Crystal Energy Landscape Research Articles

Contrasting conformational behaviors of molecules XXXI and XXXII in the seventh blind test of crystal structure prediction.

Accurate modeling of conformational energies is key to the crystal structure prediction of conformational polymorphs. Focusing on molecules XXXI and XXXII from the seventh blind test of crystal structure prediction, this study employs various electronic structure methods up to the level of domain-local pair natural orbital coupled cluster singles and doubles with perturbative triples [DLPNO-CCSD(T1)] to benchmark the conformational energies and to assess their impact on the crystal energy landscapes. Molecule XXXI proves to be a relatively straightforward case, with the conformational energies from generalized gradient approximation (GGA) functional B86bPBE-XDM changing only modestly when using more advanced density functionals such as PBE0-D4, ωB97M-V, and revDSD-PBEP86-D4, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D), or DLPNO-CCSD(T1). In contrast, the conformational energies of molecule XXXII prove difficult to determine reliably, and variations in the computed conformational energies appreciably impact the crystal energy landscape. Even high-level methods such as revDSD-PBEP86-D4 and SCS-MP2D exhibit significant disagreements with the DLPNO-CCSD(T1) benchmarks for molecule XXXII, highlighting the difficulty of predicting conformational energies for complex, drug-like molecules. The best-converged predicted crystal energy landscape obtained here for molecule XXXII disagrees significantly with what has been inferred about the solid-form landscape experimentally. The identified limitations of the calculations are probably insufficient to account for the discrepancies between theory and experiment on molecule XXXII, and further investigation of the experimental solid-form landscape would be valuable. Finally, assessment of several semi-empirical methods finds r2SCAN-3c to be the most promising, with conformational energy accuracy intermediate between the GGA and hybrid functionals and a low computational cost.

Crystal Polymorph Search in the NPT Ensemble via a Deposition/Sublimation Alchemical Path.

The formulation of active pharmaceutical ingredients involves discovering stable crystal packing arrangements or polymorphs, each of which has distinct pharmaceutically relevant properties. Traditional experimental screening techniques utilizing various conditions are commonly supplemented with in silico crystal structure prediction (CSP) to inform the crystallization process and mitigate risk. Predictions are often based on advanced classical force fields or quantum mechanical calculations that model the crystal potential energy landscape but do not fully incorporate temperature, pressure, or solution conditions during the search procedure. This study proposes an innovative alchemical path that utilizes an advanced polarizable atomic multipole force field to predict crystal structures based on direct sampling of the NPT ensemble. The use of alchemical (i.e., nonphysical) intermediates, a novel Monte Carlo barostat, and an orthogonal space tempering bias combine to enhance the sampling efficiency of the deposition/sublimation phase transition. The proposed algorithm was applied to 2-((4-(2-(3,4-dichlorophenyl)ethyl)phenyl)amino)benzoic acid (Cambridge Crystallography Database Centre ID: XAFPAY) as a case study to showcase the algorithm. Each experimentally determined polymorph with one molecule in the asymmetric unit was successfully reproduced via approximately 1000 short 1 ns simulations per space group where each simulation was initiated from random rigid body coordinates and unit cell parameters. Utilizing two threads of a recent Intel CPU (a Xeon Gold 6330 CPU at 2.00 GHz), 1 ns of sampling using the polarizable AMOEBA force field can be acquired in 4 h (equating to more than 300 ns/day using all 112 threads/56 cores of a dual CPU node) within the Force Field X software (https://ffx.biochem.uiowa.edu). These results demonstrate a step forward in the rigorous use of the NPT ensemble during the CSP search process and open the door to future algorithms that incorporate solution conditions using continuum solvation methods.

Machine-Learned Potentials by Active Learning from Organic Crystal Structure Prediction Landscapes.

