The crystal structure and molecular thermal motion of urea at 12, 60 and 123 K from neutron diffraction

Machine Learning Classification of Local Environments in Molecular Crystals

Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of molecular crystals using learning models that employ either flexibly learned or handcrafted molecular representations. In the first case, we follow our earlier work on graph learning in molecular crystals, deploying an atomistic graph convolutional network combined with molecule-wise aggregation to enable per-molecule environmental classification. For the second model, we develop a new set of descriptors based on symmetry functions combined with a point-vector representation of the molecules, encoding information about the positions and relative orientations of the molecule. We demonstrate very high classification accuracy for both approaches on urea and nicotinamide crystal polymorphs and practical applications to the analysis of dynamical trajectory data for nanocrystals and solid-solid interfaces. Both architectures are applicable to a wide range of molecules and diverse topologies, providing an essential step in the exploration of complex condensed matter phenomena.

TAAM refinement on high-resolution experimental and simulated 3D ED/MicroED data for organic molecules

3D electron diffraction (3D ED), or microcrystal electron diffraction (MicroED), has become an alternative technique for determining the high-resolution crystal structures of compounds from sub-micron-sized crystals. Here, we considered L-alanine, α-glycine and urea, which are known to form good-quality crystals, and collected high-resolution 3D ED data on our in-house TEM instrument. In this study, we present a comparison of independent atom model (IAM) and transferable aspherical atom model (TAAM) kinematical refinement against experimental and simulated data. TAAM refinement on both experimental and simulated data clearly improves the model fitting statistics (R factors and residual electrostatic potential) compared to IAM refinement. This shows that TAAM better represents the experimental electrostatic potential of organic crystals than IAM. Furthermore, we compared the geometrical parameters and atomic displacement parameters (ADPs) resulting from the experimental refinements with the simulated refinements, with the periodic density functional theory (DFT) calculations and with published X-ray and neutron crystal structures. The TAAM refinements on the 3D ED data did not improve the accuracy of the bond lengths between the non-H atoms. The experimental 3D ED data provided more accurate H-atom positions than the IAM refinements on the X-ray diffraction data. The IAM refinements against 3D ED data had a tendency to lead to slightly longer X-H bond lengths than TAAM, but the difference was statistically insignificant. Atomic displacement parameters were too large by tens of percent for L-alanine and α-glycine. Most probably, other unmodelled effects were causing this behaviour, such as radiation damage or dynamical scattering.

Critical assessment of the x-ray restrained wave function approach: Advantages, drawbacks, and perspectives for density functional theory and periodic ab initio calculations

The x-ray restrained wave function (XRW) method is a quantum crystallographic technique to extract wave functions compatible with experimental x-ray diffraction data. The approach looks for wave functions that minimize the energies of the investigated systems and also reproduce sets of x-ray structure factors. Given the strict relationship between x-ray structure factors and electron distributions, the strategy practically allows determining wave functions that correspond to given (usually experimental) electron densities. In this work, the capabilities of the XRW approach were further tested. The aim was to evaluate whether the XRW technique could serve as a tool for suggesting new exchange-correlation functionals for density functional theory or refining existing ones. Additionally, the ability of the method to address the influences of the crystalline environment was also assessed. The outcomes of XRW computations were thus compared to those of traditional gas-phase, embedding quantum mechanics/molecular mechanics, and fully periodic calculations. The results revealed that, irrespective of the initial conditions, the XRW computations practically yield a consensus electron density, in contrast to the currently employed density functional approximations (DFAs), which tend to give a too large range of electron distributions. This is encouraging in view of exploiting the XRW technique to develop improved functionals. Conversely, the calculations also emphasized that the XRW method is limited in its ability to effectively address the influences of the crystalline environment. This underscores the need for a periodic XRW technique, which would allow further untangling the shortcomings of DFAs from those inherent to the XRW approach.

