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.

Heat Capacities of N-Acetyl Amides of Glycine, L-Alanine, L-Valine, L-Isoleucine, and L-Leucine.

As a follow-up to our effort to establish reliable thermodynamic data for amino acids, the heat capacity and phase behavior are reported for N-acetyl glycine amide (CAS RN: 2620-63-5), N-acetyl-L-alanine amide (CAS RN: 15962-47-7), N-acetyl-L-valine amide (CAS RN: 37933-88-3), N-acetyl-L-isoleucine amide (CAS RN: 56711-06-9), and N-acetyl-L-leucine amide (CAS RN: 28529-34-2). Prior to heat capacity measurement, thermogravimetric analysis and X-ray powder diffraction were performed to determine decomposition temperatures and initial crystal structures, respectively. The crystal heat capacities of the five N-acetyl amino acid amides were measured by Tian-Calvet calorimetry in the temperature interval (266-350 K), by power compensation DSC in the temperature interval (216-471 K), and by relaxation (heat-pulse) calorimetry in the temperature interval (2-268 K). As a result, reference heat capacities and thermodynamic functions for the crystalline phase from 0 K up to 470 K were developed.

Heat Capacities of L-Cysteine, L-Serine, L-Threonine, L-Lysine, and L-Methionine.

In an effort to establish reliable thermodynamic data for amino acids, heat capacity and phase behavior are reported for L-cysteine (CAS RN: 52-90-4), L-serine (CAS RN: 56-45-1), L-threonine (CAS RN: 72-19-5), L-lysine (CAS RN: 56-87-1), and L-methionine (CAS RN: 63-68-3). Prior to heat capacity measurements, initial crystal structures were identified by X-ray powder diffraction, followed by a thorough investigation of the polymorphic behavior using differential scanning calorimetry in the temperature range from 183 K to the decomposition temperature determined by thermogravimetric analysis. Crystal heat capacities of all five amino acids were measured by Tian-Calvet calorimetry in the temperature interval (262-358) K and by power compensation DSC in the temperature interval from 215 K to over 420 K. Experimental values of this work were compared and combined with the literature data obtained with adiabatic calorimetry. Low-temperature heat capacities of L-threonine and L-lysine, for which no or limited literature data was available, were measured using the relaxation (heat pulse) calorimetry. As a result, reference heat capacities and thermodynamic functions for the crystalline phase from near 0 K to over 420 K were developed.

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.

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.

Heat Capacities of l-Histidine, l-Phenylalanine, l-Proline, l-Tryptophan and l-Tyrosine.

In an effort to establish reliable thermodynamic data for proteinogenic amino acids, heat capacities for l-histidine (CAS RN: 71-00-1), l-phenylalanine (CAS RN: 63-91-2), l-proline (CAS RN: 147-85-3), l-tryptophan (CAS RN: 73-22-3), and l-tyrosine (CAS RN: 60-18-4) were measured over a wide temperature range. Prior to heat capacity measurements, thermogravimetric analysis was performed to determine the decomposition temperatures while X-ray powder diffraction (XRPD) and heat-flux differential scanning calorimetry (DSC) were used to identify the initial crystal structures and their possible transformations. Crystal heat capacities of all five amino acids were measured by Tian-Calvet calorimetry in the temperature interval from 262 to 358 K and by power compensation DSC in the temperature interval from 307 to 437 K. Experimental values determined in this work were then combined with the literature data obtained by adiabatic calorimetry. Low temperature heat capacities of l-histidine, for which no literature data were available, were determined in this work using the relaxation (heat pulse) calorimetry from 2 K. As a result, isobaric crystal heat capacities and standard thermodynamic functions up to 430 K for all five crystalline amino acids were developed.

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.

Volatility Study of Amino Acids by Knudsen Effusion with QCM Mass Loss Detection.

This work presents a new Knudsen effusion apparatus employing continuous monitoring of sample deposition using a quartz-crystal microbalance sensor with internal calibration by gravimetric determination of the sample mass loss. The apparatus was tested with anthracene and 1,3,5-triphenylbenzene and subsequently used for the study of sublimation behavior of several proteinogenic amino acids. Their low volatility and thermal instability strongly limit possibilities of studying their sublimation behavior and available literature data. The results presented in this work are unique in their temperature range and low uncertainty required for benchmarking theoretical studies of sublimation behavior of molecular crystals. The possibility of dimerization in the gas phase that would invalidate the effusion experiments is addressed and disproved by theoretical calculations. The enthalpy of sublimation of each amino acid is analyzed based on the contributions in two hypothetical sublimation paths involving the proton transfer in the solid and in the gas phase.

