Computing the 7Li NMR chemical shielding of hydrated Li+ using cluster calculations and time-averaged configurations from ab initio molecular dynamics simulations

NMR Spectroscopy and Multiscale Modeling Shed Light on Ion-Solvent Interactions and Ion Pairing in Aqueous NaF Solutions

The balance between ion solvation and ion pairing in aqueous solutions modulates chemical and physical processes from catalysis to protein folding. Yet, despite more than a century of investigation, experimental determination of the distribution of ion-solvation and ion-pairing states remains elusive, even for archetypal systems like aqueous alkali halides. Here, we combine nuclear magnetic resonance (NMR) spectroscopy and multiscale modeling to disentangle ion-solvent interactions from ion pairing in aqueous sodium fluoride solutions. We have developed a high-accuracy method to collect experimental NMR resonance frequencies for both ions as functions of temperature and concentration. Comparison of these data with resonance frequencies for nonassociating salts allows us to differentiate the influence of solvation and ion pairing on NMR spectra. These high-quality experimental NMR data are used to validate our modeling framework comprising polarizable force field molecular dynamics (MD) simulations and quantum chemical calculations of NMR resonance frequencies. Our experimental and theoretical resonance frequency shifts agree over a wide range of temperatures and concentrations. Structural analysis reveals how both trends are dominated by interactions with water molecules. For the more sensitive 19F nucleus, the NMR resonance frequency decreases as hydrogen bonds between fluoride and water molecules are reduced in number with increased temperature and molality. Through a detailed analysis of the theoretical NMR resonance frequencies for both ions, we show that NMR spectroscopy can distinguish both contact ion pairs and single-solvent-separated ion pairs from free ions. This quantitative framework can be applied directly to other systems.

Dynamic and relativistic effects on Pt-Pt indirect spin-spin coupling in aqueous solution studied by ab initio molecular dynamics and two- vs four-component density functional NMR calculations

Treating 195Pt nuclear magnetic resonance parameters in solution remains a considerable challenge from a quantum chemistry point of view, requiring a high level of theory that simultaneously takes into account the relativistic effects, the dynamic treatment of the solvent-solute system, and the dynamic electron correlation. A combination of Car-Parrinello molecular dynamics (CPMD) and relativistic calculations based on two-component zeroth order regular approximation spin-orbit Kohn-Sham (2c-ZKS) and four-component Dirac-Kohn-Sham (4c-DKS) Hamiltonians is performed to address the solvent effect (water) on the conformational changes and JPtPt1 coupling. A series of bridged PtIII dinuclear complexes [L1-Pt2(NH3)4(Am)2-L2]n+ (Am = α-pyrrolidonate and pivalamidate; L = H2O, Cl-, and Br-) are studied. The computed Pt-Pt coupling is strongly dependent on the conformational dynamics of the complexes, which, in turn, is correlated with the trans influence among axial ligands and with the angle N-C-O from the bridging ligands. The J-coupling is decomposed in terms of dynamic contributions. The decomposition reveals that the vibrational and explicit solvation contributions reduce JPtPt1 of diaquo complexes (L1 = L2 = H2O) in comparison to the static gas-phase magnitude, whereas the implicit solvation and bulk contributions correspond to an increase in JPtPt1 in dihalo (L1 = L2 = X-) and aquahalo (L1 = H2O; L2 = X-) complexes. Relativistic treatment combined with CPMD shows that the 2c-ZKS Hamiltonian performs as well as 4c-DKS for the JPtPt1 coupling.

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. To gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

Recent advances in the liquid-phase 6,7 Li nuclear magnetic resonance

The present review is focused on experimental methods and structural applications, including computational aspects, of classical lithium liquid-phase nuclear magnetic resonance (NMR). It consists of four parts covering accordingly a brief overview, early experimental reports (papers of up to about 2015) and more recent (papers appearing in the interim of about 2015 until 2022) results, together with very few but highly prospective computational results.

