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.

Thermodynamic Study of N-Methylformamide and N,N-Dimethyl-Formamide.

An extensive thermodynamic study of N-methylformamide (CAS RN: 123-39-7) and N,N-dimethylformamide (CAS RN: 68-12-2), is presented in this work. The liquid heat capacities of N-methylformamide were measured by Tian-Calvet calorimetry in the temperature interval (250-300) K. The vapor pressures for N-methylformamide and N,N-dimethylformamide were measured using static method in the temperature range 238 K to 308 K. The ideal-gas thermodynamic properties were calculated using a combination of the density functional theory (DFT) and statistical thermodynamics. A consistent thermodynamic description was developed using the method of simultaneous correlation, where the experimental and selected literature data for vapor pressures, vaporization enthalpies, and liquid phase heat capacities and the calculated ideal-gas heat capacities were treated together to ensure overall thermodynamic consistency of the results. The resulting vapor pressure equation is valid from the triple point to the normal boiling point temperature.

Anisotropy, segmental dynamics and polymorphism of crystalline biogenic carboxylic acids.

Carboxylic acids of the Krebs cycle possess invaluable biochemical significance. Still, there are severe gaps in the availability of thermodynamic and crystallographic data, as well as ambiguities prevailing in the literature on the thermodynamic characterization and polymorph ranking. Providing an unambiguous description of the structure, thermodynamics and polymorphism of their neat crystalline phases requires a complex multidisciplinary approach. This work presents results of an extensive investigation of the structural anisotropy of the thermal expansion and local dynamics within these crystals, obtained from a beneficial cooperation of NMR crystallography and ab initio calculations of non-covalent interactions. The observed structural anisotropy and spin-lattice relaxation times are traced to large spatial variations in the strength of molecular interactions in the crystal lattice, especially in the orientation of the hydrogen bonds. A completely resolved crystal structure for oxaloacetic acid is reported for the first time. Thanks to multi-instrumental calorimetric effort, this work clarifies phase behavior, determines third-law entropies of the crystals, and states definitive polymorph ranking for succinic and fumaric acids. These thermodynamic observations are then interpreted in terms of first-principles quasi-harmonic calculations of cohesive properties. A sophisticated model capturing electronic, thermal, and configurational-entropic effects on the crystal structure approaches captures the subtle Gibbs energy differences governing polymorph ranking for succinic and fumaric acids, representing another success story of computational chemistry.

Does Explicit Polarizability Improve Molecular Dynamics Predictions of Glass Transition Temperatures of Ionic Liquids?

Molecular dynamics simulations are used for predictions of the glass transition temperatures for a test set of five aprotic ionic liquids. Glass transitions are localized with the trend-shift method, analyzing volumetric and transport properties of bulk amorphous phases. A classical nonpolarizable all-atom OPLS force-field model developed by Canongia Lopes and Pádua (CL&P) is employed as a starting level of theory for all calculations. Alternative approaches of charge scaling and the Drude oscillator model, accounting for atomic polarizability either implicitly or explicitly, respectively, are used to investigate the sensitivity of the glass transition temperatures to induction effects. The former nonpolarizable model overestimates the glass transition temperature by tens of Kelvins (37 K on average). The charge-scaling technique yields a significant improvement, and the best estimations were achieved using polarizable simulations with the Drude model, which yielded an average deviation of 11 K. Although the volumetric data usually exhibit a lesser trend shift upon vitrification, their lower statistical uncertainty enables to predict the glass transition temperature with lower uncertainty than the ionic self-diffusivities, the temperature dependence of which is usually more scattered. Additional analyses of the simulated data were also performed, revealing that the Drude model predicts lower densities for most subcooled liquids but higher densities for the glasses than the original CL&P, and that the Drude model also invokes some longer-range organization of the subcooled liquid, greatly impacting the temperature trend of ionic self-diffusivities in the low-temperature region.

Enantiotropy of Simvastatin as a Result of Weakened Interactions in the Crystal Lattice: Entropy-Driven Double Transitions and the Transient Modulated Phase as Seen by Solid-State NMR Spectroscopy.