A primary challenge in organic molecular crystal structure prediction (CSP) is accurately ranking the energies of potential structures. While high-level solid-state density functional theory (DFT) methods allow for mostly reliable discrimination of the low-energy structures, their high computational cost is problematic because of the need to evaluate tens to hundreds of thousands of trial crystal structures to fully explore typical crystal energy landscapes. Consequently, lower-cost but less accurate empirical force fields are often used, sometimes as the first stage of a hierarchical scheme involving multiple stages of increasingly accurate energy calculations. Machine-learned interatomic potentials (MLIPs), trained to reproduce the results of ab initio methods with computational costs close to those of force fields, can improve the efficiency of the CSP by reducing or eliminating the need for costly DFT calculations. Here, we investigate active learning methods for training MLIPs with CSP datasets. The combination of active learning with the well-developed sampling methods from CSP yields potentials in a highly automated workflow that are relevant over a wide range of the crystal packing space. To demonstrate these potentials, we illustrate efficiently reranking large, diverse crystal structure landscapes to near-DFT accuracy from force field-based CSP, improving the reliability of the final energy ranking. Furthermore, we demonstrate how these potentials can be extended to more accurately model structures far from lattice energy minima through additional on-the-fly training within Monte Carlo simulations.

Thermodynamic Stability Is a Poor Indicator of Cocrystallization in Models of Organic Molecules.

Cocrystallizing a given molecule with another can be useful for adjusting the physical properties of molecules in the solid state. However, most combinations of molecules do not readily cocrystallize but form either one-component crystals or amorphous solids. Computational methods of crystal structure prediction can, in principle, identify the thermodynamically stable cocrystal and thus predict if molecules will cocrystallize or not. However, the pronounced polymorphism and tendency of many organic molecules to form disordered solids suggest that kinetic factors can play an important role in cocrystallization. The question remains: if a binary system of molecules has a thermodynamically stable cocrystal, will it indeed cocrystallize? To address this question, we simulate the crystallization of more than 2600 distinct pairs of chiral model molecules of similar size in 2D and calculate accurate crystal energy landscapes for all of them. Our analysis shows that thermodynamic criteria alone are unreliable in the prediction of cocrystallization. While the vast majority of cocrystals that form in our simulations are thermodynamically favorable, most coformer systems that have a thermodynamically stable cocrystal do not cocrystallize. We furthermore show that cocrystallization rates increase 3-fold when coformers are used that do not form well-ordered single-component crystals. Our results suggest that kinetic factors of cocrystallization are decisive in many cases.

Predictive crystallography at scale: mapping, validating, and learning from 1,000 crystal energy landscapes

Computational crystal structure prediction (CSP) is an increasingly powerful technique in materials discovery, due to its ability to reveal trends and permit insight across the possibility space of crystal structures...

Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory.

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

Exploring the Supramolecular Interactions and Thermal Stability of Dapsone:Bipyridine Cocrystals by Combining Computational Chemistry with Experimentation.

The application of computational screening methodologies based on H-bond propensity scores, molecular complementarity, molecular electrostatic potentials, and crystal structure prediction has guided the discovery of novel cocrystals of dapsone and bipyridine (DDS:BIPY). The experimental screen, which included mechanochemical and slurry experiments as well as the contact preparation, resulted in four cocrystals, including the previously known DDS:4,4'-BIPY (2:1, CC44-B) cocrystal. To understand the factors governing the formation of the DDS:2,2'-BIPY polymorphs (1:1, CC22-A and CC22-B) and the two DDS:4,4'-BIPY cocrystal stoichiometries (1:1 and 2:1), different experimental conditions (such as the influence of solvent, grinding/stirring time, etc.) were tested and compared with the virtual screening results. The computationally generated (1:1) crystal energy landscapes had the experimental cocrystals as the lowest energy structures, although distinct cocrystal packings were observed for the similar coformers. H-bonding scores and molecular electrostatic potential maps correctly indicated cocrystallization of DDS and the BIPY isomers, with a higher likelihood for 4,4'-BIPY. The molecular conformation influenced the molecular complementarity results, predicting no cocrystallization for 2,2'-BIPY with DDS. The crystal structures of CC22-A and CC44-A were solved from powder X-ray diffraction data. All four cocrystals were fully characterized by a range of analytical techniques, including powder X-ray diffraction, infrared spectroscopy, hot-stage microscopy, thermogravimetric analysis, and differential scanning calorimetry. The two DDS:2,2'-BIPY polymorphs are enantiotropically related, with form B being the stable polymorph at room temperature (RT) and form A being the higher temperature form. Form B is metastable but kinetically stable at RT. The two DDS:4,4'-BIPY cocrystals are stable at room conditions; however, at higher temperatures, CC44-A transforms to CC44-B. The cocrystal formation enthalpy order, derived from the lattice energies, was calculated as follows: CC44-B > CC44-A > CC22-A.