Reference interaction site model self-consistent field with constrained spatial electron density approach for nuclear magnetic shielding in solution

We propose a new hybrid approach combining quantum chemistry and statistical mechanics of liquids for calculating the nuclear magnetic resonance (NMR) chemical shifts of solvated molecules. Based on the reference interaction site model self-consistent field with constrained spatial electron density distribution (RISM–SCF–cSED) method, the electronic structure of molecules in solution is obtained, and the expression for the nuclear magnetic shielding tensor is derived as the second-order derivative of the Helmholtz energy of the solution system. We implemented a method for calculating chemical shifts and applied it to an adenine molecule in water, where hydrogen bonding plays a crucial role in electronic and solvation structures. We also performed the calculations of 17O chemical shifts, which showed remarkable solvent dependence. While converged results could not be sometimes obtained using the conventional method, in the present framework with RISM–SCF–cSED, an adequate representation of electron density is guaranteed, making it possible to obtain an NMR shielding constant stably. This introduction of cSED is key to extending the method’s applicability to obtain the chemical shift of various chemical species. The present demonstration illustrates our approach’s superiority in terms of numerical robustness and accuracy.

Enhancing Li-Ion Transport in Solid Electrolytes by Confined Water

Developing new oxide solid electrolytes with fast Li-ion transport and high stability is an important step to realize high-performance solid-state Li-ion batteries. Hydrate materials containing confined water widely exist in nature or can be easily synthesized. However, they have seldom been explored as Li-ion solid electrolytes due to the stereotype that the presence of water limits the electrochemical stability window of a solid electrolyte. In this work, it is demonstrated that confined water can enhance Li-ion transport while not compromising the stability window of solid electrolytes using Li-H-Ti-O quaternary compounds as an example system. Three Li-H-Ti-O quaternary compounds containing different amounts of confined water are synthesized, and their ionic conductivity and electrochemical stability are compared. The compound containing structural pseudo-water is demonstrated to have an ionic conductivity that is 2-3 order of magnitude higher than the water-free Li₄ Ti₅ O₁₂ and similar stability window. A solid-state battery is made with this new compound as the solid electrolyte, and good rate and cycling performance are achieved, which demonstrates the promise of using such confined-water-containing compounds as Li-ion solid electrolytes. The knowledge and insights gained in this work open a new direction for designing solid electrolytes for future solid-state Li-ion batteries. Broadly, by confining water into solid crystal structures, new design freedoms for tailing the properties of ceramic materials are introduced, which creates new opportunities in designing novel materials to address critical problems in various engineering fields.

Specific-Ion Effects Unveil a Route for Modulating Oxidatively Triggered Acid Systems for Reservoir Applications

On-demand in situ preparation of industrially relevant organic acids, namely, methanesulfonic acid, triflic acid, and trifluoroacetic acid, is demonstrated in this study. Sodium and potassium bromate were found to selectively oxidize a series of ammonium salts NH₄X, where X = OMs, OTf, or OTFAc, with characteristic clock reaction behavior. The redox system undergoes rapid acid formation following an extended induction time at 150 °C and is identified as a potential candidate for high-temperature oil field chemistry applications where on-demand acid placement is required. Although the reaction kinetics for acid formation from NH₄X salts where X = Cl, Br, F, or SO₄^2- follows a pK_a trend, the rates of formation of the organic acids are much slower and deviate from this trend. Furthermore, we demonstrate that the rate of acid formation can be modulated by the addition of alkali metal salts, with the strongest effect observed from LiBr. Spectroscopic studies implicate the formation of lithium bromate ion pairs that slow or altogether inhibit the oxidation of NH₄⁺. Additionally, the presence of Br^- alters the reaction path, eliminating the clock behavior and creating a pathway for Li⁺ to strongly inhibit the redox reaction. From these studies, a method for slowing ammonium oxidation under reservoir conditions to sufficiently delay acid formation until the precursors are placed in the zone of interest is identified.

