Ab Initio Theory of NMR Chemical Shifts in Solids and Liquids

1H and 13C chemical shift-structure effects in anhydrous β-caffeine and four caffeine-diacid cocrystals probed by solid-state NMR experiments and DFT calculations

By using density functional theory (DFT) calculations, we refined the H atom positions in the structures of β-caffeine (C), α-oxalic acid (OA; (COOH)2), α-(COOH)2·2H2O, β-malonic acid (MA), β-glutaric acid (GA), and I-maleic acid (ME), along with their corresponding cocrystals of 2 : 1 (2C-OA, 2C-MA) or 1 : 1 (C-GA, C-ME) stoichiometry. The corresponding 13C/1H chemical shifts obtained by gauge including projector augmented wave (GIPAW) calculations agreed overall very well with results from magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy experiments. Chemical-shift/structure trends of the precursors and cocrystals were examined, where good linear correlations resulted for all COO1H sites against the H⋯O and/or H⋯N H-bond distance, whereas a general correlation was neither found for the aliphatic/caffeine-stemming 1H sites nor any 13C chemical shift against either the intermolecular hydrogen- or tetrel-bond distance, except for the 13COOH sites of the 2C-OA, 2C-MA, and C-GA cocrystals, which are involved in a strong COOH⋯N bond with caffeine that is responsible for the main supramolecular stabilization of the cocrystal. We provide the first complete 13C NMR spectral assignment of the structurally disordered anhydrous β-caffeine polymorph. The results are discussed in relation to previous literature on the disordered α-caffeine polymorph and the ordered hydrated counterpart, along with recommendations for NMR experimentation that will secure sufficient 13C signal-resolution for reliable resonance/site assignments.

Assessing the Surface Chemistry of 2D Transition Metal Carbides (MXenes): A Combined Experimental/Theoretical 13C Solid State NMR Approach

The surface functionalization of 2D transition metal carbides or nitrides, so-called MXenes, is one of the fundamental levers allowing to deeply modify their physicochemical properties. Beyond new approaches to control this pivotal parameter, the ability to unambiguously assess their surface chemistry is thus key to expand the application fields of this large class of 2D materials. Using a combination of experiments and state of the art density functional theory calculations, we show that the NMR signal of the carbon─the element common to all MXene carbides and corresponding MAX phase precursors─is extremely sensitive to the MXene functionalization, although carbon atoms are not directly bonded to the surface groups. The simulations include the orbital part to the NMR shielding and the contribution from the Knight shift, which is crucial to achieve good correlation with the experimental data, as demonstrated on a set of reference MXene precursors. Starting with the Ti3C2Tx MXene benchmark system, we confirm the high sensitivity of the 13C NMR shift to the exfoliation process. Developing a theoretical protocol to straightforwardly simulate different surface chemistries, we show that the 13C NMR shift variations can be quantitatively related to different surface compositions and number of surface chemistry variants induced by the different etching agents. In addition, we propose that the etching agent affects not only the nature of the surface groups but also their spatial distribution. The direct correlation between surface chemistry and 13C NMR shift is further confirmed on the V2CTx, Mo2CTx, and Nb2CTx MXenes.

Refined Structures of O-Phospho-l-serine and Its Calcium Salt by New Multinuclear Solid-State NMR Crystallography Methods

