Atomic Refinement Research Articles

2,3,5-Tri-O-benzyl-d-xylofuranose

The synthesis and crystallization of 2,3,5-tri-O-benzyl-d-xylofuranose permitted us to isolate the alpha anomer with a small contamination of the beta form (ca 10%), whose first crystallographic structure obtained in the P212121 space group was determined at 100 K up to a resolution of sin θmax/λ = 0.71 Å−1 and refined to an R1 value of 0.0171 with a Hirshfeld atom refinement (HAR) approach.

Benzene and Borazine, so Different, yet so Similar: Insight from Experimental Charge Density Analysis.

Although benzene and borazine are isoelectronic and isostructural, they have very different electronic structures, mainly due to the polar nature of the B-N bond. Herein, we present an experimental study of the charge density distribution obtained from the multipole model formalism and Hirshfeld atom refinement (HAR) based on high-resolution X-ray diffraction data of borazine B3N3H6 (1) and B,B',B″-trichloroborazine (2) crystals. These data are compared to those obtained from HAR for benzene (4) and 1,3,5-trichlorobenzene (5) and further compared with values obtained from density functional theory calculations in the gas phase, where N,N',N″-trichloroborazine (3) was also included. The results confirm that, unlike benzene, borazines are only weakly aromatic with an island-like electronic delocalization within the B3N3 ring involving only the nitrogen atoms. Furthermore, delocalization indices and interacting quantum atom energy for bonded and non-bonded atoms were found to be highly suitable indicators capable of describing the origin of the discrepancies observed when the degree of aromaticity in 2 and 3 is evaluated using common aromaticity indices. Additionally, analysis of intermolecular interactions in the crystals brings further evidence of a weakly aromatic character of the borazines as it reveals surprising similarities between the crystal packing of borazine and benzene and also between B,B',B″-trichloroborazine and 1,3,5-trichlorobenzene.

π-Hole bonding in a new co-crystal hydrate of gallic acid and pyrazine: static and dynamic charge density analysis.

A new cocrystal hydrate of gallic acid with pyrazine (4GA, Py, 4H2O; GA4PyW4) was obtained and characterized by single crystal X-ray diffraction. In addition to structure determination, experimental charge density analysis was carried out in terms of Multipole Modelling (MP), X-ray wavefunction refinement (XWR) and maximum entropy method (MEM). As a part of XWR, the structural refinement via Hirshfeld atom refinement was carried out and resulted in O-H bond lengths close to values from neutron diffraction. A systematic comparison of molecular conformations and aromatic interactions in this new cocrystal hydrate was performed with other existing polymorphs of gallic acid. In GA4PyW4, the two symmetry-independent gallic acid molecules have a syn COOH orientation and form the common (COOH)2 dimeric synthon. The carboxyl C atom displays the characteristics of π-holes with electropositive regions above and below the molecular plane and engages in acceptor-donor interactions with oxygen atoms of acidic O-H groups and phenol groups of neighbouring gallic acid molecules. The signature of the π-hole was identified from experimental charge density analysis, both in static density maps in MP and XWR as well as dynamic density in MEM, but it cannot be pinned down to a specific atom-atom interaction. This study presents the first comparison between an XWR and a MEM experimental electron-density determination.

Hirshfeld atom refinement based on projector augmented wave densities with periodic boundary conditions.

Hirshfeld atom refinement (HAR) is an X-ray diffraction refinement method that, in numerous publications, has been shown to give H-atom bond lengths in close agreement with neutron diffraction derived values. Presented here is a first evaluation of an approach using densities derived from projector augmented wave (PAW) densities with three-dimensional periodic boundary conditions for HAR. The results show an improvement over refinements that neglect the crystal environment or treat it classically, while being on a par with non-periodic approximations for treating the solid-state environment quantum mechanically. A suite of functionals were evaluated for this purpose, showing that the SCAN and revSCAN functionals are most suited to these types of calculation.

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.

Crystal structure and Hirshfeld surface analysis of (S)-N-methyl-1-phenyl-ethan-1-aminium chloride.

