Refinement of K[HgI3]·H2O using non-spherical atomic form factors

The structure of K[HgI3]·H2O was redetermined at 0.70 Å resolution, and its conventional refinement is compared to a refinement using non-spherical atomic form factors.


Chemical context
It is well known that the 'independent atom model' (IAM), universally implemented in mainstream X-ray crystallography software, has the drawback of affording insufficient crystal structure models. Given that a spherical distribution of electron density around each atom is assumed, for example, by using the Cromer-Mann parameterization of the non-dispersive part of the form factors, any density involved in bonds, lone pairs and intermolecular charge transfer is completely ignored. In this context, satisfactory structure models can be obtained only on the basis of neutron diffraction data. An extreme case of discrepancy between results obtained with both radiations is the O-H bond length for the hydroxyl group in alcohols and water, which is underestimated by ca 20% by X-rays. However, neutron diffraction facilities are scarce, and even non-existent in underdeveloped countries. As a matter of fact, only 0.2% of the structures currently deposited in the CSD originate from neutron diffraction studies (Groom et al., 2016).
Within many approaches available to overcome this issue, the 'Hirshfeld atom refinement' (HAR; Capelli et al., 2014) strategy is gaining popularity. After calculating a molecular wave function for a structural model (not necessarily limited to the asymmetric unit), the electronic density functions of the so-called Hirshfeld atoms are extracted through a partitioning process (Hirshfeld, 1977), and eventually Fourier transformed, to afford non-spherical scattering factors for each individual atom in the real space and each reflection in the reciprocal space. More accurate structure factors can then be calculated during a least-squares refinement, and the full process can be iterated until convergence.
A user-friendly implementation of HAR has been recently released with OLEX2 (version 1.3) and is fully interfaced with the olex2.refine least-squares engine (Kleemiss et al., 2021). This new tool, coined as NoSpherA2 (pronounced 'Nosferatu'), is virtually universal since any element can be present in the structure. Moreover, the structure can be disordered, with atoms in special positions, squeezed with a solvent mask, or can include restrained parts. Twinned crystals can also be handled in the same way as single crystals, by computing a single wave function for each twin component. Finally, data resolution is not a concern, as long as atomic resolution is achieved [d min = 0.84 Å , corresponding to (sin /) max = 0.6 Å À1 ]. At worst, a data set with no information at all about aspherical local densities would give a Hirshfeld refinement close to that obtained with Cromer-Mann form factors.
So far, HAR has been used mainly for organic compounds, for at least two reasons. Many accurate orbital basis sets are available for light elements and, more significantly, this class of molecules is the most interesting one for such refinements: organic compounds include a large variety of chemical bonds (, , aromatic, 2c-3e bonds, etc.) and heteroatoms frequently bear electron lone pairs. The structural model obtained via HAR is thus expected to be greatly improved compared to that derived from a traditional refinement with spherical densities.
We used NoSpherA2 to refine the crystal structure of a material including both heavy and light elements, with the aim of assessing whether a non-spherical refinement is suitable and useful for such materials. The matter has been already studied for challenging compounds, namely transition-metal hydrides (Woiń ska et al., 2021;Kleemiss et al., 2021), and is now extended to an iodidomercurate hydrate, K[HgI 3 ]ÁH 2 O.

