First-principles modeling of molecular crystals: structures and stabilities, temperature and pressure

Bond Lengths and Dipole Moments of Diatomic Molecules under Isotropic Pressure with the XP-PCM and GOSTSHYP Models

While high-pressure chemistry has a well-established history, methods to simulate pressure at the single-molecule level have been somewhat lacking. The current work aims at comparing two static models (XP-PCM and GOSTSHYP) to apply isotropic pressure to single molecules, focusing on the equilibrium bond length and electric dipole moment of diatomic molecules. Numerical challenges arising in the potential energy surface using the XP-PCM method were examined, and a pragmatic approach was followed to mitigate these. The definition of the cavity was scrutinized, and two approaches to retrieve the isotropic character that could potentially be lost when using the standard methodology were suggested. Subsequently, equilibrium bond lengths under pressure were evaluated, showing reasonable agreement between GOSTSHYP and XP-PCM, but some discrepancies persist. A Taylor series analysis introduced elsewhere was then applied to rationalize the observed trends in terms of the bond surface. Finally, the dipole moment was shown to be highly sensitive to the cavity definition, and qualitative agreement necessitates the use of our adapted procedure.

On the importance of low-frequency modes in predicting pressure-induced phase transitions

The occurrence of ultra-low frequency oscillation mode as observed by means of periodic DFT calculations at Γ point in a molecular crystal at ambient conditions can be a valuable predictor of imminent pressure-induced phase transition. We illustrate it with a series of polymorphs of diacetyl-pyrenes, for two of which such soft-modes indicated the trajectory of pressure-induced structural reorganization at ≈0.8 GPa. Notably, susceptibility to pressure-induced phase transformations could not be predicted based on material's thermodynamic characteristics, and there were no unequivocal clues in their crystal packing.

How Accurate Are Simulations and Experiments for the Lattice Energies of Molecular Crystals?

Molecular crystals play a central role in a wide range of scientific fields, including pharmaceuticals and organic semiconductor devices. However, they are challenging systems to model accurately with computational approaches because of a delicate interplay of intermolecular interactions such as hydrogen bonding and Van der Waals dispersion forces. Here, by exploiting recent algorithmic developments, we report the first set of diffusion Monte Carlo lattice energies for all 23 molecular crystals in the popular and widely used X23 dataset. Comparisons with previous state-of-the-art lattice energy predictions (on a subset of the dataset) and a careful analysis of experimental sublimation enthalpies reveals that high-accuracy computational methods are now at least as reliable as (computationally derived) experiments for the lattice energies of molecular crystals. Overall, this work demonstrates the feasibility of high-level explicitly correlated electronic structure methods for broad benchmarking studies in complex condensed phase systems, and signposts a route towards closer agreement between experiment and simulation.

Neutron scattering and neural-network quantum molecular dynamics investigation of the vibrations of ammonia along the solid-to-liquid transition

Vibrational spectroscopy allows us to understand complex physical and chemical interactions of molecular crystals and liquids such as ammonia, which has recently emerged as a strong hydrogen fuel candidate to support a sustainable society. We report inelastic neutron scattering measurement of vibrational properties of ammonia along the solid-to-liquid phase transition with high enough resolution for direct comparisons to ab-initio simulations. Theoretical analysis reveals the essential role of nuclear quantum effects (NQEs) for correctly describing the intermolecular spectrum as well as high energy intramolecular N-H stretching modes. This is achieved by training neural network models using ab-initio path-integral molecular dynamics (PIMD) simulations, thereby encompassing large spatiotemporal trajectories required to resolve low energy dynamics while retaining NQEs. Our results not only establish the role of NQEs in ammonia but also provide general computational frameworks to study complex molecular systems with NQEs.

Global machine learning potentials for molecular crystals

Molecular crystals are difficult to model with accurate first-principles methods due to large unit cells. On the other hand, accurate modeling is required as polymorphs often differ by only 1 kJ/mol. Machine learning interatomic potentials promise to provide accuracy of the baseline first-principles methods with a cost lower by orders of magnitude. Using the existing databases of the density functional theory calculations for molecular crystals and molecules, we train global machine learning interatomic potentials, usable for any molecular crystal. We test the performance of the potentials on experimental benchmarks and show that they perform better than classical force fields and, in some cases, are comparable to the density functional theory calculations.

First-Principles Models of Polymorphism of Pharmaceuticals: Maximizing the Accuracy-to-Cost Ratio

Accuracy and sophistication of in silico models of structure, internal dynamics, and cohesion of molecular materials at finite temperatures increase over time. Applicability limits of ab initio polymorph ranking that would be feasible at reasonable costs currently represent crystals of moderately sized molecules (less than 20 nonhydrogen atoms) and simple unit cells (containing rather only one symmetry-irreducible molecule). Extending the applicability range of the underlying first-principles methods to larger systems with a real-life significance, and enabling to perform such computations in a high-throughput regime represent additional challenges to be tackled in computational chemistry. This work presents a novel composite method that combines the computational efficiency of density-functional tight-binding (DFTB) methods with the accuracy of density-functional theory (DFT). Being rooted in the quasi-harmonic approximation, it uses a cheap method to perform all of the costly scans of how static and dynamic characteristics of the crystal vary with respect to its volume. Such data are subsequently corrected to agree with a higher-level model, which must be evaluated only at a single volume of the crystal. It thus enables predictions of structural, cohesive, and thermodynamic properties of complex molecular materials, such as pharmaceuticals or organic semiconductors, at a fraction of the original computational cost. As the composite model retains the solid physical background, it suffers from a minimum accuracy deterioration compared to the full treatment with the costly approach. The novel methodology is demonstrated to provide consistent results for the structural and thermodynamic properties of real-life molecular crystals and their polymorph ranking.