O-phospho-l-serine (Pser) and its Ca salt, Ca[O-phospho-l-serine]·H2O (CaPser), play important roles for bone mineralization and were recently also proposed to account for the markedly improved bone-adhesive properties of Pser-doped calcium phosphate-based cements for biomedical implants. However, the hitherto few proposed structural models of Pser and CaPser were obtained by X-ray diffraction, thereby leaving the proton positions poorly defined. Herein, we refine the Pser and CaPser structures by density functional theory (DFT) calculations and contrast them with direct interatomic-distance constraints from two-dimensional (2D) nuclear magnetic resonance (NMR) correlation experimentation at fast magic-angle spinning (MAS), encompassing double-quantum-single-quantum (2Q-1Q) 1H NMR along with heteronuclear 13C{1H} and 31P{1H} correlation NMR experiments. The Pser and CaPser structures before and after refinements by DFT were validated against sets of NMR-derived effective 1H-1H, 1H-31P, and 1H-13C distances, which confirmed the improved accuracy of the refined structures. Each distance set was derived from one sole 2D NMR experiment applied to a powder without isotopic enrichment. The distances were extracted without invoking numerical spin-dynamics simulations or approximate phenomenological models. We highlight the advantages and limitations of the new distance-extraction procedure. Isotropic 1H, 13C, and 31P chemical shifts obtained by DFT calculations using the gauge including projector augmented wave (GIPAW) method agreed very well with the experimental results. We discuss the isotropic and anisotropic 13C and 31P chemical-shift parameters in relation to the previous literature, where most data on CaPser are reported herein for the first time.

Structural Refinement of Carbimazole by NMR Crystallography

The characterization of the three-dimensional structure of solids is of major importance, especially in the pharmaceutical field. In the present work, NMR crystallography methods are applied with the aim to refine the crystal structure of carbimazole, an active pharmaceutical ingredient used for the treatment of hyperthyroidism and Grave’s disease. Starting from previously reported X-ray diffraction data, two refined structures were obtained by geometry optimization methods. Experimental ¹H and ¹³C isotropic chemical shift measured by the suitable ¹H and ¹³C high-resolution solid state NMR techniques were compared with DFT-GIPAW calculated values, allowing the quality of the obtained structure to be experimentally checked. The refined structure was further validated through the analysis of ¹H-¹H and ¹H-¹³C 2D NMR correlation experiments. The final structure differs from that previously obtained from X-ray diffraction data mostly for the position of hydrogen atoms.

Revving up 13C NMR shielding predictions across chemical space: benchmarks for atoms-in-molecules kernel machine learning with new data for 134 kilo molecules

The requirement for accelerated and quantitatively accurate screening of nuclear magnetic resonance spectra across the small molecules chemical compound space is two-fold: (1) a robust ‘local’ machine learning (ML) strategy capturing the effect of the neighborhood on an atom’s ‘near-sighted’ property—chemical shielding; (2) an accurate reference dataset generated with a state-of-the-art first-principles method for training. Herein we report the QM9-NMR dataset comprising isotropic shielding of over 0.8 million C atoms in 134k molecules of the QM9 dataset in gas and five common solvent phases. Using these data for training, we present benchmark results for the prediction transferability of kernel-ridge regression models with popular local descriptors. Our best model, trained on 100k samples, accurately predicts isotropic shielding of 50k ‘hold-out’ atoms with a mean error of less than 1.9 ppm. For the rapid prediction of new query molecules, the models were trained on geometries from an inexpensive theory. Furthermore, by using a Δ-ML strategy, we quench the error below 1.4 ppm. Finally, we test the transferability on non-trivial benchmark sets that include benchmark molecules comprising 10–17 heavy atoms and drugs.

First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds II: the orthorhombic phases MgB7 and MgB12C2 and the boron modification γ-B28

