Gas Uptake and Thermodynamics in Porous Liquids Elucidated by 129Xe NMR

We exploited 129Xe NMR to investigate xenon gas uptake and dynamics in a porous liquid formed by dissolving porous organic cages in a cavity-excluded solvent. Quantitative 129Xe NMR shows that when the amount of xenon added to the sample is lower than the amount of cages present (subsaturation), the porous liquid absorbs almost all xenon atoms from the gas phase, with 30% of the cages occupied with a Xe atom. A simple two-site exchange model enables an estimate of the chemical shift of 129Xe in the cages, which is in good agreement with the value provided by first-principles modeling. T2 relaxation times allow the determination of the exchange rate of Xe between the solvent and cage sites as well as the activation energies of the exchange. The 129Xe NMR analysis also enables determination of the free energy of confinement, and it shows that Xe binding is predominantly enthalpy-driven.

Unexpected NMR shieldings of sp- and sp2-hybridized carbon atoms in graphyne systems

Graphynes (GYs) are two-dimensional alloptropic forms of carbon consisting of periodically arranged sp- and sp²-hybridized carbon atoms in a planar structure. Graphynes can be formally created from graphene by inserting sp-hybridized carbon links into selected points of the graphene lattice. Depending on where the links are introduced, several forms of graphynes have been proposed with properties that make them potential candidates for new generation electronics or for applications in chemical processes. Since the applications of each form of GY depend on its structure, it is of interest to experimentally distinguish different forms of graphynes. In this paper we propose nuclear magnetic resonance (NMR) as a potential method of choice for such distinction. We computationally investigate on the DFT level the ¹³C-NMR chemical shifts for α-, β-, γ-, rhombic, and 6,6,12-graphynes, and α- and γ-graphdiynes. We perform the calculations both in periodic systems and with approximate finite models. The results show that NMR chemical shifts in graphynes are dependent on the structure and reflect the local bonding around the carbon nucleus. Interestingly, NMR shifts of several graphynes show anomalous values, differing significantly from shifts found in typical sp²-hybridized systems. We analyze these results in terms of local structural parameters and qualitatively investigate the possible origins of these anomalous NMR shifts. The results show that NMR is a viable method for determining the structure of graphynes and their finite precursor molecules.

Hyper-CEST NMR of metal organic polyhedral cages reveals hidden diastereomers with diverse guest exchange kinetics

Guest capture and release are important properties of self-assembling nanostructures. Over time, a significant fraction of guests might engage in short-lived states with different symmetry and stereoselectivity and transit frequently between multiple environments, thereby escaping common spectroscopy techniques. Here, we investigate the cavity of an iron-based metal organic polyhedron (Fe-MOP) using spin-hyperpolarized ¹²⁹Xe Chemical Exchange Saturation Transfer (hyper-CEST) NMR. We report strong signals unknown from previous studies that persist under different perturbations. On-the-fly delivery of hyperpolarized gas yields CEST signatures that reflect different Xe exchange kinetics from multiple environments. Dilute pools with ~ 10⁴-fold lower spin numbers than reported for directly detected hyperpolarized nuclei are readily detected due to efficient guest turnover. The system is further probed by instantaneous and medium timescale perturbations. Computational modeling indicates that these signals originate likely from Xe bound to three Fe-MOP diastereomers (T, C₃, S₄). The symmetry thus induces steric effects with aperture size changes that tunes selective spin manipulation as it is employed in CEST MRI agents and, potentially, impacts other processes occurring on the millisecond time scale.

Direct magnetic-field dependence of NMR chemical shift

It is proven with experiments and computations the significant contribution of the direct field effect on the ⁵⁹Co chemical shift in Co(acac)₃ dissolved in CDCl₃.

NMR relaxation and modelling study of the dynamics of SF6 and Xe in porous organic cages

The porous solid formed from organic CC3 cage molecules has exceptional performance for rare gas separation. NMR spectroscopy provides a way to reveal the dynamical details by using experimental relaxation and diffusion measurements. Here, we investigated T₁ and T₂ relaxation as well as diffusion of ¹²⁹Xe and SF₆ gases in the CC3-R molecular crystal at various temperatures and magnetic field strengths. Advanced relaxation modelling made it possible to extract various important dynamical parameters for gases in CC3-R, such as exchange rates, activation energies and mobility rates of xenon, occupancies of the cavities, rotational correlational times, effective relaxation rates, and diffusion coefficients of SF₆.

