Beyond Isotropic Tumbling Models: Nuclear Spin Relaxation in Liquids from First Principles

Computing the frequency-dependent NMR relaxation of 1H nuclei in liquid water

We present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular nuclear magnetic resonance (NMR) dipole-dipole relaxation rates of spin 1/2 nuclei from Molecular Dynamics (MD) simulations. This approach avoids the alterations caused by the well-known finite-size effects of translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows for the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilization of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [L.-P. Hwang and J. H. Freed, J. Chem. Phys. 63, 4017-4025 (1975)] and its combination with data from MD simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theory is also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent intermolecular and intramolecular dipolar NMR relaxation rates of 1H nuclei in liquid water at 273 and 298 K based on the simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the 1H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

Unified Description of Proton NMR Relaxation in Water, Acetonitrile, and Methane from Molecular Dynamics Simulations in the Liquid, Supercritical, and Gas Phases

A comprehensive calculation of proton NMR relaxation in water, acetonitrile, and methane across a wide range of the phase diagram is provided via ab initio and force-field-based molecular dynamics simulations. The formalism used for the spin-rotation (SR) contribution to relaxation is developed for use with any molecular symmetry and utilizes the full molecular SR tensors, which are calculated from first-principles via Kohn-Sham (KS) DFT. In combination with calculations of the dipolar contribution, near-quantitative agreement with total measured relaxation rates is achieved.

Quadrupolar 23Na+ NMR relaxation as a probe of subpicosecond collective dynamics in aqueous electrolyte solutions

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.

Molecular dynamics simulations vs field-cycling NMR relaxometry: Structural relaxation mechanisms in the glass-former glycerol revisited

We combine field-cycling (FC) relaxometry and molecular dynamics (MD) simulations to study the rotational and translational dynamics associated with the glassy slowdown of glycerol. The ¹H NMR spin-lattice relaxation rates R₁(ω) probed in the FC measurements for different isotope-labelled compounds are computed from the MD trajectories for broad frequency and temperature ranges. We find high correspondence between experiment and simulation. Concerning the rotational motion, we observe that the aliphatic and hydroxyl groups show similar correlation times but different stretching parameters, while the overall reorientation associated with the structural relaxation remains largely isotropic. Additional analysis of the simulation results reveals that transitions between different molecular configurations are slow on the time scale of the structural relaxation at least at sufficiently high temperatures, indicating that glycerol rotates at a rigid entity, but the reorientation is slower for elongated than for compact conformers. The translational contribution to R₁(ω) is well described by the force-free hard sphere model. At sufficiently low frequencies, universal square-root laws provide access to the molecular diffusion coefficients. In both experiment and simulation, the time scales of the rotational and translational motions show an unusually large separation, which is at variance with the Stokes-Einstein-Debye relation. To further explore this effect, we investigate the structure and dynamics on various length scales in the simulations. We observe that a prepeak in the static structure factor S(q), which is related to a local segregation of aliphatic and hydroxyl groups, is accompanied by a peak in the correlation times τ(q) from coherent scattering functions.

Quadrupolar NMR Relaxation of Aqueous 127I-, 131Xe, and 133Cs+: A First-Principles Approach from Dynamics to Properties

Quadrupolar NMR relaxation rates were computed for aqueous ¹³³Cs⁺, ¹³¹Xe, and ¹²⁷I^- via Kohn-Sham (KS) density functional theory-based ab initio molecular dynamics and KS calculations of the electric field gradient (EFG) tensors along the trajectories. The resulting rates are within a factor of 1-3 of the experimental values and can be compared to available results from classical dynamics and EFGs from electrostatic models with corrections via Sternheimer antishielding factors. Relativistic effects are shown to have an enhancing effect on the magnitude of the EFGs. An analysis of the EFGs was carried out in terms of localized molecular orbitals to elucidate contributions from the solvent versus solute polarization and assess the validity of the Sternheimer approximation for these systems.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

The Sodium Anion Is Strongly Perturbed in the Condensed Phase Even Though It Appears Like a Free Ion in Nuclear Magnetic Resonance Experiments

