Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction

The prediction of crystal structures from first-principles requires highly accurate energies for large numbers of putative crystal structures. High accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest, so that the associated computational costs are prohibitive. Here, we apply statistical machine learning to predict expensive hybrid functional DFT (PBE0) calculations using a multifidelity approach to re-evaluate the energies of crystal structures predicted with an inexpensive force field. The method uses an autoregressive Gaussian process, making use of less expensive GGA DFT (PBE) calculations to bridge the gap between the force field and PBE0 energies. The method is benchmarked on the crystal structure landscapes of three small, hydrogen-bonded organic molecules and shown to produce accurate predictions of energies and crystal structure ranking using small numbers of the most expensive calculations; the PBE0 energies can be predicted with errors of less than 1 kJ mol^-1 with between 4.2 and 6.8% of the cost of the full calculations. As the model that we have developed is probabilistic, we discuss how the uncertainties in predicted energies impact the assessment of the energetic ranking of crystal structures.

Heterogeneous nucleation of polymorphs on polymer surfaces: polymer-molecule interactions using a heterogeneous dielectric solvation model

We have investigated the mechanism of the nucleation of acetaminophen on poly(methyl-methacrylate) and poly(vinyl-acetate) utilizing a combination of quantum mechanical computations and electrostatic models. We have used a heterogeneous dielectric solvation model to determine the stability of different orientations of acetaminophen on polymer surfaces. We find that for the nucleation of acetaminophen on the polymer surfaces in vacuum, the most stable orientation is a flat orientation. For the nucleation process in solution where acetaminophen and the polymer surface are surrounded by a solvent, we find that the heterogeneous dielectric solvation model predicts that a sideways orientation is the most stable orientation.

Predicting Nucleation of Isonicotinamide from the Solvent-Solute Interactions of Isonicotinamide in Common Organic Solvents

The interactions of isonicotinamide (INA) with seven common solvents (acetic acid, acetonitrile, acetone, chloroform, ethyl acetate, and methanol) have been studied to examine solute-solvent effects on the nucleation of INA from these solvents. In a simple model of 1:1 solute-solvent interactions, the strongest INA-solvent interaction is with acetic acid (binding energy, Δ E_bind = -64.05 kJ mol^-1) and the weakest is with chloroform (Δ E_bind = -24.85 kJ mol^-1). This arises since acetic acid and INA form a hydrogen-bonding motif containing two moderate strength N-H···O hydrogen bonds, while chloroform and INA have a single weak C-H···O hydrogen bond. Taking acetic acid, chloroform, and methanol, the solvents with the strongest, the weakest, and an intermediate strength INA-solvent binding energy, the solvation of INA was studied to compare it with the 1:1 model. Acetic acid has the strongest binding energy (-872.24 kJ mol^-1) and solvation energy (-341.20 kJ mol^-1) with chloroform binding energy (-517.72 kJ mol^-1) and solvation energy (-199.05 kJ mol^-1). Methanol has intermediate binding energy (-814.19 kJ mol^-1) and solvation energies (-320.81 kJ mol^-1). These results further confirm the recent the findings which indicate that the key trends in solvent-solute interactions can be determined from a simple and efficient 1:1 dimer model and can be used to predict ease of nucleation with stronger binding energies correlating to slower, more difficult nucleation. A limit of this model is revealed by considering alcohol and acid solvents with longer alkyl chains.

A crystal structure prediction enigma solved: the gallic acid monohydrate system - surprises at 10 K

The seemingly unpredictable structure of gallic acid monohydrate form IV has been investigated using accurate X-ray diffraction measurements at temperatures of 10 and 123 K. The measurements demonstrate that the structure is commensurately modulated at 10 K and disordered at higher temperatures. Aided by charge-density modeling and periodic DFT calculations we show that the disorder gives a substantial stabilization of the structure.

Diabat Interpolation for Polymorph Free-Energy Differences

Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.

Molecular insights into the formation of drug-monoacyl phosphatidylcholine solid dispersions for oral delivery

