The effect of intermolecular interactions on the electric field gradients in solid ammonia, tetrazole and imidazole

The many-body expansion approach to ab initio calculation of electric field gradients in molecular crystals

Accurate calculation of electric field gradients (EFGs) in molecular crystals, despite big advances in ab initio techniques, is still a challenge. Here, we present a new approach to calculate the EFGs in molecular crystals by employing the many-body expansion (MBE) technique with electrostatic embedding. This allows for (i) a reduction in the computational cost or an alternative increase in the level of theory (we use the MP2/6-311++G) and (ii) the ability to monitor EFG convergence by progressively adding more surrounding molecules and/or adding higher many-body interactions. We focus on the ¹⁴N EFG and study four (model) compounds in more detail: solid nitrogen, ethylamine, methylamine, and ammonia. Solid nitrogen is rather insensitive to neighbors; for ethylamine and methylamine, the 3-body interactions are found sufficient for a converged EFG, whereas for ammonia, even the inclusion of 5-body interactions is insufficient although convergence is anticipated. We then validate our technique by comparing the experimental and ab initio¹⁴N EFGs for 116 organic compounds utilizing their known crystal structures and published EFG. Overall, we find a very good agreement, with a small EFG rms error, which is probably due to other sources, rather than the MBE approximation.

A model to describe the inhomogeneous broadening of NQR lines in chlorohalobenzenes with orientational or substitutional disorder

A simple model to explain the NQR lineshape in solids with orientational disorder or substitutional disorder is presented. The particular case of m-chlorobromobenzene is studied. It is based on the assumption that Bromine atoms, of m-chlorobromobenzene molecules, behave as point defects in the m-dichlorobenzene lattice that modify the crystalline Electric Field Gradient. The model is also tested successfully in solid solutions of p-dichlorobenzene-p-dibromobenzene, where Bromine atoms of p-dibromobenzene molecules are assumed to be homogeneously distributed in the p-dichlorobenzene lattice. The lineshape, of others disordered chlorohalobenzenes, are also analyzed. Also, a characterization of m-chlorobromobenzene dynamics is included. In particular, there is no evidence of molecular reorientations as it is observed in the disordered phases of o-chlorobromobenzene.

14N NQR lineshape in nanocrystals: An ab initio investigation of urea

¹⁴N nuclear quadrupole resonance (NQR) lineshapes mostly contain information of low interest, although in nanocrystals they may display some unexpected behaviour. In this work, we present an ab initio computational study of the ¹⁴N NQR lineshapes in urea nanocrystals as a function of the nanocrystal size and geometry, focusing on the surface induced broadening of the lineshapes. The lineshapes were obtained through a calculation of the electric field gradient for each nitrogen site in the nanocrystal separately, taking into account the individual crystal field by embedding the molecule of interest in a suitable lattice of point multipoles representing other urea molecules in the nanocrystal. The small influence of distant molecules is found with a series expansion, using the in-crystal Sternheimer shieldings which we also calculated ab initio. We have considered nanocrystals with two geometries: a sphere and a cube, with characteristic sizes between 5 and 100 nm. Our calculations suggest that there is a dramatic difference between the linewidths for the two geometries. For spheres, we find a steep drop in linewidths at ∼10 nm; at 5 nm the linewidth is ∼11 kHz, whereas for sizes above 20 nm the linewidth is practically negligible (<100 Hz). For cubes, on the other hand, we find a steady 1/size decrease, from 12 kHz at 10 nm to 1.2 kHz at 100 nm. This analysis is important for ¹⁴N NQR spectroscopy of crystalline pharmaceuticals, where nanoparticles are increasingly more often embedded in some sort of matrix. Although this is only a theoretical analysis, we believe that this work can serve as a guidance for the forthcoming experimental analysis.

New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds.

Investigation of structure and dynamics in the sodium metallocenes CpNa and CpNa·THF via solid-state NMR, X-ray diffraction and computational modelling

Solid-state (23) Na NMR spectra of two organometallic complexes, cyclopentadienylsodium (CpNa) and the tetrahydrofuran (THF) solvate of CpNa (CpNa·THF), are presented. Analytical simulations of experimental spectra and calculated (23) Na electric-field gradient (EFG) tensors confirm that both complexes are present in microcrystalline samples of CpNa recrystallized from THF. For the solvate, (23) Na NMR experiments at 9.4 T and 11.7 T elucidate sodium chemical shielding (CS) tensor parameters, and establish that the EFG and CS tensor frames are non-coincident. Single-crystal X-ray diffraction (XRD) experiments are used to determine the crystal structure of CpNa·THF: Cmca (a = 9.3242(15) Å, b = 20.611(3) Å, c = 9.8236(14) Å, α = β = γ = 90° , V = 1887.9(5)Å(3) , Z = 8). For CpNa, (23) Na NMR data acquired at multiple field strengths establish sodium CS tensor parameters more precisely than in previous reports. Variable-temperature (VT) powder XRD (pXRD) experiments determine the temperature dependence of the CpNa unit cell parameters. The combination of (23) Na quadrupolar NMR parameters, pXRD data and calculations of (23) Na EFG tensors is used to examine various models of dynamic motion in the solid state. It is proposed that the sodium atom in CpNa undergoes an anisotropic, temperature-dependent, low frequency motion within the ab crystallographic plane, in contrast with previous models.