Based on the work on referencing 11B nuclear magnetic resonance (NMR) spectra for molecular icosahedral boranes and the subsequent transfer to the rhombohedral boron-rich borides of the α-rB12 type, we show that the magic angle spinning (MAS) NMR spectra of boron-rich borides with four or five symmetry-independent boron atoms can also be calculated. The calculations are performed on the level of density functional theory (DFT) using the gauge-including projector-augmented wave (GIPAW) approach. As model compounds o-MgB12C2 and MgB7 are used, for which the experimental spectra could be calculated in excellent agreement with a deviation of 1 to 2 ppm. Based on the calculations, the different B atoms can be assigned to the respective signals, taking into account the quadrupolar coupling constants Cq from computation of the electric field gradient (EFG) with its main axis Vzz. It is shown that due to the specific geometric conditions of icosahedra, the magnitudes of Vzz for the boron atoms involved in exohedral B-B bonds to neighbouring icosahedra depend only on the valence electron density of the bond critical point and the distance. This also applies to the bonds to the interstitial B2 unit in MgB7, but not to bonds to the heteroatom of the C2 dumbbell in o-MgB12C2. Both results are in line with our previous observations for the rhombohedral species (α-rB12; B12X2 with X = P, As, O). Finally, the spectrum of γ-B28 was calculated, whose structure also contains B12 icosahedra and interstitial B2 dumbbells. Here, a very similar bonding situation is found for the icosahedron, but the calculations show that the situation for the B2 unit is clearly different. In general, the only parameter that needs to be varied to fit calculated and measured spectra is the linewidth, as this cannot be calculated. For the cases of o-MgB12C2 and MgB7 signal areas are related to corresponding site multiplicities. A prerequisite for the successful application of the chosen method seems to be the presence of a semiconductor with a sufficiently large band gap, which is the case for the compounds investigated.

Automated fragmentation quantum mechanical calculation of 13C and 1H chemical shifts in molecular crystals

In this work, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach was applied to calculate the ¹³C and ¹H nuclear magnetic resonance (NMR) chemical shifts in molecular crystals. Two benchmark sets of molecular crystals were selected to calculate the NMR chemical shifts. Systematic investigation was conducted to examine the convergence of AF-QM/MM calculations and the impact of various density functionals with different basis sets on the NMR chemical shift prediction. The result demonstrates that the calculated NMR chemical shifts are close to convergence when the distance threshold for the QM region is larger than 3.5 Å. For ¹³C chemical shift calculations, the mPW1PW91 functional is the best density functional among the functionals chosen in this study (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB98, and OPBE), while the OB98 functional is more suitable for the ¹H NMR chemical shift prediction of molecular crystals. Moreover, with the B3LYP functional, at least a triple-ζ basis set should be utilized to accurately reproduce the experimental ¹³C and ¹H chemical shifts. The employment of diffuse basis functions will further improve the accuracy for ¹³C chemical shift calculations, but not for the ¹H chemical shift prediction. We further proposed a fragmentation scheme of dividing the central molecule into smaller fragments. By comparing with the results of the fragmentation scheme using the entire central molecule as the core region, the AF-QM/MM calculations with the fragmented central molecule can not only achieve accurate results but also reduce the computational cost. Therefore, the AF-QM/MM approach is capable of predicting the ¹³C and ¹H NMR chemical shifts for molecular crystals accurately and effectively, and could be utilized for dealing with more complex periodic systems such as macromolecular polymers and biomacromolecules. The AF-QM/MM program for molecular crystals is available at https://github.com/shiman1995/NMR.

First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds I: the rhombohedral boron modifications and B12X2 (X = P, As, O)

In the present study, solid-state nuclear magnetic resonance (NMR) spectra under magic angle spinning conditions of the rhombohedral structures α-B and B12P2 are reported together with the corresponding parameter sets from first principles calculations on α-B B12X2 (X = P, As, O). With the combination of density functional theory (DFT) and the gauge-including projector-augmented wave (GIPAW) approach as the theoretical tools at hand the computed 11B parameters lead to unambiguous explanation of the measurements. Thereby, we overcome common obstacles of processing recorded NMR spectra of solid-state compounds with several crystallographic positions, in particular non-trivial signal assignments and parameter determination due to peak overlap or even unexpected intensity/area ratios. In fact, we find very good agreement between the theoretical results and measured spectra without applying fitting procedures. Using the Perdew-Burke-Ernzerhof (PBE) functional, the results of the common construction types for pseudopotentials and referencing methods for the chemical shift determination are compared. Suggestions and conclusions from experimental 11B NMR studies on parameters according to the icosahedral positions are critically discussed, for instance the early suspected correlation to chemical shifts is not confirmed. Regarding the electric field gradient (EFG) a detailed explanation for obtaining small deviations amongst all investigated structures of the icosahedral polar sites compared to the equatorial sites is given. Our results show an important link between the exohedral bonding situation of compounds with icosahedral structure elements and the main axis of the EFG and therefore, also measurable quadrupole coupling constants if certain geometrical conditions are fulfilled. Finally, this work also contributes to establishing the number of unique sites measured by solid-state NMR methods within the modification of β-B.

