Multinuclear Residual Quadrupolar Couplings for Structure and Assignment

Most stable isotopes have a nuclear spin >1/2, but the quadrupole interaction poses challenge on their detection by nuclear magnetic resonance (NMR). On the other hand, the quadrupole interaction is a rich source of structural information that may be exploited for solution NMR in the form of residual quadrupolar couplings (RQCs) of weakly oriented samples. While 2H RQCs are now well established for structure verification and enantiomeric discrimination of organic molecules, we will in this article highlight some recent work on RQCs of other nuclei (especially 7Li and 11B).

Can simple 'molecular' corrections outperform projector augmented-wave density functional theory in the prediction of 35 Cl electric field gradient tensor parameters for chlorine-containing crystalline systems?

Many-body expansion (MBE) fragment approaches have been applied to accurately compute nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent examples demonstrate that electric field gradient (EFG) tensor parameters can be accurately calculated for 14 N and 17 O. A key additional development is the simple molecular correction (SMC) approach, which uses two one-body fragment (i.e., isolated molecule) calculations to adjust NMR parameter values established using 'benchmark' projector augmented-wave (PAW) density functional theory (DFT) values. Here, we apply a SMC using the hybrid PBE0 exchange-correlation (XC) functional to see if this can improve the accuracy of calculated 35 Cl EFG tensor parameters. We selected eight organic and two inorganic crystal structures and considered 15 chlorine sites. We find that this SMC improves the accuracy of computed values for both the 35 Cl quadrupolar coupling constant (CQ ) and the asymmetry parameter ( η Q ) by approximately 30% compared with benchmark PAW DFT values. We also assessed a SMC that offers local improvements not only in terms of the quality of the XC functional but simultaneously in the quality of the description of relativistic effects via the inclusion of spin-orbit effects. As the inorganic systems considered contain heavy atoms bonded to the chlorine atoms, we find further improvements in the accuracy of calculated 35 Cl EFG tensor parameters when both a hybrid functional and spin-orbit effects are included in the SMC. On the contrary, for chlorine-containing organics, the inclusion of spin-orbit relativistic effects using a SMC does not improve the accuracy of computed 35 Cl EFG tensor parameters.

Fast and Accurate Electric Field Gradient Calculations in Molecular Solids With Density Functional Theory

Modern approaches for calculating electric field gradient (EFF) tensors in molecular solids rely upon plane-wave calculations employing periodic boundary conditions (PBC). In practice, models employing PBCs are limited to generalized gradient approximation (GGA) density functionals. Hybrid density functionals applied in the context of gauge-including atomic orbital (GIAO) calculations have been shown to substantially improve the accuracy of predicted NMR parameters. Here we propose an efficient method that effectively combines the benefits of both periodic calculations and single-molecule techniques for predicting electric field gradient tensors in molecular solids. Periodic calculations using plane-wave basis sets were used to model the crystalline environment. We then introduce a molecular correction to the periodic result obtained from a single-molecule calculation performed with a hybrid density functional. Single-molecule calculations performed using hybrid density functionals were found to significantly improve the agreement of predicted 17O quadrupolar coupling constants (C q ) with experiment. We demonstrate a 31% reduction in the RMS error for the predicted 17O C q values relative to standard plane-wave methods using a carefully constructed test set comprised of 22 oxygen-containing molecular crystals. We show comparable improvements in accuracy using five different hybrid density functionals and find predicted C q values to be relatively insensitive to the choice of basis set used in the single molecule calculation. Finally, the utility of high-accuracy 17O C q predictions is demonstrated by examining the disordered 4-Nitrobenzaldehyde crystal structure.

Evaluation of the properties in an infinite crystal

The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630-651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400-408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision-performance balance.

Extraordinary Light-Induced Local Angular Momentum near Metallic Nanoparticles

The intense local field induced near metallic nanostructures provides strong enhancements for surface-enhanced spectroscopies, a major focus of plasmonics research over the past decade. Here we consider that plasmonic nanoparticles can also induce remarkably large electromagnetic field gradients near their surfaces. Sizeable field gradients can excite dipole-forbidden transitions in nearby atoms or molecules and provide unique spectroscopic fingerprinting for chemical and bimolecular sensing. Specifically, we investigate how the local field gradients near metallic nanostructures depend on geometry, polarization, and wavelength. We introduce the concept of the local angular momentum (LAM) vector as a useful figure of merit for the design of nanostructures that provide large field gradients. This quantity, based on integrated fields rather than field gradients, is particularly well-suited for optimization using numerical grid-based full wave electromagnetic simulations. The LAM vector has a more compact structure than the gradient matrix and can be straightforwardly associated with the angular momentum of the electromagnetic field incident on the plasmonic structures.

Does a Molecule-Specific Density Functional Give an Accurate Electron Density? The Challenging Case of the CuCl Electric Field Gradient

In the framework of determining system-specific long-range corrected density functionals, the question is addressed whether such functionals, tuned to satisfy the condition -ε(HOMO) = IP or other energetic criteria, provide accurate electron densities. A nonempirical physically motivated two-dimensional tuning of range-separated hybrid functionals is proposed and applied to the particularly challenging case of a molecular property that depends directly on the ground-state density: the copper electric field gradient (EFG) in CuCl. From a continuous range of functional parametrizations that closely satisfy -ε(HOMO) = IP and the correct asymptotic behavior of the potential, the one that best fulfills the straight-line behavior of E(N), the energy as a function of a fractional electron number N, was found to provide the most accurate electron density as evidenced by calculated EFGs. The functional also performs well for related Cu systems.

Ozone model for bonding of an O2 to heme in oxyhemoglobin

Several rather different models of the Fe-o2 bond in oxyhemoglobin have previously been proposed, none of which provide a satisfactory explanation of several properties. We propose a new model for the bonding of an O2 to the Fe of myoglobin and hemoglobin and report ab initio generalized valence bond and configuration interaction calculations on FeO2 that corroborate this model. Our model is based closely upon the bonding in ozone which recent theoretical studies have shown to be basically a biradical with a singlet state stabilized by a three-center four-electron pi bond. In this model, the facile formation and dissociation of the Fe-O2 bond is easily rationalized since the O2 always retains its triplet ground state character. The ozone model leads naturally to a large negative electric field gradient (in agreement with Mössbauer studies) and to z-polarized (perpendicular to the heme) charge transfer transitions. It also suggests that the 1.3 eV transition, present in HbO2 and absent in HbCO, is due to a porphyrin-to-Fe transition, analogous to that of ferric hemoglobins (e.g., HbCN).