Solvated sodium anions (Na^-) were thought to behave essentially like isolated gas-phase ions that interact only weakly with their environments. For example, ²³Na NMR signals for solvated Na^- are very sharp, despite the potential for strong quadrupolar broadening. The sharp NMR signals appear to indicate a nearly spherical electron density of the ion. For the present study, ab initio molecular dynamics simulations and quadrupolar relaxation rate calculations were carried out for the Na^-/Na⁺ [2.2.2]cryptand system solvated in methylamine, followed by detailed analyses of the electric field gradient at the sodium nuclei. It is found that Na^- does not behave like a quasi-free ion interacting only weakly with its environment. Rather, the filled 3s shell of Na^- interacts weakly with the ion's own core and the nucleus, causing Na^- to appear in NMR experiments like a free ion.

How to calculate charge mobility in molecular materials from surface hopping non-adiabatic molecular dynamics - beyond the hopping/band paradigm

Charge transport in high mobility organic semiconductors is in an intermediate regime between small polaron hopping and band transport limits. We have recently shown that surface hopping non-adiabatic molecular dynamics is a powerful method for prediction of charge transport mechanisms in organic materials and for near-quantitative prediction of charge mobilities at room temperature where the effects of nuclear zero-point motion and tunneling are still relatively small [S. Giannini et al., Nat. Commun., 2019, 10, 3843]. Here we assess and critically discuss the extensions to Tully's original method that have led to this success: (i) correction for missing electronic decoherence, (ii) detection of trivial crossings and (iii) removal of decoherence correction-induced spurious charge transfer. If any one of these corrections is not included, the charge mobility diverges with system size, each for different physical reasons. Yet if they are included, convergence with system size, detailed balance and good internal consistency are achieved.

Proton NMR relaxation from molecular dynamics: intramolecular and intermolecular contributions in water and acetonitrile

Accurate ¹H NMR relaxation rates for protons in pure water and acetonitrile are computed via ab initio and force field molecular dynamics. Dipole–dipole and spin-rotation mechanisms are considered.

Quadrupolar 14N NMR Relaxation from Force-Field and Ab Initio Molecular Dynamics in Different Solvents

Quadrupolar NMR spin relaxation rates and corresponding line widths were computed for the quadrupolar nucleus ¹⁴N for neat acetonitrile as well as for 1-methyl-1,3-imidazole and 1-methyl-1,3,4-triazole in different solvents. Molecular dynamics (MD) was performed with forces from the Kohn-Sham (KS) theory (ab initio MD) and force-field molecular mechanics (classical MD), followed by KS electric field gradient (EFG) calculations. For acetonitrile the agreement of the ¹⁴N line width with experiment is very good. Relative line widths for the azole nitrogens are improved over simpler approximations used previously in conjunction with single-point calculations at the multiconfigurational self-consistent field level. Overall, the NMR line widths are computed within a factor of 2 of the experimental values, giving access to reasonable estimates both of the dynamic EFG variance in the solvated systems as well as the associated correlation times that determine the relaxation rates.

Quadrupolar NMR Relaxation from ab Initio Molecular Dynamics: Improved Sampling and Cluster Models versus Periodic Calculations

Quadrupolar NMR relaxation rates are computed for ¹⁷O and ²H nuclei of liquid water, and of ²³Na⁺, and ³⁵Cl^- in aqueous solution via Kohn-Sham (KS) density functional theory ab initio molecular dynamics (aiMD) and subsequent KS electric field gradient (EFG) calculations along the trajectories. The calculated relaxation rates are within about a factor of 2 of experimental results and improved over previous aiMD simulations. The relaxation rates are assessed with regard to the lengths of the simulations as well as configurational sampling. The latter is found to be the more limiting factor in obtaining good statistical sampling and is improved by averaging over many equivalent nuclei of a system or over several independent trajectories. Further, full periodic plane-wave basis calculations of the EFGs are compared with molecular-cluster atomic-orbital basis calculations. The two methods deliver comparable results with nonhybrid functionals. With the molecular-cluster approach, a larger variety of electronic structure methods is available. For chloride, the EFG computations benefit from using a hybrid KS functional.