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.

Ideal-gas thermodynamic properties of proteinogenic aliphatic amino acids calculated by R1SM approach.

In this work, a R1SM approach was applied for the calculation of ideal-gas thermodynamic properties of five amino acids with aliphatic side chains: glycine, alanine, valine, leucine, and isoleucine. The first step of the calculation was an extensive conformational analysis that located several conformers not reported previously. A new systematic and user-friendly nomenclature of the conformers was introduced, and the stable conformers were clearly assigned with the previously used labeling where possible. Stability and calculated relative energies of the conformers were compared between various levels of theory and with several experimental studies, demonstrating a good performance of the selected B3LYP-D3/6-311+G(2df,p) level of theory. As a second step, the theoretically calculated vibrational frequencies were compared to the previously reported experimental spectra to verify the performance of the applied double-linear scaling factor. Finally, ideal-gas heat capacities, enthalpies, and absolute entropies were calculated, accounting for all stable conformers using the R1SM model. The resulting thermodynamic data are presented for the first time, since they cannot be determined experimentally and their rigorous calculation requires a complex thermodynamic model.

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.

First-principles calculation of ideal-gas thermodynamic properties of long-chain molecules by R1SM approach-Application to n-alkanes.

First-principles calculations, coupled with statistical thermodynamics, can provide ideal-gas thermodynamic properties but get complicated and less reliable with an increasing number of conformers. An approach designed for calculation of ideal-gas thermodynamic properties of long-chain molecules, R1SM, and its simplified version, sR1SM, is tested in this work by calculation of ideal-gas heat capacities and entropies for a homologous series of n-alkanes up to n-tetradecane. The R1SM approach incorporates the rigid rotor-harmonic oscillator approximation in combination with a correction for internal rotations of methyl tops using the one-dimensional hindered rotor scheme and the mixing model accounting for the population of conformers based on the Boltzmann distribution. The R1SM approach is applicable for compounds with up to hundreds of conformers, while the simplified sR1SM approach can be used for molecules with up to 105 conformers when coupled with rules for enumeration of stable conformers and estimation scheme for their energies. The obtained results for n-alkanes are compared with experimental values and previously employed computational schemes. As the conformational behavior and conformer energies are inherent parts of the proposed approaches, a thorough conformational study of n-alkanes is performed and compared with experiments and the Tasi rules for enumeration of n-alkane conformers. Finally, the standard uncertainty of the R1SM-calculated ideal-gas thermodynamic properties is estimated based on the error propagation from the used input quantities and approximations as well as on comparison to experimental values and amounts to less than 1% for both ideal-gas heat capacity and standard ideal-gas entropy.

Polymorphism and thermophysical properties of L- and DL-menthol.

The thermodynamic properties, phase behavior, and kinetics of polymorphic transformations of racemic (DL-) and enantiopure (L-) menthol were studied using a combination of advanced experimental techniques, including static vapor pressure measurements, adiabatic calorimetry, Tian-Calvet calorimetry, differential scanning calorimetry (DSC), and variable-temperature X-ray powder diffraction. Several concomitant polymorphs (α, ß, γ, and δ forms) were observed and studied. A continuous transformation to the stable α form was detected by DSC and monitored in detail using X-ray powder diffraction. A long-term coexistence of the stable crystalline form with the liquid phase was observed. The vapor pressure measurements of both compounds were performed using two static apparatus over a temperature range from 274 K to 363 K. Condensed-phase heat capacities were measured by adiabatic and Tian-Calvet calorimetry in the wide temperature interval from 5 K to 368 K. Experimental data of L- and DL-menthol are compared mutually as well as with available literature results. The thermodynamic functions of crystalline and liquid L-menthol between 0 K and 370 K were calculated from the calorimetric results. The thermodynamic properties in the ideal-gas state were obtained by combining statistical thermodynamics and quantum chemical calculations based on a thorough conformational analysis. Calculated ideal-gas heat capacities and experimental data on vapor pressure and condensed-phase heat capacity were treated simultaneously to obtain a consistent thermodynamic description. Based on the obtained results, the phase diagrams of L-menthol and DL-menthol were suggested.