Accurate Bond Lengths to Hydrogen Atoms from Single-Crystal X-ray Diffraction by Including Estimated Hydrogen ADPs and Comparison to Neutron and QM/MM Benchmarks

Tools to enable the study and translation of supramolecular amphiphiles

This tutorial review focuses on providing a summary of the key techniques used for the characterisation of supramolecular amphiphiles and their self-assembled aggregates; from the understanding of low-level molecular interactions, to materials analysis, use of data to support computer-aided molecular design and finally, the translation of this class of compounds for real world application, specifically within the clinical setting. We highlight the common methodologies used for the study of traditional amphiphiles and build to provide specific examples that enable the study of specialist supramolecular systems. This includes the use of nuclear magnetic resonance spectroscopy, mass spectrometry, X-ray scattering techniques (small- and wide-angle X-ray scattering and single crystal X-ray diffraction), critical aggregation (or micelle) concentration determination methodologies, machine learning, and various microscopy techniques. Furthermore, this review provides guidance for working with supramolecular amphiphiles in in vitro and in vivo settings, as well as the use of accessible software programs, to facilitate screening and selection of druggable molecules. Each section provides: a methodology overview - information that may be derived from the use of the methodology described; a case study - examples for the application of these methodologies; and a summary section - providing methodology specific benefits, limitations and future applications.

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.

Insights into Proton Dynamics in a Photofunctional Salt-Cocrystal Continuum: Single-Crystal X-ray, Neutron Diffraction, and Hirshfeld Atom Refinement

X-ray diffraction, neutron diffraction, and theoretical calculations were used to investigate the relationship between the optical properties and degree of protonation in acid-base complexes. We prepared five acid-base complexes by using a pyridine-modified pyrrolopyrrole derivative and salicylic acid. Two of the prepared acid-base complexes were polymorphs of guest-free crystals with green emission; the other three were guest-inclusion crystals with yellow emission containing CH₂ Cl₂ , CH₂ Br₂ , or C₂ H₄ Cl₂ . The presence or absence of guests caused the emission to change color, altering the hydrogen bond strength between the acid-base complexes. Accurate N⋅⋅⋅H distances between the pyridyl moiety and the carboxy group over the temperature range 123 to 273 K were 1.40 Å for the guest-free crystals and 1.25 Å for the guest-inclusion crystals. Our findings contribute to a better understanding of the complex relationship between photofunction and proton dynamics in acid-base complexes.

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.

A rare case of a 2:2:1 ternary cocrystal of pyridine sulfides and trithiocyanuric acid

We report a rare case of a 2:2:1 ternary cocrystal consisting of two trithiocyanuric acid molecules, two bis(pyridin-4-yl) sulfide molecules and 1,4-bis(pyridin-4-yl)tetrasulfane, namely, 1,3,5-triazinane-2,4,6-trithione-4-(pyridin-4-ylsulfanyl)pyridine-1,4-bis(pyridin-4-yl)tetrasulfane (2/2/1), 2C₃H₃N₃S₃·2C₁₀H₈N₂S·C₁₀H₈N₂S₄. This interesting crystal structure with five neutral molecules per asymmetric unit was synthesized and characterized by means of X-ray diffraction (XRD) experiments and quantum-chemical modelling. Among various specific interactions, hydrogen and halogen bridges have a significant role in stabilizing the crystal structure. In particular, the role played by stacking interactions has been revealed by structure analysis and theoretical calculations. Crystallization was spontaneous and reproducible. One of the components, 1,4-bis(pyridin-4-yl)tetrasulfane, has been characterized by XRD for the first time.

The advanced treatment of hydrogen bonding in quantum crystallography

Although hydrogen bonding is one of the most important motifs in chemistry and biology, H-atom parameters are especially problematic to refine against X-ray diffraction data. New developments in quantum crystallography offer a remedy. This article reports how hydrogen bonds are treated in three different quantum-crystallographic methods: Hirshfeld atom refinement (HAR), HAR coupled to extremely localized molecular orbitals and X-ray wavefunction refinement. Three different compound classes that form strong intra- or intermolecular hydrogen bonds are used as test cases: hydrogen maleates, the tripeptide l-alanyl-glycyl-l-alanine co-crystallized with water, and xylitol. The differences in the quantum-mechanical electron densities underlying all the used methods are analysed, as well as how these differences impact on the refinement results.

Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K

The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)max = 1.143 Å-1 are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ-3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long-range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least-squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.

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.

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.

Studying the hydrogen atom position in the strong-short intermolecular hydrogen bond of pure and 5-substituted 9-hydroxyphenalenones by invariom refinement and ONIOM cluster computations

The solid-state structures of three H-bonded enol forms of 5-substituted 9-hydroxyphenalenones were investigated to accurately determine the H atom positions of the intramolecular hydrogen bond. For this purpose, single-crystal X-ray diffraction (SC-XRD) data were evaluated by invariom-model refinement. In addition, QM/MM computations of central molecules in their crystal environment show that results of an earlier standard independent atom model refinement, which pointed to the presence of a resonance-assisted hydrogen bond in unsubstituted 9-hydroxyphenalone, are misleading: in all our three and the earlier solid-state structures the lowest energy form is that of an asymmetric hydrogen bond (CS form). Apparent differences of results from SC-XRD and other analytical methods are explained.

