Ab initio crystal structure predictions for flexible hydrogen-bonded molecules. Part II. Accurate energy minimization

Hybrid classical/machine-learning force fields for the accurate description of molecular condensed-phase systems

Electronic structure methods offer in principle accurate predictions of molecular properties, however, their applicability is limited by computational costs. Empirical methods are cheaper, but come with inherent approximations and are dependent on the quality and quantity of training data. The rise of machine learning (ML) force fields (FFs) exacerbates limitations related to training data even further, especially for condensed-phase systems for which the generation of large and high-quality training datasets is difficult. Here, we propose a hybrid ML/classical FF model that is parametrized exclusively on high-quality ab initio data of dimers and monomers in vacuum but is transferable to condensed-phase systems. The proposed hybrid model combines our previous ML-parametrized classical model with ML corrections for situations where classical approximations break down, thus combining the robustness and efficiency of classical FFs with the flexibility of ML. Extensive validation on benchmarking datasets and experimental condensed-phase data, including organic liquids and small-molecule crystal structures, showcases how the proposed approach may promote FF development and unlock the full potential of classical FFs.

Quantum Mechanical-Based Stability Evaluation of Crystal Structures for HIV-Targeted Drug Cabotegravir

The long-acting parenteral formulation of the HIV integrase inhibitor cabotegravir (GSK744) is currently being developed to prevent HIV infections, benefiting from infrequent dosing and high efficacy. The crystal structure can affect the bioavailability and efficacy of cabotegravir. However, the stability determination of crystal structures of GSK744 have remained a challenge. Here, we introduced an ab initio protocol to determine the stability of the crystal structures of pharmaceutical molecules, which were obtained from crystal structure prediction process starting from the molecular diagram. Using GSK744 as a case study, the ab initio predicted that Gibbs free energy provides reliable further refinement of the predicted crystal structures and presents its capability for becoming a crystal stability determination approach in the future. The proposed work can assist in the comprehensive screening of pharmaceutical design and can provide structural predictions and stability evaluation for pharmaceutical crystals.

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

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

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.

The Structural Details of Aspirin Molecules and Crystals

We revisit, in the key of structural chemistry, one of the most known and important drugs: the aspirin. Although apparently simple, the factors determining the molecular structure and supramolecular association in crystals are not trivial. We addressed the problem from experimental and theoretical sides, considering issues from X-ray measurements and results of first-principle reconstruction of molecule and lattices by ab initio calculations. Some puzzling problems can give headaches to specialists and intrigue the general public. Thus, the reported polymorphism of aspirin is disputed, a so-called form II being alleged as a result of misinterpretation. At the same time, were presented evidences that the structure of common form I can be disrupted by domains where the regular packing is changed to the pattern of form II. The problems appear even at the level of independent molecule: the most stable conformation computed by various techniques of electronic structure differs from those encountered in crystals. Because the energy difference between the related conformational isomers (computed as most stable vs. the experimental structure) is small, about 1 kcal/mol, comprised in the error bars of used methods, the unresting question is whether the modelling is imprecise, or the supramolecular factors are mutating the conformational preferences. By a detective following of the issue, the intermolecular effects were made responsible for the conformation of the molecule in crystal. The presented problems were gathered from literature results, debates, glued with modelling and analysis redone by ourselves, in order to secure the unitary view of the considered prototypic topic.

Crystal structure prediction of rigid molecules

A non-polarizable force field based on atomic multipoles fit to reproduce experimental crystal properties andab initiogas-phase dimers is described. The Ewald method is used to calculate both long-range electrostatic and 1/r6dispersion energies of crystals. The dispersion energy of a crystal calculated by a cutoff method is shown to converge slowly to the exact Ewald result. A method for constraining space-group symmetry during unit-cell optimization is derived. Results for locally optimizing 4427 unit cells including volume, cell parameters, unit-cell r.m.s.d. and CPU timings are given for both flexible and rigid molecule optimization. An algorithm for randomly generating rigid molecule crystals is described. Using the correct experimentally determined space group, the average and maximum number of random crystals needed to find the correct experimental structure is given for 2440 rigid single component crystals. The force field energy rank of the correct experimental structure is presented for the same set of 2440 rigid single component crystals assuming the correct space group. A complete crystal prediction is performed for two rigid molecules by searching over the 32 most probable space groups.