Accurate and efficient polymorph energy ranking with XDM-corrected hybrid DFT

Pairing the XDM dispersion model with hybrid density functionals shows significant improvements in the computed crystal energy landscapes for 4 of the 26 compounds appearing in the first six blind tests of crystal structure prediction.

An analytical method to quantify the statistics of energy landscapes in random solid solutions

Recent studies of concentrated solid solutions have highlighted the role of varied solute interactions in the determination of a wide variety of mesoscale properties. These solute interactions emerge as spatial fluctuations in potential energy, which arise from local variations in the chemical environment. Although observations of potential energy fluctuations are well documented in the literature, there remains a paucity of methods to determine their statistics. Here, we present a set of analytical equations to quantify the statistics of potential energy landscapes in randomly arranged solid solutions. Our approach is based on a reparameterization of the relations of the embedded-atom method in terms of the solute coordination environment. The final equations are general and can be applied to different crystal lattices and energy landscapes, provided the systems of interest can be described by sets of coordination relations. We leverage these statistical relations to study the cohesive energy and generalized planar fault energy landscapes of several different solid solutions. Analytical predictions are validated using molecular statics simulations, which find excellent agreement in most cases. The outcomes of this analysis provide new insights into phase stability and the interpretation of ‘local’ planar fault energies in solid solutions, which are topics of ongoing discussion within the community.

Efficient Crystal Structure Prediction for Structurally Related Molecules with Accurate and Transferable Tailor-Made Force Fields.

Crystal structure prediction (CSP) is generally used to complement experimental solid form screening and applied to individual molecules in drug development. The fast development of algorithms and computing resources offers the opportunity to use CSP earlier and for a broader range of applications in the drug design cycle. This study presents a novel paradigm of CSP specifically designed for structurally related molecules, referred to as Quick-CSP. The approach prioritizes more accurate physics through robust and transferable tailor-made force fields (TMFFs), such that significant efficiency gains are achieved through the reduction of expensive ab initio calculations. The accuracy of the TMFF is increased by the introduction of electrostatic multipoles, and the fragment-based force field parameterization scheme is demonstrated to be transferable for a family of chemically related molecules. The protocol is benchmarked with structurally related compounds from the Bromodomain and Extraterminal (BET) domain inhibitors series. A new convergence criterion is introduced that aims at performing only as many ab initio optimizations of crystal structures as required to locate the bottom of the crystal energy landscape within a user-defined accuracy. The overall approach provides significant cost savings ranging from three- to eight-fold less than the full-CSP workflow. The reported advancements expand the scope and utility of the underlying CSP building blocks as well as their novel reassembly to other applications earlier in the drug design cycle to guide molecule design and selection.

Global analysis of the energy landscapes of molecular crystal structures by applying the threshold algorithm

Polymorphism in molecular crystals has important consequences for the control of materials properties and our understanding of crystallization. Computational methods, including crystal structure prediction, have provided important insight into polymorphism, but have usually been limited to assessing the relative energies of structures. We describe the implementation of the Monte Carlo threshold algorithm as a method to provide an estimate of the energy barriers separating crystal structures. By sampling the local energy minima accessible from multiple starting structures, the simulations yield a global picture of the crystal energy landscapes and provide valuable information on the depth of the energy minima associated with crystal structures. We present results from applying the threshold algorithm to four polymorphic organic molecular crystals, examine the influence of applying space group symmetry constraints during the simulations, and discuss the relationship between the structure of the energy landscape and the intermolecular interactions present in the crystals.

Crystal Energy Landscape of Nifedipine by Experiment and Computer Prediction

Crystal Energy Landscape of Nifedipine by Experiment and Computer Prediction

Expanding the Solid Form Landscape of Bipyridines.

Two bipyridine isomers (2,2′- and 4,4′-), used as coformers and ligands in coordination chemistry, were subjected to solid form screening and crystal structure prediction. One anhydrate and a formic acid disolvate were crystallized for 2,2′-bipyridine, whereas multiple solid-state forms, anhydrate, dihydrate, and eight solvates with carboxylic acids, including a polymorphic acetic acid disolvate, were found for the 4,4′-isomer. Seven of the solvates are reported for the first time, and structural information is provided for six of the new solvates. All twelve solid-state forms were investigated comprehensively using experimental [thermal analysis, isothermal calorimetry, X-ray diffraction, gravimetric moisture (de)sorption, and IR spectroscopy] and computational approaches. Lattice and interaction energy calculations confirmed the thermodynamic driving force for disolvate formation, mediated by the absence of H-bond donor groups of the host molecules. The exposed location of the N atoms in 4,4′-bipyridine facilitates the accommodation of bigger carboxylic acids and leads to higher conformational flexibility compared to 2,2′-bipyridine. For the 4,4′-bipyridine anhydrate ↔ hydrate interconversion hardly any hysteresis and a fast transformation kinetics are observed, with the critical relative humidity being at 35% at room temperature. The computed anhydrate crystal energy landscapes have the 2,2′-bipyridine as the lowest energy structure and the 4,4′-bipyridine among the low-energy structures and suggest a different crystallization behavior of the two compounds.