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.

Fast energy minimization of the CCDC drug-subset structures by molecule-in-cluster computations allows independent structure validation and model completion

Optimizing structures with computations on clusters of molecules permits generation of structure-specific restraints for refinement and structure validation.

User-Friendly Quantum Mechanics: Applications for Drug Discovery

Quantum mechanics (QM) methods provide a fine description of receptor-ligand interactions and of chemical reactions. Their use in drug design and drug discovery is increasing, especially for complex systems including metal ions in the binding sites, for the design of highly selective inhibitors, for the optimization of bi-specific compounds, to understand enzymatic reactions, and for the study of covalent ligands and prodrugs. They are also used for generating molecular descriptors for predictive QSAR/QSPR models and for the parameterization of force fields. Thanks to the continuous increase of computational power offered by GPUs and to the development of sophisticated algorithms, QM methods are becoming part of the standard tools used in computer-aided drug design (CADD). We present the most used QM methods and software packages, and we discuss recent representative applications in drug design and drug discovery.

Hydrogen atoms in bridging positions from quantum crystallographic refinements: influence of hydrogen atom displacement parameters on geometry and electron density

Hydrogen atom positions can be obtained accurately from X-ray diffraction data of hydrogen maleate salts via Hirshfeld atom refinement.

Fast and Accurate Quantum Crystallography: From Small to Large, from Light to Heavy

The coupling of the crystallographic refinement technique Hirshfeld atom refinement (HAR) with the recently constructed libraries of extremely localized molecular orbitals (ELMOs) gives rise to the new quantum-crystallographic method HAR-ELMO. This method is significantly faster than HAR but as accurate and precise, especially concerning the free refinement of hydrogen atoms from X-ray diffraction data, so that the first fully quantum-crystallographic refinement of a protein is presented here. However, the promise of HAR-ELMO exceeds large molecules and protein crystallography. In fact, it also renders possible electron-density investigations of heavy elements in small molecules and facilitates the detection and isolation of systematic errors from physical effects.

Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)₂] and dicyanomercury(II) [Hg(CN)₂]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)₂ and Hg(CN)₂, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

Role of H-Optimization in the Computed Intermolecular Interactions and Charge-Transfer Integrals in Diketopyrrolopyrroles

Small organic conjugated systems displaying one-dimensional stacking motifs in the solid state that facilitate charge propagation are highly desirable. Noncovalent interactions, although weak, can synergistically provide those supramolecular architectures with large binding energies and associated thermal integrity. Amongst the plethora of intermolecular interactions contributing toward the overall lattice energy and stability of the charge-propagation supramolecular architectures, H-bonding interactions are well-known to play a pivotal role. Despite their critical contribution, the positions of hydrogen atoms in X-ray crystallographic data are parameterized, which can lead to significant changes in the computed intermolecular interactions. Herein, we report for the first time an analysis of the role that the optimization of the H atoms in X-ray structures has in the computed intermolecular interactions energies in diketopyrrolopyrroles (DPPs). A large dataset comprising 94 dimer pairs from 19 different DPP-based systems, including three pigment analogues, was employed. In total, more than 1400 H-X chemical bonds were considered and optimized using the M06-2X density functional at the 6-311G(d) level. Intermolecular interactions were computed for the H-optimized geometries and compared to those from nonoptimized counterparts. We report that in 35 out of the 94 dimer pairs investigated (37%), the computed intermolecular interactions were at least 2.5 kJ mol^-1 larger on progression to the H-optimized geometries. In turn, lower computed values were yielded upon H-optimization computed for 8 out of the 94 dimer pairs (8%), with one case exhibiting a difference greater than 2.5 kJ mol^-1. In line with the negligible changes to electron density and wavefunction overlap, the computed changes on the transfer integrals for the hole and electron were always lower than 1 kJ mol^-1. The observed changes to computed intermolecular interactions can play a critical role in determining the thermal integrity of the supramolecular structures and charge propagation channels, and thus in the absence of neutron diffraction data, H atoms should be optimized prior to computation. We envisage that the results herein will be of interest to the extensive scientific community devoted to the understanding of intermolecular interactions in organic conjugated systems and the realization of superior charge-transfer-mediating materials, and given the plethora of intermolecular interactions investigated, the results are not solely limited to DPP-based architectures.

Complementary bonding analysis of the N–Si interaction in pentacoordinated silicon compounds using quantum crystallography

The unique combination of quantum crystallography and complementary bonding analysis is used to investigate the bonding of pentacoordinated silicon atoms.

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.

