A theoretical-electron-density databank using a model of real and virtual spherical atoms

Hirshfeld atom refinement and dynamical refinement of hexagonal ice structure from electron diffraction data

Reaching beyond the commonly used spherical atomic electron density model allows one to greatly improve the accuracy of hydrogen atom structural parameters derived from X-ray data. However, the effects of atomic asphericity are less explored for electron diffraction data. In this work, Hirshfeld atom refinement (HAR), a method that uses an accurate description of electron density by quantum mechanical calculation for a system of interest, was applied for the first time to the kinematical refinement of electron diffraction data. This approach was applied here to derive the structure of ordinary hexagonal ice (Ih). The effect of introducing HAR is much less noticeable than in the case of X-ray refinement and it is largely overshadowed by dynamical scattering effects. It led to only a slight change in the O-H bond lengths (shortening by 0.01 Å) compared with the independent atom model (IAM). The average absolute differences in O-H bond lengths between the kinematical refinements and the reference neutron structure were much larger: 0.044 for IAM and 0.046 Å for HAR. The refinement results changed considerably when dynamical scattering effects were modelled - with extinction correction or with dynamical refinement. The latter led to an improvement of the O-H bond length accuracy to 0.021 Å on average (with IAM refinement). Though there is a potential for deriving more accurate structures using HAR for electron diffraction, modelling of dynamical scattering effects seems to be a necessary step to achieve this. However, at present there is no software to support both HAR and dynamical refinement.

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.

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.

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 (P_val, κ, κ′, P_lm) 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.

Fragmentation and transferability in Hirshfeld atom refinement

Hirshfeld atom refinement (HAR) is one of the most effective methods for obtaining accurate structural parameters for hydrogen atoms from X-ray diffraction data. Unfortunately, it is also relatively computationally expensive, especially for larger molecules due to wavefunction calculations. Here, a fragmentation approach has been tested as a remedy for this problem. It gives an order of magnitude improvement in computation time for larger organic systems and is a few times faster for metal-organic systems at the cost of only minor differences in the calculated structural parameters when compared with the original HAR calculations. Fragmentation was also applied to polymeric and disordered systems where it provides a natural solution to problems that arise when HAR is applied. The concept of fragmentation is closely related to the transferable aspherical atom model (TAAM) and allows insight into possible ways to improve TAAM. Hybrid approaches combining fragmentation with the transfer of atomic densities between chemically similar atoms have been tested. An efficient handling of intermolecular interactions was also introduced for calculations involving fragmentation. When applied in fragHAR (a fragmentation approach for polypeptides) as a replacement for the original approach, it allowed for more efficient calculations. All of the calculations were performed with a locally modified version of Olex2 combined with a development version of discamb2tsc and ORCA. Care was taken to efficiently use the power of multicore processors by simple implementation of load-balancing, which was found to be very important for lowering computational time.

Refinements on electron diffraction data of β-glycine in MoPro: a quest for an improved structure model

The advancement in 3D electron diffraction (3D ED) techniques that lead to a revolution in molecular structure determination using nano-sized crystals is now achieving atomic resolution. The structures can be obtained from 3D ED data with tools similar to those used for X-ray structure determination. In this context, the MoPro software, originally designed for structure and charge density refinements using X-ray diffraction data, has been adapted. Structure refinement on 3D ED data was achieved via implementation of electron scattering factors available in the literature and by application of the Mott–Bethe equation to X-ray scattering factors computed from the multipolar atom model. The multipolar model was parametrized using the transferable pseudoatom databanks ELMAM2 and UBDB. Applying the independent atom model (IAM), i.e. spherical neutral atom refinement, to 3D ED data on β-glycine in MoPro resulted in structure and refinement statistics comparable to those obtained from other well known software. Use of the transferred aspherical atom model (TAAM) led to improvement of the refinement statistics and a better fit of the model to the 3D ED data as compared with the spherical atom refinement. The anisotropic displacement parameters of non-H atoms appear underestimated by typically 0.003 Å2 for the non-H atoms in IAM refinement compared with TAAM. Thus, MoPro is shown to be an effective tool for crystal structure refinement on 3D ED data and allows use of a spherical or a multipolar atom model. Electron density databases can be readily transferred with no further modification needed when the Mott–Bethe equation is applied.

Charge density studies of multicentre two-electron bonding of an anion radical at non-ambient temperature and pressure

The variation of charge density of two-electron multicentre bonding (pancake bonding) between semi-quinone radicals with pressure and temperature was studied on a salt of 5,6-di-chloro-2,3-di-cyano-semi-quinone radical anion (DDQ) with 4-cyano-N-methyl-pyridinium cation (4-CN) using the Transferable Aspheric Atom Model (TAAM) refinement. The pancake-bonded radical dimers are stacked by non-bonding π-interactions. With rising pressure, the covalent character of interactions between radicals increases, and above 2.55 GPa, the electron density indicates multicentric covalent interactions throughout the stack. The experimental charge densities were verified and corroborated by periodic DFT computations. The TAAM approach has been tested and validated for atomic resolution data measured at ambient pressure; this work shows this approach can also be applied to diffraction data obtained at pressures up to several gigapascals.

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.

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.

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.

Polarization of Electron Density Databases of Transferable Multipolar Atoms

Polarizability is a key molecular property involved in either macroscopic (i.e., dielectric constant) and microscopic properties (i.e., interaction energies). In rigid molecules, this property only depends on the ability of the electron density (ED) to acquire electrostatic moments in response to applied electric fields. Databases of transferable electron density fragments are a cheap and efficient way to access molecular EDs. This approach is rooted in the relative conservation of the atomic ED between different molecules, termed transferability principle. The present work discusses the application of this transferability principle to the polarizability, an electron density-derived property, partitioned in atomic contributions using the Quantum Theory of Atoms In Molecules topology. The energetic consequences of accounting for in situ deformation (polarization) of database multipolar atoms are investigated in detail by using a high-quality quantum chemical benchmark.

The upcoming subatomic resolution revolution

Subatomic resolution macromolecular crystallography has been revealing the most fascinating details of macromolecular structures for many years. This most extreme form of macromolecular crystallography is going through rapid changes. A new generation of superbrilliant X-ray sources and detectors is facilitating the rapid acquisition of high-quality datasets. Equally important, a new breed of methods and highly integrated advanced computational tools for structure refinement and analysis is poised to change the way we use subatomic resolution data and reposition high-resolution macromolecular crystallography in medicinal chemistry studies. Subatomic resolution macromolecular crystallography may soon be a routine source of detailed molecular information besides precise geometries, including binding energies and other chemical descriptors, opening new possibilities of application.