Decoding Van der Waals Impact on Chirality Transfer in Perovskite Structures: Density Functional Theory Insights

Chiral organic-inorganic perovskites exhibit unique physicochemical properties driven by the symmetry of monovalent organic cations. However, an atomistic understanding of how chiral cations transfer their chirality to the inorganic framework and the role played by van der Waals (vdW) interactions in this process is still incomplete. In this work, we report a theoretical investigation, based on density functional theory calculations within the Perdew-Burke-Ernzerhof (PBE) formulation for the exchange-correlation functional, into the role of the vdW interactions in the chirality transfer process. For that, we selected several vdW corrections, namely, Grimme (D2, D3, D3(BJ)), Tkatchenko-Scheffler (TS, TS+SCS, TS+HSI), density-dependent energy correction (dDsC), and many-body scattering (MBD) energy method correction. For the chiral perovskite systems, we selected a set of chiral organic-inorganic perovskites with several dimensions, namely, from zero-dimensional to three-dimensional, each having enantiomers with R and S configurations. Based on a statistical treatment of the relative errors of all lattice parameters with respect to experimental data, we found that D3, D3(BJ), TS, TS+SCS, TS+HSI, and MBD vdW are the most accurate corrections to describe the equilibrium structural properties of chiral perovskites using the PBE method. We identify chirality-induced sequential asymmetries of distorted octahedrons and propose angular descriptors to quantify them, where the orientations of these distortions depend on the R or S nature of the chiral cations. Furthermore, we demonstrate the importance of accurate vdW interactions in precisely describing these asymmetric distortions. By means of binding energies and charge-transfer analysis, we show that the impact of vdW corrections on the charge distribution leads to a subtle strengthening of hydrogen bonds between chiral cations and inorganic octahedra, resulting in an increase in the binding energy. Finally, we identified that the Rashba-Dresselhaus effect in two-dimensionality is refined by vdW interactions.

Multimer Embedding Approach for Molecular Crystals up to Harmonic Vibrational Properties

Accurate calculations of molecular crystals are crucial for drug design and crystal engineering. However, periodic high-level density functional calculations using hybrid functionals are often prohibitively expensive for the relevant systems. These expensive periodic calculations can be circumvented by the usage of embedding methods in which, for instance, the periodic calculation is only performed at a lower-cost level and then monomer energies and dimer interactions are replaced by those of the higher-level method. Herein, we extend such a multimer embedding approach to enable energy corrections for trimer interactions and the calculation of harmonic vibrational properties up to the dimer level. We evaluate this approach for the X23 benchmark set of molecular crystals by approximating a periodic hybrid density functional (PBE0+MBD) by embedding multimers into less expensive calculations using a generalized-gradient approximation functional (PBE+MBD). We show that trimer interactions are crucial for accurately approximating lattice energies within 1 kJ/mol and might also be needed for further improvement of lattice constants and hence cell volumes. Finally, the vibrational properties are already very well captured at the monomer and dimer level, making it possible to approximate vibrational free energies at room temperature within 1 kJ/mol.

Benchmark Data Set of Crystalline Organic Semiconductors

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r2SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r2SCAN-D3. Our results show that r2SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

Can Spin-Component Scaled MP2 Achieve kJ/mol Accuracy for Cohesive Energies of Molecular Crystals?

Attaining kJ/mol accuracy in cohesive energy for molecular crystals is a persistent challenge in computational materials science. In this study, we evaluate second-order Møller-Plesset perturbation theory (MP2) and its spin-component scaled models for calculating cohesive energies for 23 molecular crystals (X23 data set). Using periodic boundary conditions and Brillouin zone sampling, we converge results to the thermodynamic and complete basis set limits, achieving an accuracy of about 2 kJ/mol (0.5 kcal/mol), which is rarely achieved in previous MP2 calculations for molecular crystals. When compared to experimental data, our results have a mean absolute error of 12.9 kJ/mol, comparable to Density Functional Theory with the PBE functional and TS dispersion correction. By separately scaling the opposite-spin and same-spin correlation energy components, using predetermined parameters, we reduce the mean absolute error to 9.5 kJ/mol. Further fine-tuning of these scaling parameters specifically for the X23 data set brings the mean absolute error down to 7.5 kJ/mol.

Review of Applications of Density Functional Theory (DFT) Quantum Mechanical Calculations to Study the High-Pressure Polymorphs of Organic Crystalline Materials

Since its inception, chemistry has been predominated by the use of temperature to generate or change materials, but applications of pressure of more than a few tens of atmospheres for such purposes have been rarely observed. However, pressure is a very effective thermodynamic variable that is increasingly used to generate new materials or alter the properties of existing ones. As computational approaches designed to simulate the solid state are normally tuned using structural data at ambient pressure, applying them to high-pressure issues is a highly challenging test of their validity from a computational standpoint. However, the use of quantum chemical calculations, typically at the level of density functional theory (DFT), has repeatedly been shown to be a great tool that can be used to both predict properties that can be later confirmed by experimenters and to explain, at the molecular level, the observations of high-pressure experiments. This article's main goal is to compile, analyze, and synthesize the findings of works addressing the use of DFT in the context of molecular crystals subjected to high-pressure conditions in order to give a general overview of the possibilities offered by these state-of-the-art calculations.