Numerical study of disorder on the orbital magnetization in two dimensions

The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by using this method on the Haldane model in two dimensions, which can be tuned between a normal insulator or a Chern insulator at half filling. The effects of increasing disorder on OM for both cases are simulated. Energy renormalization shifts are observed in the weak disorder regime and topologically trivial case, which was predicted by a self-consistentT-matrix approximation. Besides this, two other phenomena can be seen. One is the localization trend of the band orbital magnetization. The other is the remarkable contribution from topological chiral states arising from nonzero Chern number or large value of integrated Berry curvature. If the fermi energy is fixed at the gap center of the clean system, there is an enhancement of |M| at the intermediate disorder, for both cases of normal and Chern insulators, which can be attributed to the disorder induced topological metal state before localization.

GIAO versus GIPAW: Comparison of Methods To Calculate 11B NMR Shifts of Icosahedral Closo-Heteroboranes toward Boron-Rich Borides

In this work, we perform first-principle density functional theory calculations with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional to compare the results of the gauge-including atomic orbital (GIAO) method with the gauge-including projector-augmented wave (GIPAW) approach for isotropic ¹¹B nuclear magnetic resonance shifts. GIPAW had been used successfully for the theoretical calculation of nuclear magnetic parameters of ¹¹B species in strong ionic solid-phase compounds such as borates but had been applied very rarely to structures where boron is mainly involved in complex covalent bonding situations, for example, in icosahedra of boron-rich borides. Thus, we investigate the accuracy of both well-known methods and reliability of the effective treatment of core electrons on a test set containing 16 experimentally known closo-(hetero)dodecaboranes. In general, we find very good agreement between GIAO and GIPAW when compared to experimental observations. However, accidental degeneracies of the shift values are better predicted by GIPAW. The optimized molecular geometries on the PBE level agree well with gaseous electron diffraction data and lead to theoretical isotropic chemical ¹¹B shifts with root-mean-square errors of 2.1 and 1.0 ppm depending on the used model of converting absolute shieldings to chemical shifts. The comparison with results from hybrid functionals (B3LYP, B3LYP-D2, and PBE0) shows a minor improvement in accuracy, which is in agreement with ¹³C shifts of sp³-hybridized species. In order to prove the reliability of the conversion parameters obtained by PBE, we report the calculated ¹¹B shifts of 1,2-, 1,7-, and 1,12-PCB₁₀H₁₁ with GIAO and GIPAW to our knowledge for the first time. Additionally, Bader's analysis is carried out on the converged electron density for all boron species within the molecular test set, yielding no simple direct relation between charge and isotropic shifts.

Investigation of 205 Tl NMR shielding, structural, and electronical properties in thallium halides by applying PBE-GGA, YS-PBE0 and mBJ functionals

We report the structural, electronical, and heavy nuclear ²⁰⁵ Tl Nuclear Magnetic Resonance (NMR) shielding properties of thallium halides TlX (X = F, Cl, Br, and I) by the first principles calculation. The Perdew-Burke-Ernzerhof Generalized Gradient Approximation, Yukawa Screened-PBE0 hybrid functional, and modified Becke-Johnson (mBJ) functionals including the relativistic and spin-orbit coupling effects are applied for calculation of the exchange-correlation potentials. Calculated PDOS spectra display that the valence band is composed of the X-s, Tl-5d, X-p, and Tl-6s states, and these states play an important role in ²⁰⁵ Tl NMR shielding. Our findings indicate that the nuclear magnetic shielding parameters depend on the electronic properties. Obtained results by mBJ show that there is a close agreement between the experimental and the calculated NMR parameters.