In crystalline molecular solids, in the absence of strong intermolecular interactions, entropy-driven processes play a key role in the formation of dynamically modulated transient phases. Specifically, in crystalline simvastatin, the observed fully reversible enantiotropic behavior is associated with multiple order-disorder transitions: upon cooling, the dynamically disordered high-temperature polymorphic Form I is transformed to the completely ordered low-temperature polymorphic Form III via the intermediate (transient) modulated phase II. This behavior is associated with a significant reduction in the kinetic energy of the rotating and flipping ester substituents, as well as a decrease in structural ordering into two distinct positions. In transient phase II, the conventional three-dimensional structure is modulated by periodic distortions caused by cooperative conformation exchange of the ester substituent between the two states, which is enabled by weakened hydrogen bonding. Based on solid-state NMR data analysis, the mechanism of the enantiotropic phase transition and the presence of the transient modulated phase are documented.

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.

Decay of hydrogen bonding in mixtures of aliphatic heptanols and bistriflimide ionic liquids.

Hydrogen bonding in liquids of the constitution isomers of heptan-1-ol mixed with 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids (ILs), [Cnmim][NTf2], is investigated using both computational and experimental techniques. All-atom non-polarizable molecular-dynamics (MD) simulations predict that the hydrogen bonds gradually decay with increasing temperature. This decay is more pronounced for the branched alcohols and in the presence of the ionic liquids. The primary and linear isomer, heptan-1-ol, and its tertiary and bulky analogue 3-ethylpentan-3-ol are identified as the opposite extremes of the spectrum of hydrogen bonding stability in the bulk liquid. While neat heptan-1-ol exhibits strong hydrogen bonding at 350 K, 3-ethylpentan-3-ol is prone to hydrogen bonding decay already at 300 K. The presence of ionic liquids is found to affect the hydrogen bonding comparably as a 50 K temperature increase. Since the heat capacities of the associating liquids are very sensitive to any variation in hydrogen bonding strength and to the character of the hydrogen-bonded clusters in the bulk liquid, the calorimetric effort provides useful experimental data to confirm the results predicted by MD simulations. In this work, excess heat capacity is measured for equimolar single-phase mixtures of alcohols and ILs, and it differs largely in its sign and magnitude for individual heptanol isomers. Temperature trends of the excess heat capacities suggest that the stability of hydrogen bonding for individual heptanol isomers is temperature-shifted, based on their capability of hydrogen bonding. The predicted hierarchy of hydrogen bonding in individual alcohols and its impact on the excess heat capacity trends are qualitatively confirmed via thermodynamic modelling of the associative contribution to the excess heat capacities. These terms are found to predetermine the observed non-monotonous excess heat capacity trends.

Does Explicit Polarizability Improve Simulations of Phase Behavior of Ionic Liquids?

Molecular dynamics simulations are performed for a test set of 20 aprotic ionic liquids to investigate whether including an explicit polarizability model in the force field leads to higher accuracy and reliability of the calculated phase behavior properties, especially the enthalpy of fusion. A classical nonpolarizable all-atom optimized potentials for liquid simulations (OPLS) force-field model developed by Canongia Lopes and Pádua (CL&P) serves as a reference level of theory. Polarizability is included either in the form of Drude oscillators, resulting in the CL&P-D models, or in the framework of the atomic multipole optimized energetics for biomolecular application (AMOEBA) force field with polarizable atomic sites. Benchmarking of the calculated fusion enthalpy values against the experimental data reveals that overall the nonpolarizable CL&P model and polarizable CL&P-D models perform similarly with average deviations of about 30%. However, fusion enthalpies from the CL&P-D models exhibit a stronger correlation with their experimental counterparts. The least successful predictions are interestingly obtained from AMOEBA (deviation ca. 60%), which may indicate that a reparametrization of this force-field model is needed to achieve improved predictions of the fusion enthalpy. In general, all FF models tend to underestimate the fusion enthalpies. In addition, quantum chemical calculations are used to compute the electronic cohesive energies of the crystalline phases of the ionic liquids and of the interaction energies within the ion pair. Significant positive correlations are found between the fusion enthalpy and the cohesive energies. The character of the present anions predetermines the magnitude of individual mechanistic components of the interaction energy and related enthalpic and cohesive properties.

