Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

NMR Crystallography of the Polymorphs of Metergoline

Two polymorphs of the drug compound metergoline (C25H29N3O2) were investigated in detail by solid-state NMR measurements. The results have been analysed by an advanced procedure, which uses experimental input together with the results of quantum chemical calculations that were performed for molecular crystals. In this way, it was possible to assign the total of 40 1H–13C correlation pairs in a highly complex system, namely, in the dynamically disordered polymorph with two independent molecules in the unit cell of a large volume of 4234 Å3. For the simpler polymorph, which exhibits only small-amplitude motions and has just one molecule in the unit cell with a volume of 529.0 Å3, the values of the principal elements of the 13C chemical shift tensors were measured. Additionally, for this polymorph, a set of crystal structure predictions were generated, and the {13C, 1H} isotropic and 13C anisotropic chemical shielding data were computed while using the gauge-including projector augmented-wave approach combined with the “revised Perdew-Burke-Ernzerhof“ exchange-correlation functional (GIPAW-RPBE). The experimental and theoretical results were combined in an application of the newly developed strategy to polymorph discrimination. This research thus opens up new routes towards more accurate characterization of the polymorphism of drug formulations.

Stability of Hydrogen Hydrates from Second-Order Møller-Plesset Perturbation Theory

The formation of gas hydrates and clathrates critically depends on the interaction between the host water network and the guest gas species. Density functional calculations can struggle to quantitatively capture these dispersion-type interactions. Here, we report wave function-based calculations on hydrogen hydrates that combine periodic Hartree-Fock with a localized treatment of electronic correlation. We show that local second-order Møller-Plesset perturbation theory (LMP2) reproduces the stability of the different filled-ice-like hydrates in excellent agreement with experimental data. In contrast to various dispersion-corrected density functional theory implementations, LMP2 correctly identifies the pressures needed to stabilize the C₀, C₁, and C₂ hydrates and does not find a spurious region of stability for an ice-I_h-based dihydrate. Our results suggest that LMP2 or similar approaches can provide quantitative insights into the mechanisms of formation and eventual decomposition of molecular host-guest compounds.

Control and prediction of the organic solid state: a challenge to theory and experiment†

The ability of theoretical chemists to quantitatively model the weak forces between organic molecules is being exploited to predict their crystal structures and estimate their physical properties. Evolving crystal structure prediction methods are increasingly being used to aid the design of organic functional materials and provide information about thermodynamically plausible polymorphs of speciality organic materials to aid, for example, pharmaceutical development. However, the increasingly sophisticated experimental studies for detecting the range of organic solid-state behaviours provide many challenges for improving quantitative theories that form the basis for the computer modelling. It is challenging to calculate the relative thermodynamic stability of different organic crystal structures, let alone understand the kinetic effects that determine which polymorphs can be observed and are practically important. However, collaborations between experiment and theory are reaching the stage of devising experiments to target the first crystallization of new polymorphs or create novel organic molecular materials.

Communication: Accurate description of interaction energies and three-body effects in weakly bound molecular complexes by PBE-QIDH models

We apply a recently developed parameter-free double-hybrid density functional belonging to the quadratic-integrand double-hybrid model to calculate association energies (ΔE) and three-body effects (Δ³E) arising from intermolecular interactions in weakly bound supramolecular complexes (i.e., the dataset 3B-69). The model behaves very accurately for trimer association energies and is found to outperform widely used density functional approximations while approaching the accuracy of more costly ab initio methods for three-body effects. The results are further improved when we add some specific corrections for the remaining dispersion interactions, D3(BJ) or VV10 for two-body effects and Axilrod-Teller-Muto for three-body effects, leading to marginal deviations (less than 1 kcal/mol for ΔE and around 0.03-0.04 kcal/mol for Δ³E) with respect to benchmark results.

