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.

Role of dispersion interactions in the polymorphism and entropic stabilization of the aspirin crystal.

Aspirin has been used and studied for over a century but has only recently been shown to have an additional polymorphic form, known as form II. Since the two observed solid forms of aspirin are degenerate in terms of lattice energy, kinetic effects have been suggested to determine the metastability of the less abundant form II. Here, first-principles calculations provide an alternative explanation based on free-energy differences at room temperature. The explicit consideration of many-body van der Waals interactions in the free energy demonstrates that the stability of the most abundant form of aspirin is due to a subtle coupling between collective electronic fluctuations and quantized lattice vibrations. In addition, a systematic analysis of the elastic properties of the two forms of aspirin rules out mechanical instability of form II as making it metastable.

Long-range correlation energy calculated from coupled atomic response functions.

An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.

Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals.

The development and application of computational methods for studying molecular crystals, particularly density-functional theory (DFT), is a large and ever-growing field, driven by their numerous applications. Here we expand on our recent study of the importance of many-body van der Waals interactions in molecular crystals [A. M. Reilly and A. Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013)], with a larger database of 23 molecular crystals. Particular attention has been paid to the role of the vibrational contributions that are required to compare experiment sublimation enthalpies with calculated lattice energies, employing both phonon calculations and experimental heat-capacity data to provide harmonic and anharmonic estimates of the vibrational contributions. Exact exchange, which is rarely considered in DFT studies of molecular crystals, is shown to have a significant contribution to lattice energies, systematically improving agreement between theory and experiment. When the vibrational and exact-exchange contributions are coupled with a many-body approach to dispersion, DFT yields a mean absolute error (3.92 kJ/mol) within the coveted "chemical accuracy" target (4.2 kJ/mol). The role of many-body dispersion for structures has also been investigated for a subset of the database, showing good performance compared to X-ray and neutron diffraction crystal structures. The results show that the approach employed here can reach the demanding accuracy of crystal-structure prediction and organic material design with minimal empiricism.

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.

Modeling crystal growth from solution with molecular dynamics simulations: approaches to transition rate constants.

The feasibility of using the molecular dynamics (MD) simulation technique to study crystal growth from solution quantitatively, as well as to obtain transition rate constants, has been studied. The dynamics of an interface between a solution of Lennard-Jones particles and the (100) face of an fcc lattice comprised of solute particles have been studied using MD simulations, showing that MD is, in principle, capable of following growth behavior over large supersaturation and temperature ranges. Using transition state theory, and a nearest-neighbor approximation growth and dissolution rate constants have been extracted from equilibrium MD simulations at a variety of temperatures. The temperature dependence of the rates agrees well with the expected transition state theory behavior.

A Piezoelectric Ionic Cocrystal of Glycine and Sulfamic Acid.

Cocrystallization of two or more molecular compounds can dramatically change the physicochemical properties of a functional molecule without the need for chemical modification. For example, coformers can enhance the mechanical stability, processability, and solubility of pharmaceutical compounds to enable better medicines. Here, we demonstrate that amino acid cocrystals can enhance functional electromechanical properties in simple, sustainable materials as exemplified by glycine and sulfamic acid. These coformers crystallize independently in centrosymmetric space groups when they are grown as single-component crystals but form a noncentrosymmetric, electromechanically active ionic cocrystal when they are crystallized together. The piezoelectricity of the cocrystal is characterized using techniques tailored to overcome the challenges associated with measuring the electromechanical properties of soft (organic) crystals. The piezoelectric tensor of the cocrystal is mapped using density functional theory (DFT) computer models, and the predicted single-crystal longitudinal response of 2 pC/N is verified using second-harmonic generation (SHG) and piezoresponse force microscopy (PFM). The experimental measurements are facilitated by polycrystalline film growth that allows for macroscopic and nanoscale quantification of the longitudinal out-of-plane response, which is in the range exploited in piezoelectric technologies made from quartz, aluminum nitride, and zinc oxide. The large-area polycrystalline film retains a damped response of ≥0.2 pC/N, indicating the potential for application of such inexpensive and eco-friendly amino acid-based cocrystal coatings in, for example, autonomous ambient-powered devices in edge computing.

Determination of the experimental equilibrium structure of solid nitromethane using path-integral molecular dynamics simulations.

Path-integral molecular dynamics (PIMD) simulations with an empirical interaction potential have been used to determine the experimental equilibrium structure of solid nitromethane at 4.2 and 15 K. By comparing the time-averaged molecular structure determined in a PIMD simulation to the calculated minimum-energy (zero-temperature) molecular structure, we have derived structural corrections that describe the effects of thermal motion. These corrections were subsequently used to determine the equilibrium structure of nitromethane from the experimental time-averaged structure. We find that the corrections to the intramolecular and intermolecular bond distances, as well as to the torsion angles, are quite significant, particularly for those atoms participating in the anharmonic motion of the methyl group. Our results demonstrate that simple harmonic models of thermal motion may not be sufficiently accurate, even at low temperatures, while molecular simulations employing more realistic potential-energy surfaces can provide important insight into the role and magnitude of anharmonic atomic motions.

