Revisiting the Van Vleck second moment for characterizing molecular motion in organic solids.

Van Vleck's classic theory of the second moment of lineshapes in 1H nuclear magnetic resonance (NMR) is reworked in a form that allows the effect of rapid molecular motion on second moments to be calculated in a semi-analytical fashion. This is much more efficient than existing approaches and also extends previous analyses of (non-dynamic) dipolar networks in terms of site-specific root-sum-square dipolar couplings. The non-local nature of the second moment means that it can discriminate between overall motions that are difficult to discriminate using alternative approaches, such as measurements of NMR relaxation. The value of reviving second moment studies is illustrated on the plastic solids diamantane and triamantane. In the case of triamantane, straightforward measurements of 1H lineshapes on milligram samples show that the molecules in the higher temperature phase undergo multi-axis jumps, information that is not accessible either to diffraction studies or to alternative NMR approaches. The efficiency of the computational methods means that the second moments can be calculated using a readily extensible and open-source Python code.

Operando NMR electrochemical gating studies of ion dynamics in PEDOT:PSS.

Although organic mixed ionic-electronic conductors are widely proposed for use in bioelectronics, energy generation/storage and neuromorphic computing, our fundamental understanding of the charge-compensating interactions between the ionic and electronic carriers and the dynamics of ions remains poor, particularly for hydrated devices and on electrochemical cycling. Here we show that operando 23Na and 1H nuclear magnetic resonance (NMR) spectroscopy can quantify cation and water movement during the doping/dedoping of films comprising the widely used mixed conductor poly(3,4-ethylene dioxythiophene) poly(styrene sulfonate) (PEDOT:PSS). A distinct 23Na quadrupolar splitting is observed due to the partial ordering of the PSS chains within the PEDOT:PSS-rich domains, with respect to the substrate. Operando 23Na NMR studies reveal a close-to-linear correlation between the quadrupolar splitting and the charge stored, which is quantitatively explained by a model in which the holes on the PEDOT backbone are bound to the PSS SO3- groups; an increase in hole concentration during doping inversely correlates with the number of Na+ ions bound to the PSS chains within the PEDOT-rich ordered domains, leading to a decrease in ions within the ordered regions and a decrease in quadrupolar splitting. The Na+-to-electron coupling efficiency, measured via 23Na NMR intensity changes, is close to 100% when using a 1 M NaCl electrolyte. Operando 1H NMR spectroscopy confirms that the Na+ ions injected into/extracted from the wet films are hydrated. These findings shed light on the working principles of organic mixed conductors and demonstrate the utility of operando NMR spectroscopy in revealing structure-property relationships in electroactive polymers.

Testing, tracing and isolation in compartmental models.

Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computational efficiency is such that it can be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.

Computational prediction of muon stopping sites: A novel take on the unperturbed electrostatic potential method.

Finding the stopping site of the muon in a muon-spin relaxation experiment is one of the main problems of muon spectroscopy, and computational techniques that make use of quantum chemistry simulations can be of great help when looking for this stopping site. The most thorough approach would require the use of simulations, such as Density Functional Theory (DFT), to test and optimize multiple possible sites, accounting for the effect that the added muon has on its surroundings. However, this can be computationally expensive and sometimes unnecessary. Hence, in this work, we present a software implementation of the Unperturbed Electrostatic Potential (UEP) Method: an approach used for finding the muon stopping site in crystalline materials. The UEP method requires only one DFT calculation, necessary to compute the electronic density. This, in turn, is used to calculate the minima of the crystalline material's electrostatic potential and the estimates of the muon stopping site, relying on the approximation that the muon's presence does not significantly affect its surroundings. One of the main UEP's assumptions is that the muon stopping site will be one of the crystalline material's electrostatic potential minima. In this regard, we also propose some symmetry-based considerations about the properties of this crystalline material's electrostatic potential, in particular, which sites are more likely to be its minima and why the unperturbed approximation may be sufficiently robust for them. We introduce the Python software package pymuon-suite and the various utilities it provides to facilitate these calculations, and finally, we demonstrate the effectiveness of the method with some chosen example systems.