Genarris: Random generation of molecular crystal structures and fast screening with a Harris approximation

We present Genarris, a Python package that performs configuration space screening for molecular crystals of rigid molecules by random sampling with physical constraints. For fast energy evaluations, Genarris employs a Harris approximation, whereby the total density of a molecular crystal is constructed via superposition of single molecule densities. Dispersion-inclusive density functional theory is then used for the Harris density without performing a self-consistency cycle. Genarris uses machine learning for clustering, based on a relative coordinate descriptor developed specifically for molecular crystals, which is shown to be robust in identifying packing motif similarity. In addition to random structure generation, Genarris offers three workflows based on different sequences of successive clustering and selection steps: the "Rigorous" workflow is an exhaustive exploration of the potential energy landscape, the "Energy" workflow produces a set of low energy structures, and the "Diverse" workflow produces a maximally diverse set of structures. The latter is recommended for generating initial populations for genetic algorithms. Here, the implementation of Genarris is reported and its application is demonstrated for three test cases.

Simplified DFT methods for consistent structures and energies of large systems

Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium-sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.

Ab initio prediction of the polymorph phase diagram for crystalline methanol

Organic crystals frequently adopt multiple distinct polymorphs exhibiting different properties. The ability to predict not only what crystal forms might occur, but under what experimental thermodynamic conditions those polymorphs are stable would be immensely valuable to the pharmaceutical industry and others. Starting only from knowledge of the experimental crystal structures, this study successfully predicts the methanol crystal polymorph phase diagram from first-principles quantum chemistry, mapping out the thermodynamic regions of stability for three polymorphs over the range 0-400 K and 0-6 GPa. The agreement between the predicted and experimental phase diagrams corresponds to predicting the relative polymorph free energies to within ∼0.5 kJ mol-1 accuracy, which is achieved by employing fragment-based second-order Møller-Plesset perturbation theory and coupled cluster theory plus a quasi-harmonic treatment of the phonons.

Uncovering the Connection Between Low-Frequency Dynamics and Phase Transformation Phenomena in Molecular Solids

The low-frequency motions of molecules in the condensed phase have been shown to be vital to a large number of physical properties and processes. However, in the case of disordered systems, it is often difficult to elucidate the atomic-level details surrounding these phenomena. In this work, we have performed an extensive experimental and computational study on the molecular solid camphor, which exhibits a rich and complex structure-dynamics relationship, and undergoes an order-disorder transition near ambient conditions. The combination of x-ray diffraction, variable temperature and pressure terahertz time-domain spectroscopy, ab initio molecular dynamics, and periodic density functional theory calculations enables a complete picture of the phase transition to be obtained, inclusive of mechanistic, structural, and thermodynamic phenomena. Additionally, the low-frequency vibrations of a disordered solid are characterized for the first time with atomic-level precision, uncovering a clear link between such motions and the phase transformation. Overall, this combination of methods allows for significant details to be obtained for disordered solids and the associated transformations, providing a framework that can be directly applied for a wide range of similar systems.

Estimations of energy of noncovalent bonding from integrals over interatomic zero-flux surfaces: Correlation trends and beyond

Bonding energies of 50 associates composed by neutral molecules (atoms) and bounded by various weak noncovalent interactions are calculated within the DFT framework using the PBE0/aug-cc-pVTZ combination. The electronic virial and electron density values at bond critical points together with their integrals over interatomic surfaces are tested to check their ability to estimate bonding energies. Two correlations schemes dealing with integrals over interatomic surface are suggested to estimate bonding energy of any noncovalent interaction. The physical meaning of explored and several known correlations is discussed. Methods to estimate interatomic surface integrals of electronic virial and electron density are proposed. © 2018 Wiley Periodicals, Inc.

