Predicting crystal form stability under real-world conditions.

The physicochemical properties of molecular crystals, such as solubility, stability, compactability, melting behaviour and bioavailability, depend on their crystal form1. In silico crystal form selection has recently come much closer to realization because of the development of accurate and affordable free-energy calculations2-4. Here we redefine the state of the art, primarily by improving the accuracy of free-energy calculations, constructing a reliable experimental benchmark for solid-solid free-energy differences, quantifying statistical errors for the computed free energies and placing both hydrate crystal structures of different stoichiometries and anhydrate crystal structures on the same energy landscape, with defined error bars, as a function of temperature and relative humidity. The calculated free energies have standard errors of 1-2 kJ mol-1 for industrially relevant compounds, and the method to place crystal structures with different hydrate stoichiometries on the same energy landscape can be extended to other multi-component systems, including solvates. These contributions reduce the gap between the needs of the experimentalist and the capabilities of modern computational tools, transforming crystal structure prediction into a more reliable and actionable procedure that can be used in combination with experimental evidence to direct crystal form selection and establish control5.

How many ritonavir cases are there still out there?

Based on a thorough and critical analysis of the commercial crystal structure prediction studies of 41 pharmaceutical compounds, we conclude that for between 15 and 45% of all small-molecule drugs currently on the market the most stable experimentally observed polymorph is not the thermodynamically most stable crystal structure and that the appearance of the latter is kinetically hindered.

The importance of configurational disorder in crystal structure prediction: the case of loratadine.

Loratadine, an over-the-counter antihistamine medication, has two known monotropically related polymorphs, both of which feature disorder. A combined experimental and computational approach using variable temperature single crystal X-ray diffraction (VT-SCXRD) analysis and dispersion corrected density functional theory (DFT-D) reveals that the nature of the disorder in each form is markedly different and cannot be described by a simple isolated-site model with thermally populated conformations in either of the two cases. In Form I, the ethyl carbamate functionality adopts two different configurations, with adjacent moieties interacting along one-dimensional chains. The most stable arrangement features alternating configurations, but because of the low energetic cost of stacking faults, the domain sizes are short and an average crystal structure is observed experimentally. The configurational free energy of the disordered structure is lower than the energy of the two corresponding ordered crystal structures, but the energy decrease is dominated by the lower lattice energy of the alternating arrangement with a small entropic contribution. In Form II, the flexible cycloheptane bridge adopts two different configurations. The disorder is not an equilibrium property but is instead frozen-in during the crystallisation process. The configurational free energy of the disordered structure falls in between the lattice energies of the two corresponding ordered structures. The two ordered components of each disordered structure are all found in a crystal structure prediction (CSP) study with the GRACE programme. However, the experimentally observed stability relationship is only reproduced when the energy contribution of disorder is taken into account. The disordered model of Form I is found to be lower in energy than all the other predicted structures and there is no indication of a missing, thermodynamically more stable, form. The case of loratadine demonstrates that experimentally observed disorder close to 50/50 does not necessarily correspond to a free energy decrease by kT ln 2.

Empirical van der Waals corrections to solid-state density functional theory: Iodine and phosphorous containing molecular crystals.

Parameters are derived for a molecular mechanics type dispersive correction to solid-state density functional theory calculations on molecular crystals containing iodine and phosphorous. The molecular C(6) coefficients are derived from photoabsorption differential oscillator strength spectra determined from accurate (e,e) dipole spectra. The cross-over parameters, which ensure correct behavior at short internuclear distances, are obtained by fitting predicted crystal lattice parameters to experimental data. The accuracy of the parameterization is assessed by optimizing the experimental structures of several additional phosphorous and iodine containing molecular crystals and by examining the relative stabilities of the known polymorphs of phosphorous pentoxide and the stabilities of different packings of an iodine containing molecular crystal, 2,9-bis(iodo)anthanthrone, which has been the subject of a crystal structure prediction study. Optimizations of the experimental crystal structures did not lead to significant geometric deviations. The optimized experimental structure of 2,9-bis(iodo)anthanthrone is the lowest energy packing found, indicating a satisfactory description of both energy and structure for these molecular crystals.

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.

Progress in crystal structure prediction.

