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

Aspherical atom refinements on X-ray data of diverse structures including disordered and covalent organic framework systems: a time-accuracy trade-off

Aspherical atom refinement is the key to achieving accurate structure models, displacement parameters, hydrogen-bond lengths and analysis of weak interactions, amongst other examples. There are various quantum crystallographic methods to perform aspherical atom refinement, including Hirshfeld atom refinement (HAR) and transferable aspherical atom model (TAAM) refinement. Both HAR and TAAM have their limitations and advantages, the former being more accurate and the latter being faster. With the advent of non-spherical atoms in Olex2 (NoSpherA2), it is now possible to overcome some limitations, like treating disorder, twinning and network structures, in aspherical refinements using HAR, TAAM or both together. TAAM refinement in NoSpherA2 showed significant improvement in refinement statistics compared with independent atom model (IAM) refinements on a diverse set of X-ray diffraction data. The sensitivity of TAAM towards poor data quality and disorder was observed in terms of higher refinement statistics for such structures. A comparison of IAM with TAAM and HAR in NoSpherA2 indicated that the time taken by TAAM refinements was of the same order of magnitude as that taken by IAM, while in HAR the time taken using a minimal basis set was 50 times higher than for IAM and rapidly increased with increasing size of the basis sets used. The displacement parameters for hydrogen and non-hydrogen atoms were very similar in both HAR and TAAM refinements. The hydrogen-bond lengths were slightly closer to neutron reference values in the case of HAR with higher basis sets than in TAAM. To benefit from the advantages of each method, a new hybrid refinement approach has been introduced, allowing a combination of IAM, HAR and TAAM in one structure refinement. Refinement of coordination complexes involving metal-organic compounds and network structures such as covalent organic frameworks and metal-organic frameworks is now possible in a hybrid mode such as IAM-TAAM or HAR-TAAM, where the metal atoms are treated via either the IAM or HAR method and the organic part via TAAM, thus reducing the computational costs without compromising the accuracy. Formal charges on the metal and ligand can also be introduced in hybrid-mode refinement.

Refinement of anomalous dispersion correction parameters in single-crystal structure determinations

Correcting for anomalous dispersion is part of any refinement of an X-ray dif-fraction crystal structure determination. The procedure takes the inelastic scattering in the diffraction experiment into account. This X-ray absorption effect is specific to each chemical compound and is particularly sensitive to radiation energies in the region of the absorption edges of the elements in the compound. Therefore, the widely used tabulated values for these corrections can only be approximations as they are based on calculations for isolated atoms. Features of the unique spatial and electronic environment that are directly related to the anomalous dispersion are ignored, although these can be observed spectroscopically. This significantly affects the fit between the crystallographic model and the measured intensities when the excitation wavelength in an X-ray diffraction experiment is close to an element's absorption edge. Herein, we report on synchrotron multi-wavelength single-crystal X-ray diffraction, as well as X-ray absorption spectroscopy experiments which we performed on the mol-ecular compound Mo(CO)₆ at energies around the molybdenum K edge. The dispersive (f') and absorptive (f'') terms of the anomalous dispersion can be refined as independent parameters in the full-matrix least-squares refinement. This procedure has been implemented as a new feature in the well-established OLEX2 software suite. These refined parameters are in good agreement with the independently recorded X-ray absorption spectrum. The resulting crystallographic models show significant improvement compared to those employing tabulated values.

Application of the Molecular Invariom Model for the Study of Interactions Involving Fluorine Atoms in the {$${\text{Yb}}_{{\text{2}}}^{{{\text{II}}}}$$(μ2-OCH(CF3)2)3(μ3-OCH(CF3)2)2YbIII(OCH(CF3)2)2(THF)(Et2O)} Complex

Abstract

The electron density distributions obtained by the quantum-chemical (density functional theory) calculations and molecular invariom model in the trimeric ytterbium complex with the hexafluoroisopropoxide ligands {$${\text{Yb}}_{{\text{2}}}^{{{\text{II}}}}$$(μ2-OR)3(μ3-OR)2YbIII(OR)2(THF)(Et2O)} (I) (where R is CH(CF3)2, and THF is tetrahydrofuran) are compared. The main topological characteristics of the electron density at the critical points (3, –1) corresponding to the interactions of the ytterbium atoms in the coordination sphere obtained using two studied approaches demonstrate excellent agreement. The maximum divergence between the density functional calculations and molecular invariom model is observed for the intramolecular interactions involving the fluorine atoms (F···F, F···H, and F···O) in the structure of complex I. Geometry optimization leads to a higher number of these interactions in the complex. The energy corresponding to these interactions also increases. However, the main topological characteristics for the F···X interactions (X = F, H, O), which can be localized in the framework of both methods, remain within the transferability index range. An analysis of the deformation electron density shows that the Fδ–···Fδ– interactions are determined by the correspondence of the region of electron density concentration on one of the fluorine atoms to the region of electron density depletion on the second fluorine atom regardless of the method of measuring the electron density distribution.

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.

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.