Simulating thermal motion in crystalline phase-I ammonia.

Path-integral molecular dynamics have been used to simulate the phase-I crystalline form of ammonia, using an empirical force field. This method allows quantum-mechanical effects on the average geometry and vibrational quantities to be evaluated. When these are used to adjust the output of a high-temperature density functional theory simulation, the results are consistent with those given by the most recent structural refinement based on powder neutron diffraction data. It is clear that the original refinement overestimated thermal motion, and therefore also overestimated the equilibrium N-{H/D} bond length.

What makes the huge 31P-31P coupling constants in S(PF2)2 and Se(PF2)2 vary so much with temperature?

The enormous temperature dependence of the (2)J(PP) coupling constants in S(PF(2))(2) and Se(PF(2))(2) has been explained by a theoretical investigation of their conformations and NMR coupling constants. In contrast, the coupling in O(PF(2))(2) is almost invariant. Gas electron diffraction data for S(PF(2))(2) have been reinterpreted. The results show that two conformers, with C(s) and C(2v) symmetry, exist for the S and Se compounds. The C(s) and C(2v) conformers have very different (2)J(PP) coupling constants (-12.6 and 395.2 Hz for S(PF(2))(2) at B3LYP/aug-cc-pVQZ) and thermal interconversion of these conformers explains the experimental behavior.

Experimental equilibrium structures: application of molecular dynamics simulations to vibrational corrections for gas electron diffraction.

A general method is described that allows experimental equilibrium structures to be determined from gas electron diffraction (GED) data. Distance corrections, starting values for amplitudes of vibration and anharmonic "Morse" constants (all required for a GED refinement) have been extracted from molecular dynamics (MD) simulations. For this purpose MD methods have significant advantages over traditional force-field methods, as they can more easily be performed for large molecules, and, as they do not rely on extrapolation from equilibrium geometries, they are highly suitable for molecules with large-amplitude and anharmonic modes of vibration. For the test case Si(8)O(12)Me(8), where the methyl groups rotate and large deformations of the Si(8)O(12) cage are observed, the MD simulations produced results markedly superior to those obtained using force-field methods. The experimental equilibrium structure of Si(8)O(12)H(8) has also been determined, demonstrating the use of empirical potentials rather than DFT methods when such potentials exist. We highlight the one major deficiency associated with classical MD--the absence of quantum effects--which causes some light-atom bonded-pair amplitudes of vibration to be significantly underestimated. However, using C(3)N(3)Cl(3) and C(3)N(3)H(3) as examples, we show that path-integral MD simulations can overcome these problems. The distance corrections and amplitudes of vibration obtained for C(3)N(3)Cl(3) are almost identical to those obtained from force-field methods, as we would expect for such a rigid molecule. In the case of C(3)N(3)H(3), for which an accurate experimental structure exists, the use of path-integral methods more than doubles the C-H amplitude of vibration.

Efficient DNA Condensation by a C3 -Symmetric Codeine Scaffold.

A novel tripodal codeine scaffold (CC3) was rationally designed using computational methods as a DNA condensing alkaloid. Separation of the piperidine nitrogen atoms in CC3 is considerably larger at 14.36 Šthan previously reported tripodal opioids allowing for enhanced aggregation of larger DNA plasmids (>4,000 bp). The scaffold undergoes protonation at physiological pH that allows for controlled compaction and release of nucleic acids. Condensation is inhibited under basic conditions and nucleic acid release can be achieved by modulating the ionic strength. Zeta potential experiments indicate stabilised DNA particles at low alkaloid loading with AFM measurements showing particles sizes with a height of 103 nm and diameter of 350 nm. Since condensation is a prerequisite for the cellular uptake of DNA, this new class of alkaloid represents a novel nucleic acid condensation agent with potential gene therapy applications.

Quantitative Prediction of Optical Absorption in Molecular Solids from an Optimally Tuned Screened Range-Separated Hybrid Functional.

We show that fundamental gaps and optical spectra of molecular solids can be predicted quantitatively and nonempirically within the framework of time-dependent density functional theory (TDDFT) using the recently developed optimally tuned screened range-separated hybrid (OT-SRSH) functional approach. In this scheme, the electronic structure of the gas-phase molecule is determined by optimal tuning of the range-separation parameter in a range-separated hybrid functional. Screening and polarization in the solid state are taken into account by adding long-range dielectric screening to the functional form, with the modified functional used to perform self-consistent periodic-boundary calculations for the crystalline solid. We provide a comprehensive benchmark for the accuracy of our approach by considering the X23 set of molecular solids and comparing results obtained from TDDFT with those obtained from many-body perturbation theory in the GW-BSE approximation. We additionally compare results obtained from dielectric screening computed within the random-phase approximation to those obtained from the computationally more efficient many-body dispersion approach and find that this influences the fundamental gap but has little effect on the optical spectra. Our approach is therefore robust and can be used for studies of molecular solids that are typically beyond the reach of computationally more intensive methods.

