Toward Calculations of the 129Xe Chemical Shift in Xe@C60 at Experimental Conditions: Relativity, Correlation, and Dynamics

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.

Isomer-Dependent Escape Rate of Xenon from a Water-Soluble Cryptophane Cage Studied by Ab Initio Molecular Dynamics

The escape of xenon from the anti and syn diastereomers of hexacarboxylic-cryptophane-222 in water has been studied by ab initio molecular dynamics simulations. The structures of both complexes, when the xenon atom is trapped inside their cages, have been compared and show no major differences. The free-energy profiles corresponding to the escape reaction have been calculated with the Blue Moon ensemble method using the distance between Xe and the center of mass of the cage as the reaction coordinate. The resulting free-energy barriers are very different; the escape rate is much faster in the case of the syn diastereomer, in agreement with experimental data obtained in hyperpolarized 129 Xe NMR. Our simulations reveal the mechanistic details for each diastereomer and provide an explanation for the different in-out xenon rates based on the solvation structure around the cages.

Computational NMR spectroscopy of 205 Tl

We have investigated the NMR chemical shift of 205 Tl in several thallium compounds, ranging from small covalent Tl(I) and Tl(III) molecules to supramolecular complexes with large organic ligands and some thallium halides. NMR calculations were run at the ZORA relativistic level, with and without spin-orbit coupling using few selected GGA and hybrid functionals, namely BP86, PBE, B3LYP, and PBE0. We also tested solvent effects both at the optimization level and at the NMR calculation step. At the ZORA-SO-PBE0 (COSMO) level of theory we find a very good performance of the computational protocol that allows to discard or retain possible structures/conformations based on the agreement between the calculated chemical shift and the experimental value.

NMR chemical shift of confined 129Xe: coordination number, paramagnetic channels and molecular dynamics in a cryptophane-A biosensor

Advances in hyperpolarisation and indirect detection have enabled the development of xenon nuclear magnetic resonance (NMR) biosensors (XBSs) for molecule-selective sensing in down to picomolar concentration. Cryptophanes (Crs) are popular cages for hosting the Xe "spy". Understanding the microscopic host-guest chemistry has remained a challenge in the XBS field. While early NMR computations of XBSs did not consider the important effects of host dynamics and explicit solvent, here we model the motionally averaged, relativistic NMR chemical shift (CS) of free Xe, Xe in a prototypic CrA cage and Xe in a water-soluble CrA derivative, each in an explicit H2O solvent, over system configurations generated at three different levels of molecular dynamics (MD) simulations. We confirm the "contact-type" character of the Xe CS, arising from the increased availability of paramagnetic channels, magnetic couplings between occupied and virtual orbitals through the short-ranged orbital hyperfine operator, when neighbouring atoms are in contact with Xe. Remarkably, the Xe CS in the present, highly dynamic and conformationally flexible situations is found to depend linearly on the coordination number of the Xe atom. We interpret the high- and low-CS situations in terms of the magnetic absorption spectrum and choose our preference among the used MD methods based on comparison with the experimental CS. We check the role of spin-orbit coupling by comparing with fully relativistic CS calculations. The study outlines the computational workflow required to realistically model the CS of Xe confined in dynamic cavity structures under experimental conditions, and contributes to microscopic understanding of XBSs.

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.

Local energy decomposition analysis and molecular properties of encapsulated methane in fullerene (CH4@C60)

