Theoretical and experimental studies of the charge density in urea

Extension of the lattice-based aggregation-volume-bias Monte Carlo approach to molecular crystals: Quantitative calculations on the thermodynamic stability of the urea polymorphs

Motivated by the recent success in using a latticed-based version of the aggregation-volume-bias Monte Carlo method to determine the thermodynamic stabilities of both bcc and fcc clusters formed by Lennard-Jones particles, this approach is extended to the calculation of the nucleation-free energies of solid clusters formed by urea at 300 K in two different polymorphs, i.e., form I and form IV. In addition to the lattice confinement, the constraint on the molecular orientation was found necessary to ensure that the clusters sampled in these simulations are in the corresponding form. A model that can reproduce the experimental properties such as density and lattice parameters of form I at ambient conditions is used in this study. From the size dependencies of the free energies obtained for a finite set of clusters studied, the free energies of clusters at other sizes, including an infinitely large cluster, were extrapolated. At the infinite size, equivalent to a bulk solid, form I was found to be more stable than form IV, which agrees with the experimental results. In addition, form I was found to be thermodynamically stable throughout the entire cluster size range investigated here, which contradicts the previous finding that small form I clusters are unstable from the crystal nucleation simulation studies.

Assessment of GAFF and OPLS Force Fields for Urea: Crystal and Aqueous Solution Properties

Molecular simulations such as Monte Carlo, molecular dynamics, and metadynamics have been used to provide insight into crystallization phenomena, including nucleation and crystal growth. However, these simulations depend on the force field used, which models the atomic and molecular interactions, to adequately reproduce relevant material properties for the phases involved. Two widely used force fields, the General AMBER Force Field (GAFF) and the Optimized Potential for Liquid Simulations (OPLS), including several variants, have previously been used for studying urea crystallization. In this work, we investigated how well four different versions of the GAFF force field and five different versions of the OPLS force field reproduced known urea crystal and aqueous solution properties. Two force fields were found to have the best overall performance: a specific urea charge-optimized GAFF force field and the original all-atom OPLS force field. It is recommended that a suitable testing protocol involving both solution and solid properties, such as that used in this work, is adopted for the validation of force fields used for simulations of crystallization phenomena.

Crystal engineering of a co-crystal of antipyrine and 2-chlorobenzoic acid: relative energetic contributions based on multipolar refinement

The growth and stability of a new 1 : 1 antipyrene–dichlorobenzoic acid cocrystal system has been analyzed in terms of electron density analysis and electrostatic interaction energy contributions.

Dipole Moment Enhancement in Molecular Crystals from X-ray Diffraction Data

Although reliable determination of the molecular dipole moment from experimental charge density analyses on molecular crystals is a challenging undertaking, these values are becoming increasingly common experimental results. We collate all known experimental determinations and use this database to identify broad trends in the dipole moment enhancements implied by these measurements as well as outliers for which enhancements are pronounced. Compelling evidence emerges that molecular dipole moments from X-ray diffraction data can provide a wealth of information on the change in the molecular charge distribution that results from crystal formation. Most importantly, these experiments are unrivalled in their potential to provide this information in such detail and deserve to be exploited to a much greater extent. The considerable number of experimental determinations now available has enabled us to pinpoint those studies that merit further attention, either because they point unequivocally to a considerable enhancement in the crystal (of 50 % or more), or because the experimental determinations suggest enhancements of 100 % or more--much larger than independent theoretical estimates. In both cases further detailed experimental and theoretical studies are indicated.

Geometry optimization of periodic systems using internal coordinates

An algorithm is proposed for the structural optimization of periodic systems in internal (chemical) coordinates. Internal coordinates may include in addition to the usual bond lengths, bond angles, out-of-plane and dihedral angles, various "lattice internal coordinates" such as cell edge lengths, cell angles, cell volume, etc. The coordinate transformations between Cartesian (or fractional) and internal coordinates are performed by a generalized Wilson B-matrix, which in contrast to the previous formulation by Kudin et al. [J. Chem. Phys. 114, 2919 (2001)] includes the explicit dependence of the lattice parameters on the positions of all unit cell atoms. The performance of the method, including constrained optimizations, is demonstrated on several examples, such as layered and microporous materials (gibbsite and chabazite) as well as the urea molecular crystal. The calculations used energies and forces from the ab initio density functional theory plane wave method in the projector-augmented wave formalism.

Simulating micrometre-scale crystal growth from solution

Understanding crystal growth is essential for controlling the crystallization used in industrial separation and purification processes. Because solids interact through their surfaces, crystal shape can influence both chemical and physical properties. The thermodynamic morphology can readily be predicted, but most particle shapes are actually controlled by the kinetics of the atomic growth processes through which assembly occurs. Here we study the urea-solvent interface at the nanometre scale and report kinetic Monte Carlo simulations of the micrometre-scale three-dimensional growth of urea crystals. These simulations accurately reproduce experimentally observed crystal growth. Unlike previous models of crystal growth, no assumption is made that the morphology can be constructed from the results for independently growing surfaces or from an a priori specification of surface defect concentration. This approach offers insights into the role of the solvent, the degree of supersaturation, and the contribution that extended defects (such as screw dislocations) make to crystal growth. It also connects observations made at the nanometre scale, through in situ atomic force microscopy, with those made at the macroscopic level. If extended to include additives, the technique could lead to the computer-aided design of crystals.