Transferable Hirshfeld atom model for rapid evaluation of aspherical atomic form factors

Form factors based on aspherical models of atomic electron density have brought great improvement in the accuracies of hydrogen atom parameters derived from X-ray crystal structure refinement. Today, two main groups of such models are available, the banks of transferable atomic densities parametrized using the Hansen-Coppens multipole model which allows for rapid evaluation of atomic form factors and Hirshfeld atom refinement (HAR)-related methods which are usually more accurate but also slower. In this work, a model that combines the ideas utilized in the two approaches is tested. It uses atomic electron densities based on Hirshfeld partitions of electron densities, which are precalculated and stored in a databank. This model was also applied during the refinement of the structures of five small molecules. A comparison of the resulting hydrogen atom parameters with those derived from neutron diffraction data indicates that they are more accurate than those obtained with the Hansen-Coppens based databank, and only slightly less accurate than those obtained with a version of HAR that neglects the crystal environment. The advantage of using HAR becomes more noticeable when the effects of the environment are included. To speed up calculations, atomic densities were represented by multipole expansion with spherical harmonics up to l = 7, which used numerical radial functions (a different approach to that applied in the Hansen-Coppens model). Calculations of atomic form factors for the small protein crambin (at 0.73 Å resolution) took only 68 s using 12 CPU cores.

Quantifying the Relevance of Long-Range Forces for Crystal Nucleation in Water

Understanding nucleation from aqueous solutions is of fundamental importance in a multitude of fields, ranging from materials science to biophysics. The complex solvent-mediated interactions in aqueous solutions hamper the development of a simple physical picture, elucidating the roles of different interactions in nucleation processes. In this work, we make use of three complementary techniques to disentangle the role played by short- and long-range interactions in solvent-mediated nucleation. Specifically, the first approach we utilize is the local molecular field (LMF) theory to renormalize long-range Coulomb electrostatics. Second, we use well-tempered metadynamics to speed up rare events governed by short-range interactions. Third, the deep learning-based State Predictive Information Bottleneck approach is employed in analyzing the reaction coordinate of the nucleation processes obtained from the LMF treatment coupled with well-tempered metadynamics. We find that the two-step nucleation mechanism can largely be captured by the short-range interactions, while the long-range interactions further contribute to the stability of the primary crystal state under ambient conditions. Furthermore, by analyzing the reaction coordinate obtained from the combined LMF-metadynamics treatment, we discern the fluctuations on different time scales, highlighting the need for long-range interactions when accounting for metastability.

Dataset for the phase equilibria and PXRD studies of urea as a green thermodynamic inhibitor of sII gas hydrates

The equilibrium conditions of sII methane/propane hydrates have been experimentally determined for the C3H8/CH4-H2O-urea system. The equilibrium dissociation temperatures and pressures of sII hydrates span a wide P,T-range (266.7-293.9 K; 0.87-9.49 MPa) and were measured by varying the feed mass fraction of urea in solution from 0 to 50 mass%. The experimental points at feed urea concentration ≤ 40 mass% correspond to the V-Lw-H equilibrium (gas-aqueous urea solution-gas hydrate). A four-phase V-Lw-H-Su equilibrium (with an additional phase of solid urea) was observed because the solubility limit of urea in water was reached for all points at a feed mass fraction of 50 mass% and for one point at 40 mass% (266.93 K). Gas hydrate equilibria were measured using a high-pressure rig GHA350 under isochoric conditions with rapid fluid stirring and slow ramp heating of 0.1 K/h. Each measured point represents complete dissociation of the sII hydrate. The phase equilibrium data was compared with the literature reported for the C3H8/CH4-H2O and CH4-H2O-urea systems. A comprehensive analysis of the thermodynamic inhibition effect of urea to sII C3H8/CH4 hydrates on pressure and concentration of the inhibitor was carried out. The phase composition of the samples was analyzed by powder X-ray diffractometry at 173 K.

Quantitative matching of crystal structures to experimental powder diffractograms

The identification and classification of crystal structures is fundamental in materials science, as the crystal structure is an inherent factor of what gives solid materials their properties. Being able to identify the same crystallographic form from unique origins (e.g. different temperatures, pressures, or in silico-generated) is a complex challenge. While our previous work has focused on comparison of simulated powder diffractograms from known crystal structures, herein is presented the variable-cell experimental powder difference (VC-xPWDF) method to match collected powder diffractograms of unknown polymorphs to both experimental crystal structures from the Cambridge Structural Database and in silico-generated structures from the Control and Prediction of the Organic Solid State database. The VC-xPWDF method is shown to correctly identify the most similar crystal structure to both moderate and "low" quality experimental powder diffractograms for a set of 7 representative organic compounds. Features of the powder diffractograms that are more challenging for the VC-xPWDF method are discussed (i.e. preferred orientation), and comparison with the FIDEL method showcases the advantage of VC-xPWDF provided the experimental powder diffractogram can be indexed. The VC-xPWDF method should allow rapid identification of new polymorphs from solid-form screening studies, without requiring single-crystal analysis.

