On modelling disordered crystal structures through restraints from molecule-in-cluster computations, and distinguishing static and dynamic disorder

Distinguishing disorder into static and dynamic based on multi-temperature X-ray or neutron diffraction experiments is the current state of the art, but is only descriptive, not predictive. Here, several disordered structures are revisited from the Cambridge Crystallographic Data Center 'drug subset', the Cambridge Structural Database and own earlier work, where experimental intensities of Bragg diffraction data were available. Using the molecule-in-cluster approach, structures with distinguishable conformations were optimized separately, as extracted from available or generated disorder models of the respective disordered crystal structures. Re-combining these 'archetype structures' by restraining positional and constraining displacement parameters for conventional least-squares refinement, based on the optimized geometries, then often achieves a superior fit to the experimental diffraction data compared with relying on experimental information alone. It also simplifies and standardizes disorder refinement. Ten example structures were analysed. It is observed that energy differences between separate disorder conformations are usually within a small energy window of RT (T = crystallization temperature). Further computations classify disorder into static or dynamic, using single experiments performed at one single temperature, and this was achieved for propionamide.

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.

Electron densities of two cyclononapeptides from invariom application

The nonapeptides cyclo(Val-Leu-Pro-Ile-Leu-Leu-Leu-Val-Leu) (I) and cyclo(Val-Leu-Pro-Ala-Leu-Leu-Leu-Val-Leu) (II) were identified as promising candidates for the development as potential anti-cancer drugs. We report a re-refinement of deposited single-crystal X-ray diffraction data with aspherical scattering factors from the invariom database. A subsequent evaluation of the molecular electron density distribution and of the differences in their molecular electrostatic potentials provides insight in their activities. The sequences differ only in residue 4, Ile in (I) and Ala in (II). Since the anti-tumor potency is reduced for the Ala peptide (II), the causes for the differences seen in activity between (I) and (II) were examined from a structural and from an electron density (ED) point of view. The exchange at residue 4 does not lead to significant changes in molecular geometry. Molecular Hirshfeld surfaces and electrostatic potential (ESP) isosurfaces show accumulations of intermolecular interactions in regions adjacent to the Ile/Ala residues indicating preferred interactions with a potential receptor in these regions. The concentrations of intermolecular interactions were localized on the Hirshfeld surfaces through an extended basin of ED concentration close to the Ile/Ala residues. Differences in the electrostatic potentials (ESPs) between (I) and (II) were only found at the Ile/Ala site and were very close to zero otherwise.

Aspherical scattering factors for SHELXL - model, implementation and application

A new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.

Azulene revisited: solid-state structure, invariom modeling and lattice-energy minimization of a classical example of disorder

The molecular and solid-state structure of azulene both raise fundamental questions. Therefore, the disordered crystal structure of azulene was re-refined with invariom non-spherical atomic scattering factors from new single-crystal X-ray diffraction data with a resolution of d = 0.45 Å. An unconstrained refinement results in a molecular geometry with C s symmetry. Refinements constrained to fulfill C 2v symmetry, as observed in the gas phase and in high-level ab initio calculations, lead to similar figures of merit and residual densities as unconstrained ones. Such models are consistent with the structures from microwave spectroscopy and electron diffraction, albeit they are not the same. It is shown that for the disorder present in azulene, the invariom model describes valence electron density as successfully as it does for non-disordered structures, although the disorder still leads to high correlations mainly between positional parameters. Lattice-energy minimizations on a variety of ordered model structures using dispersion-corrected DFT calculations reveal that the local deviations from the average structure are small. Despite the molecular dipole moment there is no significant molecular ordering in any spatial direction. A superposition of all ordered model structures leads to a calculated average structure, which explains not only the experimental determined atomic coordinates, but also the apparently unusual experimental anisotropic displacement parameters.

The truth is out there: the metal-π interactions in crystal of Cr(CO)3(pcp) as revealed by the study of vibrational smearing of electron density

The vibrational smearing of electron density was studied in the crystal of complex of Cr(CO)3 with [2.2]paracyclophane. The combination of theoretical and experimental methods, including periodic calculations and screening of DFT calculated and multipole-decomposed electron densities, was utilized to reveal the vibrational smearing of electron density and its influence on the multipole-constructed electron density. The multipole model, commonly used to treat the high-resolution X-ray diffraction data, was shown to be rather inaccurate in description of electron density and its vibrational smearing in metal-π complex where the interchange between diatomic interactions can occur. Namely, some bond critical points can be hidden while analyzing multipole-decomposed electron density with proved effects of vibrational smearing even if the deconvolution problem is overcome by using the invariom approach. On the contrary, the recently proposed “clouds of critical point variation” (CCPV) approach is demonstrated as the route to gather all reasonable bonding trends and to reconstruct static electron density pattern in metal-π complexes.

Using invariom modelling to distinguish correct and incorrect central atoms in `duplicate structures' with neighbouring 3d elements

Modelling coordination compounds has been shown to be feasible using the invariom method; for the best fit to a given set of diffraction data, additional steps other than using lookup tables of scattering factors need to be carried out. Here such procedures are applied to a number of `duplicate structures', where structures of two or more supposedly different coordination complexes with identical ligand environments, but with different 3d metal ions, were published. However, only one metal atom can be plausibly correct in these structures, and other spectroscopic data are unavailable. Using aspherical scattering factors, a structure can be identified as correct from the deposited Bragg intensities alone and modelling only the ligand environment often suffices to make this distinction. This is not possible in classical refinements using the independent atom model. Quantum-chemical computations of the better model obtained after aspherical-atom refinement further confirm the assignment of the element in the respective figures of merit.