Calculation of Diamagnetic Susceptibility Tensors of Organic Crystals: From Coronene to Pharmaceutical Polymorphs

Understanding why crystallization in strong magnetic fields can lead to new polymorphs requires methods to calculate the diamagnetic response of organic molecular crystals. We develop the calculation of the macroscopic diamagnetic susceptibility tensor, χ^cryst, for organic molecular crystals using periodic density functional methods. The crystal magnetic susceptibility tensor, χ^cryst, for all experimentally known polymorphs, and its molecular counterpart, χ^mol, are calculated for flexible pharmaceuticals such as carbamazepine, flufenamic acid, and chalcones, and rigid molecules, such as benzene, pyridine, acridine, anthracene, and coronene, whose molecular magnetic properties have been traditionally studied. A tensor addition method is developed to approximate the crystal diamagnetic susceptibility tensor, χ^cryst, from the molecular one, χ^mol, giving good agreement with those calculated directly using the more costly periodic density functional method for χ^cryst. The response of pharmaceutical molecules and crystals to magnetic fields, as embodied by χ^cryst, is largely determined by the packing in the crystal, as well as the molecular conformation. The anisotropy of χ^cryst can vary considerably between polymorphs though the isotropic terms are fairly constant. The implications for developing a computational method for predicting whether crystallization in a magnetic field could produce a novel or different polymorph are discussed.

Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

DFT calculations for structural prediction and applications of intercalated lamellar compounds

This review lists some relevant types of intercalated lamellar materials and applications of DFT calculations in these materials.

127I NMR calculations in binary metal iodides by PBE-GGA, YS-PBE0 and mBJ exchange correlation potentials

We have calculated Nuclear Magnetic Resonance (NMR) spectroscopy for ¹²⁷I (quadrupolar nuclei I=5/2) in binary metal iodides XI (X=Li, Na, K, Rb and Cs) by using PBE- GGA, YS- PBE0 and mBJ exchange correlation potentials. The results show that the nature of bonds between Iodine and metal atoms are ionic. The main contribution in NMR spectroscopy is related to the induced current inside the atomic sphere and the remainder of the unit cell volume contributes only a few ppm. Obtained NMR shifts are compared with the NMR shielding data and the NMR shielding for metal-p band varies across the series about 221ppm. Density of states results indicate that the largest contribution in the shielding comes from the I-core electrons (1s and 4d). The NMR shielding graphs show that there are negative linear correlation with slope -1.18, -1.16 and -1.01 by PBE- GGA, YS- PBE0 and mBJ, respectively. The computed results by mBJ are in good agreement with the experimental values.

Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term Hm and a field term Hf, and show that both Hm and Hf have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge.

Ab Initio Quality NMR Parameters in Solid-State Materials Using a High-Dimensional Neural-Network Representation

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful experimental tools to probe the local atomic order of a wide range of solid-state compounds. However, due to the complexity of the related spectra, in particular for amorphous materials, their interpretation in terms of structural information is often challenging. These difficulties can be overcome by combining molecular dynamics simulations to generate realistic structural models with an ab initio evaluation of the corresponding chemical shift and quadrupolar coupling tensors. However, due to computational constraints, this approach is limited to relatively small system sizes which, for amorphous materials, prevents an adequate statistical sampling of the distribution of the local environments that is required to quantitatively describe the system. In this work, we present an approach to efficiently and accurately predict the NMR parameters of very large systems. This is achieved by using a high-dimensional neural-network representation of NMR parameters that are calculated using an ab initio formalism. To illustrate the potential of this approach, we applied this neural-network NMR (NN-NMR) method on the (17)O and (29)Si quadrupolar coupling and chemical shift parameters of various crystalline silica polymorphs and silica glasses. This approach is, in principal, general and has the potential to be applied to predict the NMR properties of various materials.