Collective water dynamics in the first solvation shell drive the NMR relaxation of aqueous quadrupolar cations

Using molecular simulations, we analyze the microscopic processes driving the Nuclear Magnetic Resonance (NMR) relaxation of quadrupolar cations in water. The fluctuations of the Electric Field Gradient (EFG) experienced by alkaline and magnesium cations, which determine the NMR relaxation time, are mainly due to the dynamics of water molecules in their solvation shell. The dynamics of the ion plays a less important role, with the exception of the short-time dynamics in the lighter Li⁺ case, for which rattling in the solvent cage results in oscillations of the EFG autocorrelation function (ACF). Several microscopic mechanisms that may a priori contribute to the decay of the EFG-ACF occur in fact over too long time scales: entrance/exit of individual water molecules into/from the solvation shell, rotation of a molecule around the ion, or reorientation of the molecule. In contrast, the fluctuations of the ion-water distance are clearly correlated to that of the EFG. Nevertheless, it is not sufficient to consider a single molecule due to the cancellations arising from the symmetry of the solvation shell. The decay of the EFG-ACF, hence NMR relaxation, is in fact governed by the collective symmetry-breaking fluctuations of water in the first solvation shell.

Prediction of low-field nuclear singlet lifetimes with molecular dynamics and quantum-chemical property surface

Molecular dynamics and quantum chemistry methods are implemented to quantify nuclear spin-1/2 pair singlet-state relaxation rates. Illustrated is the relevant spin-internal-motion mechanism (SIM).

On the microscopic fluctuations driving the NMR relaxation of quadrupolar ions in water

Nuclear Magnetic Resonance (NMR) relaxation is sensitive to the local structure and dynamics around the probed nuclei. The Electric Field Gradient (EFG) is the key microscopic quantity to understand the NMR relaxation of quadrupolar ions, such as (7)Li(+), (23)Na(+), (25)Mg(2+), (35)Cl(-), (39)K(+), or (133)Cs(+). Using molecular dynamics simulations, we investigate the statistical and dynamical properties of the EFG experienced by alkaline, alkaline Earth, and chloride ions at infinite dilution in water. Specifically, we analyze the effect of the ionic charge and size on the distribution of the EFG tensor and on the multi-step decay of its auto-correlation function. The main contribution to the NMR relaxation time arises from the slowest mode, with a characteristic time on the picosecond time scale. The first solvation shell of the ion plays a dominant role in the fluctuations of the EFG, all the more that the ion radius is small and its charge is large. We propose an analysis based on a simplified charge distribution around the ion, which demonstrates that the auto-correlation of the EFG, hence the NMR relaxation time, reflects primarily the collective translational motion of water molecules in the first solvation shell of the cations. Our findings provide a microscopic route to the quantitative interpretation of NMR relaxation measurements and open the way to the design of improved analytical theories for NMR relaxation for small ionic solutes, which should focus on water density fluctuations around the ion.

Solid-state NMR in macromolecular systems: insights on how molecular entities move

The function of synthetic and natural macromolecularsystems critically depends on the packing and dynamics of the individual components of a given system. Not only can solid-state NMR provide structural information with atomic resolution, but it can also provide a way to characterize the amplitude and time scales of motions over broad ranges of length and time. These movements include molecular dynamics, rotational and translational motions of the building blocks, and also the motion of the functional species themselves, such as protons or ions. This Account examines solid-state NMR methods for correlating dynamics and function in a variety of chemical systems. In the early days, scientists thought that the rotationalmotions reflected the geometry of the moving entities. They described these phenomena as jumps about well-defined axes, such as phenyl flips, even in amorphous polymers. Later, they realized that conformational transitions in macromolecules happen in a much more complex way. Because the individual entities do not rotate around well-defined axes, they require much less space. Only recently researchers have appreciated the relative importance of large angle fluctuations of polymers over rotational jumps. Researchers have long considered that cooperative motions might be at work, yet only recently they have clearly detected these motions by NMR in macromolecular and supramolecular systems. In correlations of dynamics and function, local motions do not always provide the mechanism of long-range transport. This idea holds true in ion conduction but also applies to chain transport in polymer melts and semicrystalline polymers. Similar chain motions and ion transport likewise occur in functional biopolymers, systems where solid-state NMR studies are also performed. In polymer science, researchers have appreciated the unique information on molecular dynamics available from advanced solid-state NMR at times, where their colleagues in the biomacromolecular sciences have emphasized structure. By contrast, following X-ray crystallographers, researchers studying proteins using solution NMR introduced the combination of NMR with computer simulation before that became common practice in solid-state NMR. Today's simulation methods can handle partially ordered or even disordered systems common in synthetic polymers. Thus, the multitechnique approaches employed in NMR of synthetic and biological macromolecules have converged. Therefore, this Account will be relevant to both researchers studying synthetic macromolecular and supramolecular systems and those studying biological complexes.

