Abstract
Hirshfeld atom refinement (HAR) is a novel X-ray structure refinement technique that employs aspherical atomic scattering factors obtained from stockholder partitioning of a theoretically determined tailor-made static electron density. HAR overcomes many of the known limitations of independent atom modelling (IAM), such as too short element-hydrogen distances, r(X-H), or too large atomic displacement parameters (ADPs). This study probes the accuracy and precision of anisotropic hydrogen and non-hydrogen ADPs and of r(X-H) values obtained from HAR. These quantities are compared and found to agree with those obtained from (i) accurate neutron diffraction data measured at the same temperatures as the X-ray data and (ii) multipole modelling (MM), an established alternative method for interpreting X-ray diffraction data with the help of aspherical atomic scattering factors. Results are presented for three chemically different systems: the aromatic hydro-carbon rubrene (orthorhombic 5,6,11,12-tetra-phenyl-tetracene), a co-crystal of zwitterionic betaine, imidazolium cations and picrate anions (BIPa), and the salt potassium hydrogen oxalate (KHOx). The non-hydrogen HAR-ADPs are as accurate and precise as the MM-ADPs. Both show excellent agreement with the neutron-based values and are superior to IAM-ADPs. The anisotropic hydrogen HAR-ADPs show a somewhat larger deviation from neutron-based values than the hydrogen SHADE-ADPs used in MM. Element-hydrogen bond lengths from HAR are in excellent agreement with those obtained from neutron diffraction experiments, although they are somewhat less precise. The residual density contour maps after HAR show fewer features than those after MM. Calculating the static electron density with the def2-TZVP basis set instead of the simpler def2-SVP one does not improve the refinement results significantly. All HARs were performed within the recently introduced HARt option implemented in the Olex2 program. They are easily launched inside its graphical user interface following a conventional IAM.
Highlights
X-ray diffraction experiments provide access to the thermally smeared electron-density distribution, which is generally approximated as a convolution of a static electron density with a probability density function for the motion of the nuclei (Stewart & Feil, 1980)
If the effects of chemical bonding are taken into account with non-spherical static atomic electron densities, the refined atomic positions and anisotropic displacement parameters (ADPs) may differ favourably from those obtained with the independent atom model (IAM)
It has been shown that the anisotropic displacement parameters from Hirshfeld atom refinement (HAR ADPs) for non-hydrogen atoms in three organic molecular crystals, rubrene, BIPa and KHOx, are as accurate and precise as the ADPs from multipolar refinements or from neutron diffraction data
Summary
X-ray diffraction experiments provide access to the thermally smeared electron-density distribution, which is generally approximated as a convolution of a static electron density with a probability density function for the motion of the nuclei (Stewart & Feil, 1980). If the effects of chemical bonding are taken into account with non-spherical static atomic electron densities, the refined atomic positions and anisotropic displacement parameters (ADPs) may differ favourably from those obtained with the IAM. Hydrogen–element bond distances in IAMs are underestimated by about 0.1 Abecause the single electron of the H atom has to account for both the density around the proton and that in the hydrogen– element bond. Such were some of the original motivations for introducing the so-called X–N refinements, where X-ray data are refined with hydrogen positions and ADPs fixed at the values obtained from neutron diffraction data (Coppens, 1967; Figgis et al, 1993). MM refinement of the ADPs of hydrogen atoms is possible only in exceptional cases (Zhurov et al, 2011); it is not normally considered a viable option in multipole refinements (Hoser et al, 2009)
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