Discriminating and understanding molecular crystal polymorphism

Polymorph discrimination for a molecular crystal has long been a challenging task, which, nonetheless, is a major concern in the pharmaceutical industry. In this work, we have investigated polymorph discrimination on three different molecular crystals, tetrolic acid, oxalic acid, and oxalyl dihydrazide, covering both packing polymorphism and conformational polymorphism. To gain more understanding, we have performed energy decomposition analysis based on many-body expansion, and have compared the results from the XO-PBC method, that is, the eXtended ONIOM method (XO) with the periodic boundary condition (PBC), with those from some commonly used dispersion corrected density functional theory (DFT-D) methods. It is shown here that, with the XYG3 doubly hybrid functional chosen as the target high level to capture the intra- and short-range intermolecular interactions, and the periodic PBE as the basic low level to take long range interactions into account, the XO-PBC(XYG3:PBE) method not only obtains the correct experimental stability orderings, but also predicts reasonable polymorph energy ranges for all three cases. Our results have demonstrated the usefulness of the present theoretical methods, in particular XO-PBC, while highlighted the importance of a better treatment of different kinds of interactions to be beneficial to polymorph control.

XDM-corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy

Molecular crystals are important for many applications, including energetic materials, organic semiconductors, and the development and commercialization of pharmaceuticals. The exchange-hole dipole moment (XDM) dispersion model has shown good performance in the calculation of relative and absolute lattice energies of molecular crystals, although it has traditionally been applied in combination with plane-wave/pseudopotential approaches. This has limited XDM to use with semilocal functional approximations, which suffer from delocalization error and poor quality conformational energies, and to systems with a few hundreds of atoms at most due to unfavorable scaling. In this work, we combine XDM with numerical atomic orbitals, which enable the efficient use of XDM-corrected hybrid functionals for molecular crystals. We test the new XDM-corrected functionals for their ability to predict the lattice energies of molecular crystals for the X23 set and 13 ice phases, the latter being a particularly stringent test. A composite approach using a XDM-corrected, 25% hybrid functional based on B86bPBE achieves a mean absolute error of 0.48 kcal mol^-1 per molecule for the X23 set and 0.19 kcal mol^-1 for the total lattice energies of the ice phases, compared to recent diffusion Monte-Carlo data. These results make the new XDM-corrected hybrids not only far more computationally efficient than previous XDM implementations, but also the most accurate density-functional methods for molecular crystal lattice energies to date.

Controlling anisotropic properties by manipulating the orientation of chiral small molecules

Chiral π-conjugated molecules bring new functionality to technological applications and represent an exciting, rapidly expanding area of research. Their functional properties, such as the absorption and emission of circularly polarized light or the transport of spin-polarized electrons, are highly anisotropic. As a result, the orientation of chiral molecules critically determines the functionality and efficiency of chiral devices. Here we present a strategy to control the orientation of a small chiral molecule (2,2'-dicyano[6]helicene) by the use of organic and inorganic templating layers. Such templating layers can either force 2,2'-dicyano[6]helicene to adopt a face-on orientation and self-assemble into upright supramolecular columns oriented with their helical axis perpendicular to the substrate, or an edge-on orientation with parallel-lying supramolecular columns. Through such control, we show that low- and high-energy chiroptical responses can be independently 'turned on' or 'turned off'. The templating methodologies described here provide a simple way to engineer orientational control and, by association, anisotropic functional properties of chiral molecular systems for a range of emerging technologies.

A density-functional benchmark of vibrational free-energy corrections for molecular crystal polymorphism

Many crystal structure prediction protocols only concern themselves with the electronic energy of molecular crystals. However, vibrational contributions to the free energy ( Fvib) can be significant in determining accurate stability rankings for crystal candidates. While force-field studies have been conducted to gauge the magnitude of these free-energy corrections, highly accurate results from quantum mechanical methods, such as density-functional theory (DFT), are desirable. Here, we introduce the PV17 set of 17 polymorphic pairs of organic molecular crystals, for which plane wave DFT is used to calculate the vibrational free energies and free-energy differences (Δ Fvib) between each pair. Our DFT results confirm that the vibrational free-energy corrections are small, having a mean value of 1.0 kJ/mol and a maximum value of 2.3 kJ/mol for the PV17 set. Furthermore, we assess the accuracy of a series of lower-cost DFT, semi-empirical, and force-field models for computing Δ Fvib that have been proposed in the literature. It is found that calculating Fvib using the Γ-point frequencies does not provide Δ Fvib values of sufficiently high quality. In addition, Δ Fvib values calculated using various approximate methods have mean absolute errors relative to our converged DFT results of equivalent or larger magnitude than the vibrational free-energy corrections themselves. Thus, we conclude that, in a crystal structure prediction protocol, it is preferable to forego the inclusion of vibrational free-energy corrections than to estimate them with any of the approximate methods considered here.