Composite and Low-Cost Approaches for Molecular Crystal Structure Prediction

Molecular crystal structure prediction (CSP) requires evaluating differences in lattice energy between candidate crystal structures accurately and efficiently. In this work, we explore and compare several low-cost alternatives to dispersion-corrected density-functional theory (DFT) in the plane-waves/pseudopotential approximation, the most accurate and general approach used for CSP at present. Three types of low-cost methods are considered: DFT with a small basis set of finite-support numerical orbitals (the SIESTA method), dispersion-corrected Gaussian small or minimal-basis-set Hartree-Fock and DFT with additional empirical corrections (HF-3c and PBEh-3c), and self-consistent-charge dispersion-corrected density-functional tight binding (SCC-DFTB3-D3). In addition, we study the performance of composite methods that comprise a geometry optimization using a low-cost approach followed by a single-point calculation using the accurate but comparatively expensive B86bPBE-XDM functional. All methods were tested for their abilities to produce absolute lattice energies, relative lattice energies, and crystal geometries. We show that assessing various methods by their ability to produce absolute lattice energies can be misleading and that relative lattice energies are a much better indicator of performance in CSP. The EE14 set of relative solubilities of homochiral and heterochiral chiral crystals is proposed for relative lattice-energy benchmarking. Our results show that PBE-D2 plus a DZP basis set of numerical orbitals coupled with a final B86bPBE-XDM single-point calculation gives excellent performance at a fraction of the cost of a full B86bPBE-XDM calculation, although the results are sensitive to the particular details of the computational protocol. The B86bPBE-XDM//PBE-D2/DZP method was subsequently tested in a practical CSP application from our recent work on the crystal structure of the enantiopure and racemate forms of 1-aza[6]helicene, a chiral organic semiconductor. Our results show that this multilevel method is able to correctly reproduce the energy ranking of both crystal forms.

Terahertz spectroscopy of 2,4,6-trinitrotoluene molecular solids from first principles

We present a computational analysis of the terahertz spectra of the monoclinic and the orthorhombic polymorphs of 2,4,6-trinitrotoluene. Very good agreement with experimental data is found when using density functional theory that includes Tkatchenko–Scheffler pair-wise dispersion interactions. Furthermore, we show that for these polymorphs the theoretical results are only weakly affected by many-body dispersion contributions. The absence of dispersion interactions, however, causes sizable shifts in vibrational frequencies and directly affects the spatial character of the vibrational modes. Mode assignment allows for a distinction between the contributions of the monoclinic and orthorhombic polymorphs and shows that modes in the range from 0 to ca. 3.3 THz comprise both inter- and intramolecular vibrations, with the former dominating below ca. 1.5 THz. We also find that intramolecular contributions primarily involve the nitro and methyl groups. Finally, we present a prediction for the terahertz spectrum of 1,3,5-trinitrobenzene, showing that a modest chemical change leads to a markedly different terahertz spectrum.

GAtor: A First-Principles Genetic Algorithm for Molecular Crystal Structure Prediction

We present the implementation of GAtor, a massively parallel, first-principles genetic algorithm (GA) for molecular crystal structure prediction. GAtor is written in Python and currently interfaces with the FHI-aims code to perform local optimizations and energy evaluations using dispersion-inclusive density functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for molecular crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented in GAtor by using machine learning to cluster the dynamically updated population by structural similarity and then employing a cluster-based fitness function. Evolutionary niching promotes uniform sampling of the potential energy surface by evolving several subpopulations, which helps overcome initial pool biases and selection biases (genetic drift). The various settings offered by GAtor increase the likelihood of locating numerous low-energy minima, including those located in disconnected, hard to reach regions of the potential energy landscape. The best structures generated are re-relaxed and re-ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chemically diverse set of four past blind test targets, characterized by different types of intermolecular interactions. The experimentally observed structures and other low-energy structures are found for all four targets. In particular, for Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z' = 2 structure with P1̅ symmetry and a scaffold packing motif, which has not been reported previously.

Fast and accurate quantum Monte Carlo for molecular crystals

Computational approaches based on the fundamental laws of quantum mechanics are now integral to almost all materials design initiatives in academia and industry. If computational materials science is genuinely going to deliver on its promises, then an electronic structure method with consistently high accuracy is urgently needed. We show that, thanks to recent algorithmic advances and the strategy developed in our manuscript, quantum Monte Carlo yields extremely accurate predictions for the lattice energies of materials at a surprisingly modest computational cost. It is thus no longer a technique that requires a world-leading computational facility to obtain meaningful results. While we focus on molecular crystals, the significance of our findings extends to all classes of materials.

Computer simulation plays a central role in modern-day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated ab initio electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers subchemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high-accuracy methods.