Phospholipid-based formulations provide a key technology to formulate poorly water-soluble drugs. A recent interest has been in using phospholipids with a high content of monoacyl phosphatidylcholine (monoacyl PC) due to its ability to form mixed micelles of mono- and di-acylphospholipids upon aqueous dispersion. The present work focused on binary drug- monoacyl PC systems (at about equimolar ratio) with respect to screening of solid dispersion feasibility. It was tested whether or not a molecular rule of thumb can predict the desirable absence of drug crystallinity in the products. Subsequently, molecular simulations were performed to gain a better understanding of molecular association between drugs and monoacyl PC. Finally, the glass-forming ability (GFA) of pure drugs was considered with respect to solid dispersion formation. All products were obtained from a solvent-evaporation process and subsequent analysis of potential drug crystallinity was measured with X-ray powder diffraction and differential scanning calorimetry. Molecular simulations were making use of a Monte Carlo algorithm and molecular properties relevant for GFA were calculated. As a result, the dataset of 28 drugs confirmed an earlier proposed empirical rule that enthalpy of fusion and logP were important for solid dispersion formation, while some relevance was also evidenced for drug energies of frontal orbitals. Interestingly, the Monte Carlo simulations revealed several likely associations between drug and phospholipid rather than a well-defined single complex formation. However, drug-excipient interactions were still pivotal, since GFA of pure drug could not predict solid dispersion formation. These findings led to important molecular insights into binary solid dispersions of drug and monoacyl PC, which can guide formulators in early drug product development.

Crystal structure landscape of conformationally flexible organo-fluorine compounds

The crystal structure landscape of an unsubstituted benzanilide was generated and a number of hypothetical structures were accessed with experimentally obtained crystal structures of mono-, di-, tetra- and penta-fluorobenzanilides.

New organic–inorganic hybrid compounds constructed from polyoxometalates and transition metal mixed-organic-ligand complexes

Five compounds constructed from different polyoxoanions and metal mixed-organic complexes of carboxylates and nitrogen-containing ligands have been synthesized and characterized.

Crystal structure and prediction

The notion of structure is central to the subject of chemistry. This review traces the development of the idea of crystal structure since the time when a crystal structure could be determined from a three-dimensional diffraction pattern and assesses the feasibility of computationally predicting an unknown crystal structure of a given molecule. Crystal structure prediction is of considerable fundamental and applied importance, and its successful execution is by no means a solved problem. The ease of crystal structure determination today has resulted in the availability of large numbers of crystal structures of higher-energy polymorphs and pseudopolymorphs. These structural libraries lead to the concept of a crystal structure landscape. A crystal structure of a compound may accordingly be taken as a data point in such a landscape.

Why don't we find more polymorphs?

Crystal structure prediction (CSP) studies are not limited to being a search for the most thermodynamically stable crystal structure, but play a valuable role in understanding polymorphism, as shown by interdisciplinary studies where the crystal energy landscape has been explored experimentally and computationally. CSP usually produces more thermodynamically plausible crystal structures than known polymorphs. This article illustrates some reasons why: because (i) of approximations in the calculations, particularly the neglect of thermal effects (see §1.1); (ii) of the molecular rearrangement during nucleation and growth (see §1.2); (iii) the solid-state structures observed show dynamic or static disorder, stacking faults, other defects or are not crystalline and so represent more than one calculated structure (see §1.3); (iv) the structures are metastable relative to other molecular compositions (see §1.4); (v) the right crystallization experiment has not yet been performed (see §1.5) or (vi) cannot be performed (see §1.6) and the possibility (vii) that the polymorphs are not detected or structurally characterized (see §1.7). Thus, we can only aspire to a general predictive theory for polymorphism, as this appears to require a quantitative understanding of the kinetic factors involved in all possible multi-component crystallizations. For a specific molecule, analysis of the crystal energy landscape shows the potential complexity of its crystallization behaviour.

The nucleation of inosine: the impact of solution chemistry on the appearance of polymorphic and hydrated crystal forms

This contribution concerns the issue of crystal nucleation in the polymorphic and hydrate forming system inosine-water. A combination of computational and experimental tools have been used to explore the relationship between solution phase inosine species and the structural synthons as found in its crystal structures. It is evident that the initial nucleation of a metastable polymorph at temperatures above 10 degrees C is directed by dimeric self-association as revealed through proton NMR. At lower temperatures a dihydrate structure becomes the most stable solid phase and in this region of the phase diagram this is the only form that appears even though the solution species remain unchanged. This can only be rationalised in terms of a combination of water binding to the solution dimers and the thermodynamic stability of the hydrate crystal structure.

Accurate Predictions of Crystal Densities Using Quantum Mechanical Molecular Volumes

A quantum mechanically based procedure for estimation of crystal densities of neutral and ionic crystals is presented. In this method, volumes within 0.001 electrons/bohr3 isosurfaces of electron density for the constituent isolated neutral and ionic molecules are calculated to define the molecular volume or formula unit volumes used in predicting the crystal density. The B3LYP density functional theory in conjunction with the 6-31G** basis set were employed to generate the electron densities. The suitability of this method of crystal density prediction was assessed by subjecting a large number (289) of molecular and ionic crystals to the procedure and comparing results with experimental information. The results indicate that, for neutral molecular crystals, the root-mean-square (rms) deviation from experiment is within 4%, whereas the rms deviation is somewhat larger for the 71 ionic crystals evaluated (within 5%).