Ab Initio Crystal Structure Prediction of the Energetic Materials LLM-105, RDX, and HMX

Crystal structure prediction (CSP) is performed for the energetic materials (EMs) LLM-105 and α-RDX, as well as the α and β conformational polymorphs of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), using the genetic algorithm (GA) code, GAtor, and its associated random structure generator, Genarris. Genarris and GAtor successfully generate the experimental structures of all targets. GAtor's symmetric crossover scheme, where the space group symmetries of parent structures are treated as genes inherited by offspring, is found to be particularly effective. However, conducting several GA runs with different settings is still important for achieving diverse samplings of the potential energy surface. For LLM-105 and α-RDX, the experimental structure is ranked as the most stable, with all of the dispersion-inclusive density functional theory (DFT) methods used here. For HMX, the α form was persistently ranked as more stable than the β form, in contrast to experimental observations, even when correcting for vibrational contributions and thermal expansion. This may be attributed to insufficient accuracy of dispersion-inclusive DFT methods or to kinetic effects not considered here. In general, the ranking of some putative structures is found to be sensitive to the choice of the DFT functional and the dispersion method. For LLM-105, GAtor generates a putative structure with a layered packing motif, which is desirable thanks to its correlation with low sensitivity. Our results demonstrate that CSP is a useful tool for studying the ubiquitous polymorphism of EMs and shows promise of becoming an integral part of the EM development pipeline.

Development of a Crystallization-Induced Diastereomer Transformation of Oxime Isomers for the Asymmetric Synthesis of (1S,6R)-3,9-Diazabicyclo[4.2.1]nonane

Herein we report a practical crystallization-induced diastereomer transformation (CIDT) of oxime isomers for the scalable asymmetric synthesis of the bicyclic diamine (1S,6R)-3,9-diazabicyclo[4.2.1]nonane derivative that serves as a valuable building block in medicinal chemistry. The developed approach utilizes (S)-phenylethylamine as a chiral auxiliary handle for CIDT, and the starting nortropinone derivative is prepared in one step from commercially available materials. The resulting E-oxime is subjected to a stereospecific Beckmann rearrangement, followed by reduction of the resulting lactam with LiAlH4 to afford the monoprotected (1S,6R)-3,9-diazabicyclo[4.2.1]nonane derivative. The development of the CIDT and understanding of the mechanistic implications leading to the high selectivity are reported.

Cocrystal Synthesis through Crystal Structure Prediction

Crystal structure prediction (CSP) is an invaluable tool in the pharmaceutical industry because it allows to predict all the possible crystalline solid forms of small-molecule active pharmaceutical ingredients. We have used a CSP-based cocrystal prediction method to rank ten potential cocrystal coformers by the energy of the cocrystallization reaction with an antiviral drug candidate, MK-8876, and a triol process intermediate, 2-ethynylglyclerol. For MK-8876, the CSP-based cocrystal prediction was performed retrospectively and successfully predicted the maleic acid cocrystal as the most likely cocrystal to be observed. The triol is known to form two different cocrystals with 1,4-diazabicyclo[2.2.2]octane (DABCO), but a larger solid form landscape was desired. CSP-based cocrystal screening predicted the triol-DABCO cocrystal as rank one, while a triol-l-proline cocrystal was predicted as rank two. Computational finite-temperature corrections enabled determination of relative crystallization propensities of the triol-DABCO cocrystals with different stoichiometries and prediction of the triol-l-proline polymorphs in the free-energy landscape. The triol-l-proline cocrystal was obtained during subsequent targeted cocrystallization experiments and was found to exhibit an improved melting point and deliquescence behavior over the triol-free acid, which could be considered as an alternative solid form in the synthesis of islatravir.

Modeling coarse-grained van der Waals interactions using dipole-coupled anisotropic quantum Drude oscillators

The Quantum Drude Oscillator (QDO) model is a promising candidate for accurately calculating the van der Waals (vdW) interaction. Anisotropic QDO models have recently been used to represent quantum fluctuations of molecular fragments rather than that of single atoms. While this model promises accurate calculation of vdW energy, there is significant room for improvements, such as incorporating a proper fragmentation method, higher-order dispersion corrections, and so forth. The present work attempts to gauge dipole-dipole interactions' ability without fragmentation. A suitable anisotropic damping function is also introduced to work with anisotropic QDO. This revised model accurately predicts the binding energies of vdW complexes for most of the systems considered. This work indicates the limit of dipole approximation for an anisotropic QDO-based model.

Towards practical and massively parallel quantum computing emulation for quantum chemistry

Quantum computing is moving beyond its early stage and seeking for commercial applications in chemical and biomedical sciences. In the current noisy intermediate-scale quantum computing era, the quantum resource is too scarce to support these explorations. Therefore, it is valuable to emulate quantum computing on classical computers for developing quantum algorithms and validating quantum hardware. However, existing simulators mostly suffer from the memory bottleneck so developing the approaches for large-scale quantum chemistry calculations remains challenging. Here we demonstrate a high-performance and massively parallel variational quantum eigensolver (VQE) simulator based on matrix product states, combined with embedding theory for solving large-scale quantum computing emulation for quantum chemistry on HPC platforms. We apply this method to study the torsional barrier of ethane and the quantification of the protein-ligand interactions. Our largest simulation reaches 1000 qubits, and a performance of 216.9 PFLOP/s is achieved on a new Sunway supercomputer, which sets the state-of-the-art for quantum computing emulation for quantum chemistry.