Experimental X-ray Charge Density Studies on the Binary Carbonyls Cr(CO)6, Fe(CO)5, and Ni(CO)4

The experimental charge densities in the binary carbonyls Cr(CO)(6) (1), Fe(CO)(5) (2), and Ni(CO)(4) (3) have been investigated on the basis of high-resolution X-ray diffraction data collected at 100 K. The nature of the metal-ligand interactions has been studied by means of deformation densities and by topological analyses using the Atoms in Molecules (AIM) approach of Bader. A detailed comparison between the experimental results and theoretical results from previous work and from gas-phase and periodic DFT/B3LYP calculations shows excellent agreement, both on a qualitative and quantitative level. An examination of the kappa-restricted multipole model (KRMM) for Cr(CO)(6), using theoretically derived structure factors, showed it to provide a somewhat worse fit than a model with freely refined kappa' values. The experimental atomic graphs for the metal atoms in 2 and 3 were found to be dependent on the multipole model used for that atom. In the case of compound 2, restriction of the multipole populations according to idealized site symmetry of D(3h) gave an atomic graph in essential agreement with the theoretical gas-phase study. For compound 3, all multipole models fail to reproduce the atomic graph obtained from the theoretical gas-phase study. The atomic quadrupole moments for the C atoms in all compounds were consistent with significant pi back-donation from the metal atoms.

Urea: Anab initioand force field study of the gas and solid phases

We have studied the gaseous and solid phases of urea using both quantum mechanics calculation and force field simulation methods. Our ab initio calculations confirmed experimental observations that urea structure is planar in the crystal, but nonplanar in the gas phase. Based on electron structure analysis, we suggest that the significant difference between these two structures in different environments can be qualitatively explained by two resonance structures. The planar structure is more polarized than the nonplanar one, and the former is stabilized in the solid phases due to strong electrostatic interactions. We found classical force field method is incapable to represent such strong polarization effect. Using molecular dynamics simulations with a force field optimized for condensed phases, we calculated the crystalline structures of urea in the temperature range of 12 to 293 K. The densities as well as cell parameters are within 2% deviation from the experimental data in the temperature range.

Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning

Accurate and fast evaluation of electrostatic interactions in molecular systems is still one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry, including molecular recognition, protein modeling and drug design. One of the most convenient and accurate approaches is based on a Buckingham-type approximation that uses the multipole moment expansion of molecular/atomic charge distributions. In the mid-1980s it was shown that the pseudoatom model commonly used in experimental X-ray charge density studies can be easily combined with the Buckingham-type approach for calculation of electrostatic interactions, plus atom-atom potentials for evaluation of the total interaction energies in molecular systems. While many such studies have been reported, little attention has been paid to the accuracy of evaluation of the purely electrostatic interactions as errors may be absorbed in the semiempirical atom-atom potentials that have to be used to account for exchange repulsion and dispersion forces. This study is aimed at the evaluation of the accuracy of the calculation of electrostatic interaction energies with the Buckingham approach. To eliminate experimental uncertainties, the atomic moments are based on theoretical single-molecule electron densities calculated at various levels of theory. The electrostatic interaction energies for a total of 11 dimers of alpha-glycine, N-acetylglycine and L-(+)-lactic acid structures calculated according to Buckingham with pseudoatom, stockholder and atoms-in-molecules moments are compared with those evaluated with the Morokuma-Ziegler energy decomposition scheme. For alpha-glycine a comparison with direct "pixel-by-pixel" integration method, recently developed Gavezzotti, is also made. It is found that the theoretical pseudoatom moments combined with the Buckingham model do predict the correct relative electrostatic interactions energies, although the absolute interaction energies are underestimated in some cases. The good agreement between electrostatic interaction energies computed with Morokuma-Ziegler partitioning, Gavezzotti's method, and the Buckingham approach with atoms-in-molecules moments demonstrates that reliable and accurate evaluation of electrostatic interactions in molecular systems of considerable complexity is now feasible.

Wave functions derived from experiment. V. Investigation of electron densities, electrostatic potentials, and electron localization functions for noncentrosymmetric crystals

The constrained Hartree-Fock method using experimental X-ray diffraction data is extended and applied to the case of noncentrosymmetric molecular crystals. A new way to estimate the errors in derived properties as a derivative with respect to added Gaussian noise is also described. Three molecular crystals are examined: ammonia [NH(3)], urea [CO(NH(2))(2)], and alloxan [(CO)(4)(NH)(2)]. The energetic and electrical properties of these molecules in the crystalline state are presented. In all cases, an enhancement of the dipole moment is observed upon application of the experimental constraint. It is found that the phases of the structure factors are robustly determined by the constrained Hartree-Fock model, even in the presence of simulated noise. Plots of the electron density, electrostatic potential, and the electron localization function for the molecules in the crystal are displayed. In general, relative to the Hartree-Fock model, there is a depletion of charge around hydrogen atoms and lone pair regions, and a build-up of charge within the molecular framework near nuclei, directed along the bonds. The electron localization function plots reveal an increase in the pair density between vicinal hydrogen atoms.