A Solid-State 39K and 13C NMR Study of Polymeric Potassium Metallocenes

The quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) and double frequency sweep (DFS)/QCPMG pulse sequences are applied in order to acquire the first solid-state 39K NMR spectra of organometallic complexes, the polymeric main group metallocenes cyclopentadienyl potassium (CpK) and pentamethylcyclopentadienyl potassium (Cp*K). Piecewise QCPMG NMR techniques are used to acquire a high S/N 39K spectrum of the broad central transition of Cp*K, which is ca. 200 kHz in breadth. Analytical and numerical simulations indicate that there is a significant quadrupolar interaction present at both potassium nuclei (C(Q)(39K) = 2.55(6)/2.67(8) MHz and 4.69(8) MHz for CpK (static/MAS) and Cp*K, respectively). Experimental quadrupolar asymmetry parameters suggest that both structures are bent about the potassium atoms (eta(Q)(39K) = 0.28(3)/0.29(3) for CpK (static/MAS) and eta(Q)(39K) = 0.30(3) for Cp*K). Variable-temperature (VT) 39K NMR experiments on CpK elucidate temperature-dependent changes in quadrupolar parameters which can be rationalized in terms of alterations of bond distances and angles with temperature. 13C CP/MAS NMR experiments are conducted upon both samples to quantify the carbon chemical shielding anisotropy (CSA) at the Cp' ring carbon atoms. Ab initio carbon CSA and 39K electric-field gradient (EFG) and CSA calculations are conducted and discussed for the CpK complex, in order to correlate the experimental NMR parameters with molecular structure in CpK and Cp*K. 39K DFS/QCPMG and 13C CP/MAS experiments prove invaluable for probing molecular structure, temperature-dependent structural changes, and the presence of impurities in these systems.

Anisotropic NMR interaction tensors in the decamethylaluminocenium cation

Solid-state NMR experiments, analytical and numerical simulations of solid NMR powder patterns, ab initio self-consistent field and hybrid density functional theory calculations, and single-crystal X-ray diffraction are used to characterize the molecular structure and anisotropic NMR interaction tensors in the bis(pentamethylcyclopentadienyl)aluminum cation, [Cp(2)Al](+). This highly symmetric main group metallocene has a structure analogous to that of ferrocene and the cobaltocenium cation. The single-crystal X-ray diffraction structure is reported for [Cp(2)Al][AlCl(4)]. Solid-state (27)Al[(1)H] magic-angle spinning and static NMR experiments are used to study the aluminum chemical shielding and electric field gradient tensors, revealing axial symmetry in both cases with a large chemical shielding span of Omega = 83(3) ppm and a small nuclear quadrupole coupling constant, C(Q)((27)Al) = 0.86(10) MHz. Carbon-13 CPMAS NMR experiments in combination with ab initio calculations and simulations of the effects of chemical exchange on (13)C static powder patterns reveal dynamic rotation of rings and suggest a low internal rotational barrier for this process. Theoretical computations of interaction tensors using the Gaussian 98 and Amsterdam Density Functional software packages are in good agreement with experiment and lend insight into the molecular origin of these NMR interactions. Orientations of the NMR tensors determined from theory, the large chemical shielding span, and the very small value of C(Q)((27)Al) can all be rationalized in terms of the high molecular symmetry.

A definitive example of aluminum-27 chemical shielding anisotropy

Solid-state 27Al NMR spectra have been obtained for a crystalline 1:1 complex of AlCl3 and OPCl3. Aluminum chloride phosphoryl chloride, AlCl3 . OPCl3 (1), is unusual in that the Al-O-P bond angle is close to 180 degrees. From analysis of the 27Al MAS NMR spectra, it was determined that the 27Al nuclear quadrupole coupling constant is 6.0(1) MHz, the asymmetry in the electric field gradient (efg) tensor is 0.15(2), and the isotropic chemical shift, deltaiso(27Al), is 88(1) ppm. Solid-state 27Al NMR of a stationary sample reveals a line shape affected by a combination of anisotropic chemical shielding and second-order quadrupolar interactions. Analysis of this spectrum yields a chemical shift anisotropy of 60(1) ppm and orientations of the chemical shift and electric field gradient tensors in the molecular frame. Experimental results are compared with those calculated using ab initio Hartree-Fock and density functional theory. Copyright 1998 Academic Press.