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.

Theoretical 3D electron diffraction electrostatic potential maps of proteins modeled with a multipolar pseudoatom data bank.

The availability of atomic resolution experimental maps of electrostatic potential from 3D electron diffraction (3D ED) extends the possibility of investigating the electrostatic potential beyond the determination of non-H-atom positions. However, accurate tools to calculate this potential for macromolecules, without the use of expensive quantum calculations, are lacking. The University at Buffalo Data Bank (UBDB) gathers atom types that can be used to calculate accurate electrostatic potential maps via structure-factor calculations. Here, the transferable aspherical atom model (TAAM) is applied with UBDB to investigate theoretically obtained electrostatic potential maps of lysozyme and proteinase K, and compare them with experimental maps from 3D ED. UBDB better reproduces the molecular electrostatic potential of molecules within their entire volume compared with the neutral spherical models used in the popular independent atom model (IAM). Additionally, the theoretical electron-density maps of the studied proteins are shown and compared with the electrostatic potential maps. The atomic displacement parameters (B factors) may affect the electrostatic potential maps in a different way than in the case of electron-density maps. The computational method presented in this study could potentially facilitate the interpretation of the less resolved regions of cryo-electron microscopy density maps and pave the way for distinguishing between different ions/water molecules in the active sites of macromolecules in high-resolution structures, which is of interest for drug-design purposes.

Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Impact of Surrounding Atoms on Electron Density from Cluster Analysis.

The multipole model (MM) uses an aspherical approach to describe electron density and can be used to interpret data from X-ray diffraction in a more accurate manner than using the spherical approximation. The MATTS (multipolar atom types from theory and statistical clustering) data bank gathers MM parameters specific for atom types in proteins, nucleic acids, and organic molecules. However, it was not fully understood how the electron density of particular atoms responds to their surroundings and which factors describe the electron density in molecules within the MM. In this work, by applying clustering using descriptors available in the MATTS data bank, that is, topology and multipole parameters, we found the topology features with the biggest impact on the multipole parameters: the element of the central atom, the number of first neighbors, and planarity of the group. The similarities in the spatial distribution of electron density between and within atom type classes revealed distinct and unique atom types. The quality of existing types can be improved by adding better parametrization, definitions, and local coordinate systems. Future development of the MATTS data bank should lead to a wider range of atom types necessary to construct the electron density of any molecule.

Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Restructurization and Extension of UBDB.

A fast and accurate operational model of electron density is crucial in many scientific disciplines including crystallography, molecular biology, pharmaceutical, and structural chemistry. In quantum crystallography, the aspherical refinement of crystal structures is becoming increasingly popular because of its accurate description in terms of physically meaningful properties. The transferable aspherical atom model (TAAM) is quick and precise, though it requires a robust algorithm for atom typing and coverage of the most popular atom types present in small organic molecules. Thus, the University at Buffalo Databank (UBDB) has been renamed to the Multipolar Atom Types from Theory and Statistical clustering (MATTS) data bank, broadened, restructured, and implemented into the software DiSCaMB with 651 atom types obtained from 2316 small-molecule crystal structures containing C, H, N, O, P, S, F, Cl, and Br atoms. MATTS2021 data bank now covers most of the small molecules, peptides, RNA, DNA, and some frequently occurring cations and anions in biological, pharmaceutical, and organic materials, including the majority of known crystal structures composed of the above elements. The multipole model parameters (Pval, κ, κ', Plm) obtained for different atom types were greatly influenced by neighboring atom types, hybridization, geometrical strain in the ring system, and charges on the molecule. Contrary to previous findings, the atoms showing variable oxidation states and ions deviate from the linear dependence of monopole-derived charges on the expansion-contraction κ parameter.

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 (dmin ≤ 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.

Refinement of organic crystal structures with multipolar electron scattering factors.

A revolution in resolution is occurring now in electron microscopy arising from the development of methods for imaging single particles at cryogenic temperatures and obtaining electron diffraction data from nanocrystals of small organic molecules or macromolecules. Near-atomic or even atomic resolution of molecular structures can be achieved. The basis of these methods is the scattering of an electron beam due to the electrostatic potential of the sample. To analyse these high-quality experimental data, it is necessary to use appropriate atomic scattering factors. The independent atom model (IAM) is commonly used although various more advanced models, already known from X-ray diffraction, can also be applied to enhance the analysis. In this study a comparison is presented of IAM and TAAM (transferable aspherical atom model), the latter with the parameters of the Hansen-Coppens multipole model transferred from the University at Buffalo Databank (UBDB). By this method, TAAM takes into account the fact that atoms in molecules are partially charged and are not spherical. Structure refinements were performed on a carbamazepine crystal using electron structure-factor amplitudes determined experimentally [Jones et al. (2018). ACS Cent. Sci. 4, 1587-1592] or modelled with theoretical quantum-mechanical methods. The results show the possibilities and limitations of the TAAM method when applied to electron diffraction. Among others, the method clearly improves model fitting statistics, when compared with IAM, and allows for reliable refinement of atomic thermal parameters. The improvements are more pronounced with poorer-resolution diffraction data.

An insight into real and average structure from diffuse X-ray scattering - a case study.

Two-dimensional diffuse X-ray scattering from an organic salt [N-(3-(2,6-dimethylanilino)-1-methylbut-2-enylidene)-2,6-dimethylanilinium chloride, C21H27N2(+)Cl(-)] was interpreted with the help of an analytical model of diffuse scattering. An analysis of the relationship between symmetry and diffuse scattering for the studied system has been undertaken. The symmetry of the system explains the extinction pattern, taking the form of curves, on the diffuse scattering planes. We have also tested the relationship between the average structure model and scattering intensities. Two models, differing in their representation of overlapping atoms, were used. In the case of diffuse scattering the difference between resulting intensities is immense, while for the Bragg intensities it is much smaller. This sensitivity of diffuse scattering could potentially be used to improve the description of the average structure.

Compact multipolar representation of the electrostatic potential for flexible molecules.

A new method for generating a compact multipolar representation of the electrostatic potential (EP) for flexible molecules is presented. The method is based on a constrained minimization of the difference between the quantum mechanical and the classical EP. The fitting procedure used adopts the least absolute shrinkage and selection operator technique [R. Tibshirani, J. Roy. Stat. Soc. B 58, 267 (1996)] which can be seen as penalized ordinary least squares. The penalty function optimized for the particular molecule of interest effectively removes redundant multipoles. It is shown that the use of multiple conformations is crucial for the predictive ability of the EP model for flexible molecules. The multipole local coordinate systems are chosen in a way that best reflects the key conformational changes. It was demonstrated that such an approach improves the predictive ability of EP models. It also allows to exploit equivalence of atoms in the calculation of multipoles components. In the case of polar flexible molecules, the augmentation of the EP model based on charges by higher multipoles decreases the relative root mean square error by a factor of 1.5-5. The corresponding effect of enlargement of the set of multipoles was significantly reduced.