A conventional and chemometric analytical approach to solving urea determination with accuracy and precision

Urea is an essential molecule usually detected using spectroscopy, particularly ultraviolet and visible spectroscopy (UV-vis). However, its detection represents a not always fully acknowledged issue. Its concentration dependency has raised questions about the reliability of the UV-vis results. Derivatization reactions, common alternatives to achieve accuracy and precision with UV-vis measurements, still represent an additional step in the measurement process. Besides the problems mentioned earlier, urea forms complex mixtures in aqueous mediums. Therefore, this work proposes to investigate the accuracy and precision of urea determination by UV-vis spectroscopy in the pure form and derivatized with para-dimethylaminobenzaldehyde. The results show that UV-vis spectroscopy could not quantify urea in both forms with precision and accuracy. On the other hand, when applying multivariate curve resolution with alternating least squares (MCR-ALS) to the UV-vis data, the pure urea analytical signal is mathematically separated. Then, those parameters of merit were successfully achieved.

How do density functionals affect the Hirshfeld atom refinement?

In this work, the effect of mixing different amounts of Hartree-Fock (HF) exchange with hybrid density functionals applied to the Hirshfeld atom refinement (HAR) of urea and oxalic acid dihydrate is explored. Together, the influence of using different basis sets, methods (including MP2 and HF) and cluster sizes (to model bulk effects) is studied. The results show that changing the amount of HF exchange, no matter the level of theory, has an impact almost exclusively on the H atom refinement parameters. Contrary to pure quantum mechanical calculations where good geometries are obtained with intermediate HF exchange mixtures, in the HAR the best match with neutron diffraction reference values is not necessarily found for these admixtures. While the non-hydrogen covalent bond lengths are insensitive to the combination of method or basis set employed, the X-H bond lengths always increase proportionally to the HF exchange for the analysed systems. This outcome is opposite to what is normally observed from geometry optimisations, i.e., shorter bonds are obtained with greater HF exchange. Additionally, the thermal ellipsoids tend to shrink with larger HF exchange, especially for the H atoms involved in strong hydrogen bonding. Thus, it may be the case that the development of density functionals or basis sets suitable for quantum crystallography should take a different path than those fitted for quantum chemistry calculations.

Hirshfeld atom refinement based on projector augmented wave densities with periodic boundary conditions

Hirshfeld atom refinement (HAR) is an X-ray diffraction refinement method that, in numerous publications, has been shown to give H-atom bond lengths in close agreement with neutron diffraction derived values. Presented here is a first evaluation of an approach using densities derived from projector augmented wave (PAW) densities with three-dimensional periodic boundary conditions for HAR. The results show an improvement over refinements that neglect the crystal environment or treat it classically, while being on a par with non-periodic approximations for treating the solid-state environment quantum mechanically. A suite of functionals were evaluated for this purpose, showing that the SCAN and revSCAN functionals are most suited to these types of calculation.

High Energy Density Shape Memory Polymers Using Strain-Induced Supramolecular Nanostructures

Shape memory polymers are promising materials in many emerging applications due to their large extensibility and excellent shape recovery. However, practical application of these polymers is limited by their poor energy densities (up to ∼1 MJ/m³). Here, we report an approach to achieve a high energy density, one-way shape memory polymer based on the formation of strain-induced supramolecular nanostructures. As polymer chains align during strain, strong directional dynamic bonds form, creating stable supramolecular nanostructures and trapping stretched chains in a highly elongated state. Upon heating, the dynamic bonds break, and stretched chains contract to their initial disordered state. This mechanism stores large amounts of entropic energy (as high as 19.6 MJ/m³ or 17.9 J/g), almost six times higher than the best previously reported shape memory polymers while maintaining near 100% shape recovery and fixity. The reported phenomenon of strain-induced supramolecular structures offers a new approach toward achieving high energy density shape memory polymers.