Solvent effect on the 195Pt NMR properties in pyridonate-bridged PtIII dinuclear complex derivatives investigated by ab initio molecular dynamics and localized orbital analysis

An ab initio molecular dynamics investigation of the solvent effect (water) on the structural parameters, ¹⁹⁵Pt NMR spin-spin coupling constants (SSCCs) and chemical shifts of a series of pyridonate-bridged Pt^III dinuclear complexes is performed using Kohn-Sham (KS) Car-Parrinello molecular dynamics (CPMD) and relativistic hybrid KS NMR calculations. The indirect solvent effect (via structural changes) has a dramatic effect on the ¹J_PtPt SSCCs. The complexes exhibit a strong trans influence in solution, where the Pt-Pt bond lengthens with increasing axial ligand σ-donor strength. In the diaqua complex, where the solvent effect is more pronounced, the SSCCs averaged for CPMD configurations with explicit plus implicit solvation agree much better with the experimental data, while the calculations for static geometry and CPMD unsolvated configurations show large deviations with respect to experiment. The combination of CPMD with hybrid KS NMR calculations provides a much more realistic computational model that reproduces the large magnitudes of ¹J_PtPt and ¹⁹⁵Pt chemical shifts. An analysis of ¹J_PtPt in terms of localized and canonical orbitals shows that the SSCCs are driven by changes in the s-character of the natural atomic orbitals of Pt atoms, which affect the 'Fermi contact' mechanism.

A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations

This review focuses on a combination of ab initio molecular dynamics (aiMD) and NMR parameters calculations using quantum mechanical methods. The advantages of such an approach in comparison to the commonly applied computations for the structures optimized at 0 K are presented. This article was designed as a convenient overview of the applied parameters such as the aiMD type, DFT functional, time step, or total simulation time, as well as examples of previously studied systems. From the analysis of the published works describing the applications of such combinations, it was concluded that including fast, small-amplitude motions through aiMD has a noticeable effect on the accuracy of NMR parameters calculations.

Mechanistic implications of Li-S cell function through modification of organo-sulfur cathode architectures

Copolymeric organo-sulfur based electrodes provide a unique framework to explore and subsequently improve lithium-sulfur (Li-S) cells. There is a general difference in the way copolymers trap lithium during cell function compared to inorganic carbon-sulfur composites. Using a chain-like polyterpene copolymeric architecture involving the copolymerization of squalene monomer with sulfur (poly(S-r-squalene)), the first evidence for distinguishable differences in the entrapment of lithiated species, when using different copolymeric architectures, is provided. Investigation of poly(S-r-squalene) as an active cathode material via X-ray Absorption Near-Edge Structure (XANES) spectroscopy and high-resolution solid-state Nuclear Magnetic Resonance (NMR) reveal notable differences compared to previously studied poly(S-r-DIB) (proposed to have a less branched architecture) between the lithium environments present during electrochemistry that can be directly linked to the copolymeric structural features. Subtle but pertinent effects based on the copolymeric architecture related to the solid-electrolyte interphase (SEI) formed from the electrolytic components are also uncovered through these techniques. This work offers a comprehensive study on poly(S-r-squalene) and reveals that foundational inverse vulcanisation conditions such as choice of crosslinking monomer can dramatically impact lithium transport and SEI formation for the copolymeric electrode.

Al27 NMR chemical shift of Al(OH)4 - calculated from first principles: Assessment of error cancellation in chemically distinct reference and target systems

Predicting accurate nuclear magnetic resonance chemical shieldings relies upon cancellation of different types of errors between the theoretically calculated shielding constant of the analyte of interest and the reference. Often, the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral trivalent cation Al(H₂O)₆ ³⁺, accounting for ab initio intrinsic errors. However, the use of this species as a reference for the chemically distinct tetrahedral anion Al(OH)₄ ^- requires an understanding of how these errors cancel in order to define the limits of accurately predicting Al27 chemical shielding in Al(OH)₄ ^-. In this work, we estimate the absolute shielding of the Al27 nucleus in Al(OH)₄ ^- at the coupled cluster level (515.1 ± 5.3 ppm). Shielding sensitivity to the choice of method approximation and atomic basis sets used has been evaluated. Solvent and thermal effects are assessed through ensemble averaging techniques using ab initio molecular dynamics. The contribution of each type of intrinsic error is assessed for the Al(H₂O)₆ ³⁺ and Al(OH)₄ ^- ions, revealing significant differences that fundamentally hamper the ability to accurately calculate the Al27 chemical shift of Al(OH)₄ ^- from first principles.

Hydration Mimicry by Membrane Ion Channels

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if these protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry concept depends on understanding the hydration structure and free energies of metal ions in water in order to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water and the molecular quasi-chemical theory that provides hydration free energies. In doing so, we note some current views of ion binding to membrane channels and suggest new physical chemical calculations and experiments that might further clarify the hydration mimicry concept.