Inside information on xenon adsorption in porous organic cages by NMR

A solid porous molecular crystal formed from an organic cage, CC3, has unprecedented performance for the separation of rare gases. Here, xenon was used as an internal reporter providing extraordinarily versatile information about the gas adsorption phenomena in the cage and window cavities of the material. 129Xe NMR measurements combined with state-of-the-art quantum chemical calculations allowed the determination of the occupancies of the cavities, binding constants, thermodynamic parameters as well as the exchange rates of Xe between the cavities. Chemical exchange saturation transfer (CEST) experiments revealed a minor window cavity site with a significantly lower exchange rate than other sites. Diffusion measurements showed significantly reduced mobility of xenon with loading. 129Xe spectra also revealed that the cage cavity sites are preferred at lower loading levels, due to more favourable binding, whereas window sites come to dominate closer to saturation because of their greater prevalence.

Clathrate Structure Determination by Combining Crystal Structure Prediction with Computational and Experimental 129 Xe NMR Spectroscopy

An approach is presented for the structure determination of clathrates using NMR spectroscopy of enclathrated xenon to select from a set of predicted crystal structures. Crystal structure prediction methods have been used to generate an ensemble of putative structures of o- and m-fluorophenol, whose previously unknown clathrate structures have been studied by ¹²⁹ Xe NMR spectroscopy. The high sensitivity of the ¹²⁹ Xe chemical shift tensor to the chemical environment and shape of the crystalline cavity makes it ideal as a probe for porous materials. The experimental powder NMR spectra can be used to directly confirm or reject hypothetical crystal structures generated by computational prediction, whose chemical shift tensors have been simulated using density functional theory. For each fluorophenol isomer one predicted crystal structure was found, whose measured and computed chemical shift tensors agree within experimental and computational error margins and these are thus proposed as the true fluorophenol xenon clathrate structures.

Ratcheting rotation or speedy spinning: EPR and dynamics of Sc3C2@C80

First principles modelling graphically explains how changes in the Sc-trimer motion cause the curious temperature dependence of Sc₃C₂@C₈₀ EPR spectra.

Orienting spins in dually doped monolayer MoS2: from one-sided to double-sided doping

Single- and double-sided doped monolayer MoS₂show electron spin alignments with their origins beyond explanations of the existing models.

DFT calculations in the assignment of solid-state NMR and crystal structure elucidation of a lanthanum(iii) complex with dithiocarbamate and phenanthroline

Structure of a novel rare-earth lanthanum(iii) complex resolved by a combination of DFT modelling, NMR spectroscopy, and single crystal XRD.

Encapsulation of xenon by a self-assembled Fe4L6 metallosupramolecular cage

We report (129)Xe NMR experiments showing that a Fe4L6 metallosupramolecular cage can encapsulate xenon in water with a binding constant of 16 M(-1). The observations pave the way for exploiting metallosupramolecular cages as economical means to extract rare gases as well as (129)Xe NMR-based bio-, pH, and temperature sensors. Xe in the Fe4L6 cage has an unusual chemical shift downfield from free Xe in water. The exchange rate between the encapsulated and free Xe was determined to be about 10 Hz, potentially allowing signal amplification via chemical exchange saturation transfer. Computational treatment showed that dynamical effects of Xe motion as well as relativistic effects have significant contributions to the chemical shift of Xe in the cage and enabled the replication of the observed linear temperature dependence of the shift.

Xenon NMR of liquid crystals confined to cylindrical nanocavities: a simulation study

Coarse-grained simulations show that the ¹²⁹Xe NMR shielding reflects the smooth changes of orientational order in liquid crystals confined to nanocavities.

Curie-type paramagnetic NMR relaxation in the aqueous solution of Ni(ii)

The magnetic field of the Curie spin manifests itself as both the pNMR shielding tensor and Curie relaxation, in analogy with CSA relaxation theory.

Chemical distinction by nuclear spin optical rotation

Nuclear spin optical rotation (NSOR) arising from the Faraday effect constitutes a novel, advantageous method for detection of nuclear magnetic resonance, provided that a distinction is seen between different chemical surroundings of magnetic nuclei. Efficient first-principles calculations for isolated water, ethanol, nitromethane, and urea molecules at standard laser wavelengths reveal a range of NSOR for different molecules and inequivalent nuclei, indicating the existence of an optical chemical shift. 1H results for H2O(l) are in excellent agreement with recent pioneering experiments. We also evaluate, for the same systems, the Verdet constants of Faraday rotation due to an external magnetic field. Calculations of NSOR in ethanol and a 11-cis-retinal protonated Schiff base imply an enhanced chemical distinction between chromophores at laser wavelengths approaching optical resonance.