Infrared spectra of amorphous and crystalline urea ices

Urea is a molecule of great interest in chemistry and biology. In particular, it is considered a key building block in prebiotic chemistry on Earth. The hypothesis of its possible exogenous origin has been reinforced after the recent detection of this molecule in the interstellar medium, where it is believed to form in the ice mantles of dust grains. In this work the infrared spectra of urea ices and urea:H₂O ice mixtures have been studied both experimentally and theoretically. Urea ices were generated by vapour deposition at temperatures between 10 K and 270 K. It was found that an amorphous phase is formed at temperatures below 200 K. A theoretical modelling of crystalline urea and of a tentative amorphous urea solid phase, as well as of amorphous urea:H₂O ice mixtures, has been performed. The corresponding infrared spectra were simulated with density functional theory. The main spectral features observed in the various solid samples are interpreted with the help of the theoretical results. Infrared band strengths are also provided for amorphous and crystalline urea. The infrared spectroscopic information given in this work is expected to be useful for the detection and quantification of urea in astrophysical ices.

Remarkable Conversion of 2-Thioxo-2,3-dihydroquinazolin-4(1H)-ones into the Corresponding Quinazoline-2,4(1H,3H)-diones: Spectroscopic Analysis and X-Ray Crystallography

A simple and efficient new synthetic method to obtain 3-substituted quinazolin-2,4-diones 9–16 by the reaction of 3-substituted 2-thioxo-quinazolin-4-ones 1–8 with sodamide under mild conditions was presented. The structure of the newly synthesized compounds was determined by infrared spectroscopy, UV-visible spectroscopy, nuclear magnetic resonance, and single-crystal X-ray crystallographic analysis. The crystal structure of 6-methyl-3-phenylquinazoline-2,4(1H,3H)-dione (11) [C15H12N2O2: MF = 252.27, triclinic, P-1, a = 7.8495 (13) Å, b = 12.456 (2) Å, c = 13.350 (2) Å, α = 103.322 (3)°, β = 90.002 (3)°, γ = 102.671 (4)°, V = 1237.5 (3) Å3, Z = 4, R = 0.0592, wR = 0.1699, S = 1.039] was determined. In the crystal cell, two identical conformers of compound 11 were found connected by intramolecular hydrogen bonds, responsible for the favourable occurrence of these two independent molecules.

Controlling the aqueous growth of urea crystals with different growth inhibitors: a molecular-scale study

Molecular scale understanding of the mechanism of solution-mediated nucleation and the growth of crystalline materials in the presence of growth inhibitors together with the process parameters continues to attract the interest of the scientific community though much headway has been made in recent years. Growth inhibitors can be added to solution of a crystallizing parent molecule to alter the rate of growth of different crystal faces, size and shape of the crystalline materials. In this work, we investigated the effects of a number of shape-controlling inhibitors, such as acetone, biuret and biurea, on the growth kinetics of the various faces of aqueous-grown urea crystals as a means to predictably control the crystal growth morphology. We combined the adsorption energy landscape of various auxiliaries with the kinetics of the molecular growth processes to develop an analytical model to compute the rate of growth as a function of supersaturation and the additive concentration. The model relates the kinetic and thermodynamic aspects of the adsorption of the solute, solvent and additive to provide a quantitative description of the crystal growth. Ab initio periodic dispersion-corrected density functional theory using the hybrid exchange-correlation functional was employed to determine the interfacial structure of the adsorption of various auxiliaries at crystalline surfaces. The calculated adsorption energies of different auxiliaries were employed to examine the role played by these auxiliaries during the aqueous crystallization of urea crystals containing small amounts of additives. Our results showed that the growth of (110), (111) and (1̄1̄1̄) faces were nearly unaltered by the addition of moderate amounts of acetone as it has lower adsorption energies with the surfaces of these faces. Nevertheless, the presence of acetone in the solution reasonably impeded the growth of the (001) face. The addition of biuret or biurea in the solution led to a higher adsorption energy at (001) and (111) faces. Consequently, the low concentration of these additives severely obstructed the growth of (001) and (111) faces as most of the adsorption sites were occupied by these additives. On the other hand, these additives were weakly adsorbed at the (110) face and, hence, the growth of the (110) face largely remained unaltered. Moreover, unlike biuret, biurea considerably inhibited the growth of the (1̄1̄1̄) face. Our results are in agreement with the experimental and computational results reported in the literature.