Decoding Supramolecular Packing Patterns from Computed Anisotropic Deformability Maps of Molecular Crystals

The ability to encode and embed desired mechanical properties into active pharmaceutical ingredient solid forms would significantly advance drug development. In recent years, computational methods, particularly dispersion-corrected density functional theory (DFT), have come of age, opening the possibility of reliably predicting and rationally engineering the mechanical response of molecular crystals. Here, many-body dispersion and Tkatchenko-Scheffler dispersion-corrected DFT were used to calculate the elastic constants of a series of archetypal systems, including paracetamol and aspirin polymorphs and model hydrogen-bonded urea and π-π-bound benzene crystals, establishing their structure-mechanics relations. Both methods showed semiquantitative and excellent qualitative agreement with experiment. The calculations revealed that the plane of maximal Young's modulus generally coincides with extended H-bond or π-π networks, showing how programmable supramolecular packing dictates the mechanical behavior. In a pharmaceutical setting, these structure-mechanics relations can steer the molecular design of solid forms with improved physicochemical and compression properties.

Predicting the structures and vibrational spectra of molecular crystals containing large molecules with the generalized energy-based fragmentation approach

The generalized energy-based fragmentation (GEBF) approach under periodic boundary conditions (PBCs) has been developed to facilitate calculations of molecular crystals containing large molecules. The PBC-GEBF approach can help predict structures and properties of molecular crystals at different theory levels by performing molecular quantum chemistry calculations on a series of non-periodic subsystems constructed from the studied systems. A more rigorous formula of the forces on translational vectors of molecular crystals was proposed and implemented, enabling more reliable predictions of crystal structures. Our benchmark results on several typical molecular crystals show that the PBC-GEBF approach could reproduce the forces on atoms and the translational vectors and the optimized crystal structures from the corresponding conventional periodic methods. The improved PBC-GEBF approach is then applied to predict the crystal structures and vibrational spectra of two molecular crystals containing large molecules. The PBC-GEBF approach can provide a satisfactory description on the crystal structure of a molecular crystal containing 312 atoms in a unit cell at density-fitting second-order Møller-Plesset perturbation theory and density functional theory (DFT) levels and the infrared vibrational spectra of another molecular crystal containing 864 atoms in a unit cell at the DFT level. The PBC-GEBF approach is expected to be a promising theoretical tool for electronic structure calculations on molecular crystals containing large molecules.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Performance of Dispersion-Inclusive Density Functional Theory Methods for Energetic Materials

Molecular crystals of energetic materials (EMs) are denser than typical molecular crystals and are characterized by distinct intermolecular interactions between nitrogen-containing moieties. To assess the performance of dispersion-inclusive density functional theory (DFT) methods, we have compiled a data set of experimental sublimation enthalpies of 31 energetic materials. We evaluate the performance of three methods: the semilocal Perdew-Burke-Ernzerhof (PBE) functional coupled with the pairwise Tkatchenko-Scheffler (TS) dispersion correction, PBE with the many-body dispersion (MBD) method, and the PBE-based hybrid functional (PBE0) with MBD. Zero-point energy contributions and thermal effects are described using the quasi-harmonic approximation (QHA), including explicit treatment of thermal expansion, which we find to be non-negligible for EMs. The lattice energies obtained with PBE0+MBD are the closest to experimental sublimation enthalpies with a mean absolute error of 9.89 kJ/mol. However, the state-of-the-art treatment of vibrational and thermal contributions makes the agreement with experiment worse. Pressure-volume curves are also examined for six representative materials. For pressure-volume curves, all three methods provide reasonable agreement with experimental data with mean absolute relative errors of 3% or less. Most of the intermolecular interactions typical of EMs, namely nitro-amine, nitro-nitro, and nitro-hydrogen interactions, are more sensitive to the choice of the dispersion method than to the choice of the exchange-correlation functional. The exception is π-π stacking interactions, which are also very sensitive to the choice of the functional. Overall, we find that PBE+TS, PBE+MBD, and PBE0+MBD do not perform as well for energetic materials as previously reported for other classes of molecular crystals. This highlights the importance of testing dispersion-inclusive DFT methods for diverse classes of materials and the need for further method development.

A Hybrid Machine Learning Approach for Structure Stability Prediction in Molecular Co-crystal Screenings

Co-crystals are a highly interesting material class as varying their components and stoichiometry in principle allows tuning supramolecular assemblies toward desired physical properties. The in silico prediction of co-crystal structures represents a daunting task, however, as they span a vast search space and usually feature large unit cells. This requires theoretical models that are accurate and fast to evaluate, a combination that can in principle be accomplished by modern machine-learned (ML) potentials trained on first-principles data. Crucially, these ML potentials need to account for the description of long-range interactions, which are essential for the stability and structure of molecular crystals. In this contribution, we present a strategy for developing Δ-ML potentials for co-crystals, which use a physical baseline model to describe long-range interactions. The applicability of this approach is demonstrated for co-crystals of variable composition consisting of an active pharmaceutical ingredient and various co-formers. We find that the Δ-ML approach offers a strong and consistent improvement over the density functional tight binding baseline. Importantly, this even holds true when extrapolating beyond the scope of the training set, for instance in molecular dynamics simulations under ambient conditions.