Pairwise additivity in the nuclear magnetic resonance interactions of atomic xenon

Nuclear magnetic resonance (NMR) of atomic (129/131)Xe is used as a versatile probe of the structure and dynamics of various host materials, due to the sensitivity of the Xe NMR parameters to intermolecular interactions. The principles governing this sensitivity can be investigated using the prototypic system of interacting Xe atoms. In the pairwise additive approximation (PAA), the binary NMR chemical shift, nuclear quadrupole coupling (NQC), and spin-rotation (SR) curves for the xenon dimer are utilized for fast and efficient evaluation of the corresponding NMR tensors in small xenon clusters Xe(n) (n = 2-12). If accurate, the preparametrized PAA enables the analysis of the NMR properties of xenon clusters, condensed xenon phases, and xenon gas without having to resort to electronic structure calculations of instantaneous configurations for n > 2. The binary parameters for Xe(2) at different internuclear distances were obtained at the nonrelativistic Hartree-Fock level of theory. Quantum-chemical (QC) calculations at the corresponding level were used to obtain the NMR parameters of the Xe(n) (n = 2-12) clusters at the equilibrium geometries. Comparison of PAA and QC data indicates that the direct use of the binary property curves of Xe(2) can be expected to be well-suited for the analysis of Xe NMR in the gaseous phase dominated by binary collisions. For use in condensed phases where many-body effects should be considered, effective binary property functions were fitted using the principal components of QC tensors from Xe(n) clusters. Particularly, the chemical shift in Xe(n) is strikingly well-described by the effective PAA. The coordination number Z of the Xe site is found to be the most important factor determining the chemical shift, with the largest shifts being found for high-symmetry sites with the largest Z. This is rationalized in terms of the density of virtual electronic states available for response to magnetic perturbations.

Xe129 chemical shift by the perturbational relativistic method: Xenon fluorides

(129)Xe nuclear shielding tensor is calculated at the leading-order, one-electron Breit-Pauli perturbation theory (BPPT) level for the xenon fluorides XeF(+), XeF(2), XeF(3) (+), and XeF(4) that cover the large nuclear magnetic resonance chemical shift range of this nucleus. BPPT is found to improve the shift range and relative shifts as compared to the nonrelativistic (NR) theory. While the full BPPT expansion consists of 16 relativistic terms, 5 of them are responsible for the entire chemical shift and shielding anisotropy. The remaining terms are practically isotropic, corelike contributions that are significant for the absolute shielding constant but cancel for the relative chemical shifts. The five principal terms are due to the spin-orbit-modified wave function allowing the Fermi contact and spin-dipole hyperfine interactions to be coupled to the orbital Zeeman interaction, as well as three distinct scalar relativistic modifications of the NR paramagnetic shielding: wave function change due to mass-velocity and Darwin interactions and the relativistic modification of the orbital hyperfine interaction. A very good agreement with the experimental shifts is obtained for XeF(2) and the particularly challenging XeF(+) species when both the NR and the five main relativistic terms are calculated at electron-correlated ab initio levels of theory. The performance of density-functional theory (DFT) with different pure and hybrid exchange-correlation functionals (with increasing exact exchange admixture) is tested against the ab initio data for each individual contribution. It is shown that DFT has difficulties in the description of paramagnetic shielding, already and especially in the NR contribution, which causes a large discrepancy of DFT results with experiment for xenon fluorides. In contrast, the DFT errors for the relativistic terms cancel out to the extent that a fairly good approximation of the total relativistic shift and anisotropy contributions may be obtained. A combination of high-level ab initio NR calculation with hybrid DFT estimates of the five main BPPT terms is proposed for reasonable estimates of xenon chemical shift in molecules. For the difficult cases such as the present XeF(+) and XeF(3) (+) cations, correlated ab initio calculations are unavoidable throughout. None of the other currently available relativistic methods, either at the fully relativistic or a variationally stable quasirelativistic levels of theory, surpasses the quality of the present approach for Xe shifts in these systems.

Nuclear Magnetic Resonance Chemical Shifts and Quadrupole Couplings for Different Hydrogen-Bonding Cases Occurring in Liquid Water: A Computational Study

Nuclear magnetic resonance (NMR) parameters are determined theoretically for the oxygen and hydrogen/deuterium nuclei of differently hydrogen-bonded water molecules in liquid water at 300 K. The parameters are the chemical shift, the shielding anisotropy, the asymmetry parameter of shielding, the nuclear quadrupole coupling constant, and the asymmetry parameter of the nuclear quadrupole coupling. We sample instantaneous configurations from a Car-Parrinello molecular dynamics simulation and feed nuclear coordinates into a quantum chemical program for the calculation of NMR parameters using density-functional theory with the three-parameter hybrid exchange-correlation (B3LYP) functional. In the subsequent analysis, molecules are divided into groups according to the number of hydrogen bonds they possess, and the full average NMR tensors are calculated separately for each group. The classification of the hydrogen-bonding cases is performed using a simple distance-based criterion. The analysis reveals in detail how the NMR tensors evolve as the environment changes gradually from gas to liquid upon increasing the number of hydrogen bonds to the molecule of interest. Liquid-state distributions of the instantaneous values of the NMR properties show a wide range of values for each hydrogen-bonding species with significant overlap between the different cases. Our study shows how local changes in the environment, along with classical thermal averaging, affect the NMR parameters in liquid water. For example, a broken or alternatively extra hydrogen bond induces major changes in the NMR tensors, and the effect is more pronounced for hydrogen or deuterium than for oxygen. The data sheds light on the usefulness of NMR experiments in investigating the local coordination of liquid water.