Multipole electron densities and structural parameters from synchrotron powder X-ray diffraction data obtained with a MYTHEN detector system (OHGI)

Powder X-ray diffraction has some inherent advantages over traditional single-crystal X-ray diffraction in accurately determining electron densities and structural parameters due to the lower requirements for sample crystallinity, simpler corrections and measurement simultaneity. For some simple inorganic materials, it has been shown that these advantages can compensate for disadvantages such as peak overlap and error-prone background subtraction. Although it is challenging to extend powder X-ray diffraction-based electron-density studies to organic materials with significant peak overlap, previous results using a dedicated vacuum diffractometer with a large image-plate camera (AVID) demonstrated that it can be done. However, the vacuum setup with the off-line detector system was found to prohibit a widespread use. Fast microstrip detectors, which have been employed at a number of powder diffraction beamlines, have the potential to facilitate electron-density studies. Nevertheless, no electron-density studies even for materials with slight peak overlap have been performed with microstrip detectors. One of the most critical problems has been a difference in sensitivity between microstrip channels, which substantially defines the dynamic range of a detector. Recently, a robust approach to this problem has been developed and applied to a total scattering measurement system (OHGI) with 15 MYTHEN microstrip modules. In the present study, synchrotron powder X-ray diffraction data obtained with OHGI are evaulated in terms of multipole electron densities and structural parameters (atomic positions and displacement parameters). These results show that, even without a dedicated setup and perfect samples, electron-density modelling can be carried out on high-quality powder X-ray diffraction data. However, it was also found that the required prior information about the sample prohibits widespread use of the method. With the presently obtainable data quality, electron densities of molecular crystals in general are not reliably obtained from powder data, but it is an excellent, possibly superior, alternative to single-crystal measurements for small-unit-cell inorganic solids. If aspherical atomic scattering factors can be obtained from other means (multipole databases, theoretical calculations), then atomic positions (including for hydrogen) and anisotropic atomic displacement parameters (non-hydrogen atoms) of excellent accuracy can be refined from synchrotron powder X-ray diffraction data on organic crystals.

Hirshfeld atom like refinement with alternative electron density partitions

Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree-Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.

TAAM: a reliable and user friendly tool for hydrogen-atom location using routine X-ray diffraction data

Hydrogen is present in almost all of the molecules in living things. It is very reactive and forms bonds with most of the elements, terminating their valences and enhancing their chemistry. X-ray diffraction is the most common method for structure determination. It depends on scattering of X-rays from electron density, which means the single electron of hydrogen is difficult to detect. Generally, neutron diffraction data are used to determine the accurate position of hydrogen atoms. However, the requirement for good quality single crystals, costly maintenance and the limited number of neutron diffraction facilities means that these kind of results are rarely available. Here it is shown that the use of Transferable Aspherical Atom Model (TAAM) instead of Independent Atom Model (IAM) in routine structure refinement with X-ray data is another possible solution which largely improves the precision and accuracy of X-H bond lengths and makes them comparable to averaged neutron bond lengths. TAAM, built from a pseudoatom databank, was used to determine the X-H bond lengths on 75 data sets for organic molecule crystals. TAAM parametrizations available in the modified University of Buffalo Databank (UBDB) of pseudoatoms applied through the DiSCaMB software library were used. The averaged bond lengths determined by TAAM refinements with X-ray diffraction data of atomic resolution (d_min ≤ 0.83 Å) showed very good agreement with neutron data, mostly within one single sample standard deviation, much like Hirshfeld atom refinement (HAR). Atomic displacements for both hydrogen and non-hydrogen atoms obtained from the refinements systematically differed from IAM results. Overall TAAM gave better fits to experimental data of standard resolution compared to IAM. The research was accompanied with development of software aimed at providing user-friendly tools to use aspherical atom models in refinement of organic molecules at speeds comparable to routine refinements based on spherical atom model.

Can We Predict the Pressure Induced Phase Transition of Urea? Application of Quantum Molecular Dynamics

Crystalline urea undergoes polymorphic phase transition induced by high pressure. Form I, which is the most stable form at normal conditions and Form IV, which is the most stable form at 3.10 GPa, not only crystallize in various crystal systems but also differ significantly in the unit cell dimensions. The aim of this study was to determine if it is possible to predict polymorphic phase transitions by optimizing Form I at high pressure and Form IV at low pressure. To achieve this aim, a large number of periodic density functional theory (DFT) calculations were performed using CASTEP. After geometry optimization of Form IV at 0 GPa Form I was obtained, performing energy minimization of Form I at high pressure did not result in Form IV. However, employing quantum molecular isothermal–isobaric (NPT) dynamics calculations enabled to accurately predict this high-pressure transformation. This study shows the potential of different approaches in predicting the polymorphic phase transition and points to the key factors that are necessary to achieve the success.

