Identifying pragmatic quasi-harmonic electronic structure approaches for modeling molecular crystal thermal expansion

Sublimation of pyridine derivatives: fundamental aspects and application for two-component crystal screening

The saturated vapour pressures of five heterocyclic compounds containing the pyridine fragment, namely, three isomers of aminopyridine (2-aminopyridine (2AmPy), 3-aminopyridine (3AmPy), and 4-aminopyridine (4AmPy)); 3-hydroxypyridine (3OHPy) and 2-(1H-imidazol-2-yl)pyridine (ImPy), were measured at appropriate temperature intervals using a transpiration (inert gas flow) method. The standard molar enthalpies, entropies, and Gibbs energies of sublimation for all the studied substances were determined. Among the compounds studied, the largest value of ΔH298sub was observed for ImPy. The influence of substitution and the effects of hydrogen bonds in the crystal lattices on sublimation parameters are discussed herein. The reliable dependences relating ΔG298sub to Tfus and ΔH298sub to ΔG298sub were plotted. A comparative analysis of several calculation schemes for the estimation of sublimation enthalpy and Gibbs free energy was carried out. Thermodynamic parameters obtained in this study were applied for the evaluation of cocrystallisation thermodynamic functions for two-component crystals (virtual screening) on the basis of the studied substituted pyridines.

First-Principles Models of Polymorphism of Pharmaceuticals: Maximizing the Accuracy-to-Cost Ratio

Accuracy and sophistication of in silico models of structure, internal dynamics, and cohesion of molecular materials at finite temperatures increase over time. Applicability limits of ab initio polymorph ranking that would be feasible at reasonable costs currently represent crystals of moderately sized molecules (less than 20 nonhydrogen atoms) and simple unit cells (containing rather only one symmetry-irreducible molecule). Extending the applicability range of the underlying first-principles methods to larger systems with a real-life significance, and enabling to perform such computations in a high-throughput regime represent additional challenges to be tackled in computational chemistry. This work presents a novel composite method that combines the computational efficiency of density-functional tight-binding (DFTB) methods with the accuracy of density-functional theory (DFT). Being rooted in the quasi-harmonic approximation, it uses a cheap method to perform all of the costly scans of how static and dynamic characteristics of the crystal vary with respect to its volume. Such data are subsequently corrected to agree with a higher-level model, which must be evaluated only at a single volume of the crystal. It thus enables predictions of structural, cohesive, and thermodynamic properties of complex molecular materials, such as pharmaceuticals or organic semiconductors, at a fraction of the original computational cost. As the composite model retains the solid physical background, it suffers from a minimum accuracy deterioration compared to the full treatment with the costly approach. The novel methodology is demonstrated to provide consistent results for the structural and thermodynamic properties of real-life molecular crystals and their polymorph ranking.

Multimer Embedding Approach for Molecular Crystals up to Harmonic Vibrational Properties

Accurate calculations of molecular crystals are crucial for drug design and crystal engineering. However, periodic high-level density functional calculations using hybrid functionals are often prohibitively expensive for the relevant systems. These expensive periodic calculations can be circumvented by the usage of embedding methods in which, for instance, the periodic calculation is only performed at a lower-cost level and then monomer energies and dimer interactions are replaced by those of the higher-level method. Herein, we extend such a multimer embedding approach to enable energy corrections for trimer interactions and the calculation of harmonic vibrational properties up to the dimer level. We evaluate this approach for the X23 benchmark set of molecular crystals by approximating a periodic hybrid density functional (PBE0+MBD) by embedding multimers into less expensive calculations using a generalized-gradient approximation functional (PBE+MBD). We show that trimer interactions are crucial for accurately approximating lattice energies within 1 kJ/mol and might also be needed for further improvement of lattice constants and hence cell volumes. Finally, the vibrational properties are already very well captured at the monomer and dimer level, making it possible to approximate vibrational free energies at room temperature within 1 kJ/mol.

Along the road to Crystal Structure Prediction (CSP) of pharmaceutical-like molecules

Computational methods used for predicting crystal structures of organic compounds are mature enough to be routinely used with many rigid and semi-rigid organic molecules. The usefulness of Crystal Structure Prediction...