The Calculation of NMR Chemical Shifts in Periodic Systems Based on Gauge Including Atomic Orbitals and Density Functional Theory

We present here a method that can calculate NMR shielding tensors from first principles for systems with translational invariance. Our approach is based on Kohn-Sham density functional theory and gauge-including atomic orbitals. Our scheme determines the shielding tensor as the second derivative of the total electronic energy with respect to an external magnetic field and a nuclear magnetic moment. The induced current density due to a periodic perturbation from nuclear magnetic moments is obtained through numerical differentiation, whereas the influence of the responding perturbation in terms of the external magnetic field is evaluated analytically. The method is implemented into the periodic program BAND. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn-Sham potential fully without the use of effective core potentials. Results from calculations of NMR shielding constants based on the present approach are presented for isolated molecules as well as systems with one-, two- and three-dimensional periodicity. The reported values are compared to experiment and results from calculations on cluster models.

NMR Shielding in Metals Using the Augmented Plane Wave Method

We present calculations of solid state NMR magnetic shielding in metals, which includes both the orbital and the complete spin response of the system in a consistent way. The latter contains an induced spin-polarization of the core states and needs an all-electron self-consistent treatment. In particular, for transition metals, the spin hyperfine field originates not only from the polarization of the valence s-electrons, but the induced magnetic moment of the d-electrons polarizes the core s-states in opposite direction. The method is based on DFT and the augmented plane wave approach as implemented in the WIEN2k code. A comparison between calculated and measured NMR shifts indicates that first-principle calculations can obtain converged results and are more reliable than initially concluded based on previous publications. Nevertheless large k-meshes (up to 2 000 000 k-points in the full Brillouin-zone) and some Fermi-broadening are necessary. Our results show that, in general, both spin and orbital components of the NMR shielding must be evaluated in order to reproduce experimental shifts, because the orbital part cancels the shift of the usually highly ionic reference compound only for simple sp-elements but not for transition metals. This development paves the way for routine NMR calculations of metallic systems.

Exploring the ring current of carbon nanotubes by first-principles calculations

Ring current is a fundamental concept to understand the nuclear magnetic resonance (NMR) properties and aromaticity for conjugated systems, such as carbon nanotubes (CNTs). Employing the recently developed gauge including projector augmented wave (GIPAW) method, we studied the ring currents of CNTs systematically and visualized their distribution. The ring current patterns are determined by the semiconducting or metallic properties of CNTs. The discrepancy is mainly caused by the axial component of external magnetic fields, whereas the radial component induced ring currents are almost independent of the electronic structures of CNTs, where the intensities of the ring currents are linearly related to the diameters of the CNTs. Although the ring currents induced by the radial component are more intense than those by the axial component, only the latter determines the overall NMR responses and aromaticity of the CNTs as well. Furthermore, the semiconducting CNTs are more aromatic than their metallic counterparts due to the existence of delocalized ring currents on the semiconducting CNTs. These fundamental features are of vital importance for the development of CNT-based nanoelectronics and applications in magnetic fields.