Multipole electron densities and atomic displacement parameters in urea from accurate powder X-ray diffraction

Electron density determination based on structure factors obtained through powder X-ray diffraction has so far been limited to high-symmetry inorganic solids. This limit is challenged by determining high-quality structure factors for crystalline urea using a bespoke vacuum diffractometer with imaging plates. This allows the collection of data of sufficient quality to model the electron density of a molecular system using the multipole method. The structure factors, refined parameters as well as chemical bonding features are compared with results from the high-quality synchrotron single-crystal study by Birkedal et al. [Acta Cryst. (2004), A60, 371-381] demonstrating that powder X-ray diffraction potentially provides a viable alternative for electron density determination in simple molecular crystals where high-quality single crystals are not available.

Measurement of Electric Fields Experienced by Urea Guest Molecules in the 18-Crown-6/Urea (1:5) Host-Guest Complex: An Experimental Reference Point for Electric-Field-Assisted Catalysis

High-resolution synchrotron and neutron single-crystal diffraction data of 18-crown-6/(pentakis)urea measured at 30 K are combined, with the aim of better appreciating the electrostatics associated with intermolecular interactions in condensed matter. With two 18-crown-6 molecules and five different urea molecules in the crystal, this represents the most ambitious combined X-ray/synchrotron and neutron experimental charge density analysis to date on a cocrystal or host-guest system incorporating such a large number of unique molecules. The dipole moments of the five urea guest molecules in the crystal are enhanced considerably compared to values determined for isolated molecules, and 2D maps of the electrostatic potential and electric field show clearly how the urea molecules are oriented with dipole moments aligned along the electric field exerted by their molecular neighbors. Experimental electric fields in the range of 10-19 GV m^-1, obtained for the five different urea environments, corroborate independent measurements of electric fields in the active sites of enzymes and provide an important experimental reference point for recent discussions focused on electric-field-assisted catalysis.

Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene

Anisotropic displacement parameters (ADPs) are commonly used in crystallography, chemistry, and related fields to describe and quantify thermal motion of atoms. Within the very recent years, these ADPs have become predictable by lattice dynamics in combination with first-principles theory. Here, we study four very different molecular crystals, namely, urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene, by first-principles theory to assess the quality of ADPs calculated in the quasi-harmonic approximation. In addition, we predict both the thermal expansion and thermal motion within the quasi-harmonic approximation and compare the predictions with the experimental data. Very reliable ADPs are calculated within the quasi-harmonic approximation for all four cases up to at least 200 K, and they turn out to be in better agreement with the experiment than those calculated within the harmonic approximation. In one particular case, ADPs can even reliably be predicted up to room temperature. Our results also hint at the importance of normal-mode anharmonicity in the calculation of ADPs.

First principles crystal engineering of nonlinear optical materials. I. Prototypical case of urea

The crystalline materials with nonlinear optical (NLO) properties are critically important for several technological applications, including nanophotonic and second harmonic generation devices. Urea is often considered to be a standard NLO material, due to the combination of non-centrosymmetric crystal packing and capacity for intramolecular charge transfer. Various approaches to crystal engineering of non-centrosymmetric molecular materials were reported in the literature. Here we propose using global lattice energy minimization to predict the crystal packing from the first principles. We developed a methodology that includes the following: (1) parameter derivation for polarizable force field AMOEBA; (2) local minimizations of crystal structures with these parameters, combined with the evolutionary algorithm for a global minimum search, implemented in program USPEX; (3) filtering out duplicate polymorphs produced; (4) reoptimization and final ranking based on density functional theory (DFT) with many-body dispersion (MBD) correction; and (5) prediction of the second-order susceptibility tensor by finite field approach. This methodology was applied to predict virtual urea polymorphs. After filtering based on packing similarity, only two distinct packing modes were predicted: one experimental and one hypothetical. DFT + MBD ranking established non-centrosymmetric crystal packing as the global minimum, in agreement with the experiment. Finite field approach was used to predict nonlinear susceptibility, and H-bonding was found to account for a 2.5-fold increase in molecular hyperpolarizability to the bulk value.