Tuning the quasi-harmonic treatment of crystalline ionic liquids within the density functional theory

Five ionic liquids are selected for benchmarking the performance of quasi-harmonic density functional theory (DFT) calculations of structural, phonon, and thermodynamic properties of their crystals. Data predicted by individual computational setups are sorted, establishing a distinct hierarchy among the first-principles approaches. PBE-D3 and B3LYP-D3 functionals are coupled with various plane wave and Gaussian-type orbital (GTO) basis sets. Propagation of the basis set superposition error and of the imperfections of both functionals into finite-temperature properties is discussed in detail. PBE-D3 together with a triple-zeta GTO basis set often yields the most accurate predictions of predicted molar volume and heat capacity with errors at 1% and 8%, respectively, representing the state-of-the-art for quasi-harmonic DFT calculations for crystalline ionic liquids. Fortuitous error cancellation between the basis-set superposition (overbinding) and PBE imperfection (overexpanding) strongly affects the overall accuracy, unlike the case of B3LYP/GTO calculations, impeding systematic convergence of the methodology towards higher accuracy.

Modeling the α- and β-resorcinol phase boundary via combination of density functional theory and density functional tight-binding

The ability to predict not only what organic crystal structures might occur but also the thermodynamic conditions under which they are the most stable would be extremely useful for discovering and designing new organic materials. The present study takes a step in that direction by predicting the temperature- and pressure-dependent phase boundary between the α and β polymorphs of resorcinol using density functional theory (DFT) and the quasi-harmonic approximation. To circumvent the major computational bottleneck associated with computing a well-converged phonon density of states via the supercell approach, a recently developed approximation is employed, which combines a supercell phonon density of states from dispersion-corrected third-order density functional tight binding [DFTB3-D3(BJ)] with frequency corrections derived from a smaller B86bPBE-XDM functional DFT phonon calculation on the crystallographic unit cell. This mixed DFT/DFTB quasi-harmonic approach predicts the lattice constants and unit cell volumes to within 1%-2% at lower pressures. It predicts the thermodynamic phase boundary in almost perfect agreement with the experiment, although this excellent agreement does reflect fortuitous cancellation of errors between the enthalpy and entropy of transition.

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.

Novel Physics-Based Ensemble Modeling Approach That Utilizes 3D Molecular Conformation and Packing to Access Aqueous Thermodynamic Solubility: A Case Study of Orally Available Bromodomain and Extraterminal Domain Inhibitor Lead Optimization Series

Drug design with patient centricity for ease of administration and pill burden requires robust understanding of the impact of chemical modifications on relevant physicochemical properties early in lead optimization. To this end, we have developed a physics-based ensemble approach to predict aqueous thermodynamic crystalline solubility, with a 2D chemical structure as the input. Predictions for the bromodomain and extraterminal domain (BET) inhibitor series show very close match (0.5 log unit) with measured thermodynamic solubility for cases with low crystal anisotropy and good match (1 log unit) for high anisotropy structures. The importance of thermodynamic solubility is clearly demonstrated by up to a 4 log unit drop in solubility compared to kinetic (amorphous) solubility in some cases and implications thereof, for instance on human dose. We have also demonstrated that incorporating predicted crystal structures in thermodynamic solubility prediction is necessary to differentiate (up to 4 log unit) between solubility of molecules within the series. Finally, our physics-based ensemble approach provides valuable structural insights into the origins of 3-D conformational landscapes, crystal polymorphism, and anisotropy that can be leveraged for both drug design and development.

Diabat method for polymorph free energies: Extension to molecular crystals

Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences.