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.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

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.

Modelling organic crystal structures using distributed multipole and polarizability-based model intermolecular potentials

Crystal structure prediction for organic molecules requires both the fast assessment of thousands to millions of crystal structures and the greatest possible accuracy in their relative energies. We describe a crystal lattice simulation program, DMACRYS, emphasizing the features that make it suitable for use in crystal structure prediction for pharmaceutical molecules using accurate anisotropic atom-atom model intermolecular potentials based on the theory of intermolecular forces. DMACRYS can optimize the lattice energy of a crystal, calculate the second derivative properties, and reduce the symmetry of the spacegroup to move away from a transition state. The calculated terahertz frequency k = 0 rigid-body lattice modes and elastic tensor can be used to estimate free energies. The program uses a distributed multipole electrostatic model (Q, t = 00,...,44s) for the electrostatic fields, and can use anisotropic atom-atom repulsion models, damped isotropic dispersion up to R(-10), as well as a range of empirically fitted isotropic exp-6 atom-atom models with different definitions of atomic types. A new feature is that an accurate model for the induction energy contribution to the lattice energy has been implemented that uses atomic anisotropic dipole polarizability models (alpha, t = (10,10)...(11c,11s)) to evaluate the changes in the molecular charge density induced by the electrostatic field within the crystal. It is demonstrated, using the four polymorphs of the pharmaceutical carbamazepine C(15)H(12)N(2)O, that whilst reproducing crystal structures is relatively easy, calculating the polymorphic energy differences to the accuracy of a few kJ mol(-1) required for applications is very demanding of assumptions made in the modelling. Thus DMACRYS enables the comparison of both known and hypothetical crystal structures as an aid to the development of pharmaceuticals and other speciality organic materials, and provides a tool to develop the modelling of the intermolecular forces involved in molecular recognition processes.

Crystal structure prediction of flexible molecules using parallel genetic algorithms with a standard force field

This article describes the application of our distributed computing framework for crystal structure prediction (CSP) the modified genetic algorithms for crystal and cluster prediction (MGAC), to predict the crystal structure of flexible molecules using the general Amber force field (GAFF) and the CHARMM program. The MGAC distributed computing framework includes a series of tightly integrated computer programs for generating the molecule's force field, sampling crystal structures using a distributed parallel genetic algorithm and local energy minimization of the structures followed by the classifying, sorting, and archiving of the most relevant structures. Our results indicate that the method can consistently find the experimentally known crystal structures of flexible molecules, but the number of missing structures and poor ranking observed in some crystals show the need for further improvement of the potential.

A strategy for predicting the crystal structures of flexible molecules: the polymorphism of phenobarbital

A computational exploration of the low energy crystal structures of the pharmaceutical molecule phenobarbital is presented as a test of an approach for the crystal structure prediction of flexible molecules. Traditional transferable force field methods of modelling flexible molecules are unreliable for the level of accuracy required in crystal structure prediction and we outline a strategy for improving the evaluation of relative energies of large sets of crystal structures. The approach involves treating the molecule as a set of linked rigid units, whose conformational energy is expressed as a function of the relative orientations of the rigid groups. The conformational energy is calculated by electronic structure methods and the intermolecular interactions using an atomic multipole description of electrostatics. A key consideration in our approach is the scalability to more typical pharmaceutical molecules of higher molecular weight with many more atoms and degrees of flexibility. Based on our calculations, crystal structures are proposed for the as-yet uncharacterised forms IV and V, as well as further polymorphs of phenobarbital.