NMR characterization of hydrocarbon adsorption on calcite surfaces: a first principles study

The electronic and coordination environment of minerals surfaces, as calcite, are very difficult to characterize experimentally. This is mainly due to the fact that there are relatively few spectroscopic techniques able to detect Ca(2+). Since calcite is a major constituent of sedimentary rocks in oil reservoir, a more detailed characterization of the interaction between hydrocarbon molecules and mineral surfaces is highly desirable. Here we perform a first principles study on the adsorption of hydrocarbon molecules on calcite surface (CaCO3 (101¯4)). The simulations were based on Density Functional Theory with Solid State Nuclear Magnetic Resonance (SS-NMR) calculations. The Gauge-Including Projector Augmented Wave method was used to compute mainly SS-NMR parameters for (43)Ca, (13)C, and (17)O in calcite surface. It was possible to assign the peaks in the theoretical NMR spectra for all structures studied. Besides showing different chemical shifts for atoms located on different environments (bulk and surface) for calcite, the results also display changes on the chemical shift, mainly for Ca sites, when the hydrocarbon molecules are present. Even though the interaction of the benzene molecule with the calcite surface is weak, there is a clearly distinguishable displacement of the signal of the Ca sites over which the hydrocarbon molecule is located. A similar effect is also observed for hexane adsorption. Through NMR spectroscopy, we show that aromatic and alkane hydrocarbon molecules adsorbed on carbonate surfaces can be differentiated.

Extended Czjzek model applied to NMR parameter distributions in sodium metaphosphate glass

The extended Czjzek model (ECM) is applied to the distribution of NMR parameters of a simple glass model (sodium metaphosphate, NaPO3) obtained by molecular dynamics (MD) simulations. Accurate NMR tensors, electric field gradient (EFG) and chemical shift anisotropy (CSA) are calculated from density functional theory (DFT) within the well-established PAW/GIPAW framework. The theoretical results are compared to experimental high-resolution solid-state NMR data and are used to validate the considered structural model. The distributions of the calculated coupling constant C(Q) is proportional to |V(zz)| and the asymmetry parameter η(Q) that characterize the quadrupolar interaction are discussed in terms of structural considerations with the help of a simple point charge model. Finally, the ECM analysis is shown to be relevant for studying the distribution of CSA tensor parameters and gives new insight into the structural characterization of disordered systems by solid-state NMR.

A study of hydrogen microstructure in amorphous silicon via inversion of nuclear magnetic resonance spectra

We present an inverse approach for studying hydrogen microstructure in amorphous silicon. The approach consists of generating a prior distribution (of spins/hydrogen) by inverting experimental nuclear magnetic resonance (NMR) data, which is subsequently superimposed on a network of amorphous silicon. The resulting network is then relaxed using a total-energy functional to obtain a stable, low-energy configuration such that the initial spin distribution is minimally perturbed. The efficacy of this approach is demonstrated by generating model configurations that not only have the correct NMR spectra but also satisfy simultaneously experimental structural, electronic and vibrational properties of hydrogenated amorphous silicon.

Interpretation of crystal effects on NMR chemical shift tensors: electron and shielding deformation densities

The relationship between the NMR observables and the supramolecular structure of any system is not straightforward. In this work we examine the influence of the crystal packing for three purine derivatives (hypoxanthine, theobromine, and 6-(2-methoxy)benzylaminopurine) on the principal components of the NMR chemical shift tensors (CSTs). We employ density functional calculations to obtain various molecular properties (the ground-state electron density, the magnitudes and orientations of the components of NMR chemical shift tensor, and the spatial distribution of the isotropic magnetic shielding) for the isolated molecules and for the molecules embedded in supramolecular clusters modeling the crystal environment and evaluate their differences. The concept has enabled us to rationalize the effect of the crystal packing on the NMR CSTs in terms of the redistribution of the ground-state electron density induced by intermolecular interactions in the solid state.