Ab initio determination of crystal stability of di-p-tolyl disulfide

With the rapid growth of energy demand and the depletion of existing energy resources, the new materials with superior performances, low costs and environmental friendliness for energy production and storage are explored. Di-p-tolyl disulfide (p-Tol2S2) is a typical lubricating material, which has been applied in the field of energy storage. The conformational properties and phase transformations of p-Tol2S2 have been studied by pioneers, but their polymorphs and the polymorphism induced crystal structure changes require further analysis. In this study, we perform the crystal structural screening, prediction and optimization of p-Tol2S2 crystal with quantum mechanical calculations, i.e., density functional theory (DFT) and second-order Møller–Plesset perturbation (MP2) methods. A series of crystal structures with different molecular arrangements are generated based on the crystal structure screening. As compared to long-established lattice energy calculation, we take an advantage of using more accurate technique, which is Gibbs free energy calculation. It considers the effects of entropy and temperature to predict the crystal structures and energy landscape. By comparing the Gibbs free energies between predicted and experimental structures, we found that phase α is the most stable structure for p-Tol2S2 crystal at ambient temperature and standard atmospheric pressure. Furthermore, we provide an efficient method to discriminate different polymorphs that are otherwise difficult to be identified based on the Raman/IR spectra. The proposed work enable us to evaluate the quality of various crystal polymorphs rapidly.

Dapsone Form V: A Late Appearing Thermodynamic Polymorph of a Pharmaceutical.

Five anhydrate polymorphs (forms I-V) and the isomorphic dehydrate (Hydehy) of dapsone (4,4'-diaminodiphenyl sulfone or DDS) were prepared and characterized in an interdisciplinary experimental and computational study, elucidating the kinetic and thermodynamic stabilities, solid form interrelationships, and structural features of the known forms I-IV, the novel polymorph form V, and Hydehy. Calorimetric measurements, solubility experiments, and lattice energy calculations revealed that form V is the thermodynamically stable polymorph from absolute zero to at least 90 °C. At higher temperatures, form II, and then form I, becomes the most stable DDS solid form. The computed 0 K stability order (lattice energy calculations) was confirmed with calorimetric measurements as follows, V (most stable) > III > Hydehy > II > I > IV (least stable). The discovery of form V was complicated by the fact that the metastable but kinetically stabilized form III shows a higher nucleation and growth rate. By combining laboratory powder X-ray diffraction data and ab initio calculations, the crystal structure of form V ( P21/ c, Z' = 4) was solved, with a high energy DDS conformation allowing a denser packing and more stable intermolecular interactions, rationalizing the formation of a high Z' structure. The structures of the forms I and IV, only observed from the melt and showing distinct packing features compared to the forms II, III, and V, were derived from the computed crystal energy landscapes. Dehydration modeling of the DDS hydrate led to the Hydehy structure. This study expands our understanding about the complex crystallization behavior of pharmaceuticals and highlights the big challenge in solid form screening, especially that there is no clear end point.

Olanzapine Form IV: Discovery of a New Polymorphic Form Enabled by Computed Crystal Energy Landscapes

Olanzapine is a polymorphic drug molecule that has been extensively studied, with over 60 structures reported in the Cambridge Structural Database. All anhydrous and solvated forms of olanzapine known to date contain the SC0 dimer packing motif. In this study, a new screening approach was adopted involving heat-induced forced crystallization from a polymer-based molecular dispersion of olanzapine. Simultaneous differential scanning calorimetry–powder X-ray diffraction was used to heat the amorphous dispersion and to identify a novel physical form from diffraction and heat flow data. Comparison of the diffraction data with those from a computed crystal energy landscape allowed the crystal structure to be determined. The result was the discovery of a new polymorph, form IV, which does not use the SC0 motif. Hence, while dimer formation is the dominant process that defines crystal packing for olanzapine formed from solution, it seems that molecularly dispersing the drug in a polymeric matrix permits crystallization of alternative motifs. Having identified form IV, it proved possible to scale up the synthesis and demonstrate its enhanced dissolution properties over form I.