Weak Intermolecular CH···N Hydrogen Bonding: Determination of 13CH-15N Hydrogen-Bond Mediated J Couplings by Solid-State NMR Spectroscopy and First-Principles Calculations.

Weak hydrogen bonds are increasingly hypothesized to play key roles in a wide range of chemistry from catalysis to gelation to polymer structure. Here, 15N/13C spin-echo magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) experiments are applied to "view" intermolecular CH···N hydrogen bonding in two selectively labeled organic compounds, 4-[15N] cyano-4'-[13C2] ethynylbiphenyl (1) and [15N3,13C6]-2,4,6-triethynyl-1,3,5-triazine (2). The synthesis of 2-15N3,13C6 is reported here for the first time via a multistep procedure, where the key element is the reaction of [15N3]-2,4,6-trichloro-1,3,5-triazine (5) with [13C2]-[(trimethylsilyl)ethynyl]zinc chloride (8) to afford its immediate precursor [15N3,13C6]-2,4,6-tris[(trimethylsilyl)ethynyl]-1,3,5-triazine (9). Experimentally determined hydrogen-bond-mediated 2hJCN couplings (4.7 ± 0.4 Hz (1) and 4.1 ± 0.3 Hz (2)) are compared with density functional theory (DFT) gauge-including projector augmented wave (GIPAW) calculations, whereby species-independent coupling values 2hKCN (29.0 × 1019 kg m-2 s-2 A-2 (1) and 27.9 × 1019 kg m-2 s-2 A-2 (2)) quantitatively demonstrate the J couplings for these "weak" CH···N hydrogen bonds to be of a similar magnitude to those for conventionally observed NH···O hydrogen-bonding interactions in uracil (2hKNO: 28.1 and 36.8 × 1019 kg m-2 s-2 A-2). Moreover, the GIPAW calculations show a clear correlation between increasing 2hJCN (and 3hJCN) coupling and reducing C(H)···N and H···N hydrogen-bonding distances, with the Fermi contact term accounting for at least 98% of the isotropic 2hJCN coupling.

Comparison between density functional theory and density functional tight binding approaches for finding the muon stopping site in organic molecular crystals.

Finding the possible stopping sites for muons inside a crystalline sample is a key problem of muon spectroscopy. In a previous study, we suggested a computational approach to this problem when dealing with muonium, the pseudoatom formed by a positive muon that has captured an electron, using density functional theory software in combination with a random structure searching approach that relies on a Poisson sphere distribution. In this work, we test this methodology further by applying it to muonium in three organic molecular crystal model systems: durene, bithiophene, and tetracyanoquinodimethane. Using the same sets of random structures, we compare the performance of density functional theory software CASTEP and the much faster lower level approximation of Density Functional Tight Binding provided by DFTB+ combined with the use of the 3ob-3-1 parameter set. We show the benefits and limitations of such an approach, and we propose the use of DFTB+ as a viable alternative to more cumbersome simulations for routine site-finding in organic materials. Finally, we introduce the Muon Spectroscopy Computational Project software suite, a library of Python tools meant to make these methods standardized and easy to use.

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13 C-13 C dipolar couplings.

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed 1 H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using 13 C-13 C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although 13 C-13 C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.

A Picture of Disorder in Hydrous Wadsleyite-Under the Combined Microscope of Solid-State NMR Spectroscopy and Ab Initio Random Structure Searching.

