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

The crystal structure model for potassium tri­iodido­mercurate(II) monohydrate, K[HgI₃]·H₂O, based on single-crystal data, was reported 50 years ago [Nyqvist & Johansson (1971). Acta Chem. Scand. 25, 1615–1629]. We have now redetermined this structure with X-ray diffraction data at 0.70 Å resolution collected at 153 K using Ag Kα radiation. Combined quantum mechanical methods (ORCA) and computation of non-spherical scattering form factors (NoSpherA2) allowed the refinement of the shape of the water mol­ecule with anisotropic H atoms, despite the presence of heavy elements in the crystal. The refined shape of the water mol­ecule via this Hirshfeld refinement is close to that determined for liquid water by neutron diffraction experiments. Moreover, the Laplacian of the electron density clearly shows how electron density accumulates along the O—H σ-valence bonds in the water mol­ecule.

1. 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 θ/λ)_max = 0.6 Å⁻¹]. 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 (σ, π, 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 (Woińska et al., 2021; Kleemiss et al., 2021), and is now extended to an iodido­mercurate hydrate, K[HgI₃]·H₂O.

2. Structural commentary

The crystal structure of potassium tri­iodido­mercurate(II) monohydrate, K[HgI₃]·H₂O, 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 Kα radiation, we now obtained the same structure at 0.70 Å resolution in the same space group, Pna2₁ (Fig. 1 and Table 1). The Hg atoms form distorted [HgI₄] tetra­hedra sharing one corner and giving a chain structure along the a-axis direction. Water mol­ecules bridge K⁺ cations and are sandwiched between these chains, at normal distances, K—OH₂ ≃ 2.75 Å. The cations are seven-coordinate, a common coordination number for K⁺, characterized by its large ionic radius. The three-dimensional structure is completed by K⁺ cations bridg­ing [HgI₄] tetra­hedra in neighbouring chains. The water mol­ecules are oriented in such a way that O—H⋯I hydrogen bonds are formed with two I atoms on the edge of an [HgI₄] tetra­hedron.

Table 1
Experimental details

Crystal data
Chemical formula	K[HgI3]·H2O
Mr	638.41
Crystal system, space group	Orthorhombic, Pna21
Temperature (K)	153
a, b, c (Å)	8.5810 (2), 9.2648 (3), 11.4073 (4)
V (Å^3)	906.89 (5)
Z	4
Radiation type	Ag Kα, λ = 0.56083 Å
μ (mm^−1)	14.87
Crystal size (mm)	0.06 × 0.05 × 0.03
Data collection
Diffractometer	Stoe Stadivari
Absorption correction	Multi-scan (X-AREA; Stoe & Cie, 2019)
Tmin, Tmax	0.064, 0.132
No. of measured, independent and observed [I > 2σ(I)] reflections	29699, 2720, 2179
Rint	0.070
(sin θ/λ)max (Å^−1)	0.714
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.021, 0.038, 0.87
No. of reflections	2720
No. of parameters	74
No. of restraints	21
H-atom treatment	All H-atom parameters refined
Δρmax, Δρmin (e Å^−3)	1.17, −1.26
Absolute structure	Flack (1983)
Absolute structure parameter	0.033 (11)
Computer programs: X-AREA (Stoe & Cie, 2019), SHELXT2018/2 (Sheldrick, 2015a), olex2.refine 1.3 (Bourhis et al., 2015), OLEX2 (Dolomanov et al., 2009), Mercury (Macrae et al., 2020) and publCIF (Westrip, 2010).

Figure 1 Part of the crystal structure of the title compound. Colour code: orange = [HgI4] tetra­hedra, purple = I, green = K, red = O, pale green = H.

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) Ų, respectively. For this preliminary refinement, hydrogen bonds were determined with large uncertainties for O—H⋯I 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 [KHgI₃·H₂O]₂ was used as a structure model, in order to take into account O—H⋯I 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.

Figure 2 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.