New Tricks of the Trade for Crystal Structure Refinement

Accurate crystal structures and their experimental uncertainties, determined by X-ray diffraction/neutron diffraction techniques, are vital for crystal engineering studies, such as polymorph stability and crystal morphology calculations. Because of differences in crystal growth and data measurement conditions, crystallographic databases often contain multiple entries of varying quality of the same compound. The choice of the most reliable and best quality crystal structure from many very similar structures remains an unresolved problem, especially for nonexperts. In addition, while crystallographers can make use of some professional software (i.e., Materials Studio) for structure refinement, noncrystallographers may not have access to it. In the present paper, we propose a simple method to study the sensitivity of the crystal lattice energy to changes in the structural parameters, which creates a diagnostic tool to test the quality of crystal structure files and to improve the low-quality structures based on lattice energy distribution. Thus, noncrystallographers could take the proposed idea and program/optimize crystal structure by themselves. They can have their in-house program to determine the reliability of the selected crystal data and then use the best quality data or carry out structural optimization for low-quality data. The proposed method will benefit a broad cross-section of scientific researchers, especially those in solid-state and physical chemistry.

Thermal properties of molecular crystals through dispersion-corrected quasi-harmonic ab initio calculations: the case of urea

An ab initio quantum-mechanical theoretical framework is presented to compute the thermal properties of molecular crystals. The present strategy combines dispersion-corrected density-functional-theory (DFT-D), harmonic phonon dispersion, quasi-harmonic approximation to the lattice dynamics for thermal expansion and thermodynamic functions, and quasi-static approximation for anisotropic thermo-elasticity. The proposed scheme is shown to reliably describe thermal properties of the urea molecular crystal by a thorough comparison with experimental data.

Quantum crystallographic charge density of urea

Standard X-ray crystallography methods use free-atom models to calculate mean unit-cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density model of crystalline urea was calculated using high-level quantum theory and was refined against publicly available ultra-high-resolution experimental Bragg data, including the effects of atomic displacement parameters. The resulting quantum crystallographic model was compared with models obtained using spherical atom or multipole methods. Despite using only the same number of free parameters as the spherical atom model, the agreement of the quantum model with the data is comparable to the multipole model. The static, theoretical crystalline charge density of the quantum model is distinct from the multipole model, indicating the quantum model provides substantially new information. Hydrogen thermal ellipsoids in the quantum model were very similar to those obtained using neutron crystallography, indicating that quantum crystallography can increase the accuracy of the X-ray crystallographic atomic displacement parameters. The results demonstrate the feasibility and benefits of integrating fully periodic quantum charge density calculations into ultra-high-resolution X-ray crystallographic model building and refinement.

Adducts of urea with pyrazines

The adducts urea:2,3-dimethylpyrazine (1:1) (1), urea:2-methylpyrazine (2:1) (2), urea:2,6-dimethylpyrazine (2:1) (3), urea:2,5-dimethylpyrazine (2:3) (4) and urea:2,5-dimethylpyrazine (2:1) (5), together with the related adduct methylthiourea:2-methylpyrazine (1:1) (6), were prepared and their structures determined. In all cases, the basic motif of the packing is a urea (or thiourea for 6) ribbon consisting of linked R 2 2 ${\rm{R}}_2^2$ (8) rings, to which the pyrazines are often attached by bifurcated hydrogen bond systems. Adducts 1–3 present standard packing patterns of 1:1 or 2:1 urea solvates. Adduct 4 consists of layers of standard 1:1 ribbons, between which are regions of interspersed pyrazines, connected to the main layers by C–H⋯N interactions. Adduct 5 contains the standard ribbons linked by pyrazines in one direction and (urea⋯pyrazine⋯urea) spacers in the other direction. The methylthiourea adduct 6 consists of the usual ribbons with pyrazines attached by two-centre hydrogen bonds (the methyl substituent blocks the formation of bifurcated systems).

The importance of cooperative interactions and a solid-state paradigm to proteins: what Peptide chemists can learn from molecular crystals

Proteins and peptides in solution or in vivo share properties with both liquids and solids. More often than not, they are studied using the liquid paradigm rather than that of a solid. Studies of molecular crystals illustrate how the use of a solid paradigm may change the way that we consider these important molecules. Cooperative interactions, particularly those involving H-bonding, play much more important roles in the solid than in the liquid paradigms, as molecular crystals clearly illustrate. Using the solid rather than the liquid paradigm for proteins and peptides includes these cooperative interactions while application of the liquid paradigm tends to ignore or minimize them. Use of the solid paradigm has important implications for basic principles that are often implied about peptide and protein chemistry, such as the importance of entropy in protein folding and the nature of the hydrophobic effect. Understanding the folded states of peptides and proteins (especially alpha-helices) often requires the solid paradigm, whereas understanding unfolded states does not. Both theoretical and experimental studies of the energetics of protein and peptide folding require comparison to a suitable standard. Our perspective on these energetics depends on the reasonable choice of reference. The use of multiple reference states, particularly that of component amino acids in the gas phase, is proposed.