First principles NMR study of fluorapatite under pressure

NMR is the technique of election to probe the local properties of materials. Herein we present the results of density functional theory (DFT) ab initio calculations of the NMR parameters for fluorapatite (FAp), a calcium orthophosphate mineral belonging to the apatite family, by using the GIPAW method (Pickard and Mauri, 2001). Understanding the local effects of pressure on apatites is particularly relevant because of their important role in many solid state and biomedical applications. Apatites are open structures, which can undergo complex anisotropic deformations, and the response of NMR can elucidate the microscopic changes induced by an applied pressure. The computed NMR parameters proved to be in good agreement with the available experimental data. The structural evaluation of the material behavior under hydrostatic pressure (from -5 to +100 kbar) indicated a shrinkage of the diameter of the apatitic channel, and a strong correlation between NMR shielding and pressure, proving the sensitivity of this technique to even small changes in the chemical environment around the nuclei. This theoretical approach allows the exploration of all the different nuclei composing the material, thus providing a very useful guidance in the interpretation of experimental results, particularly valuable for the more challenging nuclei such as (43)Ca and (17)O.

An improved scheme for the calculation of NMR chemical shifts in periodic systems based on gauge including atomic orbitals and density functional theory

We report here on an improved first principles method that can determine NMR shielding tensors for periodic systems. Our scheme evaluates the shielding tensor as the second derivative of the total electronic energy with respect to a nuclear magnetic moment and an external magnetic field. Both the induced current density J(α) due to the first perturbation from the nuclear magnetic moment as well as the interaction of J(α) with the second perturbation in the form of an external magnetic field are evaluated analytically. Our approach is based on Kohn–Sham density functional theory and gauge-including atomic orbitals. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn–Sham potential fully without the use of effective core potentials. The method is implemented into the periodic program BAND. The new scheme represents an improvement over a previously proposed method in that use can be made of the zero-order Kohn–Sham orbitals from a calculation based on a primitive cell instead of a supercell. Further, J(α) is evaluated analytically rather than by a finite difference approach. The improvements reduce the required computational time by up to two orders of magnitude for three-dimensional systems. Such a reduction is made possible by the fact that we are using atomic centered basis functions. The new implementation is further able to take into account scalar relativistic effects within the zero-order regular approximation. Results from calculations of NMR shielding constants based on the present approach are presented for systems with one-, two-, and three-dimensional periodicity. The reported values are compared to experiment and results from the previously proposed scheme.

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.

Magnetic response of single-walled carbon nanotubes induced by an external magnetic field

Using first-principles density functional calculations, magnetically induced currents are obtained for zigzag single-walled carbon nanotubes. Clear differences and trends in current flow are observed between the different nanotube families. In particular, for a magnetic field applied along the tube axis, the current response of the λ = 0 infinite nanotubes is paramagnetic, whereas for λ = 1 and 2 nanotubes, the response is diamagnetic. The results are used to predict and interpret the significant changes in NMR properties for small molecules encapsulated inside a tube.

Dynamical effects in ab initio NMR calculations: classical force fields fitted to quantum forces

NMR chemical shifts for an L-alanine molecular crystal are calculated using ab initio plane wave density functional theory. Dynamical effects including anharmonicity may be included by averaging chemical shifts over an ensemble of structural configurations generated using molecular dynamics (MD). The time scales required mean that ab initio MD is prohibitively expensive. Yet the sensitivity of chemical shifts to structural details requires that the methodologies for performing MD and calculating NMR shifts be consistent. This work resolves these previously competing requirements by fitting classical force fields to reproduce ab initio forces. This methodology is first validated by reproducing the averaged chemical shifts found using ab initio molecular dynamics. Study of a supercell of L-alanine demonstrates that finite size effects can be significant when accounting for dynamics.

First-principles calculations of NMR parameters for phosphate materials

In this short review, we discuss the ability to reproduce NMR parameters in the case of phosphates materials through electronic structure calculation within density functional theory linear response. Indeed, the gauge-including projector-augmented wave is today largely used by the solid-state NMR community as a tool for structural determination and it has been applied to a large variety of materials. We emphasise on the crucial points that should be taken into account to perform such calculations. In particular, we discuss the influence of the electronic structure and of the geometry on the calculation of NMR parameters. To illustrate the review, we present experimental and theoretical comparison of (31)P, (1)H and (23)Na NMR data on a series of sodium phosphate systems.