Further Validation of Quantum Crystallography Approaches

Abstract

Quantum crystallography is a fast-developing multidisciplinary area of crystallography. In this work, we analyse the influence of different charge density models (i.e., the multipole model (MM), Hirshfeld atom refinement (HAR), and the transferable aspherical atom model (TAAM)), modelling of the thermal motion of hydrogen atoms (anisotropic, isotropic, and with the aid of SHADE or NoMoRe), and the type of radiation used (Mo Kα and Cu Kα) on the final results. To achieve this aim, we performed a series of refinements against X-ray diffraction data for three model compounds and compared their final structures, geometries, shapes of ADPs, and charge density distributions. Our results were also supported by theoretical calculations that enabled comparisons of the lattice energies of these structures. It appears that geometrical parameters are better described (closer to the neutron values) when HAR is used; however, bonds to H atoms more closely match neutron values after MM or TAAM refinement. Our analysis shows the superiority of the NoMoRe method in the description of H-atom ADPs. Moreover, the shapes of the ADPs of H atoms, as well as their electron density distributions, were better described with low-resolution Cu Kα data in comparison to low-resolution Mo Kα data.

Keywords: Hirshfeld atom refinement; charge density; multipole model; normal mode refinement; transferable aspherical atom model.

Figure 1

Labelling of atoms and visualisation and comparison of atomic ADPs in molecular structures of the studied compounds 1, 2, and 3 obtained with the MM and HAR–NoMoRe refinements and neutron diffraction. Anisotropic atomic displacement ellipsoids are drawn at the 50% probability level.

Figure 2

Differences between ADP values resulting from neutron and MM refinements for 1, 2, and 3. PEANUT plots for HAR_aniso, HAR_NoMoRe, HAR_SHADE, and TAAM_SHADE are available in the Supplementary Materials (Figures S27–S29). Scale is equal to 2.0. The colour red represents ADPs larger than neutron ADPs, whereas blue represents ADPs smaller than neutron ADPs. Selected values of similarity index (S_HX, where x is an atom number) were added to the plots.

Figure 3

Summary of the modelling of H atoms in the MM, HAR, and TAAM methods.

Figure 4

Fractal dimension plots for MM, HAR_SHADE, and TAAM_SHADE refinements of 1. Fractal dimension plots for all analysed compounds and methods are available in the Supplementary Materials (Figures S5–S7).

Figure 5

Comparison of the O–C bonds for IAM, MM, HAR, and TAAM refinements of 1. The values on the plot represent the difference between the analysed model and the neutron data (in Å). Plotlines have no physical meaning, but aid in visual analysis. For each plot, estimated standard deviations within +/−1 ESD are included. For comparison, plots of O–C bonds for 2 and 3 are available in the Supplementary Materials (see Figure S8).

Figure 6

Comparison of C–H bonds for MM, HAR, and TAAM refinements of 2. The values on the plot represent the difference between a given analysed model and the neutron data. Plotlines have no physical meaning, but aid in visual analysis. For clarity, +/−1 ESD intervals were added to selected bonds (C4–H4 and C5–H5B). Restraints were applied for MM and TAAM refinements. Plots for the comparison of C–H bonds in 1 and 3 are available in Supplementary Figure S11.

Figure 7

Comparison of H–C–H angles for MM, IAM, HAR, and TAAM refinements of 2. Plot values represent the difference between values obtained with the analysed model and the neutron data, in degrees. Plotlines have no physical meaning, but aid in visual analysis. For each plot, estimated standard deviations were added. Plots for the comparison of H–C–H angles for 1 and 3 are available in Supplementary Figure S26.

Figure 8

Differences between the ADPs of the neutron data and the analysed models for HAR_NoMoRe and HAR_aniso refinements of 1, 2, and 3. A two-step overlay algorithm and 2.0 scale were applied using PEANUT software. Selected similarity index values (S_HX, where x is an atom number) were added to the plots. PEANUT plots for MM, HAR_aniso, HAR_NoMoRe, HAR_SHADE, and TAAM_SHADE are available in the Supplementary Materials (Figures S27–S29).

Figure 9

Residual density maps for HAR_SHADE and TAAM_SHADE refinements of 3Mo, 3Cu, and 3-cutoff. Maps are presented with contour levels with intervals of ±0.05 eÅ⁻³. All residual density maps for the analysed compounds are available in the Supplementary Materials (Figures S2–S4).