The Earth's transition zone, at depths of 410-660 km, while being composed of nominally anhydrous magnesium silicate minerals, may be subject to significant hydration. Little is known about the mechanism of hydration, despite the vital role this plays in the physical and chemical properties of the mantle, leading to a need for improved structural characterization. Here we present an ab initio random structure searching (AIRSS) investigation of semihydrous (1.65 wt % H2O) and fully hydrous (3.3 wt % H2O) wadsleyite. Following the AIRSS process, k-means clustering was used to select sets of structures with duplicates removed, which were then subjected to further geometry optimization with tighter constraints prior to NMR calculations. Semihydrous models identify a ground-state structure (Mg3 vacancies, O1-H hydroxyls) that aligns with a number of previous experimental observations. However, predicted NMR parameters fail to reproduce low-intensity signals observed in solid-state NMR spectra. In contrast, the fully hydrous models produced by AIRSS, which enable both isolated and clustered defects, are able to explain observed NMR signals via just four low-enthalpy structures: (i) a ground state, with isolated Mg3 vacancies and O1-H hydroxyls; (ii/iii) edge-sharing Mg3 vacancies with O1-H and O3-H species; and (iv) edge-sharing Mg1 and Mg3 vacancies with O1-H, O3-H, and O4-H hydroxyls. Thus, the combination of advanced structure searching approaches and solid-state NMR spectroscopy is able to provide new and detailed insight into the structure of this important mantle mineral.

Computational applications of the many-interacting-worlds interpretation of quantum mechanics.

While historically many quantum-mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a great deal of interest has arisen in quantum effects in nuclear dynamics as well. Due to the computational difficulty of solving the Schrödinger equation in full, these effects are often treated with approximate methods. In this paper, we present an algorithm to tackle these problems using an extension to the many-interacting-worlds approach to quantum mechanics. This technique uses a kernel function to rebuild the probability density, and therefore, in contrast with the approximation presented in the original paper, it can be naturally extended to n-dimensional systems. This opens up the possibility of performing quantum ground-state searches with steepest-descent methods, and it could potentially lead to real-time quantum molecular-dynamics simulations. The behavior of the algorithm is studied in different potentials and numbers of dimensions and compared both to the original approach and to exact Schrödinger equation solutions whenever possible.

Computational prediction of muon stopping sites using ab initio random structure searching (AIRSS).

The stopping site of the muon in a muon-spin relaxation experiment is in general unknown. There are some techniques that can be used to guess the muon stopping site, but they often rely on approximations and are not generally applicable to all cases. In this work, we propose a purely theoretical method to predict muon stopping sites in crystalline materials from first principles. The method is based on a combination of ab initio calculations, random structure searching, and machine learning, and it has successfully predicted the MuT and MuBC stopping sites of muonium in Si, diamond, and Ge, as well as the muonium stopping site in LiF, without any recourse to experimental results. The method makes use of Soprano, a Python library developed to aid ab initio computational crystallography, that was publicly released and contains all the software tools necessary to reproduce our analysis.

Visualising crystal packing interactions in solid-state NMR: Concepts and applications.

In this article, we introduce and apply a methodology, based on density functional theory and the gauge-including projector augmented wave approach, to explore the effects of packing interactions on solid-state nuclear magnetic resonance (NMR) parameters. A visual map derived from a so-termed "magnetic shielding contribution field" can be made of the contributions to the magnetic shielding of a specific site-partitioning the chemical shift to specific interactions. The relation to the established approaches of examining the molecule to crystal change in the chemical shift and the nuclear independent chemical shift is established. The results are applied to a large sample of 71 molecular crystals and three further specific examples from supermolecular chemistry and pharmaceuticals. This approach extends the NMR crystallography toolkit and provides insight into the development of both cluster based approaches to the predictions of chemical shifts and for empirical predictions of chemical shifts in solids.

Ab initio random structure searching of organic molecular solids: assessment and validation against experimental data.

