Comparison of different strategies for modelling hydrogen atoms in charge density analyses

The quality of various approximation methods for modelling anisotropic displacement parameters (ADPs) for hydrogen atoms was investigated in a comparative study. A multipole refinement was performed against high-resolution single crystal X-ray data of 9-diphenylthiophosphoranylanthracene (SPAnH) and 9,10-bis-diphenylthiophosphoranylanthracene·toluene (SPAnPS). Hydrogen-atom parameters and structural properties derived from our collected neutron data sets were compared with those obtained from the SHADE-server, the software APD-Toolkit based on the invariom database, the results from Hirshfeld atom refinement conducted in the OLEX2 GUI (HARt), and the results of anisotropic hydrogen refinement within XD2016. Additionally, a free refinement of H-atom positions against X-ray data was performed with fixed ADPs from various methods. The resulting C—H bond distances were compared with distances from neutron diffraction experiments and the HARt results. Surprisingly, the refinement of anisotropic hydrogen displacement parameters against the X-ray data yielded the smallest deviations from the neutron values. However, the refinement of bond-directed quadrupole parameters turned out to be vital for the quality of the resulting ADPs. In both model structures, SHADE and, to a lesser extent, APD-Toolkit showed problems in dealing with atoms bonded to carbon atoms with refined Gram-Charlier parameters for anharmonic motion. The HARt method yields the most accurate C—H bond distances compared to neutron data results. Unconstrained refinement of hydrogen atom positions using ADPs derived from all other used approximation methods showed that even with well approximated hydrogen ADPs, the resulting distances were still significantly underestimated.

CAPOW: a standalone program for the calculation of optimal weighting parameters for least-squares crystallographic refinements

The rigorous analysis of crystallographic models, refined through the use of least-squares minimization, is founded on the expectation that the data provided have a normal distribution of residuals. Processed single-crystal diffraction data rarely exhibit this feature without a weighting scheme being applied. These schemes are designed to reflect the precision and accuracy of the measurement of observed reflection intensities. While many programs have the ability to calculate optimal parameters for applied weighting schemes, there are still programs that do not contain this functionality, particularly when moving beyond the spherical atom model. For this purpose,CAPOW(calculation and plotting of optimal weights), a new program for the calculation of optimal weighting parameters for aSHELXLweighting scheme, is presented and an example of its application in a multipole refinement is given.

Validation of experimental charge-density refinement strategies: when do we overfit?

A cross-validation method is supplied to judge between various strategies in multipole refinement procedures. Its application enables straightforward detection of whether the refinement of additional parameters leads to an improvement in the model or an overfitting of the given data. For all tested data sets it was possible to prove that the multipole parameters of atoms in comparable chemical environments should be constrained to be identical. In an automated approach, this method additionally delivers parameter distributions ofkdifferent refinements. These distributions can be used for further error diagnostics,e.g.to detect erroneously defined parameters or incorrectly determined reflections. Visualization tools show the variation in the parameters. These different refinements also provide rough estimates for the standard deviation of topological parameters.

An analysis of the experimental and theoretical charge density distributions of the piroxicam–saccharin co-crystal and its constituents

Experimental and theoretical charge density of piroxicam, saccharin and their 1 : 1 co-crystal have been determined using high-resolution X-ray diffraction, multipole refinement and DFT calculations

Charge density investigations on [2,2]-paracyclophane – in data we trust

Four datasets on [2,2]-paracyclophane were collected in-house and at the Advanced Photon Source at two different temperatures for charge density investigation. Global data quality indicators such as high resolution, highI/σ(I) values, low mergingRvalues and high multiplicity were matched for all four datasets. The structural parameters did not show significant differences, but the synchrotron data depicted deficiencies in the topological analysis. In retrospect these deficiencies could be assigned to the low quality of the innermost data, which could have been identified bye.g.mergingRvalues for only these reflections. In the multipole refinement these deficiencies could be monitored usingDRK-plotand residual density analysis. In this particular example the differences in the topological parameters were relatively small but significant.

Experimental and theoretical charge density distribution in Pigment Yellow 101

The charge density distribution in 2,2′-dihydroxy-1,1′-naphthalazine (Pigment Yellow 101; P.Y.101) has been determined using high-resolution X-ray diffraction and multipole refinement, along with density functional theory calculations.

Reassessment of the electron density in Cu2O using γ-ray diffraction

The electron-density distribution in Cu2O has been critically reexamined to test controversial conclusions from earlier experimental and theoretical studies. The electron density is derivedviamultipole refinement of high-quality single-crystal diffraction data, collected at room temperature with 316.5 keV gamma radiation. Four γ-lines in the energy range 200–600 keV have been used to extrapolate extinction-free low-order structure factors. The remaining extinction corrections refine to a crystal mosaicity identical to the observed one. There is no support for anharmonic contributions to the thermal parameters. Important features of the derived electron density are (i) a partially filled d_{z^2} orbital, (ii) an incomplete ionization of Cu and O, and (iii) no interstitial Cu–Cu charge pileup, thereby refuting the covalent bonding hypothesis.

Charge-density distribution in sodium bis(4-nitrophenyl)phosphate

The electron-density distribution in sodium bis(4-nitrophenyl)phosphate has been analyzed using the multipole refinement of X-ray diffraction data and of theoretical density-functional theory (DFT) calculations. The ester P—O bonds are particularly long and their topological parameters (density at the bond critical point, Laplacian) are lower than for other P—O bonds. Some disagreement between the experimental and theoretical charges of atoms constituting the nitro groups has been observed and the possible reasons are discussed. Weak polarization effects produced by sodium cations may be observed within the phosphate fragment; they are more manifest in the case of the nitro groups.