Structural commentary
The crystal structure of potassium triiodidomercurate(II) monohydrate, K[HgI 3 ]ÁH 2 O, was reported 50 years ago, using data collected on a Philips-Norelco PAILRED diffractometer, with monochromatized Mo K radiation (1542 reflections in the 0kl-10kl half-sphere; R = 0.081 for an anisotropic model omitting H atoms; Nyqvist & Johansson, 1971). The powder diffraction pattern is also deposited in the PDF-2 database, with reference PDF 00-027-0415 (Gates-Rector & Blanton, 2019). Using low-temperature data collected with Ag K radiation, we now obtained the same structure at 0.70 Å resolution in the same space group, Pna2 1 ( Fig. 1 and Table 1    Although H atoms were visible in a difference-Fourier map, the IAM refinement carried out with SHELXL (Sheldrick, 2015b) gave an odd shape for the water molecule. Hydroxyl O-H groups were then restrained to have the same bond lengths with an effective standard deviation of 0.04 Å . Rigid bond restraints with a standard deviation of 0.008 Å for 1,2 and 1,3 distances in the K/O1/H1a/H1b fragment were also applied. Both O-H bond lengths in the water molecule converged to 0.84 (11) Å , and the H-O-H angle was too acute, 87 (10) . Moreover, isotropic displacement parameters for the H1a and H1b atoms were unbalanced, 0.06 (5) and 0.18 (9) Å 2 , respectively. For this preliminary refinement, hydrogen bonds were determined with large uncertainties for O-HÁ Á ÁI angles, 160 (12) and 159 (26) .
With the hope of improving the shape of the water molecule, a non-spherical refinement was carried out using the SHELXL model as a starting point. The wave functions were calculated using ORCA with the two-component relativistic basis set x2c-TZVPP and the generalized gradient approximation PBE functional (Neese, 2018). The least-squares refinements were then carried out with olex2.refine (Bourhis et al., 2015), while keeping the same restraints as for the SHELXL refinement. For the final calculation of non-spherical form factors with NoSpherA2, a neutral dimeric cluster [KHgI 3 ÁH 2 O] 2 was used as a structure model, in order to take into account O-HÁ Á ÁI hydrogen bonds. The final refinement was done with olex2.refine (Table 1), and a comparison of the asymmetric units for the IAM and HAR refinements is given in Fig. 2.
The heavy part of the structure is almost unchanged after HAR, as expected. When comparing bonds lengths and angles, the largest difference is observed for the K-O bonds, with a shift of 0.006 Å ; for bond angles, the largest difference between the two refinements is 0.25 for the angle K1-O1-K1 i [symmetry code: (i) x + 1 2 , Ày + 1 2 , z]. Moreover, uncer-tainties for bond lengths and angles are systematically improved with HAR. Likewise, displacement parameters for Hg, I and K atoms are almost unaffected after using nonspherical form factors. In contrast, the water molecule clearly displays a more accurate shape. Bond lengths for the O-H groups are 1.07 (6) and 1.11 (7) (Ichikawa et al., 1991;Milovanović et al., 2020). These dimensions are also consistent with the shape previously described for a water molecule bridging two K + cations in a potassium aryloxide aggregate characterized by neutron diffraction at 100 K: O-H = 0.963 (16)-1.009 (16) Å and H-O-H = 108.0 (13) (Morris et al., 2007). It was possible to refine anisotropic displacement parameters for the H atoms, although it was necessary to use rigid bond restraints for the K-OH 2 group, in order to avoid non-positive definite H atoms. In the final model, displacement ellipsoids for H atoms are well balanced (Fig. 2). The final residual map is featureless, but the deformation density map in the water molecule vicinity is insightful (Fig. 3). Ellipsoid plots of the asymmetric unit for the IAM (left) and HAR (right) models, with displacement ellipsoids at the 85% probability level. For the IAM refinement, isotropic H atoms are shown as spheres of arbitrary radius, while anisotropic H atoms in the HAR panel are shown with their refined ADPs. little to the conventional IAM approximation in those parts. Finally, the Laplacian of the electron density, r 2 , also shows expected features. Electronic density is locally concentrated over the attractive covalent O-H -bonds in the water molecule (Fig. 4), while heavy atoms display r 2 x; y; z ð Þ isosurfaces with spherical symmetry.

Discussion and conclusions
Regarding the crystal structure refinement, the drop for residuals R 1 and wR 2 is marginal with a HAR compared to a IAM refinement with SHELXL, at any resolution, since the structure-factor amplitudes are dominated by the contribution of heavy scatterers, Hg and I. However, in the present case, diffraction data contain information about the non-sphericity of the form factors for the O and H atoms, warranting a HAR. Given that computational cost associated with the calculation of the wave function increases drastically for large molecular systems or large clusters of molecules, HAR may prove challenging to implement as a day-to-day routine, as long as desktop computers are used for structure refinements. However, the refinement reported here shows that an alternative would be to perform refinements through a hybrid IAM/HAR strategy, with structure factors including conventional spherical form factors for heavy atoms, and nonspherical form factors for light atoms. Obviously, this may not apply to large organic systems, like proteins, unless supercomputing is involved (Capelli et al., 2014).

Synthesis and crystallization
Caution!! Any mercury compound poses potential health risks; appropriate safety precautions and disposal procedures must be taken to handle the complexes here reported.
The compound under study was obtained as a by-product during the synthesis of Ag 2 [HgI 4 ]. A procedure to obtain Ag 2 [HgI 4 ] single crystals involves the near saturation of K 2 [HgI 4 ] with HgI 2 and AgI in an aqueous medium (Browall et al., 1974). Potassium tetraiodomercurate(II), commonly known as Nessler reagent, was obtained by dissolving 2.603 g of KI and 3.574 g of HgI 2 in an aqueous medium, following the reaction: HgI 2 + 2 KI ! K 2 [HgI 4 ]. The resulting solution was nearly saturated with HgI 2 and subsequently with AgI. The solution was kept under constant stirring for 30 min at 323 K. After that, the solution was stored in 50 ml plastic tubes in complete darkness for one month.
The crystals obtained were washed with a 2 M solution of K 2 [HgI 4 ] and distilled water. Since the process for the preparation of these compounds contains the precursors HgI 2 and KI in an aqueous medium, this also favours the crystallization of K[HgI 3 ]ÁH 2 O within a temperature range of 273-353 K (Sieskind et al., 1998). One small crystal of K[HgI 3 ]ÁH 2 O recovered from such a crystallization was used for the present study. olex2.refine 1.3 (Bourhis et al., 2015); molecular graphics: Mercury (Macrae et al., 2020) and OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: publCIF (Westrip, 2010).