between experiment and simulations is achieved without adjustable parameters. These studies highlight the importance of considering unusual and difficult-to-control mechanisms, such as dipolar couplings to low-gamma solvent nuclei, and to residual paramagnetic species, which often can represent lifetime limiting factors. These results also point to the power of molecular dynamics simulations to provide insights into little-known NMR relaxation mechanisms. 

31 P NMR spectroscopy and the study of nuclear spin singlet relaxation phenomena are of interest in particular due to the importance of phosphorus-containing compounds in physiology. We report the generation and measurement of relaxation of 31 P singlet order in a chemically equivalent but magnetically inequivalent case. Nuclear magnetic resonance singlet state lifetimes of 31 P pairs have heretofore not been reported. Couplings between 1 H and 31 P nuclei lead to magnetic inequivalence and serve as a mechanism of singlet state population conversion within this molecule. We show that in this molecule singlet relaxation occurs at a rate significantly faster than spin–lattice relaxation, and that anticorrelated chemical shift anisotropy can account for this observation. Calculations of this mechanism, with the help of molecular dynamics simulations and ab initio calculations, provide excellent agreement with the experimental findings. This study could provide guidance for the study of 31 P singlets within other compounds, including biomolecules.