NMR absolute shielding scales and nuclear magnetic dipole moments of transition metal nuclei

This work reports new, accurate nuclear magnetic dipole moments for transition metal nuclei where the long-standing systematic error due to obsolete diamagnetic correction has been eliminated by ab initio calculations of NMR shielding constants.

Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F-) Anion Hydration

Accurate predictions of the hydration free energy for anions typically has been more challenging than that for cations. Hydrogen bond donation to the anion in hydrated clusters such as F(H₂O) _n ^- can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that even though anharmonic effects are interesting they need not be of troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed, and application of implicit solvation models to these structures can incur more serious errors than those for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

Strontium and barium in aqueous solution and a potassium channel binding site

Ion hydration structure and free energy establish criteria for understanding selective ion binding in potassium (K⁺) ion channels and may be significant to understanding blocking mechanisms as well. Recently, we investigated the hydration properties of Ba²⁺, the most potent blocker of K⁺ channels among the simple metal ions. Here, we use a similar method of combining ab initio molecular dynamics simulations, statistical mechanical theory, and electronic structure calculations to probe the fundamental hydration properties of Sr²⁺, which does not block bacterial K⁺ channels. The radial distribution of water around Sr²⁺ suggests a stable 8-fold geometry in the local hydration environment, similar to Ba²⁺. While the predicted hydration free energy of -331.8 kcal/mol is comparable with the experimental result of -334 kcal/mol, the value is significantly more favorable than the -305 kcal/mol hydration free energy of Ba²⁺. When placed in the innermost K⁺ channel blocking site, the solvation free energies and lowest energy structures of both Sr²⁺ and Ba²⁺ are nearly unchanged compared with their respective hydration properties. This result suggests that the block is not attributable to ion trapping due to +2 charge, and differences in blocking behavior arise due to free energies associated with the exchange of water ligands for channel ligands instead of free energies of transfer from water to the binding site.

Comparison of single-ion molecular dynamics in common solvents

Laying a basis for molecularly specific theory for the mobilities of ions in solutions of practical interest, we report a broad survey of velocity autocorrelation functions (VACFs) of Li⁺ and PF₆^- ions in water, ethylene carbonate, propylene carbonate, and acetonitrile solutions. We extract the memory function, γ(t), which characterizes the random forces governing the mobilities of ions. We provide comparisons controlling for the effects of electrolyte concentration and ion-pairing, van der Waals attractive interactions, and solvent molecular characteristics. For the heavier ion (PF₆^-), velocity relaxations are all similar: negative tail relaxations for the VACF and a clear second relaxation for γt, observed previously also for other molecular ions and with n-pentanol as the solvent. For the light Li⁺ ion, short time-scale oscillatory behavior masks simple, longer time-scale relaxation of γt. But the corresponding analysis of the solventberg Li⁺H₂O₄ does conform to the standard picture set by all the PF₆^- results.

Quasi-chemical theory of F-(aq): The "no split occupancies rule" revisited

We use ab initio molecular dynamics (AIMD) calculations and quasi-chemical theory (QCT) to study the inner-shell structure of F^-(aq) and to evaluate that single-ion free energy under standard conditions. Following the "no split occupancies" rule, QCT calculations yield a free energy value of -101 kcal/mol under these conditions, in encouraging agreement with tabulated values (-111 kcal/mol). The AIMD calculations served only to guide the definition of an effective inner-shell constraint. QCT naturally includes quantum mechanical effects that can be concerning in more primitive calculations, including electronic polarizability and induction, electron density transfer, electron correlation, molecular/atomic cooperative interactions generally, molecular flexibility, and zero-point motion. No direct assessment of the contribution of dispersion contributions to the internal energies has been attempted here, however. We anticipate that other aqueous halide ions might be treated successfully with QCT, provided that the structure of the underlying statistical mechanical theory is absorbed, i.e., that the "no split occupancies" rule is recognized.