Reduced-cost supercell approach for computing accurate phonon density of states in organic crystals

Phonon contributions to organic crystal structures and thermochemical properties can be significant, but computing a well-converged phonon density of states with lattice dynamics and periodic density functional theory (DFT) is often computationally expensive due to the need for large supercells. Using semi-empirical methods like density functional tight binding (DFTB) instead of DFT can reduce the computational costs dramatically, albeit with noticeable reductions in accuracy. This work proposes approximating the phonon density of states via a relatively inexpensive DFTB supercell treatment of the phonon dispersion that is then corrected by shifting the individual phonon modes according to the difference between the DFT and DFTB phonon frequencies at the Γ-point. The acoustic modes are then computed at the DFT level from the elastic constants. In several small-molecule crystal test cases, this combined approach reproduces DFT thermochemistry with kJ/mol accuracy and 1-2 orders of magnitude less computational effort. Finally, this approach is applied to computing the free energy differences between the five crystal polymorphs of oxalyl dihydrazide.

Statistical Mechanical Approximations to More Efficiently Determine Polymorph Free Energy Differences for Small Organic Molecules

Methods to efficiently determine the relative stability of polymorphs of organic crystals are highly desired in crystal structure predictions (CSPs). Current methodologies include calculating the free energy of static lattice phonons, quasi-harmonic approximations (QHA), and computing the full thermodynamic cycle using replica exchange molecular dynamics (REMD). We found that 13 out of the 29 systems minimized from experimental crystal structures restructured to a lower energy minimum when heated and annealed using REMD, a phenomenon that QHA alone cannot capture. Here, we present a series of methods that are intermediate in accuracy and expense between QHA and computing the full thermodynamic cycle, which can save 42-80% of the computational cost and introduces, on this benchmark, a relatively small (0.16 ± 0.04 kcal/mol) error relative to the full thermodynamic cycle. In particular, a method that Boltzmann weights harmonic free energies from along the trajectory of REMD replica exchange appears to be an appropriate intermediate between QHA and the full thermodynamic cycle using MD when screening crystal polymorph stability.

Sublimation Properties of α,ω-Diamines Revisited from First-Principles Calculations

Sublimation enthalpies of alkane-α,ω-diamines exhibit an odd-even pattern within their homologous series. First-principles calculations coupled with the quasi-harmonic approximation for crystals and with the conformation mixing model for the ideal gas are used to explain this phenomenon from the theoretical point of view. Crystals of the odd and even alkane-α,ω-diamines distinctly differ in their packing motifs. However, first-principles calculations indicate that it is a delicate interplay of the cohesive forces, phonons, molecular vibrations and conformational equilibrium which governs the odd-even pattern of the sublimation enthalpies within the homologous series. High molecular flexibility of the alkane-α,ω-diamines predetermines higher sensitivity of the computational model to the quality of the optimized geometries and relative conformational energies. Performance of high-throughput computational methods, such as the density functional tight binding (DFTB, GFN2-xTB) and the explicitly correlated dispersion-corrected Møller-Plesset perturbative method (MP2C-F12), are benchmarked against the consistent state-of-the-art calculations of conformational energies and interaction energies, respectively.

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.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Cohesive properties of the crystalline phases of twenty proteinogenic α-aminoacids from first-principles calculations

Cohesive properties (lattice and cohesive energy of the crystal and corresponding sublimation enthalpy) of the complete set of twenty enantiopure anhydrous proteinogenic amino acids are investigated using first-principles calculations. In contrast to neutral amino acid molecules in the vapor phase, all amino acids form crystals in their zwitterionic form. Therefore, reliable ab initio calculations of the proton transfer energy are an indispensable step of such calculations. Simplifying procedures, designed to rationalize the computational cost of the quasi-harmonic approximation, which proves too demanding if performed fully at the given quantum level of theory, are presented and tested. For this purpose, atomic multipoles (up to the quadrupoles) for the amoeba force field are parametrized for all amino acid zwitterions. While the calculated lattice energies of the amino acids range from 235-458 kJ mol-1 in absolute value, the proton transfer energies typically amount to 100-220 kJ mol-1, which translates to sublimation enthalpies ranging from 117-202 kJ mol-1, appreciably exceeding the sublimation enthalpy values common for nonionic molecular crystals. Critically assessed experimental data on sublimation enthalpies are used as a benchmark for comparison of the data calculated in this work. Cohesive properties of most amino acids calculated in this work, combining the PBE-D3(BJ)/PAW and CCSD(T)-F12/aug-cc-pVDZ levels of theory used for predictions of the lattice energies and of the proton transfer energies, respectively, exhibit a reasonable agreement with the experiment. At the same time, this work contains the first published data on cohesive properties for several enantiopure amino acids.