The title compound C9H14N+·Cl-, (1), can be synthesized starting from (S)-N-methyl-1-phenyl-ethan-1-amine (2). Compound 2 upon addition of HCl·Et2O leads to crystallization of compound 1 as colorless blocks. The configuration of compound 1 is stable as well as preserved in space group P212121. Ammonium chlorides, like the title compound, are often observed as undesirable by-products in amino-silylation of chloro-silanes. Additionally, these by-products are usually soluble in selected organic solvents, which require difficult separation steps. Therefore, detailed studies on structural features and inter-molecular inter-actions performed by Hirshfeld atom refinement (HAR) using NoSpherA2 [Kleemiss et al. (2021 ▸). Chem. Sci. 12, 1675-1692] and Hirshfeld surface analysis were used to address structural issues on that separation problem.

Energy landscape of the SARS-CoV-2 reveals extensive conformational heterogeneity.

Cryo-electron microscopy (cryo-EM) has produced a number of structural models of the SARS-CoV-2 spike, already prompting biomedical outcomes. However, these reported models and their associated electrostatic potential maps represent an unknown admixture of conformations stemming from the underlying energy landscape of the spike protein. As with any protein, some of the spike's conformational motions are expected to be biophysically relevant, but cannot be interpreted only by static models. Using experimental cryo-EM images, we present the energy landscape of the glycosylated spike protein, and identify the diversity of low-energy conformations in the vicinity of its open (so called 1RBD-up) state. The resulting atomic refinement reveal global and local molecular rearrangements that cannot be inferred from an average 1RBD-up cryo-EM model. Here we report varied degrees of “openness” in global conformations of the 1RBD-up state, not revealed in the single-model interpretations of the density maps, together with conformations that overlap with the reported models. We discover how the glycan shield contributes to the stability of these low-energy conformations. Five out of six binding sites we analyzed, including those for engaging ACE2, therapeutic mini-proteins, linoleic acid, two different kinds of antibodies, switch conformations between their known apo- and holo-conformations, even when the global spike conformation is 1RBD-up. This apo-to-holo switching is reminiscent of a conformational preequilibrium. We found only one binding site, namely that of AB-C135 remains in apo state within all the sampled free energy-minimizing models, suggesting an induced fit mechanism for the docking of this antibody to the spike.

X-ray wavefunction refinement and comprehensive structural studies on bromo-substituted analogues of 2-deoxy-d-glucose in solid state and solution.

The structural studies on two bromo-substituted derivatives of 2-deoxy-d-glucose (2-DG), namely 2-deoxy-2-bromo-d-glucose (2-BG) and 2-deoxy-2-bromo-d-mannose (2-BM) are described. 2-DG itself is an inhibitor of hexokinase, the first enzyme in the glycolysis process, playing a vital role in both cancer cell metabolism and viral replication in host cells. Because of that, 2-DG derivatives are considered as potential anti-cancer and anti-viral drugs. An X-ray quantum crystallography approach allowed us to obtain more accurate positions of hydrogen atoms by applying Hirshfeld atom refinement, providing a better description of hydrogen bonding even in the case of data from routine X-ray experiments. Obtained structures showed that the introduction of bromine at the C2 position in the pyranose ring has a minor influence on its conformation but still, it has a noticeable effect on the crystal structure. Bromine imposes the formation of a layered supramolecular landscape containing hydrogen bonds, which involves the bromine atom. Periodic DFT calculations of cohesive and interaction energies (at the B3LYP level of theory) have supported these findings and highlighted energetic changes upon bromine substitution. Based on molecular wavefunction from the refinement, we calculated the electrostatic potential, Laplacian, and ELI-D, and applied them to charge-density studies, which confirmed the geometry of hydrogen bonding and involvement of the bromine atom with these intermolecular interactions. NMR studies in the solution show that both compounds do not display significant differences in their anomeric equilibria compared to 2-DG, and the pyranose ring puckering is similar in both aqueous and solid state.

Vanishing of the atomic form factor derivatives in non-spherical structural refinement - a key approximation scrutinized in the case of Hirshfeld atom refinement.