Best practices for first-principles simulations of epitaxial inorganic interfaces

At an interface between two materials physical properties and functionalities may be achieved, which would not exist in either material alone. Epitaxial inorganic interfaces are at the heart of semiconductor, spintronic, and quantum devices. First principles simulations based on density functional theory (DFT) can help elucidate the electronic and magnetic properties of interfaces and relate them to the structure and composition at the atomistic scale. Furthermore, DFT simulations can predict the structure and properties of candidate interfaces and guide experimental efforts in promising directions. However, DFT simulations of interfaces can be technically elaborate and computationally expensive. To help researchers embarking on such simulations, this review covers best practices for first principles simulations of epitaxial inorganic interfaces, including DFT methods, interface model construction, interface structure prediction, and analysis and visualization tools.

The interplay of intra- and intermolecular errors in modeling conformational polymorphs

Conformational polymorphs of organic molecular crystals represent a challenging test for quantum chemistry because they require careful balancing of the intra- and intermolecular interactions. This study examines 54 molecular conformations from 20 sets of conformational polymorphs, along with the relative lattice energies and 173 dimer interactions taken from six of the polymorph sets. These systems are studied with a variety of van der Waals-inclusive density functionals theory models; dispersion-corrected spin-component-scaled second-order Møller–Plesset perturbation theory (SCS-MP2D); and domain local pair natural orbital coupled cluster singles, doubles, and perturbative triples [DLPNO-CCSD(T)]. We investigate how delocalization error in conventional density functionals impacts monomer conformational energies, systematic errors in the intermolecular interactions, and the nature of error cancellation that occurs in the overall crystal. The density functionals B86bPBE-XDM, PBE-D4, PBE-MBD, PBE0-D4, and PBE0-MBD are found to exhibit sizable one-body and two-body errors vs DLPNO-CCSD(T) benchmarks, and the level of success in predicting the relative polymorph energies relies heavily on error cancellation between different types of intermolecular interactions or between intra- and intermolecular interactions. The SCS-MP2D and, to a lesser extent, ωB97M-V models exhibit smaller errors and rely less on error cancellation. Implications for crystal structure prediction of flexible compounds are discussed. Finally, the one-body and two-body DLPNO-CCSD(T) energies taken from these conformational polymorphs establish the CP1b and CP2b benchmark datasets that could be useful for testing quantum chemistry models in challenging real-world systems with complex interplay between intra- and intermolecular interactions, a number of which are significantly impacted by delocalization error.

Quantifying Mechanical Properties of Molecular Crystals: A Critical Overview of Experimental Elastic Tensors

This review presents a critical and comprehensive overview of current experimental measurements of complete elastic constant tensors for molecular crystals. For a large fraction of these molecular crystals, detailed comparisons are made with elastic tensors obtained using the corrected small basis set Hartree-Fock method S-HF-3c, and these are shown to be competitive with many of those obtained from more sophisticated density functional theory plus dispersion (DFT-D) approaches. These detailed comparisons between S-HF-3c, experimental and DFT-D computed tensors make use of a novel rotation-invariant spherical harmonic description of the Young's modulus, and identify outliers among sets of independent experimental results. The result is a curated database of experimental elastic tensors for molecular crystals, which we hope will stimulate more extensive use of elastic tensor information-experimental and computational-in studies aimed at correlating mechanical properties of molecular crystals with their underlying crystal structure.

Thermal properties of energetic materials from quasi-harmonic first-principles calculations

The structure and properties at a finite temperature are critical to understand the temperature effects on energetic materials (EMs). Combining dispersion-corrected density functional theory with quasi-harmonic approximation, the thermodynamic properties for several representative EMs, including nitromethane, PETN, HMX, and TATB, are calculated. The inclusion of zero-point energy and temperature effect could significantly improve the accuracy of lattice parameters at ambient condition; the deviations of calculated cell volumes and experimental values at room temperature are within 0.62%. The calculated lattice parameters and thermal expansion coefficients with increasing temperature show strong anisotropy. In particular, the expansion rate (2.61%) of inter-layer direction of TATB is higher than intra-layer direction and other EMs. Furthermore, the calculated heat capacities could reproduce the experimental trends and enrich the thermodynamic data set at finite temperatures. The predicted isothermal and adiabatic bulk moduli could reflect the softening behavior of EMs. These results would fundamentally provide a deep understanding and serve as a reference for the experimental measurement of the thermodynamic parameters of EMs.

Modeling the α- and β-resorcinol phase boundary via combination of density functional theory and density functional tight-binding

The ability to predict not only what organic crystal structures might occur but also the thermodynamic conditions under which they are the most stable would be extremely useful for discovering and designing new organic materials. The present study takes a step in that direction by predicting the temperature- and pressure-dependent phase boundary between the α and β polymorphs of resorcinol using density functional theory (DFT) and the quasi-harmonic approximation. To circumvent the major computational bottleneck associated with computing a well-converged phonon density of states via the supercell approach, a recently developed approximation is employed, which combines a supercell phonon density of states from dispersion-corrected third-order density functional tight binding [DFTB3-D3(BJ)] with frequency corrections derived from a smaller B86bPBE-XDM functional DFT phonon calculation on the crystallographic unit cell. This mixed DFT/DFTB quasi-harmonic approach predicts the lattice constants and unit cell volumes to within 1%-2% at lower pressures. It predicts the thermodynamic phase boundary in almost perfect agreement with the experiment, although this excellent agreement does reflect fortuitous cancellation of errors between the enthalpy and entropy of transition.