A Solid-State Chemist's View of the Crystal Polymorphism of Organic Compounds

In a survey of some structural and energetic aspects of crystal polymorphism, definitions are proposed, and a method for generating an unequivocal fingerprint of the cohesive pattern of an organic crystal structure is presented. The method identifies the electronic nature of molecule-molecule interactions in crystals, and its application requires a minimal training in basic crystallography and molecular modeling. The analysis suggests that thermodynamic and physical properties of polymorphs of organic crystals are quite often very similar, and sometimes depend on morphology as well as on crystal structure. It is also suggested that real polymorphism should be distinguished from the many defective or modulated structural variations often appearing in the crystallization of weakly bound molecular materials.

Crystal engineering of active pharmaceutical ingredients to improve solubility and dissolution rates

The increasing prevalence of poorly soluble drugs in development provides notable risk of new products demonstrating low and erratic bioavailability with consequences for safety and efficacy, particularly for drugs delivered by the oral route of administration. Although numerous strategies exist for enhancing the bioavailability of drugs with low aqueous solubility, the success of these approaches is not yet able to be guaranteed and is greatly dependent on the physical and chemical nature of the molecules being developed. Crystal engineering offers a number of routes to improved solubility and dissolution rate, which can be adopted through an in-depth knowledge of crystallisation processes and the molecular properties of active pharmaceutical ingredients. This article covers the concept and theory of crystal engineering and discusses the potential benefits, disadvantages and methods of preparation of co-crystals, metastable polymorphs, high-energy amorphous forms and ultrafine particles. Also considered within this review is the influence of crystallisation conditions on crystal habit and particle morphology with potential implications for dissolution and oral absorption.

In Silico Prediction of Drug Solubility. 3. Free Energy of Solvation in Pure Amorphous Matter

The solubility of drugs in water is investigated in a series of papers. In this work, we address the process of bringing a drug molecule from the vapor into a pure drug amorphous phase. This step enables us to actually calculate the solubility of amorphous drugs in water. In our general approach, we, on one hand, perform rigorous free energy simulations using a combination of the free energy perturbation and thermodynamic integration methods. On the other hand, we develop an approximate theory containing parameters that are easily accessible from conventional Monte Carlo simulations, thereby reducing the computation time significantly. In the theory for solvation, we assume that DeltaG* = DeltaGcav + ELJ + EC/2, where the free energy of cavity formation, DeltaGcav, in pure drug systems is obtained using a theory for hard-oblate spheroids, and ELJ and EC are the Lennard-Jones and Coulomb interaction energies between the chosen molecule and the others in the fluid. The theoretical predictions for the free energy of solvation in pure amorphous matter are in good agreement with free energy simulation data for 46 different drug molecules. These results together with our previous studies support our theoretical approach. By using our previous data for the free energy of hydration, we compute the total free energy change of bringing a molecule from the amorphous phase into water. We obtain good agreement between the theory and simulations. It should be noted that to obtain accurate results for the total process, high precision data are needed for the individual subprocesses. Finally, for eight different substances, we compare the experimental amorphous and crystalline solubility in water with the results obtained by the proposed theory with reasonable success.

Naphthylimido-Substituted Hexamolybdate: Preparation, Crystal Structures, Solvent Effects, and Optical Properties of Three Polymorphs

[(n-C4H9)4N]2[Mo6O18(N-1-C10H(6)-2-CH3)] (1) has been prepared by the reaction of 1-amino-2-methylnaphthalene hydrochloride with [(n-C4H9)4N]4[alpha-Mo8O26] in the presence of 1,3-dicyclohexylcarbodiimide. Three solvent-free crystalline phases are isolated from the mixed solvents of acetone and acetic ether. The X-ray single-crystal structures of the three phases have been determined, showing the packing and supramolecular assembly characters (pseudohigher symmetry, helical chains, and pi-pi stacking) by which the effect of solvent polarity and crystallization speed on polymorphism in organic-inorganic hybrids has been demonstrated.

In Silico Prediction of Drug Solubility: 1. Free Energy of Hydration

As a first step in the computational prediction of drug solubility the free energy of hydration, DeltaG*(vw) in TIP4P water has been computed for a data set of 48 drug molecules using the free energy of perturbation method and the optimized potential for liquid simulations all-atom force field. The simulations were performed in two steps, where first the Coulomb and then the Lennard-Jones interactions between the solute and the water molecules were scaled down from full to zero strength to provide physical understanding and simpler predictive models. The results have been interpreted using a theory assuming DeltaG*(vw) = A(MS)gamma + E(LJ) + E(C)/2 where A(MS) is the molecular surface area, gamma is the water-vapor surface tension, and E(LJ) and E(C) are the solute-water Lennard-Jones and Coulomb interaction energies, respectively. It was found that by a proper definition of the molecular surface area our results as well as several results from the literature were found to be in quantitative agreement using the macroscopic surface tension of TIP4P water. This is in contrast to the surface tension for water around a spherical cavity that previously has been shown to be dependent on the size of the cavity up to a radius of approximately 1 nm. The step of scaling down the electrostatic interaction can be represented by linear response theory.