Structure and Glass Transition Temperature of Amorphous Dispersions of Model Pharmaceuticals with Nucleobases from Molecular Dynamics.

Glass transition temperature (Tg) is an important material property, which predetermines the kinetic stability of amorphous solids. In the context of active pharmaceutical ingredients (API), there is motivation to maximize their Tg by forming amorphous mixtures with other chemicals, labeled excipients. Molecular dynamics simulations are a natural computational tool to investigate the relationships between structure, dynamics, and cohesion of amorphous materials with an all-atom resolution. This work presents a computational study, addressing primarily the predictions of the glass transition temperatures of four selected API (carbamazepine, racemic ibuprofen, indomethacin, and naproxen) with two nucleobases (adenine and cytosine). Since the classical non-polarizable simulations fail to reach the quantitative accuracy of the predicted Tg, analyses of internal dynamics, hydrogen bonding, and cohesive forces in bulk phases of pure API and their mixtures with the nucleobases are performed to interpret the predicted trends. This manuscript reveals the method for a systematic search of beneficial pairs of API and excipients (with maximum Tg when mixed). Monitoring of transport and cohesive properties of API-excipients systems via molecular simulation will enable the design of such API formulations more efficiently in the future.

Computational assessment of the crystallization tendency of 1-ethyl-3-methylimidazolium ionic liquids.

A test set of 20 1-ethyl-3-methylimidazolium ionic liquids, differing in their anions, is subjected to a computational study with an aim to interpret the experimental difficulties related to the preparation of crystalline phases of the selected species. Molecular dynamics simulations of the liquid phases, quantum-chemical symmetry-adapted perturbation theory calculations of the interaction energies within the ion pair, and density functional theory calculations of the cohesive energies of the crystal phases are used in this work to obtain the structural, energetic, and diffusion parameters of the materials. Correlations of fusion temperatures and enthalpies and temperatures of the glass transitions with 15 calculated parameters are investigated in order to interpret the trends of the phase behavior of the selected ionic liquids. Correlations of a fair significance are found between the glass transition temperatures and selected energetic, cohesive, and diffusion-related characteristics of the liquids; however, the correlations of calculated transport and some enthalpic properties are blurred by the limited accuracy of the non-polarizable CL&P force field for predicting these properties. 1-Ethyl-3-methylimidazolium acetate is found to have an exclusive position among those in the test set due to several outlying characteristics, such as the short contact distance of its counterions in the liquid, high pair interaction energies, and importance of the dispersion interactions for the collective cohesion, impeding its crystallization significantly.

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.

Cohesive Properties of Ionic Liquids Calculated from First Principles.

Low volatility of ionic liquids (ILs), being one of their most valuable properties, is also the principal factor making reliable measurements of vapor pressures and vaporization (or sublimation) enthalpies of ILs extremely difficult. Alternatively, vaporization enthalpies at the temperature of the triple point can be obtained from the enthalpies of sublimation and fusion. While the latter can be obtained calorimetrically with a fair accuracy, the former is in principle accessible through ab initio computations. This work assesses the performance of the first-principles calculations of sublimation properties of ILs. Namely, 3 compounds, coupling the 1-ethyl-3-methylimidazolium cation [emIm] with either tetrafluoroborate [BF4], hexafluorophosphate [PF6], or bis(trifluoromethylsulfonyl)imide [NTf2] anions were selected for a case study. A computational methodology, originally developed for molecular crystals, is adopted for crystals of ILs. It exploits periodic density functional theory (DFT) calculations of the unit-cell geometries and quasi-harmonic phonons and many-body expansion schemes for ab initio refinements of the lattice energies of crystalline ILs. The vapor phase is treated as the ideal gas whose properties are obtained combining the rigid rotor-harmonic oscillator model with corrections from the one-dimensional hindered rotors and molecular-dynamics simulations capturing the contributions from the interionic interaction modes. Although the given computational approach enables one to reach the chemical accuracy (4 kJ mol-1) of calculated sublimation enthalpies of simple molecular crystals, reaching the same level of accuracy for ionic liquids proves challenging as crystals of ionic liquids are bound appreciably stronger than common molecular crystals, the underlying cohesive energies of solid ionic liquids is up to 1 order of magnitude larger. Still, combination of the mentioned computational and experimental frameworks results in a novel promising scheme that is expected to generate reliable and accurate temperature-dependent data on sublimation (and vaporization) of ILs.