Neutron powder diffraction and theory-aided structure refinement of rubidium and cesium ureate

Urea (CN2H4O) is a fundamental biomolecule whose derivatives are abundant throughout chemistry. Among the latter, rubidium ureate (RbCN2H3O) and its cesium analog (CsCN2H3O) have been described only very recently and form the first structurally characterized salts of deprotonated urea. Here, we report on a neutron diffraction study on the aforementioned alkaline-metal ureates, which affords the positions for all hydrogen atoms (including full anisotropic displacement tensors) and thus allows us to gain fundamental insights into the hydrogen-bonding networks in the title compounds. The structure refinements of the experimental neutron data proceeded successfully using starting parameters from ab initio simulations of atomic positions and anisotropic displacement parameters. Such joint experimental-theoretical refinement procedures promise significant practical potential in cases where complex solids (organic, organometallic, framework materials) are studied by powder diffraction.

Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. I. Theory

This study demonstrates and tests the refinement of a lattice-dynamical model derived from periodic ab initio calculations at the Γ point against elastic diffraction data (X-ray or neutron). Refinement of only a handful of parameters is sufficient to obtain a similar agreement with the data as the conventional crystallographic model using anisotropic displacement parameters. By refinement against X-ray data, H displacement parameters are obtained which compare favourably with those from neutron diffraction experiments. The approach opens the door for evaluating thermodynamic properties, and for refinement against multi-temperature data, against inelastic diffraction data, spectroscopic information and thermal diffuse scattering data.

Simulating growth morphology of urea crystals from vapour and aqueous solution

The prediction of solvent-induced urea crystal growth shape from the internal and interfacial atomic structure was investigated. A computational model was used to calculate crystal growth morphologies from vapour and aqueous solution as a function of supersaturation; predicted growth shapes agree well with experimental observations.

Molecular-dynamics simulations of urea nucleation from aqueous solution

Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.

Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals

The development and application of computational methods for studying molecular crystals, particularly density-functional theory (DFT), is a large and ever-growing field, driven by their numerous applications. Here we expand on our recent study of the importance of many-body van der Waals interactions in molecular crystals [A. M. Reilly and A. Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013)], with a larger database of 23 molecular crystals. Particular attention has been paid to the role of the vibrational contributions that are required to compare experiment sublimation enthalpies with calculated lattice energies, employing both phonon calculations and experimental heat-capacity data to provide harmonic and anharmonic estimates of the vibrational contributions. Exact exchange, which is rarely considered in DFT studies of molecular crystals, is shown to have a significant contribution to lattice energies, systematically improving agreement between theory and experiment. When the vibrational and exact-exchange contributions are coupled with a many-body approach to dispersion, DFT yields a mean absolute error (3.92 kJ/mol) within the coveted "chemical accuracy" target (4.2 kJ/mol). The role of many-body dispersion for structures has also been investigated for a subset of the database, showing good performance compared to X-ray and neutron diffraction crystal structures. The results show that the approach employed here can reach the demanding accuracy of crystal-structure prediction and organic material design with minimal empiricism.

Reinvestigation of growth of urea thiosemicarbazone monohydrate crystal

The reaction of urea with thiosemicarbazide in 1:1 mole ratio in aqueous solution does not result in the formation of urea thiosemicarbazone monohydrate crystal, as reported by Hanumantharao, Kalainathan and Bhagavannarayana [Spectrochim. Acta A91 (2012) 345-351]. A reinvestigation of the reported reaction reveals that the crystal obtained is the starting material namely thiosemicarbazide, which has been unambiguously confirmed with the aid of infrared and (1)H NMR spectra and single crystal X-ray structure determination. Analysis of (1)H NMR spectrum reveals that thiosemicarbazide exhibits thione-thiol tautomerism in solution. In contrast, thiosemicarbazide exists as the thione tautomer in the solid state.