Molecular Conformations and Relative Stabilities Can Be as Demanding of the Electronic Structure Method as Intermolecular Calculations

We have performed a variety of high-level electronic structure calculations on two moderately sized organic molecules and found considerable sensitivity of the intramolecular potential energy surface to the method employed. The gas-phase structure of tyrosine-glycine varies qualitatively between B3LYP and MP2 optimizations, producing different close contacts between the tyrosine ring and the glycine moiety. The relative energies of the 2-(acetylamino)benzamide conformations found in its two polymorphs can vary by over 20 kJ mol-1 between MP2 and B3LYP calculations, using the same basis set. It is shown by a novel analysis that the intramolecular equivalent of basis set superposition error competes with the errors in the intramolecular dispersion in causing this sensitivity.

Ab initio crystal structure prediction?I. Rigid molecules

A new methodology for the prediction of molecular crystal structures using only the atomic connectivity of the molecule under consideration is presented. The approach is based on the global minimization of the lattice enthalpy of the crystal. The modeling of the electrostatic interactions is accomplished through a set of distributed charges that are optimally and automatically selected and positioned based on results of quantum mechanical calculations. A four-step global optimization algorithm is used for the identification of the local minima of the lattice enthalpy surface. A parallelized implementation of the algorithm permits a much more extensive search of the solution space than has hitherto been possible, allowing the identification of crystal structures in less frequently occurring space groups and with more than one molecule in the asymmetric unit. The algorithm has been applied successfully to the prediction of the crystal structures of 3-aza-bicyclo(3.3.1)nonane-2,4-dione (P2(1)/a, Z' = 1), allopurinol (P2(1)/c, Z' = 1), 1,3,4,6,7,9-hexa-azacycl(3.3.3)azine (Pbca, Z' = 2), and triethylenediamine (P6(3)/m, Z' = 1). In all cases, the experimentally known structure is among the most stable predicted structures, but not necessarily the global minimum.

Ab initio conformational studies on diols and binary diol-water systems using DFT methods. Intramolecular hydrogen bonding and 1:1 complex formation with water

Studies on the conformational equilibrium for the following diols, ethane-1,2-diol (12EG, CAS 107-21-1), 2R-D-(-)-propane-1,2-diol (12PG, CAS 4254-14-2), (2S,3S)-L-(+)-butane-2,3-diol (L23BD, CAS 19132-06-0), and (2S,3R)-meso-butane-2,3-diol (m23BD, CAS 5341-95-7), are described using Gaussian ab initio calculations involving density functional theory (DFT) methods. We also report in this article results on the stability and conformation for the 1:1 water-diol complex formed by ethane-1,2-diol, propane-1,2-diol, and L- and meso-butane-2,3-diol. The relative stability of the intramolecular (internal) hydrogen bond in a range of diols (n = 2 to 6), based on ab initio geometry optimization and determination of the -O...H- distance, dOH, and -O-H...O- angle, theta, increases through the sequence 1,2 approximately equals 2,3 < 1,3 < 1,4 approximately equals 1,5 approximately equals 1,6, as judged from the bond linearity and -O...H- separation. Quantum mechanical and topological analysis of possible intramolecular hydrogen bonding in this complete series of diols provides convincing evidence for this in diols in which the hydroxyl groups are separated by three or more carbon atoms, that is, in (n, n+m) diols for m > or = 2, but not for ethane-1,2-diol or other vicinal diols, which do not satisfy Popelier's topological and electron density criteria based on the AIM theory of Bader. Based on these criteria it is unlikely that vicinal diols are in fact capable of forming an intramolecular hydrogen bond, in spite of geometric and spectroscopic data in the literature suggesting otherwise.

Crystal structure predictions using five space groups with two independent molecules. The case of small organic acids

Crystal structure generations with two independent molecules have been performed for a series of carboxylic acids, using a slightly modified version of the OPLS force field. It was found that in this way the experimental structures with one independent molecule were produced as special cases, except for the molecules with four or more internal degrees of freedom. This work shows that a search with two independent molecules in only five space groups, although costly in computer power, can automatically also find structures with one independent molecule in many supergroups. Considering the observed abundances of structural classes, such a search should cover more than 95% of the possible homomolecular crystal structures.