Self-assembled nanostructures in ionic liquids facilitate charge storage at electrified interfaces.

Driven by the potential applications of ionic liquids (ILs) in many emerging electrochemical technologies, recent research efforts have been directed at understanding the complex ion ordering in these systems, to uncover novel energy storage mechanisms at IL-electrode interfaces. Here, we discover that surface-active ILs (SAILs), which contain amphiphilic structures inducing self-assembly, exhibit enhanced charge storage performance at electrified surfaces. Unlike conventional non-amphiphilic ILs, for which ion distribution is dominated by Coulombic interactions, SAILs exhibit significant and competing van der Waals interactions owing to the non-polar surfactant tails, leading to unusual interfacial ion distributions. We reveal that, at an intermediate degree of electrode polarization, SAILs display optimum performance, because the low-charge-density alkyl tails are effectively excluded from the electrode surfaces, whereas the formation of non-polar domains along the surface suppresses undesired overscreening effects. This work represents a crucial step towards understanding the unique interfacial behaviour and electrochemical properties of amphiphilic liquid systems showing long-range ordering, and offers insights into the design principles for high-energy-density electrolytes based on spontaneous self-assembly behaviour.

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.

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.

Porous Ionic Liquids or Liquid Metal-Organic Frameworks?

Porous liquids can be prepared from the dispersion metal-organic frameworks (MOFs) in ionic liquids (ILs). Porous liquids prepared from 5 % of ZIF-8 in a phosphonium-based ionic liquid are capable of absorbing reversibly up to 150 % more nitrogen and 100 % more methane than the pure ionic liquid.

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.

Dipole Effects on Electron Transfer are Enormous.

Molecular dipoles present important, but underutilized, methods for guiding electron transfer (ET) processes. While dipoles generate fields of Gigavolts per meter in their vicinity, reported differences between rates of ET along versus against dipoles are often small or undetectable. Herein we show unprecedentedly large dipole effects on ET. Depending on their orientation, dipoles either ensure picosecond ET, or turn ET completely off. Furthermore, favorable dipole orientation makes ET possible even in lipophilic medium, which appears counterintuitive for non-charged donor-acceptor systems. Our analysis reveals that dipoles can substantially alter the ET driving force for low solvent polarity, which accounts for these unique trends. This discovery opens doors for guiding forward ET processes while suppressing undesired backward electron transduction, which is one of the holy grails of photophysics and energy science.

Ab initio thermodynamic properties and their uncertainties for crystalline α-methanol.

To investigate the performance of quasi-harmonic electronic structure methods for modeling molecular crystals at finite temperatures and pressures, thermodynamic properties are calculated for the low-temperature α polymorph of crystalline methanol. Both density functional theory (DFT) and ab initio wavefunction techniques up to coupled cluster theory with singles, doubles, and perturbative triples (CCSD(T)) are combined with the quasi-harmonic approximation to predict energies, structures, and properties. The accuracy, reliability, and uncertainties of the individual quantum-chemical methods are assessed via detailed comparison of calculated and experimental data on structural properties (density) and thermodynamic properties (isobaric heat capacity). Performance of individual methods is also studied in context of the hierarchy of the quantum-chemical methods. The results indicate that while some properties such as the sublimation enthalpy and thermal expansivity can be modeled fairly well, other properties such as the molar volume and isobaric heat capacities are harder to predict reliably. The errors among the energies, structures, and phonons are closely coupled, and most accurate predictions here appear to arise from fortuitous error compensation among the different contributions. This study highlights how sensitive molecular crystal property predictions can be to the underlying model approximations and the significant challenges inherent in first-principles predictions of solid state structures and thermochemistry.