The results of the application of a density functional theory method incorporating dispersive corrections in the 2010 crystal structure prediction blind test are reported. The method correctly predicted four out of the six experimental structures. Three of the four correct predictions were found to have the lowest lattice energy of any crystal structure for that molecule. The experimental crystal structures for all six compounds were found during the structure generation phase of the simulations, indicating that the tailor-made force fields used for screening structures were valid and that the structure generation engine, which combines a Monte Carlo parallel tempering algorithm with an efficient lattice energy minimiser, was working effectively. For the three compounds for which the experimental crystal structures did not correspond to the lowest energy structures found, the method for calculating the lattice energy needs to be further refined or there may be other polymorphs that have not yet been found experimentally.

Towards crystal structure prediction of complex organic compounds--a report on the fifth blind test.

Following on from the success of the previous crystal structure prediction blind tests (CSP1999, CSP2001, CSP2004 and CSP2007), a fifth such collaborative project (CSP2010) was organized at the Cambridge Crystallographic Data Centre. A range of methodologies was used by the participating groups in order to evaluate the ability of the current computational methods to predict the crystal structures of the six organic molecules chosen as targets for this blind test. The first four targets, two rigid molecules, one semi-flexible molecule and a 1:1 salt, matched the criteria for the targets from CSP2007, while the last two targets belonged to two new challenging categories - a larger, much more flexible molecule and a hydrate with more than one polymorph. Each group submitted three predictions for each target it attempted. There was at least one successful prediction for each target, and two groups were able to successfully predict the structure of the large flexible molecule as their first place submission. The results show that while not as many groups successfully predicted the structures of the three smallest molecules as in CSP2007, there is now evidence that methodologies such as dispersion-corrected density functional theory (DFT-D) are able to reliably do so. The results also highlight the many challenges posed by more complex systems and show that there are still issues to be overcome.

Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations.

This paper describes the validation of a dispersion-corrected density functional theory (d-DFT) method for the purpose of assessing the correctness of experimental organic crystal structures and enhancing the information content of purely experimental data. 241 experimental organic crystal structures from the August 2008 issue of Acta Cryst. Section E were energy-minimized in full, including unit-cell parameters. The differences between the experimental and the minimized crystal structures were subjected to statistical analysis. The r.m.s. Cartesian displacement excluding H atoms upon energy minimization with flexible unit-cell parameters is selected as a pertinent indicator of the correctness of a crystal structure. All 241 experimental crystal structures are reproduced very well: the average r.m.s. Cartesian displacement for the 241 crystal structures, including 16 disordered structures, is only 0.095 Š(0.084 Šfor the 225 ordered structures). R.m.s. Cartesian displacements above 0.25 A either indicate incorrect experimental crystal structures or reveal interesting structural features such as exceptionally large temperature effects, incorrectly modelled disorder or symmetry breaking H atoms. After validation, the method is applied to nine examples that are known to be ambiguous or subtly incorrect.

Crystal structure determination of the elusive paracetamol Form III.

The previously unknown crystal structure of the elusive Form III of paracetamol has been solved using high quality laboratory X-ray powder diffraction (XRPD) data and state-of-the-art crystal structure prediction (CSP).

Significant progress in predicting the crystal structures of small organic molecules--a report on the fourth blind test.

We report on the organization and outcome of the fourth blind test of crystal structure prediction, an international collaborative project organized to evaluate the present state in computational methods of predicting the crystal structures of small organic molecules. There were 14 research groups which took part, using a variety of methods to generate and rank the most likely crystal structures for four target systems: three single-component crystal structures and a 1:1 cocrystal. Participants were challenged to predict the crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee. Three predictions were allowed for each system. The results demonstrate a dramatic improvement in rates of success over previous blind tests; in total, there were 13 successful predictions and, for each of the four targets, at least two groups correctly predicted the observed crystal structure. The successes include one participating group who correctly predicted all four crystal structures as their first ranked choice, albeit at a considerable computational expense. The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.

Reliable and practical computational description of molecular crystal polymorphs.

Reliable prediction of the polymorphic energy landscape of a molecular crystal would yield profound insight into drug development in terms of the existence and likelihood of late-appearing polymorphs. However, the computational prediction of molecular crystal polymorphs is highly challenging due to the high dimensionality of conformational and crystallographic space accompanied by the need for relative free energies to within 1 kJ/mol per molecule. In this study, we combine the most successful crystal structure sampling strategy with the most successful first-principles energy ranking strategy of the latest blind test of organic crystal structure prediction methods. Specifically, we present a hierarchical energy ranking approach intended for the refinement of relative stabilities in the final stage of a crystal structure prediction procedure. Such a combined approach provides excellent stability rankings for all studied systems and can be applied to molecular crystals of pharmaceutical importance.