Quadrupolar NMR Spin Relaxation Calculated Using Ab Initio Molecular Dynamics: Group 1 and Group 17 Ions in Aqueous Solution

Electric field gradient (EFG) fluctuations for the monoatomic ions (7)Li(+), (23)Na(+), (35)Cl(-), (81)Br(-), and (127)I(-) in aqueous solution are studied using Car-Parrinello ab initio molecular dynamics (aiMD) simulations based on density functional theory. EFG calculations are typically performed with 1024 ion-solvent configurations from the aiMD simulation, using the Zeroth Order Regular Approximation (ZORA) relativistic Hamiltonian. Autocorrelation functions for the spherical EFG tensor elements are computed, transformed into the corresponding spectral densities (under the extreme narrowing condition), and subsequently converted into NMR quadrupolar relaxation rates for the ions. The relaxation rates are compared with experimental data. The order of magnitude is correctly predicted by the simulations. The computational protocol is tested in detail for (81)Br(-).

The PAW/GIPAW approach for computing NMR parameters: a new dimension added to NMR study of solids

In 2001, Mauri and Pickard introduced the gauge including projected augmented wave (GIPAW) method that enabled for the first time the calculation of all-electron NMR parameters in solids, i.e. accounting for periodic boundary conditions. The GIPAW method roots in the plane wave pseudopotential formalism of the density functional theory (DFT), and avoids the use of the cluster approximation. This method has undoubtedly revitalized the interest in quantum chemical calculations in the solid-state NMR community. It has quickly evolved and improved so that the calculation of the key components of NMR interactions, namely the shielding and electric field gradient tensors, has now become a routine for most of the common nuclei studied in NMR. Availability of reliable implementations in several software packages (CASTEP, Quantum Espresso, PARATEC) make its usage more and more increasingly popular, maybe indispensable in near future for all material NMR studies. The majority of nuclei of the periodic table have already been investigated by GIPAW, and because of its high accuracy it is quickly becoming an essential tool for interpreting and understanding experimental NMR spectra, providing reliable assignments of the observed resonances to crystallographic sites or enabling a priori prediction of NMR data. The continuous increase of computing power makes ever larger (and thus more realistic) systems amenable to first-principles analysis. In the near future perspectives, as the incorporation of dynamical effects and/or disorder are still at their early developments, these areas will certainly be the prime target.

NMR chemical shifts as a tool to analyze first principles molecular dynamics simulations in condensed phases: the case of liquid water

We present (1)H NMR chemical shift calculations of liquid water based on first principles molecular dynamics simulations under periodic boundary conditions. We focus on the impact of computational parameters on the structural and spectroscopic data, which is an important question for understanding how sensitive the computed (1)H NMR resonances are upon variation of the simulation setup. In particular, we discuss the influence of the exchange-correlation functional and the size of the basis set, the choice for the fictitious electronic mass and the use of pseudopotentials for the nuclear magnetic resonance (NMR) calculation on one hand and the underlying Car-Parrinello-type molecular dynamics simulations on the other hand. Our findings show that the direct effect of these parameters on (1)H shifts is not big, whereas the indirect dependence via the structural data is more important. The (1)H NMR chemical shifts clearly reflect the induced structural changes, illustrating once again the sensitivity of (1)H NMR observables on small changes in the local chemical structure of complex hydrogen-bonded liquids.