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—K1ⁱ [symmetry code: (i) x + , −y + , z]. Moreover, uncertainties for bond lengths and angles are systematically improved with HAR. Likewise, displacement parameters for Hg, I and K atoms are almost unaffected after using non-spherical 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) Å for the HAR model, with an H—O—H angle of 107 (8)°. For liquid water, neutron diffraction experiments afforded O—H = 0.970 ± 0.005 Å and H—O—H = 106.1 ± 1.8° (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—OH₂ 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). A positive density close to the O atom reflects the presence of electron lone pairs, while a negative density centred on the H-atom sites indicates the positively charged character of the H atoms, as a consequence of the difference of electronegativity with the O atom. A diffuse positive density is even visible at the midpoint of the O—H bonds, related to the contribution of the covalent σ-bonds to non-spherical densities. Beyond features observed for the water mol­ecule, the deformation map is flat, confirming that a Hirshfeld refinement adds very little to the conventional IAM approximation in those parts. Finally, the Laplacian of the electron density, , also shows expected features. Electronic density is locally concentrated over the attractive covalent O—H σ-bonds in the water mol­ecule (Fig. 4), while heavy atoms display iso­surfaces with spherical symmetry.

Figure 3 HAR – IAM dynamic deformation density map in the plane of the water mol­ecule. Isolevel contours for positive density (e^−/A^3) are displayed as solid lines with the map coloured blue, while isolevel contours for negative density are displayed as dashed lines, with the map coloured red. The map was plotted with OLEX2 (Dolomanov et al., 2009).

Figure 4 Three-dimensional wire map of the Laplacian of the electron density in the vicinity of the water mol­ecule, at ±0.25 e^−/Å^5 level. The positive isosurfaces (green) show where electron density depletion occurs (valence-atomic orbital regions), while negative isosurfaces (red) show regions where electron density accumulates (bonding-electrons energy densities). The map was calculated on a 0.05 Å grid in real space and was generated with OLEX2 (Dolomanov et al., 2009).

3. Discussion and conclusions

Regarding the crystal structure refinement, the drop for resid­uals R₁ and wR₂ 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 non-spherical form factors for light atoms. Obviously, this may not apply to large organic systems, like proteins, unless super-computing is involved (Capelli et al., 2014).

4. 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 Ag₂[HgI₄]. A procedure to obtain Ag₂[HgI₄] single crystals involves the near saturation of K₂[HgI₄] with HgI₂ 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 HgI₂ in an aqueous medium, following the reaction: HgI₂ + 2 KI → K₂[HgI₄]. The resulting solution was nearly saturated with HgI₂ 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 K₂[HgI₄] and distilled water. Since the process for the preparation of these compounds contains the precursors HgI₂ and KI in an aqueous medium, this also favours the crystallization of K[HgI₃]·H₂O within a temperature range of 273–353 K (Sieskind et al., 1998). One small crystal of K[HgI₃]·H₂O recovered from such a crystallization was used for the present study.

5. Refinement details

Crystal data, data collection, and structure refinement details for the last least-squares cycle of olex2.refine are summarized in Table 1. All atoms were refined anisotropically. In the water mol­ecule, O—H bonds were restrained to have the same length, with a 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—OH₂ fragment were also applied.

Supporting information

Computing details

Data collection: X-AREA (Stoe & Cie, 2019); cell refinement: X-AREA (Stoe & Cie, 2019); data reduction: X-AREA (Stoe & Cie, 2019); program(s) used to solve structure: SHELXT2018/2 (Sheldrick, 2015a); program(s) used to refine structure: 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).