Methane has been successfully encapsulated within cages of C₆₀ fullerene, which is an appropriate model system to study confinement effects. Its chemistry and physics are also relevant for theoretical model descriptions. Here we provide insights into intermolecular interactions and predicted spectroscopic responses of the CH₄@C₆₀ complex and compared them with results from other methods and with data from the literature. Local energy decomposition analysis (LED) within the domain-based local pair natural orbital coupled cluster singles, doubles, and perturbative triples (DLPNO-CCSD(T)) framework was used, and an efficient protocol for studies of endohedral complexes of fullerenes is proposed. This approach allowed us to assess energies in relation to electronic and geometric preparation, electrostatics, exchange, and London dispersion for the CH₄@C₆₀ endohedral complex. The calculated stabilization energy of CH₄ inside the C₆₀ fullerene was -13.5 kcal mol^-1 and its magnitude was significantly larger than the latent heat of evaporation of CH₄. Evaluation of vibrational frequencies and polarizabilities of the CH₄@C₆₀ complex revealed that the infrared (IR) and Raman bands of the endohedral CH₄ were essentially "silent" due to the dielectric screening effect of C₆₀, which acted as a molecular Faraday cage. Absorption spectra in the UV-vis domain and ionization potentials of C₆₀ and CH₄@C₆₀ were predicted. They were almost identical. The calculated ¹H/¹³C NMR shifts and spin-spin coupling constants were in very good agreement with experimental data. In addition, reference DLPNO-CCSD(T) interaction energies for complexes with noble gases (Ng@C₆₀; Ng = He, Ne, Ar, Kr) were calculated. The values were compared with those derived from supramolecular MP2/SCS-MP2 calculations and estimates with London-type formulas by Pyykkö and coworkers [Phys. Chem. Chem. Phys., 2010, 12, 6187-6203], and with values derived from DFT-based symmetry-adapted perturbation theory (DFT-SAPT) by Hesselmann & Korona [Phys. Chem. Chem. Phys., 2011, 13, 732-743]. Selected points at the potential energy surface of the endohedral He₂@C₆₀ trimer were considered. In contrast to previous theoretical attempts with the DFT/MP2/SCS-MP2/DFT-SAPT methods, our calculations at the DLPNO-CCSD(T) level of theory predicted the He₂@C₆₀ trimer to be thermodynamically stable, which is in agreement with experimental observations.

An Internuclear J-Coupling of 3He Induced by Molecular Confinement

The solution-state ¹³C NMR spectrum of the endofullerene ³He@C₆₀ displays a doublet structure due to a J-coupling of magnitude 77.5 ± 0.2 mHz at 340 K between the ³He nucleus and a ¹³C nucleus of the enclosing carbon surface. The J-coupling increases in magnitude with increasing temperature. Quantum chemistry calculations successfully predict the approximate magnitude of the coupling. This observation shows that the mutual proximity of molecular or atomic species is sufficient to induce a finite scalar nuclear spin-spin coupling, providing that translational motion is restricted by confinement. The phenomenon may have applications to the study of surface interactions and to mechanically bound species.

Chemical shift extremum of 129Xe(aq) reveals details of hydrophobic solvation

The ¹²⁹Xe chemical shift in an aqueous solution exhibits a non-monotonic temperature dependence, featuring a maximum at 311 K. This is in contrast to most liquids, where the monotonic decrease of the shift follows that of liquid density. In particular, the shift maximum in water occurs at a higher temperature than that of the maximum density. We replicate this behaviour qualitatively via a molecular dynamics simulation and computing the ¹²⁹Xe chemical shift for snapshots of the simulation trajectory. We also construct a semianalytical model, in which the Xe atom occupies a cavity constituted by a spherical water shell, consisting of an even distribution of solvent molecules. The temperature dependence of the shift is seen to result from a product of the decreasing local water density and an increasing term corresponding to the energetics of the Xe-H₂O collisions. The latter moves the chemical shift maximum up in temperature, as compared to the density maximum. In water, the computed temperature of the shift maximum is found to be sensitive to both the details of the binary chemical shift function and the coordination number. This work suggests that, material parameters allowing, the maximum should be exhibited by other liquids, too.

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.

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data.

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.

3He NMR studies on helium-pyrrole, helium-indole, and helium-carbazole systems: a new tool for following chemistry of heterocyclic compounds

The (3)He nuclear magnetic shieldings were calculated for free helium atom and He-pyrrole, He-indole, and He-carbazole complexes. Several levels of theory, including Hartree-Fock (HF), Second-order Møller-Plesset Perturbation Theory (MP2), and Density Functional Theory (DFT) (VSXC, M062X, APFD, BHandHLYP, and mPW1PW91), combined with polarization-consistent pcS-2 and aug-pcS-2 basis sets were employed. Gauge-including atomic orbital (GIAO) calculated (3)He nuclear magnetic shieldings reproduced accurately previously reported theoretical values for helium gas. (3)He nuclear magnetic shieldings and energy changes as result of single helium atom approaching to the five-membered ring of pyrrole, indole, and carbazole were tested. It was observed that (3)He NMR parameters of single helium atom, calculated at various levels of theory (HF, MP2, and DFT) are sensitive to the presence of heteroatomic rings. The helium atom was insensitive to the studied molecules at distances above 5 Å. Our results, obtained with BHandHLYP method, predicted fairly accurately the He-pyrrole plane separation of 3.15 Å (close to 3.24 Å, calculated by MP2) and yielded a sizable (3)He NMR chemical shift (about -1.5 ppm). The changes of calculated nucleus-independent chemical shifts (NICS) with the distance above the rings showed a very similar pattern to helium-3 NMR chemical shift. The ring currents above the five-membered rings were seen by helium magnetic probe to about 5 Å above the ring planes verified by the calculated NICS index.