Crystal Structure Prediction Methods for Organic Molecules: State of the Art

The prediction of the crystal structures that a given organic molecule is likely to form is an important theoretical problem of significant interest for the pharmaceutical and agrochemical industries, among others. As evidenced by a series of six blind tests organized over the past 2 decades, methodologies for crystal structure prediction (CSP) have witnessed substantial progress and have now reached a stage of development where they can begin to be applied to systems of practical significance. This article reviews the state of the art in general-purpose methodologies for CSP, placing them within a common framework that highlights both their similarities and their differences. The review discusses specific areas that constitute the main focus of current research efforts toward improving the reliability and widening applicability of these methodologies, and offers some perspectives for the evolution of this technology over the next decade.

Analytical Hessians for Ewald and particle mesh Ewald electrostatics

The particle mesh Ewald (PME) method has become ubiquitous in the molecular simulation community due to its ability to deliver long range electrostatics accurately with ON  ⁡log(N) complexity. Despite this widespread use, spanning more than two decades, second derivatives (Hessians) have not been available. In this work, we describe the theory and implementation of PME Hessians, which have applications in normal mode analysis, characterization of stationary points, phonon dispersion curve calculation, crystal structure prediction, and efficient geometry optimization. We outline an exact strategy that requires O(1) effort for each Hessian element; after discussing the excessive memory requirements of such an approach, we develop an accurate, efficient approximation that is far more tractable on commodity hardware.

Reduced-cost supercell approach for computing accurate phonon density of states in organic crystals

Phonon contributions to organic crystal structures and thermochemical properties can be significant, but computing a well-converged phonon density of states with lattice dynamics and periodic density functional theory (DFT) is often computationally expensive due to the need for large supercells. Using semi-empirical methods like density functional tight binding (DFTB) instead of DFT can reduce the computational costs dramatically, albeit with noticeable reductions in accuracy. This work proposes approximating the phonon density of states via a relatively inexpensive DFTB supercell treatment of the phonon dispersion that is then corrected by shifting the individual phonon modes according to the difference between the DFT and DFTB phonon frequencies at the Γ-point. The acoustic modes are then computed at the DFT level from the elastic constants. In several small-molecule crystal test cases, this combined approach reproduces DFT thermochemistry with kJ/mol accuracy and 1-2 orders of magnitude less computational effort. Finally, this approach is applied to computing the free energy differences between the five crystal polymorphs of oxalyl dihydrazide.

Rich polymorphism in nicotinamide revealed by melt crystallization and crystal structure prediction

Overprediction is a major limitation of current crystal structure prediction (CSP) methods. It is difficult to determine whether computer-predicted polymorphic structures are artefacts of the calculation model or are polymorphs that have not yet been found. Here, we reported the well-known vitamin nicotinamide (NIC) to be a highly polymorphic compound with nine solved single-crystal structures determined by performing melt crystallization. A CSP calculation successfully identifies all six Z' = 1 and 2 experimental structures, five of which defy 66 years of attempts at being explored using solution crystallization. Our study demonstrates that when combined with our strategy for cultivating single crystals from melt microdroplets, melt crystallization has turned out to be an efficient tool for exploring polymorphic landscapes to better understand polymorphic crystallization and to more effectively test the accuracy of theoretical predictions, especially in regions inaccessible by solution crystallization.

Hydrogen-Mediated Noncovalent Interactions in Solids: What Can NMR Crystallography Tell About?

Hydrogen atoms play a crucial role in the aggregation of organic (bio)molecules through diverse number of noncovalent interactions that they mediate, such as electrostatic in proton transfer systems, hydrogen bonding, and CH-π interactions, to mention only the most prominent. To identify and adequately describe such low-energy interactions, increasingly sensitive methods have been developed over time, among which quantum chemical computations have witnessed impressive advances in recent years. For reaching the present state-of-the-art, computations had to rely on a pool of relevant experimental data, needed at least for validation, if not also for other purposes. In the case of molecular crystals, the best illustration for the synergy between computations and experiment is given by the so-called NMR crystallography approach. Originally designed to increase the confidence level in crystal structure determination of organic compounds from powders, NMR crystallography is able now to offer also a wealth of information regarding the noncovalent interactions that drive molecules to pack in a given crystalline pattern or another. This is particularly true for the noncovalent interactions which depend on the exact location of labile hydrogen atoms in the system: in such cases, NMR crystallography represents a valuable characterization tool, in some cases complementing even the standard single-crystal X-ray diffraction technique. A concise introduction in the field is made in this mini-review, which is aimed at providing a comprehensive picture with respect to the current accuracy level reached by NMR crystallography in the characterization of hydrogen-mediated noncovalent interactions in organic solids. Different types of practical applications are illustrated with the example of molecular crystals studied by our research group, but references to other representative developments reported in the literature are also made. By summarizing the major concepts and methodological progresses, the present work is also intended to be a guide to the practical potential of this relatively recent analytical tool for the scientists working in areas where crystal engineering represents the main approach for rational design of novel materials.