In Silico Prediction of Drug Solubility: 2. Free Energy of Solvation in Pure Melts

The solubility of drugs in water is investigated in a series of papers and in the current work. The free energy of solvation, DeltaG*(vl), of a drug molecule in its pure drug melt at 673.15 K (400 degrees C) has been obtained for 46 drug molecules using the free energy perturbation method. The simulations were performed in two steps where first the Coulomb and then the Lennard-Jones interactions were scaled down from full to no interaction. The results have been interpreted using a theory assuming that DeltaG*(vl) = DeltaG(cav) + E(LJ) + E(C)/2 where the free energy of cavity formation, DeltaG(cav), in these pure drug systems was obtained using hard body theories, and E(LJ) and E(C) are the Lennard-Jones and Coulomb interaction energies, respectively, of one molecule with the other ones. Since the main parameter in hard body theories is the volume fraction, an equation of state approach was used to estimate the molecular volume. Promising results were obtained using a theory for hard oblates, in which the oblate axial ratio was calculated from the molecular surface area and volume obtained from simulations. The Coulomb term, E(C)/2, is half of the Coulomb energy in accord with linear response, which showed good agreement with our simulation results. In comparison with our previous results on free energy of hydration, the Coulomb interactions in pure drug systems are weaker, and the van der Waals interactions play a more important role.

An Automated Parallel Crystallisation Search for Predicted Crystal Structures and Packing Motifs of Carbamazepine

An automated parallel crystallisation search for physical forms of carbamazepine, covering 66 solvents and five crystallisation protocols, identified three anhydrous polymorphs (forms I-III), one hydrate and eight organic solvates, including the single-crystal structures of three previously unreported solvates (N,N-dimethylformamide (1:1); hemi-furfural; hemi-1,4-dioxane). Correlation of physical form outcome with the crystallisation conditions demonstrated that the solvent adopts a relatively nonspecific role in determining which polymorph is obtained, and that the previously reported effect of a polymer template facilitating the formation of form IV could not be reproduced by solvent crystallisation alone. In the accompanying computational search, approximately half of the energetically feasible predicted crystal structures exhibit the C=O...H--N R2(2)(8)dimer motif that is observed in the known polymorphs, with the most stable correctly corresponding to form III. Most of the other energetically feasible structures, including the global minimum, have a C=O...H--N C(4) chain hydrogen bond motif. No such chain structures were observed in this or any other previously published work, suggesting that kinetic, rather than thermodynamic, factors determine which of the energetically feasible crystal structures are observed experimentally, with the kinetics apparently favouring nucleation of crystal structures based on the CBZ-CBZ R2(2)(8) motif.

Probing Structure in the Polymorphic Domain of the l-Enantiomer of N-Benzoyl-Phenylalanine by Means of 2D Solid-State NMR Spectroscopy and DFT Calculations

A study of polymorphism using a range of solid-state NMR techniques is presented. We demonstrate the existence of at least six polymorphs in a sample of N-benzoyl-L-phenylalanine. We also present methodology for the characterization of the protonation state, hydrogen bonding, and molecular conformation for the polymorphs, together with results of such a characterization for one of the polymorphs present in our sample. DFT modeling is used to investigate the separate effects hydrogen bonding and molecular conformation have on the chemical shift tensor.

Self-assembly of trimesic acid at the liquid-solid interface-a study of solvent-induced polymorphism

A scanning tunneling microscope operated under ambient conditions was utilized to study the self-assembly of trimesic acid (TMA) at the liquid-solid interface. On a graphite substrate, two different open, loosely packed, two-dimensional hydrogen-bond networks were found. Both structures exhibit a periodic arrangement of approximately 1.0 nm wide cavities, which can be used for the co-adsorption of another species (guest) within the cells of this host system. These two polymorphs ("chickenwire" and "flower" structures) differ in their molecular packing density and hydrogen-bonding schemes. Using a homologous series of alkanoic acids as solvents, ranging from butyric to nonanoic, selective self-assembly of either the "flower" or "chickenwire" forms was achieved on a graphite surface. Solubility of TMA in these acid solvents was found to decrease with increasing chain length, and the longer-chain solvents favored formation of the chickenwire polymorph structure on the surface.