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

The robust, readily available cobalt(iii) trication [Co(NH2CHPhCHPhNH2)3]3+ is a progenitor of broadly applicable chirality and prochirality sensing agents

When NMR spectra of chiral racemic organic molecules containing a Lewis basic functional group are recorded in the presence of air and water stable salts of the cobalt(iii) trication [Co((S,S)-NH2CHPhCHPhNH2)3]3+ (23+), separate signals are usually observed for the enantiomers (28 diverse examples, >12 functional groups). Several chiral molecules can be simultaneously analyzed, and enantiotopic groups in prochiral molecules differentiated (16 examples). Particularly effective are the mixed bis(halide)/tetraarylborate salts Λ-23+ 2X-BArf- (X = Cl, I; BArf = B(3,5-C6H3(CF3)2)4), which are applied in CD2Cl2 or CDCl3 at 1-100 mol% (avg 34 and 14 mol%). Job plots establish 1 : 1 binding for Λ-23+ 2Cl-BArf- and 1-phenylethyl acetate (4) or 1-phenylethanol (10), and ca. 1 : 2 binding with DMSO (CD2Cl2). Selected binding constants are determined, which range from 7.60-2.73 M-1 for the enantiomers of 10 to 28.1-22.6 M-1 for the enantiomers of 4. The NH moieties of the C2 faces of the trication are believed to hydrogen bond to the Lewis basic functional groups, as seen in the crystal structure of a hexakis(DMSO) solvate of Λ-23+ 3I-. These salts rank with the most broadly applicable chirality sensing agents discovered to date.

Intra-electron transfer induced by protonation in copper-containing nitrite reductase

Electron transfer between two Cu sites in the enzyme induced by protonation of remote catalytic residues.

Validation of X-ray Wavefunction Refinement

In this work, the quality of the electron density in crystals reconstructed by the multipolar model (MM) and by X-ray wavefunction refinement (XWR) is tested on a set of high-resolution X-ray diffraction data sets of four amino acids and six tripeptides. It results in the first thorough validation of XWR. Agreement statistics, figures of merit, residual- and deformation-density maps, as well as atomic displacement parameters are used to measure the quality of the reconstruction relative to the measured structure factors. Topological analysis of the reconstructed density is carried out to obtain atomic and bond-topological properties, which are subsequently compared to the values derived from benchmarking periodic DFT geometry optimizations. XWR is simultaneously in better agreement than the MM with both benchmarking theory and the measured diffraction pattern. In particular, the obvious problems with the description of polar bonds in the MM are significantly reduced by using XWR. Similarly, modeling of electron density in the vicinity of hydrogen atoms with XWR is visibly improved.

Experimental charge-density studies: data reduction and model quality: the more the better?

In this review, recent developments concerning data and model quality in experimental charge-density investigations from a personal view-point are described. Data quality is not only achieved by the high resolution, high I/σ(I) values, low merging R values and high multiplicity. The quality of the innermost reflections especially is crucial for mapping the density distribution of the outermost valence electrons and can be monitored by (I/σ)^asymptotic. New detector technologies seem to be promising improvements. Empirical corrections to correct for low-energy contamination of mirror-focused X-ray data and for resolution- and temperature-dependent errors caused by factors such as thermal diffuse scattering are described. Shashlik-like residual density patterns can indicate the need for an anharmonic description of the thermal motion of individual atoms. The physical reliability of the derived model must be thoroughly analysed. The derived probability density functions for the mean-squared atomic vibrational displacements especially should have only small negative values. The treatment of H atoms has been improved by methods to estimate anisotropic thermal motion. For very high resolution data, the polarization of the core density cannot be neglected. Several tools to detect systematic errors are described. A validation tool is presented that easily detects when the refinement of additional parameters yields a real improvement in the model or simply overfits the given data. In all investigated structures, it is proved that the multipole parameters of atoms with a comparable chemical environment should be constrained to be identical. The use of restraints could be a promising alternative.

Quantum crystallography

Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.

Accurate Bond Lengths to Hydrogen Atoms from Single-Crystal X-ray Diffraction by Including Estimated Hydrogen ADPs and Comparison to Neutron and QM/MM Benchmarks

Amino acid structures are an ideal test set for method-development studies in crystallography. High-resolution X-ray diffraction data for eight previously studied genetically encoding amino acids are provided, complemented by a non-standard amino acid. Structures were re-investigated to study a widely applicable treatment that permits accurate X-H bond lengths to hydrogen atoms to be obtained: this treatment combines refinement of positional hydrogen-atom parameters with aspherical scattering factors with constrained "TLS+INV" estimated hydrogen anisotropic displacement parameters (H-ADPs). Tabulated invariom scattering factors allow rapid modeling without further computations, and unconstrained Hirshfeld atom refinement provides a computationally demanding alternative when database entries are missing. Both should incorporate estimated H-ADPs, as free refinement frequently leads to over-parameterization and non-positive definite H-ADPs irrespective of the aspherical scattering model used. Using estimated H-ADPs, both methods yield accurate and precise X-H distances in best quantitative agreement with neutron diffraction data (available for five of the test-set molecules). This work thus solves the last remaining problem to obtain such results more frequently. Density functional theoretical QM/MM computations are able to play the role of an alternative benchmark to neutron diffraction.