Successful Computationally Directed Templating of Metastable Pharmaceutical Polymorphs

A strategy of using crystal structure prediction (CSP) methods to determine which, if any, isostructural template could facilitate the first crystallization of a predicted polymorph by vapor deposition is extended to the fenamate family. Mefenamic acid (MFA) and tolfenamic acid (TFA) are used as molecules with minimal chemical differences, whereas flufenamic acid (FFA) shows greater differences in the substituents. The three crystal energy landscapes were calculated, and periodic electronic structure calculations were used to confirm the thermodynamic plausibility of possible isostructural polymorphs to experimentally obtainable crystals of the other molecules. As predicted, a new polymorph, TFA form VI, was found by sublimation onto isomorphous MFA form I, using a recently developed technique. MFA and TFA form a continuous solid solution with the structure of MFA I and TFA VI at the limits, but the isomorphous MFA/FFA solid solution does not extended to a new polymorph of FFA. The novel solid solution st...

Correction: A computational exploration of the crystal energy and charge-carrier mobility landscapes of the chiral [6]helicene molecule

Correction for 'A computational exploration of the crystal energy and charge-carrier mobility landscapes of the chiral [6]helicene molecule' by Beth Rice et al., Nanoscale, 2018, 10, 1865-1876.

A computational exploration of the crystal energy and charge-carrier mobility landscapes of the chiral [6]helicene molecule.

The potential of a given π-conjugated organic molecule in an organic semiconductor device is highly dependent on molecular packing, as it strongly influences the charge-carrier mobility of the material. Such solid-state packing is sensitive to subtle differences in their intermolecular interactions and is challenging to predict. Chirality of the organic molecule adds an additional element of complexity to intuitive packing prediction. Here we use crystal structure prediction to explore the lattice-energy landscape of a potential chiral organic semiconductor, [6]helicene. We reproduce the experimentally observed enantiopure crystal structure and explain the absence of an experimentally observed racemate structure. By exploring how the hole and electron-mobility varies across the energy-structure-function landscape for [6]helicene, we find that an energetically favourable and frequently occurring packing motif is particularly promising for electron-mobility, with a highest calculated mobility of 2.9 cm2 V-1 s-1 (assuming a reorganization energy of 0.46 eV). We also calculate relatively high hole-mobility in some structures, with a highest calculated mobility of 2.0 cm2 V-1 s-1 found for chains of helicenes packed in a herringbone fashion. Neither the energetically favourable nor high charge-carrier mobility packing motifs are intuitively obvious, and this demonstrates the utility of our approach to computationally explore the energy-structure-function landscape for organic semiconductors. Our work demonstrates a route for the use of computational simulations to aid in the design of new molecules for organic electronics, through the a priori prediction of their likely solid-state form and properties.

EXPLORING STRUCTURAL ASPECTS OF NATEGLINIDE POLYMORPHS USING POWDER X-RAY DIFFRACTION

Objective: The present manuscript highlights the structural aspects of some polymorphic forms of nateglinide using powder x-ray diffraction (PXRD) pattern.Methods: All the polymorphic forms were isolated as microcrystalline powder, therefore, powder diffraction patterns was used as a tool to determine the crystal structure. For this, Reflux Plus module of BIOVIA Material Studio software was used. Polymorph prediction (PP) and crystal morphology analysis were performed to estimate the global minimum in lattice energy landscape and morphologically important (M. I.) facets, respectively. Besides this, to investigate the behavior of polymorphs in solution phase, in vitro studies (enthalpy of solution, solubility, intrinsic dissolution rate) were also performed.Results: A new form MS was prepared and characterized. The Form H, B, MS and S were found to exist in space group P-1, C2, P-4 and P-42C, respectively. These crystal structures were found to lie on local minima in crystal energy landscape. The stability ranking of nateglinide polymorphs follows the order: Form MS<Form B<Form H<Form S.Conclusion: This research work demonstrates that PXRD is a valuable alternative for determining the structure of microcrystalline powders.