Sublimation Properties of α,ω-Diamines Revisited from First-Principles Calculations

Sublimation enthalpies of alkane-α,ω-diamines exhibit an odd-even pattern within their homologous series. First-principles calculations coupled with the quasi-harmonic approximation for crystals and with the conformation mixing model for the ideal gas are used to explain this phenomenon from the theoretical point of view. Crystals of the odd and even alkane-α,ω-diamines distinctly differ in their packing motifs. However, first-principles calculations indicate that it is a delicate interplay of the cohesive forces, phonons, molecular vibrations and conformational equilibrium which governs the odd-even pattern of the sublimation enthalpies within the homologous series. High molecular flexibility of the alkane-α,ω-diamines predetermines higher sensitivity of the computational model to the quality of the optimized geometries and relative conformational energies. Performance of high-throughput computational methods, such as the density functional tight binding (DFTB, GFN2-xTB) and the explicitly correlated dispersion-corrected Møller-Plesset perturbative method (MP2C-F12), are benchmarked against the consistent state-of-the-art calculations of conformational energies and interaction energies, respectively.

NMR crystallography of molecular organics

Developments of NMR methodology to characterise the structures of molecular organic structures are reviewed, concentrating on the previous decade of research in which density functional theory-based calculations of NMR parameters in periodic solids have become widespread. With a focus on demonstrating the new structural insights provided, it is shown how "NMR crystallography" has been used in a spectrum of applications from resolving ambiguities in diffraction-derived structures (such as hydrogen atom positioning) to deriving complete structures in the absence of diffraction data. As well as comprehensively reviewing applications, the different aspects of the experimental and computational techniques used in NMR crystallography are surveyed. NMR crystallography is seen to be a rapidly maturing subject area that is increasingly appreciated by the wider crystallographic community.

Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory

Phonons are the main source of relaxation in molecular nanomagnets, and different mechanisms have been proposed in order to explain the wealth of experimental findings. However, very limited experimental investigations on phonons in these systems have been performed so far, yielding no information about their dispersions. Here we exploit state-of-the-art single-crystal inelastic neutron scattering to directly measure for the first time phonon dispersions in a prototypical molecular qubit. Both acoustic and optical branches are detected in crystals of [VO(acac)[Formula: see text]] along different directions in the reciprocal space. Using energies and polarisation vectors calculated with state-of-the-art Density Functional Theory, we reproduce important qualitative features of [VO(acac)[Formula: see text]] phonon modes, such as the presence of low-lying optical branches. Moreover, we evidence phonon anti-crossings involving acoustic and optical branches, yielding significant transfers of the spin-phonon coupling strength between the different modes.

Can We Predict the Pressure Induced Phase Transition of Urea? Application of Quantum Molecular Dynamics

Crystalline urea undergoes polymorphic phase transition induced by high pressure. Form I, which is the most stable form at normal conditions and Form IV, which is the most stable form at 3.10 GPa, not only crystallize in various crystal systems but also differ significantly in the unit cell dimensions. The aim of this study was to determine if it is possible to predict polymorphic phase transitions by optimizing Form I at high pressure and Form IV at low pressure. To achieve this aim, a large number of periodic density functional theory (DFT) calculations were performed using CASTEP. After geometry optimization of Form IV at 0 GPa Form I was obtained, performing energy minimization of Form I at high pressure did not result in Form IV. However, employing quantum molecular isothermal–isobaric (NPT) dynamics calculations enabled to accurately predict this high-pressure transformation. This study shows the potential of different approaches in predicting the polymorphic phase transition and points to the key factors that are necessary to achieve the success.

Exploring the Polymorphism of Drostanolone Propionate

2α-Methyl-4,5α-dihydrotestosterone 17β-propionate, known as drostanolone propionate or masteron, is a synthetic anabolic-androgenic steroid derived from dihydrotestosterone. The crystal structures of two polymorphs of drostanolone propionate have been determined by single crystal X-ray diffraction and both crystallizes in the monoclinic crystal system. One is belonging to the P21 space group, Z = 2, and has one molecule in the asymmetric unit while the second belongs to the I2 space group, Z = 4, and contains two molecules in the asymmetric unit. Another polymorph has been investigated by an X-ray powder diffraction method and solved by Parallel tempering/Monte Carlo technique and refined with the Rietveld method. This polymorph crystallizes in the orthorhombic P212121 space group, Z = 4 having one molecule in the asymmetric unit. The structural configuration analysis shows that the A, B, and C steroid rings exist as chair geometry, while ring D adopts a C13 distorted envelope configuration in all structures. For all polymorphs, the lattice energy has been computed by CLP (Coulomb-London-Pauli), and tight-binding density functional theory methods. Local electron correlation methods were used to estimate the role of electron correlation in the magnitude of the dimer energies. The nature of the intermolecular interactions has been analyzed by the SAPT0 energy decomposition methods as well as by Hirshfeld surfaces.

Comment on “Polymorphism of levofloxacin: structure, properties and phase transformation” by N. Wei, L. Jia, Z. Shang, J. Gong, S. Wu, J. Wang and W. Tang, CrystEngComm, 2019, , 6196–6207

A comment on a statement made by W. Tang et al. on the levofloxacin polymorphs predicted through CSP studies.

Intermolecular Interactions in Molecular Organic Crystals upon Relaxation of Lattice Parameters

Crystal structure prediction is based on the assumption that the most thermodynamically stable structure will crystallize first. The existence of other structures such as polymorphs or from counterenantiomers requires an accurate calculation of the electronic energy. Using atom-centered Gaussian basis functions in periodic Density Functional Theory (DFT) calculations in Turbomole, the performance of two dispersion-corrected functionals, PBE-D3 and B97-D, is assessed for molecular organic crystals of the X23 benchmark set. B97-D shows a MAE (mean absolute error) of 4 kJ/mol, compared to 9 kJ/mol for PBE-D3. A strategy for the convergence of lattice energies towards the basis set limit is outlined. A simultaneous minimization of molecular structures and lattice parameters shows that both methods are able to reproduce experimental unit cell parameters to within 4–5%. Calculated lattice energies, however, deviate slightly more from the experiment, i.e., by 0.4 kJ/mol after unit cell optimization for PBE-D3 and 0.5 kJ/mol for B97-D. The accuracy of the calculated lattice energies compared to the experimental values demonstrates the ability of current DFT methods to assist in the quest for possible polymorphs and enantioselective crystallization processes.