Structure and Stability of Molecular Crystals with Many-Body Dispersion-Inclusive Density Functional Tight Binding

Accurate prediction of structure and stability of molecular crystals is crucial in materials science and requires reliable modeling of long-range dispersion interactions. Semiempirical electronic structure methods are computationally more efficient than their ab initio counterparts, allowing structure sampling with significant speedups. We combine the Tkatchenko-Scheffler van der Waals method (TS) and the many-body dispersion method (MBD) with third-order density functional tight-binding (DFTB3) via a charge population-based method. We find an overall good performance for the X23 benchmark database of molecular crystals, despite an underestimation of crystal volume that can be traced to the DFTB parametrization. We achieve accurate lattice energy predictions with DFT+MBD energetics on top of vdW-inclusive DFTB3 structures, resulting in a speedup of up to 3000 times compared with a full DFT treatment. This suggests that vdW-inclusive DFTB3 can serve as a viable structural prescreening tool in crystal structure prediction.

Development of Embedded and Performance of Density Functional Methods for Molecular Crystals

We report an alternative quantum mechanical:quantum mechanical (QM:QM) method to the currently used periodic density functional calculations including dispersion and investigate its performance with respect to main structural and energetic properties of the X23 set of molecular crystals. By setting the goal of reproducing reference periodic BLYP+D3 values and by embedding BLYP+D3 into DFTB, we obtain results similar to those of periodic BLYP+D3-typically within 1-2% in lattice energies and ∼0.4% in cell volumes. The accuracy of this QM:QM method in comparison to DFTB+D and DFT+D for the X23 set of molecular crystals is discussed.

Crystal structure prediction of flexible pharmaceutical-like molecules: density functional tight-binding as an intermediate optimisation method and for free energy estimation

Successful methodologies for theoretical crystal structure prediction (CSP) on flexible pharmaceutical-like organic molecules explore the lattice energy surface to find a set of plausible crystal structures. The initial search stages of CSP studies use relatively simple lattice energy approximations as hundreds of thousands of minima have to be considered. These generated crystal structures often have poor molecular geometries, as well as inaccurate lattice energy rankings, and performing reasonably accurate but computationally affordable optimisations of the crystal structures generated in a search would be highly desirable. Here, we seek to explore whether semi-empirical quantum-mechanical methods can perform this task. We employed the dispersion-corrected tight-binding Hamiltonian (DFTB3-D3) to relax all the inter- and intra-molecular degrees of freedom of several thousands of generated crystal structures of five pharmaceutical-like molecules, saving a large amount of computational effort compared to earlier studies. The computational cost scales better with molecular size and flexibility than other CSP methods, suggesting that it could be extended to even larger and more flexible molecules. On average, this optimisation improved the average reproduction of the eight experimental crystal structures (RMSD15) and experimental conformers (RMSD1) by 4% and 23%, respectively. The intermolecular interactions were then further optimised using distributed multipoles, derived from the molecular wave-functions, to accurately describe the electrostatic components of the intermolecular energies. In all cases, the experimental crystal structures are close to the top of the lattice energy ranking. Phonon calculations on some of the lowest energy structures were also performed with DFTB3-D3 methods to calculate the vibrational component of the Helmholtz free energy, providing further insights into the solid-state behaviour of the target molecules. We conclude that DFTB3-D3 is a cost-effective method for optimising flexible molecules, bridging the gap between the approximate methods used in CSP searches for generating crystal structures and more accurate methods required in the final energy ranking.

Structural insights into a novel anticancer sulfonamide chalcone

Natural products have stood out due to their wide range of biological activities.

Evolutionary niching in the GAtor genetic algorithm for molecular crystal structure prediction

The effects of evolutionary niching are investigated for the crystal structure prediction of 1,3-dibromo-2-chloro-5-fluorobenzene.

Identifying pragmatic quasi-harmonic electronic structure approaches for modeling molecular crystal thermal expansion

Quasi-harmonic approaches provide an economical route to modeling the temperature dependence of molecular crystal structures and properties. Several studies have demonstrated good performance of these models, at least for rigid molecules, when using fragment-based approaches with correlated wavefunction techniques. Many others have found success employing dispersion-corrected density functional theory (DFT). Here, a hierarchy of models in which the energies, geometries, and phonons are computed either with correlated methods or DFT are examined to identify which combinations produce useful predictions for properties such as the molar volume, enthalpy, and entropy as a function of temperature. The results demonstrate that refining DFT geometries and phonons with single-point energies based on dispersion-corrected second-order Møller-Plesset perturbation theory can provide clear improvements in the molar volumes and enthalpies compared to those obtained from DFT alone. Predicted entropies, which are governed by vibrational contributions, benefit less clearly from the hybrid schemes. Using these hybrid techniques, the room-temperature thermochemistry of acetaminophen (paracetamol) is predicted to address the discrepancy between two experimental sublimation enthalpy measurements.