Potassium triiodidomercurate(II) monohydrate

Crystal data

K[HgI3]·H2O	Dx = 4.676 Mg m^−3
Mr = 638.41	Ag Kα radiation, λ = 0.56083 Å
Orthorhombic, Pna21	Cell parameters from 25947 reflections
a = 8.5810 (2) Å	θ = 2.2–30.8°
b = 9.2648 (3) Å	µ = 14.87 mm^−1
c = 11.4073 (4) Å	T = 153 K
V = 906.89 (5) Å^3	Block, colourless
Z = 4	0.06 × 0.05 × 0.03 mm
F(000) = 1072

Data collection

Stoe Stadivari diffractometer	2720 independent reflections
Radiation source: Sealed X-ray tube, Axo Astix-f Microfocus source	2179 reflections with I > 2σ(I)
Graded multilayer mirror monochromator	Rint = 0.070
Detector resolution: 5.81 pixels mm^-1	θmax = 23.6°, θmin = 2.2°
ω scans	h = −12→12
Absorption correction: multi-scan (X-AREA; Stoe & Cie, 2019)	k = −13→13
Tmin = 0.064, Tmax = 0.132	l = −16→16
29699 measured reflections

Refinement

Refinement on F^2	Hydrogen site location: difference Fourier map
Least-squares matrix: full	All H-atom parameters refined
R[F^2 > 2σ(F^2)] = 0.021	w = 1/[σ^2(Fo^2) + (0.0157P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.038	(Δ/σ)max = 0.0003
S = 0.87	Δρmax = 1.17 e Å^−3
2720 reflections	Δρmin = −1.25 e Å^−3
74 parameters	Extinction correction: SHELXL2018/3 (Sheldrick 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
21 restraints	Extinction coefficient: 0.00015 (5)
0 constraints	Absolute structure: Flack (1983)
Primary atom site location: dual	Absolute structure parameter: 0.033 (11)
Secondary atom site location: difference Fourier map

Special details

Refinement. Refinement using NoSpherA2, an implementation of NOn-SPHERical Atom-form-factors in Olex2. Please cite: F. Kleemiss et al. DOI 10.1039/D0SC05526C - 2020 NoSpherA2 implementation of HAR makes use of tailor-made aspherical atomic form factors calculated on-the-fly from a Hirshfeld-partitioned electron density (ED) - not from spherical-atom form factors.

The ED is calculated from a gaussian basis set single determinant SCF wavefunction - either Hartree-Fock or DFT using selected funtionals - for a fragment of the crystal. This fregment can be embedded in an electrostatic crystal field by employing cluster charges. The following options were used: SOFTWARE: ORCA PARTITIONING: NoSpherA2 INT ACCURACY: High METHOD: PBE BASIS SET: x2c-TZVPP CHARGE: 0 MULTIPLICITY: 1 RELATIVISTIC: DKH2 DATE: 2021-04-12_22-39-08

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Hg1	0.25561 (3)	0.70101 (2)	0.500694 (18)	0.02464 (6)
I1	0.25904 (7)	0.42035 (5)	0.56854 (3)	0.02692 (9)
I2	0.49597 (5)	0.77133 (3)	0.33996 (3)	0.01831 (7)
I3	0.23628 (7)	0.92253 (5)	0.65827 (3)	0.02791 (10)
K1	0.44530 (17)	0.15898 (17)	0.3610 (2)	0.0413 (4)
O1	0.6331 (5)	0.4017 (5)	0.3698 (5)	0.0321 (11)
H1a	0.634 (12)	0.437 (11)	0.459 (6)	0.034 (16)
H1b	0.607 (14)	0.498 (9)	0.316 (9)	0.06 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Hg1	0.02658 (10)	0.02249 (10)	0.02484 (11)	−0.00072 (11)	0.00067 (13)	−0.00180 (11)
I1	0.0331 (2)	0.0247 (2)	0.02295 (19)	−0.0019 (2)	−0.0010 (2)	0.00594 (16)
I2	0.01527 (15)	0.02130 (15)	0.01837 (17)	0.00014 (15)	−0.00029 (16)	0.0012 (2)
I3	0.0337 (2)	0.0264 (2)	0.0236 (2)	0.0034 (2)	−0.0026 (3)	−0.00697 (17)
K1	0.0251 (7)	0.0278 (7)	0.0711 (13)	0.0039 (5)	−0.0017 (8)	0.0034 (9)
O1	0.030 (2)	0.020 (2)	0.047 (3)	0.0026 (18)	0.002 (2)	−0.002 (2)
H1a	0.02 (4)	0.04 (2)	0.047 (10)	0.007 (15)	0.002 (7)	−0.005 (5)
H1b	0.10 (5)	0.021 (16)	0.05 (2)	0.001 (11)	−0.017 (16)	−0.003 (8)