Use of Crystal Structure Informatics for Defining the Conformational Space Needed for Predicting Crystal Structures of Pharmaceutical Molecules.

Determining the range of conformations that a flexible pharmaceutical-like molecule could plausibly adopt in a crystal structure is a key to successful crystal structure prediction (CSP) studies. We aim to use conformational information from the crystal structures in the Cambridge Structural Database (CSD) to facilitate this task. The conformations produced by the CSD Conformer Generator are reduced in number by considering the underlying rotamer distributions, an analysis of changes in molecular shape, and a minimal number of molecular ab initio calculations. This method is tested for five pharmaceutical-like molecules where an extensive CSP study has already been performed. The CSD informatics-derived set of crystal structure searches generates almost all the low-energy crystal structures previously found, including all experimental structures. The workflow effectively combines information on individual torsion angles and then eliminates the combinations that are too high in energy to be found in the solid state, reducing the resources needed to cover the solid-state conformational space of a molecule. This provides insights into how the low-energy solid-state and isolated-molecule conformations are related to the properties of the individual flexible torsion angles.

Generation of crystal structures using known crystal structures as analogues.

This analysis attempts to answer the question of whether similar molecules crystallize in a similar manner. An analysis of structures in the Cambridge Structural Database shows that the answer is yes - sometimes they do, particularly for single-component structures. However, one does need to define what we mean by similar in both cases. Building on this observation we then demonstrate how this correlation between shape similarity and packing similarity can be used to generate potential lattices for molecules with no known crystal structure. Simple intermolecular interaction potentials can be used to minimize these potential lattices. Finally we discuss the many limitations of this approach.

Hydrogen bonding at C=Se acceptors in selenoureas, selenoamides and selones.

In recent years there has been considerable interest in chalcogen and hydrogen bonding involving Se atoms, but a general understanding of their nature and behaviour has yet to emerge. In the present work, the hydrogen-bonding ability and nature of Se atoms in selenourea derivatives, selenoamides and selones has been explored using analysis of the Cambridge Structural Database and ab initio calculations. In the CSD there are 70 C=Se structures forming hydrogen bonds, all of them selenourea derivatives or selenoamides. Analysis of intramolecular geometries and ab initio partial charges show that this bonding stems from resonance-induced C(δ+)=Se(δ-) dipoles, much like hydrogen bonding to C=S acceptors. C=Se acceptors are in many respects similar to C=S acceptors, with similar vdW-normalized hydrogen-bond lengths and calculated interaction strengths. The similarity between the C=S and C=Se acceptors for hydrogen bonding should inform and guide the use of C=Se in crystal engineering.

Report on the sixth blind test of organic crystal structure prediction methods.

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

van der Waals dispersion interactions in molecular materials: beyond pairwise additivity.

van der Waals (vdW) dispersion interactions are a key ingredient in the structure, stability, and response properties of many molecular materials and essential for us to be able to understand and design novel intricate molecular systems. Pairwise-additive models of vdW interactions are ubiquitous, but neglect their true quantum-mechanical many-body nature. In this perspective we focus on recent developments and applications of methods that can capture collective and many-body effects in vdW interactions. Highlighting a number of recent studies in this area, we demonstrate both the need for and usefulness of explicit many-body treatments for obtaining qualitative and quantitative accuracy for modelling molecular materials, with applications presented for small-molecule dimers, supramolecular host-guest complexes, and finally stability and polymorphism in molecular crystals.

The integration of solid-form informatics into solid-form selection.

OBJECTIVES: To demonstrate how the use of structural informatics during drug development assists with the assessment of the risk of polymorphism and the selection of a commercial solid form. METHODS: The application of structural chemistry knowledge derived from the hundreds of thousands of crystal structures contained in the Cambridge Structural Database to drug candidates is described. Examples given show the comparison of intermolecular geometries to database-derived statistics, the use of Full Interaction Maps to assess polymorph stability and the calculation of hydrogen bond propensities to provide assurance of a stable solid form. The software tools used are included in the Cambridge Structural Database System and the Solid Form Module of Mercury. KEY FINDINGS: The early identification of an unusual supramolecular motif in the development phase of maraviroc led to further experimental work to find the most stable polymorph. Analyses of two polymorphs of a pain candidate drug demonstrated how consideration of molecular conformation and intermolecular interactions were used for the assessment of relative stability. Informatics analysis confirmed that the solid form of crizotinib, a monomorphic system, had a low risk of polymorphism. CONCLUSIONS: The application of informatics-based assessment of new chemical entities complements experimental studies and provides a deeper understanding of the qualities of the structure. The information provided by structural analyses is incorporated into the assessment of risk. Informatics techniques are quick to apply and are straightforward to use, allowing an assessment of progressing drug candidates.