Revisiting stacking interactions in tetrathiafulvalene and selected derivatives using tight-binding quantum chemical calculations and local coupled-cluster method

The engineering of supramolecular architectures needs accurate descriptions of the intermolecular interactions in crystal structures. Tetrathiafulvalene (TTF) is an effective building block used in the construction of promising functional materials. The parallel packing of the neutral TTF-TTF system was studied previously using the high-level quantum chemical method, advancing it as a valuable model system. The recently developed tight-binding quantum chemical method GFN2-xTB and local coupled-cluster method DLPNO-CCSD(T) were used to investigate the stacking interactions of TTF and selected derivatives deposited in the Cambridge Structural Database. Using the interaction energy of the TTF-TTF dimer calculated at the CCSD(T)/CBS level as the reference, the accuracies of the two methods are investigated. The energy decomposition analysis within the DLPNO-CCSD(T) framework reveals the importance of dispersion interaction in the TTF-related stacking systems. The dispersion interaction density plot vividly shows the magnitude and distribution of the dispersion interaction, providing a revealing insight into the stacking interactions in crystal structures. The results show that the GFN2-xTB and DLPNO-CCSD(T) methods could achieve accuracy at an affordable computational cost, which would be valuable in understanding the nature of parallel stacking in supramolecular systems.

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.

Cost-effective composite methods for large-scale solid-state calculations

Following the development in recent years of progressively more accurate approximations to the exchange-correlation functional, the use of density functional theory (DFT) methods to examine increasingly large and complex systems has grown, in particular for solids and other condensed matter systems. However the cost of these calculations is high, often requiring the use of specialist HPC facilities. As such, for the purpose of large-scale high-throughput screening of material properties, a hierarchy of simplified DFT methods has been proposed that allows rapid electronic structure calculation of large systems, and we have recently extended this scheme to the solid state (sol-3c). Here, we analyze the applicability and scaling of the new sol-3c DFT methods to molecules and crystals composed of light-elements, such as small proteins and model DNA-helices. Furthermore, the calculation of the electronic structure of large to very large porous systems, such as metal-organic frameworks and inorganic nanoparticles, is discussed. The new composite methods have been implemented in the CRYSTAL17 code, which efficiently implements hybrid functionals and enables routine application of the new methods to large-scale calculations of such materials with excellent performance, even with small-scale computing resources.

Crystal forms in pharmaceutical applications: olanzapine, a gift to crystal chemistry that keeps on giving

This contribution reviews the efforts of many scientists around the world to discover and structurally characterize olanzapine crystal forms, clearing up inconsistencies in the scientific and patent literature and highlighting the challenges in identifying new forms amidst 60+ known polymorphs and solvates. Owing to its remarkable solid-state chemistry, olanzapine has emerged over the last three decades as a popular tool compound for developing new experimental and computational methods for enhanced molecular level understanding of solid-state structure, form diversity and crystallization outcomes. This article highlights the role of olanzapine in advancing the fundamental understanding of crystal forms, interactions within crystal structures, and growth units in molecular crystallization, as well as influencing the way in which drugs are developed today.

Application of XDM to ionic solids: The importance of dispersion for bulk moduli and crystal geometries

Dispersion corrections are essential in the description of intermolecular interactions; however, dispersion-corrected functionals must also be transferrable to hard solids. The exchange-hole dipole moment (XDM) model has demonstrated excellent performance for non-covalent interactions. In this article, we examine its ability to describe the relative stability, geometry, and compressibility of simple ionic solids. For the specific cases of the cesium halides, XDM-corrected functionals correctly predict the energy ranking of the B1 and B2 forms, and a dispersion contribution is required to obtain this result. Furthermore, for the lattice constants of the 20 alkali halides, the performance of XDM-corrected functionals is excellent, provided that the base functional's exchange enhancement factor properly captures non-bonded repulsion. The mean absolute errors in lattice constants obtained with B86bPBE-XDM and B86bPBE-25X-XDM are 0.060 Å and 0.039 Å, respectively, suggesting that delocalization error also plays a minor role in these systems. Finally, we considered the calculation of bulk moduli for alkali halides and alkaline-earth oxides. Previous claims in the literature that simple generalized gradient approximations, such as PBE, can reliably predict experimental bulk moduli have benefited from large error cancellations between neglecting both dispersion and vibrational effects. If vibrational effects are taken into account, dispersion-corrected functionals are quite accurate (4 GPa-5 GPa average error), again, if non-bonded repulsion is correctly represented. Careful comparisons of the calculated bulk moduli with experimental data are needed to avoid systematic biases and misleading conclusions.

Overcoming the difficulties of predicting conformational polymorph energetics in molecular crystals via correlated wavefunction methods

Molecular crystal structure prediction is increasingly being applied to study the solid form landscapes of larger, more flexible pharmaceutical molecules. Despite many successes in crystal structure prediction, van der Waals-inclusive density functional theory (DFT) methods exhibit serious failures predicting the polymorph stabilities for a number of systems exhibiting conformational polymorphism, where changes in intramolecular conformation lead to different intermolecular crystal packings. Here, the stabilities of the conformational polymorphs of o-acetamidobenzamide, ROY, and oxalyl dihydrazide are examined in detail. DFT functionals that have previously been very successful in crystal structure prediction perform poorly in all three systems, due primarily to the poor intramolecular conformational energies, but also due to the intermolecular description in oxalyl dihydrazide. In all three cases, a fragment-based dispersion-corrected second-order Møller-Plesset perturbation theory (MP2D) treatment of the crystals overcomes these difficulties and predicts conformational polymorph stabilities in good agreement with experiment. These results highlight the need for methods which go beyond current-generation DFT functionals to make crystal polymorph stability predictions truly reliable.