Geometric parameters (Å, º)

Hg1—I1	2.7131 (5)	I3—K1^iv	3.659 (2)
Hg1—I2	2.8356 (5)	I3—K1^v	3.7067 (19)
Hg1—I2^i	2.8968 (5)	K1—O1^ii	2.739 (5)
Hg1—I3	2.7333 (5)	K1—O1	2.769 (5)
I1—K1^ii	3.6595 (19)	O1—H1a	1.07 (6)
I1—K1	3.745 (2)	O1—H1b	1.11 (7)
I2—K1^iii	3.6257 (16)
I3—Hg1—I1	122.189 (16)	I2^vii—K1—I1	137.19 (6)
I2—Hg1—I1	113.375 (16)	I1^viii—K1—I1	92.00 (5)
I3—Hg1—I2	107.267 (15)	I3^ix—K1—I1	148.42 (5)
I2^i—Hg1—I1	105.885 (15)	I3^x—K1—I1	77.82 (3)
I3—Hg1—I2^i	107.648 (15)	O1^ii—K1—I2^vii	85.19 (10)
I2—Hg1—I2^i	97.460 (14)	O1—K1—I2^vii	137.50 (10)
K1^ii—I1—Hg1	90.00 (3)	O1^ii—K1—I1^viii	130.89 (15)
K1—I1—Hg1	116.37 (3)	O1—K1—I1^viii	73.23 (12)
K1^iii—I2—Hg1	95.60 (3)	O1^ii—K1—I3^ix	135.32 (15)
K1^iii—I2—Hg1^vi	87.86 (3)	O1—K1—I3^ix	75.86 (11)
K1^iv—I3—Hg1	102.44 (3)	O1^ii—K1—I3^x	75.34 (12)
K1^v—I3—Hg1	86.63 (3)	O1—K1—I3^x	74.46 (12)
K1—I1—K1^ii	77.01 (4)	O1^ii—K1—I1	72.08 (12)
K1^iv—I3—K1^v	77.50 (4)	O1—K1—I1	72.56 (11)
Hg1—I2—Hg1^vi	99.816 (14)	K1—O1—K1^viii	113.65 (15)
I2^vii—K1—I1^viii	75.86 (3)	O1^ii—K1—O1	137.29 (12)
I3^ix—K1—I2^vii	70.37 (3)	H1a—O1—K1^viii	95 (5)
I3^ix—K1—I1^viii	79.52 (3)	H1a—O1—K1	106 (6)
I3^x—K1—I2^vii	131.42 (6)	H1b—O1—K1^viii	110 (6)
I3^x—K1—I1^viii	147.69 (5)	H1b—O1—K1	121 (6)
I3^ix—K1—I3^x	93.18 (5)	H1b—O1—H1a	107 (8)

Symmetry codes: (i) x−1/2, −y+3/2, z; (ii) x−1/2, −y+1/2, z; (iii) x, y+1, z; (iv) −x+1, −y+1, z+1/2; (v) −x+1/2, y+1/2, z+1/2; (vi) x+1/2, −y+3/2, z; (vii) x, y−1, z; (viii) x+1/2, −y+1/2, z; (ix) −x+1, −y+1, z−1/2; (x) −x+1/2, y−1/2, z−1/2.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1—H1a···I3^vi	1.07	2.76	3.777 (6)	158
O1—H1b···I2	1.11	2.72	3.637 (5)	140

Symmetry code: (vi) x+1/2, −y+3/2, z.