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.

The topology of fullerenes

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96-145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

The role of aromaticity in determining the molecular structure and reactivity of (endohedral metallo)fullerenes

The molecular structure and chemical reactivity of endohedral metallofullerenes can be greatly predicted and rationalized by their local and global aromaticity.

Modeling 21Ne NMR parameters for carbon nanosystems

The potential of nuclear magnetic resonance (NMR) technique in probing the structure of porous systems including carbon nanostructures filled with inert gases is analysed theoretically using accurate calculations of neon ((21) Ne) nuclear magnetic shieldings. The CBS estimates of (21) Ne NMR parameters were performed for single atom, its dimer and neon interacting with acetylene, ethylene and 1,3-cyclopentadiene. Several levels of theory including restricted Hartree-Fock (RHF), Møller-Plesset perturbation theory to the second order (MP2), density functional theory (DFT) with van Voorhis and Scuseria's t-dependent gradient-corrected correlation functional (VSXC), coupled cluster with single and doubles excitations (CCSD), with single, doubles and triples included in a perturbative way (CCSD(T)) and single, doubles and tripes excitations (CCSDT) combined with polarization-consistent aug-pcS-n series of basis sets were employed. The impact of neon confinement inside selected fullerene cages used as an NMR probe was studied at the RHF/pcS-2 level of theory. A sensitivity of neon probe to the proximity of multiple CC bonds in C2 H2 , C2 H4 , C5 H6 and inside C28 , C30 , C32 , C34 and C60 fullerenes was predicted from (21) Ne NMR parameters' changes. Copyright © 2013 John Wiley & Sons, Ltd.

Predicting the paramagnet-enhanced NMR relaxation of H₂ encapsulated in endofullerene nitroxides by density-functional theory calculations

We have investigated the structure and nuclear magnetic resonance (NMR) spectroscopic properties of some dihydrogen endofullerene nitroxides by means of density-functional theory (DFT) calculations. Quantum versus classical roto-translational dynamics of H₂ have been characterized and compared. Geometrical parameters and hyperfine couplings calculated by DFT have been input to the Solomon-Bloembergen equations to predict the enhancement of the NMR longitudinal relaxation of H₂ due to coupling with the unpaired electron. Estimating the rotational correlation time via computed molecular volumes leads to a fair agreement with experiment for the simplest derivative; the estimate is considerably improved by recourse to the calculation of the diffusion tensor. For the other more flexible congeners, the agreement is less good, which may be due to an insufficient sampling of the conformational space. In all cases, relaxation by Fermi contact and Curie mechanisms is predicted to be negligible.

3He NMR: from free gas to its encapsulation in fullerene

The (3)He nuclear magnetic shieldings were calculated for single helium atom, its dimer, simple models of fullerene cages (He@Cn), and single wall carbon nanotubes. The performances of several levels of theory (HF, MP2, DFT-VSXC, CCSD, CCSD(T), and CCSDT) were tested. Two sets of polarization-consistent basis sets were used (pcS-n and aug-pcS-n), and an estimate of (3)He nuclear magnetic shieldings in the complete basis set limit using a two-parameter fit was established. Theoretical (3)He results reproduced accurately previously reported theoretical values for helium gas, dimer, and helium probe inside several fullerene cages. Excellent agreement with experimental values was achieved. (3)He nuclear magnetic shieldings of single helium atom approaching various points of benzene ring were tested, and an impact of (3)He confinement within fullerene cages of different size on the (3)He chemical shift was determined.

Vibrational averaging of the chemical shift in crystalline α-glycine

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane-wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born-Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower-frequency vibrational modes. Temperature excitations of the lowest-frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data.

Calculation of NMR chemical shifts in organic solids: accounting for motional effects

NMR chemical shifts were calculated from first principles for well defined crystalline organic solids. These density functional theory calculations were carried out within the plane-wave pseudopotential framework, in which truly extended systems are implicitly considered. The influence of motional effects was assessed by averaging over vibrational modes or over snapshots taken from ab initio molecular dynamics simulations. It is observed that the zero-point correction to chemical shifts can be significant, and that thermal effects are particularly noticeable for shielding anisotropies and for a temperature-dependent chemical shift. This study provides insight into the development of highly accurate first principles calculations of chemical shifts in solids, highlighting the role of motional effects on well defined systems.

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.