When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-spherical? The assumption that this particular term is very close to zero is generally made in non-spherical refinements (for example, implementations of Hirshfeld atom refinement or transferable aspherical atom models), unless the form factors are refinable parameters (for example multipole modelling). To evaluate this general approximation for one specific method, a numerical differentiation was implemented within the NoSpherA2 framework to calculate the derivatives of the structure factors in a Hirshfeld atom refinement directly as accurately as possible, thus bypassing the approximation altogether. Comparing wR2 factors and atomic parameters, along with their uncertainties from the approximate and numerically differentiating refinements, it turns out that the impact of this approximation on the final crystallographic model is indeed negligible.

H-Atom Assignment and Sb-O Bonding of [Mes3SbOH][O3SPh] Confirmed by Neutron Diffraction, Multipole Modeling, and Hirshfeld Atom Refinement.

Neutron wavelength-resolved Laue diffraction experiments permit accurate refinement of the H-atom positions and anisotropic displacement parameters of [Mes3SbOH][O3SPh]. A multipole-based charge density refinement and a topological analysis of the refined electron density were also performed. Hirshfeld atom refinement (HAR) recovers the neutron-determined H-atom parameters, and the quantum-mechanical electron density used in HAR recovers the electron density topology from the refined multipole model. These results confirm that [Mes3SbOH][O3SPh] does indeed feature a hydroxystibonium cation with a nominal Sb-O single bond and not a stibine oxide with an Sb=O/Sb+-O- bond.

Cryo-EM single-particle structure refinement and map calculation using Servalcat.

In 2020, cryo-EM single-particle analysis achieved true atomic resolution thanks to technological developments in hardware and software. The number of high-resolution reconstructions continues to grow, increasing the importance of the accurate determination of atomic coordinates. Here, a new Python package and program called Servalcat is presented that is designed to facilitate atomic model refinement. Servalcat implements a refinement pipeline using the program REFMAC5 from the CCP4 package. After the refinement, Servalcat calculates a weighted Fo - Fc difference map, which is derived from Bayesian statistics. This map helps manual and automatic model building in real space, as is common practice in crystallography. The Fo - Fc map helps in the visualization of weak features including hydrogen densities. Although hydrogen densities are weak, they are stronger than in the electron-density maps produced by X-ray crystallography, and some H atoms are even visible at ∼1.8 Å resolution. Servalcat also facilitates atomic model refinement under symmetry constraints. If point-group symmetry has been applied to the map during reconstruction, the asymmetric unit model is refined with the appropriate symmetry constraints.

The influence of refinement strategies on the wavefunctions derived from an experiment

The synergy between theory and experiment found in X-ray wavefunction refinement (XWR) makes it one of the most compelling techniques available for chemical physics. The foremost benefit of XWR – obtaining wavefunctions constrained to experimental data – is at the same time its Achilles heel, because of the dependence of the results on the quality of both empirical and theoretical data. The purpose of this work is to answer the following: What is the effect of the refinement strategy and manipulation of input data on the physical properties obtained from XWR? With that in mind, cutoffs based on data resolution and F/σ(F) ratios were applied for both steps of XWR, the Hirshfeld atom refinement (HAR) and the X-ray constrained wavefunction fitting (XCW), for four selected systems: sulfur dioxide, urea, carbamazepine and oxalic acid. The effects of changing the weighting scheme or the method to transform σ(F 2) to σ(F) were also analysed. The results show that while HAR always reaches the same result, XCW is extremely sensitive to crystallographic data manipulation. This is a result of the variability of the experimental uncertainties for different resolution shells, and of not having proper standard uncertainties. Therefore, the use of distinct constraints for each resolution interval in XCW is proposed to fix this instability.

Accurate H-atom parameters for the two polymorphs of L-histidine at 5, 105 and 295 K

The crystal structure of the monoclinic polymorph of the primary amino acid L-histidine has been determined for the first time by single-crystal neutron diffraction, while that of the orthorhombic polymorph has been reinvestigated with an untwinned crystal, improving the experimental precision and accuracy. For each polymorph, neutron diffraction data were collected at 5, 105 and 295 K. Single-crystal X-ray diffraction experiments were also performed at the same temperatures. The two polymorphs, whose crystal packing is interpreted by intermolecular interaction energies calculated using the Pixel method, show differences in the energy and geometry of the hydrogen bond formed along the c direction. Taking advantage of the X-ray diffraction data collected at 5 K, the precision and accuracy of the new Hirshfeld atom refinement method implemented in NoSpherA2 were probed choosing various settings of the functionals and basis sets, together with the use of explicit clusters of molecules and enhanced rigid-body restraints for H atoms. Equivalent atomic coordinates and anisotropic displacement parameters were compared and found to agree well with those obtained from the corresponding neutron structural models.