This paper explores the capability of using the DFT-D ab initio random structure searching (AIRSS) method to generate crystal structures of organic molecular materials, focusing on a system (m-aminobenzoic acid; m-ABA) that is known from experimental studies to exhibit abundant polymorphism. Within the structural constraints selected for the AIRSS calculations (specifically, centrosymmetric structures with Z = 4 for zwitterionic m-ABA molecules), the method is shown to successfully generate the two known polymorphs of m-ABA (form III and form IV) that have these structural features. We highlight various issues that are encountered in comparing crystal structures generated by AIRSS to experimental powder X-ray diffraction (XRD) data and solid-state magic-angle spinning (MAS) NMR data, demonstrating successful fitting for some of the lowest energy structures from the AIRSS calculations against experimental low-temperature powder XRD data for known polymorphs of m-ABA, and showing that comparison of computed and experimental solid-state NMR parameters allows different hydrogen-bonding motifs to be discriminated.

Visualization and processing of computed solid-state NMR parameters: MagresView and MagresPython.

We introduce two open source tools to aid the processing and visualisation of ab-initio computed solid-state NMR parameters. The Magres file format for computed NMR parameters (as implemented in CASTEP v8.0 and QuantumEspresso v5.0.0) is implemented. MagresView is built upon the widely used Jmol crystal viewer, and provides an intuitive environment to display computed NMR parameters. It can provide simple pictorial representation of one- and two-dimensional NMR spectra as well as output a selected spin-system for exact simulations with dedicated spin-dynamics software. MagresPython provides a simple scripting environment to manipulate large numbers of computed NMR parameters to search for structural correlations.

Probing α-relaxation with nuclear magnetic resonance echo decay and relaxation: a study on nitrile butadiene rubber.

One dimensional (1)H NMR measurements have been performed to probe slow molecular motions in nitrile butadiene rubber (NBR) around its calorimetric glass transition temperature Tg. The purpose is to show how software aided data analysis can extract meaningful dynamical data from these measurements. Spin-lattice relaxation time, free induction decay (FID) and magic sandwich echo (MSE) measurements have been carried out at different values of the static field, as a function of temperature. It has been evidenced how the efficiency of the MSE signal in reconstructing the original FID exhibits a sudden minimum at a given temperature, with a slight dependence from the measuring frequency. Computer simulations performed with the software SPINEVOLUTION have shown that the minimum in the efficiency reconstruction of the MSE signal corresponds to the average motional frequency taking a value around the inter-proton coupling. The FID signals have been fitted with a truncated form of a newly derived exact correlation function for the transverse magnetization of a dipolar interacting spin pair, which allows one to avoid the restriction of the stationary and Gaussian approximations. A direct estimate of the conformational dynamics on approaching the Tg is obtained, and the results are in agreement with the analysis performed via the MSE reconstruction efficiency. The occurrence of a wide distribution of correlation frequencies for the chains motion, with a Vogel-Fulcher type temperature dependence, is addressed. A route for a fruitful study of the dynamics accompanying the glass transition by a variety of NMR measurements is thus proposed.

An exact analytical solution for the evolution of a dipole-dipole interacting system under spherical diffusion in magnetic resonance experiments.

A model system consisting of an isotropic ensemble of spin pairs, where dipole-dipole interaction is assumed to be effective only within each pair, is considered. The ideal segment connecting the spins in a couple has a fixed length but is free to rotate following a diffusion dynamics. This allows the free induction decay (FID) to be derived non-perturbatively by solving the appropriate Dyson equation associated to the problem. Motional narrowing can be described analytically in terms of only two parameters, i.e. the coupling constant of the interaction hamiltonian, b, and the orientational diffusion coefficient D. Salient features of the transverse correlation function thus obtained are discussed, and a comparison with numerical simulations performed with the software SPINEVOLUTION is presented. Interpreting b and D as effective parameters describing multiple interactions of a single spin with its neighbors in a real system, the analysis of published experimental data on poly(ethyl acrylate) has been carried out. It is found that for temperatures higher than and not too close to the glass transition, the results are the same as those found within the Anderson-Weiss approach by assuming a single time exponential decay of the average dipole-dipole interaction. On the other hand, as D tends to zero, FID oscillations characteristic of a rigid lattice show up.