Improving Predicted Nuclear Magnetic Resonance Chemical Shifts Using the Quasi-Harmonic Approximation

Ab initio nuclear magnetic resonance chemical shift prediction plays an important role in the determination or validation of crystal structures. The ability to predict chemical shifts more accurately can translate to increased confidence in the resulting chemical shift or structural assignments. Standard electronic structure predictions for molecular crystal structures neglect thermal expansion, which can lead to an appreciable underestimation of the molar volumes. This study examines this volume error and its impact on 68 ¹³C- and 28 ¹⁵N-predicted chemical shifts taken from 20 molecular crystals. It assesses the ability to recover more realistic room-temperature crystal structures using the quasi-harmonic approximation and how refining the structures impacts the chemical shifts. Several pharmaceutical molecular crystals are also examined in more detail. On the whole, accounting for quasi-harmonic expansion changes the ¹³C and ¹⁵N chemical shifts by 0.5 and 1.0 ppm on average. This, in turn, reduces the root-mean-square errors relative to experiment by 0.3 ppm for ¹³C and 0.7 ppm for ¹⁵N. Although the statistical impacts are modest, changes in individual chemical shifts can reach multiple ppm. Accounting for thermal expansion in molecular crystal chemical shift prediction may not be needed routinely, but the systematic trend toward improved accuracy with the experiment could be useful in cases where discrimination between structural candidates is challenging, as in the pharmaceutical theophylline.

Revised values for the X23 benchmark set of molecular crystals

A revised reference value set for molecular crystals: X23b; new cell volumes and lattice energies including volumetric expansion due to zero-point energy and thermal effects.

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.

Solid state photodimerization of 9-tert-butyl anthracene ester produces an exceptionally metastable polymorph according to first-principles calculations

Molecular crystal engineering seeks to tune the material properties by controlling the crystal packing.

Towards reliable ab initio sublimation pressures for organic molecular crystals - are we there yet?

Knowledge of molecular crystal sublimation equilibrium data is vital in many industrial processes, but this data can be difficult to measure experimentally for low-volatility species. Theoretical prediction of sublimation pressures could provide a useful supplement to experiment, but the exponential temperature dependence of sublimation (or any saturated vapor) pressure curve makes this challenging. An uncertainty of only a few percent in the sublimation enthalpy or entropy can propagate to an error in the sublimation pressure exceeding several orders of magnitude for a given temperature interval. Despite this fundamental difficulty, this paper performs some of the first ab initio predictions of sublimation pressure curves. Four simple molecular crystals (ethane, methanol, benzene, and imidazole) have been selected for a case study showing the currently achievable accuracy of quantum chemistry calculations. Fragment-based ab initio techniques and the quasi-harmonic approximation are used for calculations of cohesive and phonon properties of the crystals, while the vapor phase is treated by the ideal gas model. Ab initio sublimation pressure curves for model compounds are compared against their experimental counterparts. The computational uncertainties are estimated, weak points of the computational methodology are identified, and further improvements are proposed.

Ab initio prediction of the polymorph phase diagram for crystalline methanol

Organic crystals frequently adopt multiple distinct polymorphs exhibiting different properties. The ability to predict not only what crystal forms might occur, but under what experimental thermodynamic conditions those polymorphs are stable would be immensely valuable to the pharmaceutical industry and others. Starting only from knowledge of the experimental crystal structures, this study successfully predicts the methanol crystal polymorph phase diagram from first-principles quantum chemistry, mapping out the thermodynamic regions of stability for three polymorphs over the range 0-400 K and 0-6 GPa. The agreement between the predicted and experimental phase diagrams corresponds to predicting the relative polymorph free energies to within ∼0.5 kJ mol-1 accuracy, which is achieved by employing fragment-based second-order Møller-Plesset perturbation theory and coupled cluster theory plus a quasi-harmonic treatment of the phonons.