Relativistic heavy-atom effects on heavy-atom nuclear shieldings

The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.

Calculations of nuclear quadrupole coupling in noble gas–noble metal fluorides: Interplay of relativistic and electron correlation effects

The nuclear quadrupole coupling constants (NQCCs) of noble gas and noble metal nuclei in the recently found noble gas-noble metal fluorides (NgMF, where Ng=Ar,Kr,Xe and M=Cu,Ag,Au) are obtained theoretically by high-level ab initio calculations, where both relativistic and electron correlation effects are included, and compared to experimental results. Fully relativistic four-component Dirac-Hartree-Fock (DHF) calculations are carried out at the basis set limit for electric field gradient that couples with the electric quadrupole moment of the nucleus, and uncorrelated relativistic effects are extracted by comparing DHF results to nonrelativistic (NR) HF calculations. Electron correlation effects are investigated both at fully relativistic second-order Moller-Plesset (DMP2) and at NR MP2 levels of theory, as well as at the NR coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level. The validity of the approximation where relativistic effects, on the one hand, and nonrelativistically obtained correlation effects, on the other hand, are evaluated separately and assumed to be additive, is investigated by comparison with the DMP2 results. Inclusion of relativistic effects is shown to be necessary for obtaining the correct NQCC trends as the nucleus of interest and/or its neighbors become heavier. Electron correlation treatment is needed for approaching quantitative agreement with the experimental NQCCs. The assumption of additive electron correlation and relativistic effects, corresponding to the NR correlation treatment added on top of relativistic DHF data, gives qualitatively correct noble gas NQCCs. For noble metal NQCCs, correlation treatment at the relativistic level of theory is mandatory for reaching agreement with experimental results. Current work also confirms the experimental trends of NQCCs, which have been taken as an indication of nearly covalent interaction between noble gas and noble metal in the heaviest present systems, especially in XeAuF.

NMR Spectroscopy Investigation of the Cooperative Nature of the Internal Rotational Motions in Acetophenone

The proton NMR spectrum of the doubly enriched acetophenone-carbonyl,methyl-13C2 isotopomer dissolved in a liquid-crystalline solvent (LXNMR) was analyzed to yield a data set of 19 dipolar couplings. The presence of so many couplings, and in particular the dependence of some of them on the acetyl carbons enabled the investigation of the structure of the acetyl moiety and of possible cooperative motions about the aryl-carbonyl and carbonyl-methyl bonds. Methodological aspects, and approximations relating to the application of the vibrational correction procedure in the presence of large-amplitude torsional motions, are discussed. Results show that it is possible to discriminate between a continuous and a discrete conformer distribution about the angle phi(1) but not among a few proposed continuous shapes of U(iso)({phi}). In this study, the use of dipolar couplings with a non-negligible contribution from the indirect spin-spin coupling tensor J, (D(C8C9) in our case), for structural determination is extended from rigid to flexible molecules. The 1/2J(aniso)(C8C9) contribution was derived theoretically using the density functional theory linear response (DFT-LR) first-principles calculation of the J(C8C9) spin-spin coupling tensor.

Leading-order relativistic effects on nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.

Calculation of binary magnetic properties and potential energy curve in xenon dimer: Second virial coefficient of 129Xe nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order Møller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.

Nuclear Magnetic Shielding and Quadrupole Coupling Tensors in Liquid Water: A Combined Molecular Dynamics Simulation and Quantum Chemical Study

Nuclear magnetic resonance (NMR) shielding tensors for the oxygen and hydrogen nuclei, as well as nuclear quadrupole coupling tensors for the oxygen and deuterium nuclei of water in the liquid and gaseous state, are calculated using Hartree-Fock and density functional theory methods, for snapshots sampled from Car-Parrinello molecular dynamics trajectories. Clusters representing local liquid structures and instantaneous configurations of a single molecule representing low-density gas are fed into a quantum chemical program for the calculation of the NMR tensors. The average isotropic and anisotropic tensorial properties of 400 samples in both states, averaged using a common Eckart coordinate frame, are calculated from the data. We report results for the gas-to-liquid chemical shifts of (17)O and (1)H nuclei, as well as the corresponding change in the nuclear quadrupole couplings of (17)O and (2)H. Full thermally averaged shielding and quadrupole coupling tensors are reported for the gaseous and liquid-state water, for the first time in the case of liquid. Electron correlation effects, the difference of classical vs quantum mechanical rovibrational averaging, and different methods of averaging anisotropic properties are discussed.