Methyl-rotation dynamics in metal–organic frameworks probed with terahertz spectroscopy

In ZIF-8 and its cobalt analogue ZIF-67, the imidazolate methyl-groups, which point directly into the void space, have been shown to freely rotate – even down to cryogenic temperatures.

ROY revisited, again: the eighth solved structure

X-ray powder diffraction and crystal structure prediction algorithms are used in synergy to establish the crystal structure of the eighth polymorph of ROY, form R05.

Predicting the structures and associated phase transition mechanisms in disordered crystals via a combination of experimental and theoretical methods

Experimental terahertz time-domain spectroscopy and theoretical solid-state ab initio density functional theory and molecular dynamics simulations are used to elucidate the structures, dynamics, and phase transformation processes of molecular crystals undergoing a solid-state order–disorder transition.

First-principles stability ranking of molecular crystal polymorphs with the DFT+MBD approach

The ability to accurately calculate the relative stabilities of numerous polymorphs of a given molecular crystal is crucial for the success of any molecular crystal structure prediction (CSP) approach. We have recently presented a hierarchical CSP procedure based on van-der-Waals-inclusive density functional theory [Hoja et al., 2018, arXiv:1803.07503], which yields excellent stability rankings for molecular crystals involving rigid molecules, salts, co-crystals, and highly polymorphic drug-like molecules. This approach includes many-body dispersion effects, exact exchange, as well as vibrational free energies. Here, we discuss in detail the impact of these effects on the obtained stability rankings. In addition, we assess the impact of the approximations used in our hierarchical procedure. We show that our procedure is generally robust to 1-2 kJ mol-1 for the systems in the latest CSP blind test but vibrational free energies for crystals involving flexible molecules would benefit from directly including many-body dispersion interactions. In addition, we also discuss the effect of temperature on the structure of molecular crystals and a simple but effective method for estimating anharmonic effects.

Cluster-model DFT simulations of the infrared spectra of triazine-based molecular crystals

A cluster-model approach is developed to simulate the IR spectra of triazine-based molecular crystals, and the distinct hydrogen-bonding environments of the crystallographically independent molecules can be clearly revealed.

Towards the use of experimental electron densities to estimate reliable lattice energies

Lattice energies derived from experimental charge densities are critically assessed, with a view to encouraging further research of this nature.

Improved Electrostatic Embedding for Fragment-Based Chemical Shift Calculations in Molecular Crystals

Fragment-based methods predict nuclear magnetic resonance (NMR) chemical shielding tensors in molecular crystals with high accuracy and computational efficiency. Such methods typically employ electrostatic embedding to mimic the crystalline environment, and the quality of the results can be sensitive to the embedding treatment. To improve the quality of this embedding environment for fragment-based molecular crystal property calculations, we borrow ideas from the embedded ion method to incorporate self-consistently polarized Madelung field effects. The self-consistent reproduction of the Madelung potential (SCRMP) model developed here constructs an array of point charges that incorporates self-consistent lattice polarization and which reproduces the Madelung potential at all atomic sites involved in the quantum mechanical region of the system. The performance of fragment- and cluster-based ¹H, ¹³C, ¹⁴N, and ¹⁷O chemical shift predictions using SCRMP and density functionals like PBE and PBE0 are assessed. The improved embedding model results in substantial improvements in the predicted ¹⁷O chemical shifts and modest improvements in the ¹⁵N ones. Finally, the performance of the model is demonstrated by examining the assignment of the two oxygen chemical shifts in the challenging γ-polymorph of glycine. Overall, the SCRMP-embedded NMR chemical shift predictions are on par with or more accurate than those obtained with the widely used gauge-including projector augmented wave (GIPAW) model.