Tailor-made force fields for crystal-structure prediction.

A general procedure is presented to derive a complete set of force-field parameters for flexible molecules in the crystalline state on a case-by-case basis. The force-field parameters are fitted to the electrostatic potential as well as to accurate energies and forces generated by means of a hybrid method that combines solid-state density functional theory (DFT) calculations with an empirical van der Waals correction. All DFT calculations are carried out with the VASP program. The mathematical structure of the force field, the generation of reference data, the choice of the figure of merit, the optimization algorithm, and the parameter-refinement strategy are discussed in detail. The approach is applied to cyclohexane-1,4-dione, a small flexible ring. The tailor-made force field obtained for cyclohexane-1,4-dione is used to search for low-energy crystal packings in all 230 space groups with one molecule per asymmetric unit, and the most stable crystal structures are reoptimized in a second step with the hybrid method. The experimental crystal structure is found as the most stable predicted crystal structure both with the tailor-made force field and the hybrid method. The same methodology has also been applied successfully to the four compounds of the fourth CCDC blind test on crystal-structure prediction. For the five aforementioned compounds, the root-mean-square deviations between lattice energies calculated with the tailor-made force fields and the hybrid method range from 0.024 to 0.053 kcal/mol per atom around an average value of 0.034 kcal/mol per atom.

Modeling the interplay of inter- and intramolecular hydrogen bonding in conformational polymorphs.

The predicted stability differences of the conformational polymorphs of oxalyl dihydrazide and ortho-acetamidobenzamide are unrealistically large when the modeling of intermolecular energies is solely based on the isolated-molecule charge density, neglecting charge density polarization. Ab initio calculated crystal electron densities showed qualitative differences depending on the spatial arrangement of molecules in the lattice with the greatest variations observed for polymorphs that differ in the extent of inter- and intramolecular hydrogen bonding. We show that accounting for induction dramatically alters the calculated stability order of the polymorphs and reduces their predicted stability differences to be in better agreement with experiment. Given the challenges in modeling conformational polymorphs with marked differences in hydrogen bonding geometries, we performed an extensive periodic density functional study with a range of exchange-correlation functionals using both atomic and plane wave basis sets. Although such electronic structure methods model the electrostatic and polarization contributions well, the underestimation of dispersion interactions by current exchange-correlation functionals limits their applicability. The use of an empirical dispersion-corrected density functional method consistently reduces the structural deviations between the experimental and energy minimized crystal structures and achieves plausible stability differences. Thus, we have established which types of models may give worthwhile relative energies for crystal structures and other condensed phases of flexible molecules with intra- and intermolecular hydrogen bonding capabilities, advancing the possibility of simulation studies on polymorphic pharmaceuticals.

Evaluation of General and Tailor Made Force Fields via X-ray Thermal Diffuse Scattering Using Molecular Dynamics and Monte Carlo Simulations of Crystalline Aspirin.

We have performed a comparison of the experimental thermal diffuse scattering (TDS) from crystalline Aspirin (form I) to that calculated from molecular dynamics (MD) simulations based on a variety of general force fields and a tailor-made force field (TMFF). A comparison is also made with Monte Carlo (MC) simulations which use a "harmonic network" approach to describe the intermolecular interactions. These comparisons were based on the hypothesis that TDS could be a useful experimental data in validation of such simulation parameter sets, especially when calculations of dynamical properties (e.g., thermodynamic free energies) from molecular crystals are concerned. Currently such a validation of force field parameters against experimental data is often limited to calculation of specific physical properties, e.g., absolute lattice energies usually at 0 K or heat capacity measurements. TDS harvested from in-house or synchrotron experiments comprises highly detailed structural information representative of the dynamical motions of the crystal lattice. Thus, TDS is a well-suited experimental data-driven means of cross validating theoretical approaches targeted at understanding dynamical properties of crystals. We found from the results of our investigation that the TMFF and COMPASS (from the commercial software "Materials Studio") parameter sets gave the best agreement with experiment. From our homologous MC simulation analysis we are able to show that force constants associated with the molecular torsion angles are likely to be a strong contributing factor for the apparent reason why these aforementioned force fields performed better.

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

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

Energy ranking of molecular crystals using density functional theory calculations and an empirical van der waals correction.