Quantum mechanics of proteins in explicit water: The role of plasmon-like solute-solvent interactions

Quantum-mechanical van der Waals dispersion interactions play an essential role in intraprotein and protein-water interactions-the two main factors affecting the structure and dynamics of proteins in water. Typically, these interactions are only treated phenomenologically, via pairwise potential terms in classical force fields. Here, we use an explicit quantum-mechanical approach of density-functional tight-binding combined with the many-body dispersion formalism and demonstrate the relevance of many-body van der Waals forces both to protein energetics and to protein-water interactions. In contrast to commonly used pairwise approaches, many-body effects substantially decrease the relative stability of native states in the absence of water. Upon solvation, the protein-water dispersion interaction counteracts this effect and stabilizes native conformations and transition states. These observations arise from the highly delocalized and collective character of the interactions, suggesting a remarkable persistence of electron correlation through aqueous environments and providing the basis for long-range interaction mechanisms in biomolecular systems.

Impact of nuclear vibrations on van der Waals and Casimir interactions at zero and finite temperature

Recent advances in measuring van der Waals (vdW) interactions have probed forces on molecules at nanometric separations from metal surfaces and demonstrated the importance of infrared nonlocal polarization response and temperature effects, yet predictive theories for these systems remain lacking. We present a theoretical framework for computing vdW interactions among molecular structures, accounting for geometry, short-range electronic delocalization, dissipation, and collective nuclear vibrations (phonons) at atomic scales, along with long-range electromagnetic interactions in arbitrary macroscopic environments. We primarily consider experimentally relevant low-dimensional carbon allotropes, including fullerenes, carbyne, and graphene, and find that phonons couple strongly with long-range electromagnetic fields depending on molecular dimensionality and dissipation, especially at nanometric scales, creating delocalized phonon polaritons that substantially modify infrared molecular response. These polaritons, in turn, alter vdW interaction energies between molecular and macroscopic structures, producing nonmonotonic power laws and nontrivial temperature variations at nanometric separations feasible in current experiments.

Improving Predicted Nuclear Magnetic Resonance Chemical Shifts Using the Quasi-Harmonic Approximation

Ab initio nuclear magnetic resonance chemical shift prediction plays an important role in the determination or validation of crystal structures. The ability to predict chemical shifts more accurately can translate to increased confidence in the resulting chemical shift or structural assignments. Standard electronic structure predictions for molecular crystal structures neglect thermal expansion, which can lead to an appreciable underestimation of the molar volumes. This study examines this volume error and its impact on 68 ¹³C- and 28 ¹⁵N-predicted chemical shifts taken from 20 molecular crystals. It assesses the ability to recover more realistic room-temperature crystal structures using the quasi-harmonic approximation and how refining the structures impacts the chemical shifts. Several pharmaceutical molecular crystals are also examined in more detail. On the whole, accounting for quasi-harmonic expansion changes the ¹³C and ¹⁵N chemical shifts by 0.5 and 1.0 ppm on average. This, in turn, reduces the root-mean-square errors relative to experiment by 0.3 ppm for ¹³C and 0.7 ppm for ¹⁵N. Although the statistical impacts are modest, changes in individual chemical shifts can reach multiple ppm. Accounting for thermal expansion in molecular crystal chemical shift prediction may not be needed routinely, but the systematic trend toward improved accuracy with the experiment could be useful in cases where discrimination between structural candidates is challenging, as in the pharmaceutical theophylline.

Supercell calculations of the geometry and lattice energy of α-glycine crystal

Evidence about the presence of glycine in the interstellar medium (ISM) has been motivating studies aiming the understanding of the chemical behavior of this amino acid in such environment. Since glycine is expected to be predominantly found in the ISM in solid phase, this work focuses on the search for a theoretical methodology for obtaining a molecular cluster for α-glycine that provides a good description of the geometry of the unit cell and lattice energy. Calculations have been performed using the B3LYP-D3, PBE0-D3, and WB97X-D3 functionals, with def2-SVP, def2-TZVP, def2-TZVPP, and def2-QZVPP basis sets for two models: (a) the unit cell, containing 4 glycine units, and (b) the 2 × 1 × 2 expanded cell, with 16 glycine units. Corrections for the basis set superposition error have also been applied. No significant changes in geometries and lattice energy predictions from the different functionals and basis sets have been observed for each model. Nevertheless, results obtained for the larger molecular cluster are in better agreement with the experimental data. The best lattice energy prediction, obtained for the 2 × 1 × 2 supercell at the B3LYP-gCP-D3/def2-TZVPP level, is - 15.35 kcal mol^-1, with a root mean square deviation of the predicted Cartesian coordinates of the inner molecules (with respect to the experimental α-glycine unit cell geometry) of 0.966 Å. This methodology is finally recommended for future studies of similar molecular cluster, and the predicted geometry is proposed for further studies aiming to describe glycine surface reactions in the ISM.