Structural origins of the cohesive energy in metal-terpyridine oligomer thin-films

Fe^II-terpyridine based oligomers have attracted considerable interest as key constituents for the realization of highly robust, ultra-thin ordered layers of metal center oligomers (MCOs) for organic electronics applications. By using molecular simulations and nanotribology investigations, we report on the origins of the surprisingly high mechanical and thermal stability in this type of MCO layers, which finds its expression in nanowear resistance values of up to 1.5 μN for the MCO films, as well as in a thermal stability of two-terminal MCO junctions to temperatures up to ∼100 °C under electrical load. A theoretical analysis of the fundamental cohesive forces among the constituents within the context of an electrostatic model reveal that the cohesive energy is essentially based on Coulomb interactions among the ionic constituents of the oligomers, leading to an estimated cohesive energy per molar mass of 0.0132 eV mol g^-1 for MCO layers that advantageously compare to the 0.0061 eV mol g^-1 reported for pentacene crystals.

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.

Theoretical predictions suggest carbon dioxide phases III and VII are identical

Accurate electronic structure calculations for the structures and simulated Raman spectra of high-pressure carbon dioxide suggest phases III and VII are identical, and the phase diagram should be revised.

Solid carbon dioxide exhibits a rich phase diagram at high pressures. Metastable phase III is formed by compressing dry ice above ∼10–12 GPa. Phase VII occurs at similar pressures but higher temperatures, and its stability region is disconnected from III on the phase diagram. Comparison of large-basis-set quasi-harmonic second-order Møller–Plesset perturbation theory calculations and experiment suggests that the long-accepted structure of phase III is problematic. The experimental phase III and VII structures both relax to the same phase VII structure. Furthermore, Raman spectra predicted for phase VII are in good agreement with those observed experimentally for both phase III and VII, while those for the purported phase III structure agree poorly with experimental observations. Crystal structure prediction is employed to search for other potential structures which might account for phase III, but none are found. Together, these results suggest that phases III and VII are likely identical.

On the hydrogen activation by frustrated Lewis pairs in the solid state: benchmark studies and theoretical insights

Recently, the concept of small molecule activation by frustrated Lewis pairs (FLPs) has been expanded to the solid state showing a variety of interesting reactivities. Therefore, there is a need to establish a computational protocol to investigate such systems theoretically. In the present study, we selected several FLPs and applied multiple levels of theory, ranging from a semi-empirical tight-binding Hamiltonian to dispersion corrected hybrid density functionals. Their performance is benchmarked for the computation of crystal geometries, thermostatistical contributions, and reaction energies. We show that the computationally efficient HF-3c method gives accurate crystal structures and is numerically stable and sufficiently fast for routine applications. This method also gives reliable values for the thermostatistical contributions to Gibbs free energies. The meta-generalized gradient approximated TPSS-D3 evaluated in a projector augmented plane wave basis set is able to produce sufficiently accurate reaction electronic energies. The established protocol is intended to support experimental studies and to predict new reactions in the emerging field of solid-state FLPs.This article is part of the themed issue 'Frustrated Lewis pair chemistry'.

The nature of three-body interactions in DFT: Exchange and polarization effects

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar₂-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Powder diffraction and crystal structure prediction identify four new coumarin polymorphs

Coumarin, a simple, commodity chemical isolated from beans in 1820, has, to date, only yielded one solid state structure. Here, we report a rich polymorphism of coumarin grown from the melt. Four new metastable forms were identified and their crystal structures were solved using a combination of computational crystal structure prediction algorithms and X-ray powder diffraction. With five crystal structures, coumarin has become one of the few rigid molecules showing extensive polymorphism at ambient conditions. We demonstrate the crucial role of advanced electronic structure calculations including many-body dispersion effects for accurate ranking of the stability of coumarin polymorphs and the need to account for anharmonic vibrational contributions to their free energy. As such, coumarin is a model system for studying weak intermolecular interactions, crystallization mechanisms, and kinetic effects.