Revealing the medium-range structure of glassy silica using force-enhanced atomic refinement

The medium-range order structure of silicate glasses remains poorly known as it is not directly visible from conventional experiments. In turn, although atomistic simulations offer a direct access to the structure of glasses, they face several limitations, e.g., extremely high cooling rates. Here, we adopt the force-enhanced atomic refinement (FEAR) method to overcome these limitations and reveal the atomic structure of glassy silica, both at the short- and medium-range length scales. We find that FEAR yields a glass structure that simultaneously exhibits higher thermodynamic stability and enhanced agreement with experimental structure data as compared with molecular dynamics and reverse Monte Carlo simulations. Overall, we show that the increased stability enabled by FEAR primarily arises from the fact that the generated atomic configuration exhibits a more ordered medium-range structure and a lower fraction of unstable small silicate rings.

Relativistic Hirshfeld atom refinement of organo-gold(I) and organo-mercury(II) compounds

Relativistic Hirshfeld atom refinement of organo-gold(I) and organo-mercury(II) compounds

Hirshfeld atom refinement of crystal structure and Hirshfeld surface analysis of five copper(II) fenamate complexes with N,N-diethylnicotinamide

Hirshfeld atom refinement of crystal structure and Hirshfeld surface analysis of five copper(II) fenamate complexes with <i>N</i>,<i>N</i>-diethylnicotinamide

Charge-density studies of in situ crystallized liquids with Hirshfeld atom refinement, invariom model and multipole model

Charge-density studies of <i>in situ</i> crystallized liquids with Hirshfeld atom refinement, invariom model and multipole model

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.

Non-Covalent Interactions in the Biphenyl Crystal: Is the Planar Conformer a Transition State?

A combined experimental and theoretical study of the biphenyl (BP) crystal is presented. The X-ray diffraction data collected at 100 K were subjected to Hirshfeld atom and multipole refinements of the electron density, ρ(r). A theoretical exploration of the potential energy surface (PES) of the crystal was also carried out. This investigation challenges the common assumption that the planar structure of BP in the phase I crystal is an average of two twisted configurations in a double-well potential. The theoretical computations provide compelling evidence that this structure corresponds to a minimum on the PES hence to a stable molecular arrangement. Consistently, the experiment showed no evidence of positional or dynamic disorder. The intramolecular hydrogen-hydrogen bonds detected are not repulsive. The topological analysis of the experimental and theoretical ρ(r) reveals that both the intra- and intermolecular H⋅⋅⋅H and the C-H⋅⋅⋅π contacts stabilize the BP crystal.

Different Reactivities of (5-Ph2P-Ace-6-)2MeSiH toward the Rhodium(I) Chlorides [(C2H4)2RhCl]2 and [(CO)2RhCl]2. Hirshfeld Atom Refinement of a Rh–H···Si Interaction

The reaction of (5-Ph2P-Ace-6-)2MeSiH with [(C2H4)2RhCl]2 proceeded via elimination of ethylene and oxidative addition of the Si–H bond at rhodium and provided the rhodium(III) complex (5-Ph2P-Ace-6-)2MeSiRh(H)Cl (1) possessing a reverse agostic interaction of the type Rh–H···Si, which was characterized by Hirshfeld atom refinement (HAR) of single-crystal X-ray diffraction data. This technique allows the precise and accurate determination of hydrogen positions also for heavier transition-metal hydrides. The bonding situation in the Rh–H···Si interaction was further analyzed using a set of complementary bonding indicators, such as the compliance matrix analysis or real-space bonding indicators derived from the electron and electron pair densities. The reaction of (5-Ph2P-Ace-6-)2MeSiH with [(CO)2RhCl]2 occurred via elimination of hydrogen chloride and produced the rhodium(I) complex (5-Ph2P-Ace-6-)2MeSiRh(CO)2 (2).