Ion-Specific Effects in Carboxylate Binding Sites

Specific ion binding by carboxylates (-COO^-) is a broadly important topic because -COO^- is one of the most common functional groups coordinated to metal ions in metalloproteins and synthetic polymers. We apply quantum chemical methods and the quasi-chemical free-energy theory to investigate how variations in the number of -COO^- ligands in a binding site determine ion-binding preferences. We study a series of monovalent (Li⁺, Na⁺, K⁺, Cs⁺) and divalent (Zn²⁺, Ca²⁺) ions relevant to experimental work on ion channels and ionomers. Of two competing hypotheses, our results support the ligand field strength hypothesis and follow the reverse Hofmeister series for ion solvation and ion transfer from aqueous solution to binding sites with the preferred number of ligands. New insight arises from the finding that ion-binding sequences can be manipulated and even reversed just by constraining the number of carboxylate ligands in the binding sites. Our results help clarify the discrepancy in ion association between molecular ligands in aqueous solutions and ionomers, and their chemical analogues in ion-channel binding sites.

Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration

A challenge in density functional theory is developing functionals that simultaneously describe intermolecular electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-corrected ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decomposition shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amounts of charge transfer and the least polarizable waters of the density functionals studied, which mimics the lower polarizability of CCSD. When compared with experimental binding free energies, however, the exchange-corrected CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to experimental formation enthalpies. For clusters containing more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with experiment.

Octa-Coordination and the Aqueous Ba(2+) Ion

The hydration structure of Ba(2+) ion is important for understanding blocking mechanisms in potassium ion channels. Here, we combine statistical mechanical theory, ab initio molecular dynamics simulations, and electronic structure methods to calculate the hydration free energy and local hydration structure of Ba(2+)(aq). The predicted hydration free energy (-304 ± 1 kcal/mol) agrees with the experimental value (-303 kcal/mol) when a maximally occupied, unimodal inner solvation shell is treated. In the local environment defined by the first shell of hydrating waters, Ba(2+) is directly and stably coordinated by eight (8) waters. Octa-coordination resembles the crystal structure of Ba(2+) and K(+) bound in potassium ion channels, but differs from the local hydration structure of K(+)(aq) determined earlier.

99Tc NMR as a promising technique for structural investigation of biomolecules: theoretical studies on the solvent and thermal effects of phenylbenzothiazole complex

The phenylbenzothiazole compounds show antitumor properties and are highly selective. In this paper, the (99)Tc chemical shifts based on the ((99m)Tc)(CO)3 (NNO) complex conjugated to the antitumor agent 2-(4'-aminophenyl)benzothiazole are reported. Thermal and solvent effects were studied computationally by quantum-chemical methods, using the density functional theory (DFT) (DFT level BPW91/aug-cc-pVTZ for the Tc and BPW91/IGLO-II for the other atoms) to compute the NMR parameters for the complex. We have calculated the (99)Tc NMR chemical shifts of the complex in gas phase and solution using different solvation models (polarizable continuum model and explicit solvation). To evaluate the thermal effect, molecular dynamics simulations were carried, using the atom-centered density matrix propagation method at the DFT level (BP86/LanL2dz). The results highlight that the (99)Tc NMR spectroscopy can be a promising technique for structural investigation of biomolecules, at the molecular level, in different environments.

Heterogeneous Coordination Environments in Lithium-Neutralized Ionomers Identified Using 1H and 7Li MAS NMR

The carboxylic acid proton and the lithium coordination environments for precise and random Li-neutralized polyethylene acrylic acid P(E-AA) ionomers were explored using high speed solid-state ¹H and ⁷Li MAS NMR. While the ⁷Li NMR revealed only a single Li coordination environment, the chemical shift temperature variation was dependent on the precise or random nature of the P(E-AA) ionomer. The ¹H MAS NMR revealed two different carboxylic acid proton environments in these materials. By utilizing ¹H-⁷Li rotational echo double resonance (REDOR) MAS NMR experiments, it was demonstrated that the proton environments correspond to different average ¹H-⁷Li distances, with the majority of the protonated carboxylic acids having a close through space contact with the Li. Molecular dynamics simulations suggest that the shortest ¹H-⁷Li distance corresponds to un-neutralized carboxylic acids directly involved in the coordination environment of Li clusters. These solid-state NMR results show that heterogeneous structural motifs need to be included when developing descriptions of these ionomer materials.