Plane-Wave Density Functional Theory Meets Molecular Crystals: Thermal Ellipsoids and Intermolecular Interactions

Molecular compounds, organic and inorganic, crystallize in diverse and complex structures. They continue to inspire synthetic efforts and "crystal engineering", with implications ranging from fundamental questions to pharmaceutical research. The structural complexity of molecular solids is linked with diverse intermolecular interactions: hydrogen bonding with all its facets, halogen bonding, and other secondary bonding mechanisms of recent interest (and debate). Today, high-resolution diffraction experiments allow unprecedented insight into the structures of molecular crystals. Despite their usefulness, however, these experiments also face problems: hydrogen atoms are challenging to locate, and thermal effects may complicate matters. Moreover, even if the structure of a crystal is precisely known, this does not yet reveal the nature and strength of the intermolecular forces that hold it together. In this Account, we show that periodic plane-wave-based density functional theory (DFT) can be a useful, and sometimes unexpected, complement to molecular crystallography. Initially developed in the solid-state physics communities to treat inorganic solids, periodic DFT can be applied to molecular crystals just as well: theoretical structural optimizations "help out" by accurately localizing the elusive hydrogen atoms, reaching neutron-diffraction quality with much less expensive measurement equipment. In addition, phonon computations, again developed by physicists, can quantify the thermal motion of atoms and thus predict anisotropic displacement parameters and ORTEP ellipsoids "from scratch". But the synergy between experiment and theory goes much further than that. Once a structure has been accurately determined, computations give new and detailed insights into the aforementioned intermolecular interactions. For example, it has been debated whether short hydrogen bonds in solids have covalent character, and we have added a new twist to this discussion using an orbital-based theory that once more had been developed for inorganic solids. However, there is more to a crystal structure than a handful of short contacts between neighboring residues. We hence have used dimensionally resolved analyses to dissect crystalline networks in a systematic fashion, one spatial direction at a time. Initially applied to hydrogen bonding, these techniques can be seamlessly extended to halogen, chalcogen, and pnictogen bonding, quantifying bond strength and cooperativity in truly infinite networks. Finally, these methods promise to be useful for (bio)polymers, as we have recently exemplified for α-chitin. At the interface of increasingly accurate and popular DFT methods, ever-improving crystallographic expertise, and new challenging, chemical questions, we believe that combined experimental and theoretical studies of molecular crystals are just beginning to pick up speed.

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

Noncovalent van der Waals (vdW) or dispersion forces are ubiquitous in nature and influence the structure, stability, dynamics, and function of molecules and materials throughout chemistry, biology, physics, and materials science. These forces are quantum mechanical in origin and arise from electrostatic interactions between fluctuations in the electronic charge density. Here, we explore the conceptual and mathematical ingredients required for an exact treatment of vdW interactions, and present a systematic and unified framework for classifying the current first-principles vdW methods based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem (namely the Rutgers-Chalmers vdW-DF, Vydrov-Van Voorhis (VV), exchange-hole dipole moment (XDM), Tkatchenko-Scheffler (TS), many-body dispersion (MBD), and random-phase approximation (RPA) approaches). Particular attention is paid to the intriguing nature of many-body vdW interactions, whose fundamental relevance has recently been highlighted in several landmark experiments. The performance of these models in predicting binding energetics as well as structural, electronic, and thermodynamic properties is connected with the theoretical concepts and provides a numerical summary of the state-of-the-art in the field. We conclude with a roadmap of the conceptual, methodological, practical, and numerical challenges that remain in obtaining a universally applicable and truly predictive vdW method for realistic molecular systems and materials.

The application of tailor-made force fields and molecular dynamics for NMR crystallography: a case study of free base cocaine

Motional averaging has been proven to be significant in predicting the chemical shifts in ab initio solid-state NMR calculations, and the applicability of motional averaging with molecular dynamics has been shown to depend on the accuracy of the molecular mechanical force field. The performance of a fully automatically generated tailor-made force field (TMFF) for the dynamic aspects of NMR crystallography is evaluated and compared with existing benchmarks, including static dispersion-corrected density functional theory calculations and the COMPASS force field. The crystal structure of free base cocaine is used as an example. The results reveal that, even though the TMFF outperforms the COMPASS force field for representing the energies and conformations of predicted structures, it does not give significant improvement in the accuracy of NMR calculations. Further studies should direct more attention to anisotropic chemical shifts and development of the method of solid-state NMR calculations.