By combination of high level density functional theory (DFT) calculations with an empirical van der Waals correction, a hybrid method has been designed and parametrized that provides unprecedented accuracy for the structure optimization and the energy ranking of molecular crystals. All DFT calculations are carried out using the VASP program. The van der Waals correction is expressed as the sum over atom-atom pair potentials with each pair potential for two atoms A and B being the product of an asymptotic C(6,A,B)/r(6) term and a damping function d(A,B)(r). Empirical parameters are provided for the elements H, C, N, O, F, Cl, and S. Following Wu and Yang, the C(6) coefficients have been determined by least-squares fitting to molecular C(6) coefficients derived by Meath and co-workers from dipole oscillator strength distributions. The damping functions d(A,B)(r) guarantee the crossover from the asymptotic C(6,A,B)/r(6) behavior at large interatomic distances to a constant interaction energy at short distances. The careful parametrization of the damping functions is of crucial importance to obtain the correct balance between the DFT part of the lattice energy and the contribution from the empirical van der Waals correction. The damping functions have been adjusted to yield the best possible agreement between the unit cells of a set of experimental low temperature crystal structures and their counterparts obtained by lattice energy optimization using the hybrid method. On average, the experimental and the calculated unit cell lengths deviate by 1%. To assess the performance of the hybrid method with respect to the lattice energy ranking of molecular crystals, various crystal packings of ethane, ethylene, acetylene, methanol, acetic acid, and urea have been generated with Accelrys' Polymorph Predictor in a first step and optimized with the hybrid method in a second step. In five out of six cases, the experimentally observed low-temperature crystal structure corresponds to the most stable calculated structure.

Validation of molecular crystal structures from powder diffraction data with dispersion-corrected density functional theory (DFT-D).

In 2010 we energy-minimized 225 high-quality single-crystal (SX) structures with dispersion-corrected density functional theory (DFT-D) to establish a quantitative benchmark. For the current paper, 215 organic crystal structures determined from X-ray powder diffraction (XRPD) data and published in an IUCr journal were energy-minimized with DFT-D and compared to the SX benchmark. The on average slightly less accurate atomic coordinates of XRPD structures do lead to systematically higher root mean square Cartesian displacement (RMSCD) values upon energy minimization than for SX structures, but the RMSCD value is still a good indicator for the detection of structures that deserve a closer look. The upper RMSCD limit for a correct structure must be increased from 0.25 Šfor SX structures to 0.35 Šfor XRPD structures; the grey area must be extended from 0.30 to 0.40 Å. Based on the energy minimizations, three structures are re-refined to give more precise atomic coordinates. For six structures our calculations provide the missing positions for the H atoms, for five structures they provide corrected positions for some H atoms. Seven crystal structures showed a minor error for a non-H atom. For five structures the energy minimizations suggest a higher space-group symmetry. For the 225 SX structures, the only deviations observed upon energy minimization were three minor H-atom related issues. Preferred orientation is the most important cause of problems. A preferred-orientation correction is the only correction where the experimental data are modified to fit the model. We conclude that molecular crystal structures determined from powder diffraction data that are published in IUCr journals are of high quality, with less than 4% containing an error in a non-H atom.

Revisiting the blind tests in crystal structure prediction: accurate energy ranking of molecular crystals.

In the 2007 blind test of crystal structure prediction hosted by the Cambridge Crystallographic Data Centre (CCDC), a hybrid DFT/MM method correctly ranked each of the four experimental structures as having the lowest lattice energy of all the crystal structures predicted for each molecule. The work presented here further validates this hybrid method by optimizing the crystal structures (experimental and submitted) of the first three CCDC blind tests held in 1999, 2001, and 2004. Except for the crystal structures of compound IX, all structures were reminimized and ranked according to their lattice energies. The hybrid method computes the lattice energy of a crystal structure as the sum of the DFT total energy and a van der Waals (dispersion) energy correction. Considering all four blind tests, the crystal structure with the lowest lattice energy corresponds to the experimentally observed structure for 12 out of 14 molecules. Moreover, good geometrical agreement is observed between the structures determined by the hybrid method and those measured experimentally. In comparison with the correct submissions made by the blind test participants, all hybrid optimized crystal structures (apart from compound II) have the smallest calculated root mean squared deviations from the experimentally observed structures. It is predicted that a new polymorph of compound V exists under pressure.