Hydrogen bonding in the crystal structure of phurcalite, Ca2[(UO2)3O2(PO4)2]·7H2O: single-crystal X-ray study and TORQUE calculations

The crystal structure of the uranyl-phosphate mineral phurcalite is characterised by extensive hydrogen bonding. It comprises a less common type of H2O bonding in solids: a transformer H2O unit (with a three-coordinated O atom), which is not directly linked to any metal cation. This study documents the advantage of combining XRD data and TORQUE calculations, which are significantly less demanding of resources than DFT calculations..

The vast majority of uranyl phosphate structures are based on sheets of vertex-and edge-sharing uranyl polyhedra and phosphate tetrahedra. Uranyl phosphate minerals (and arsenates as well) have historically been classified/divided in two major groups, autunite and phosphuranylite groups (Krivovichev & Plá šil, 2013). They essentially differ in details of their topological arrangement of structural units, i.e. uranylanion topologies. The autunite topology comprises equatorial vertex-sharing between uranyl square bipyramids and phosphate tetrahedra. The phosphuranylite type of structures contains both uranyl pentagonal and hexagonal bipyramids within the sheets that share edges, forming chains that are cross-linked by sharing vertices and edges with phosphate tetrahedra (Burns, 2005;Lussier et al., 2016). Mineral phosphuranylite (s.s.) contains additionally one extra uranyl square bipyramid located between the sheets making it the 3D framework structure (Demartin et al., 1991).
Hydrogen bonds are of particular importance for stabilizing the largely hydrated structures of uranyl phosphates and arsenates, thus controlling their thermodynamic stabilities. Consequently, it is important to determine the details of hydrogen bonding in such minerals in order to understand their stability and the mechanisms by which they break down. Nevertheless, the direct determination of the H-atom positions in uranyl-based compounds is challenging, largely due to high absorption of X-rays and small or poorly developed crystals available for the structure analysis. Therefore, the combination of methods, usually comprised of XRD structure determination and density functional theory (DFT) optimization is often adopted (Colmenero et al., 2017(Colmenero et al., , 2018a(Colmenero et al., ,b,c, 2019a.
Here, we present a complete structure determination, including hydrogen bonding, in a complex structure of uranyl phosphate mineral phurcalite, as determined by combination of X-rays and a recently developed robust, fast real space optimization method (Ghazisaeed et al., 2018.

Sample
The natural specimen used for extraction of phurcalite crystals suitable for X-ray diffraction originates from the Shinkolobwe mine, Shaba province, Democratic Republic of Congo (Africa). Phurcalite forms long-prismatic, needle-like orthorhombic crystals of intense yellow color (Fig. 1), growing in cavities of quartz with disseminated small crystals of metatorbernite-metazeunerite series of minerals. The specimen has been deposited in the mineral collection of the Musé e National d'Histoire Naturelle in Luxembourg (specimen registration number PV025).

Single-crystal X-ray diffraction
A long-prismatic fragment (0.091 mm Â 0.012 mm Â 0.009 mm) of phurcalite crystal was selected under a polarized-light microscope and mounted on a glass fiber. The X-ray data collection was done at room temperature with a Rigaku SuperNova single-crystal diffractometer (Mo K radiation from a micro-focus X-ray tube collimated and monochromated by mirror-optics and detected by an Atlas S2 CCD detector). In line with previous structure determinations, phurcalite is found to be orthorhombic, a = 17.3785 (9) Å , b = 15.9864 (8) Å , c = 13.5477 (10) Å , V = 3763.8 (4) Å 3 and Z = 8. Integration of the diffraction data, including corrections for background, polarization and Lorentz effects were carried out with the CrysAlis RED program (Rigaku, 2019). An empirical absorption correction was applied to the data in the Jana2006 software, using spherical harmonics (Petříček et al., 2014). Crystallographic data and experimental details are given in Table 1. The structure of phurcalite was solved by the chargeflipping algorithm using the SHELXT program (Sheldrick, 2015). Structure refinement was done using the software Jana2006 with the full-matrix least-squares refinement based on F 2 . The structure solution revealed positions for all atoms except of hydrogens; those were ascertained from the difference Fourier maps. The H atoms were refined using a mix of soft constraints on O-H distances and with the U eq of each H  (Rigaku, 2015), Jana2006 (Petříček et al., 2014).
set to 1.2 times that of the donor O atom. The bond-valence sums were calculated following the procedure of Brown (2002), and using bond-valence parameters taken from Gagné & Hawthorne (2015).

TORQUE method calculations
The orientations of the H 2 O molecules were optimized with the TORQUE method, a robust and fast real-space method for determining H 2 O orientations from rotational equilibrium (Ghazisaeed et al., 2018 (Ghazisaeed et al., 2018). In the TORQUE method, the H 2 O molecules are placed such that its oxygen matches the location known from the experiment. In contrast, no prior knowledge of the location of the two hydrogens atoms (per water molecule) is needed. Their locations are obtained from the molecular H 2 O geometry, as described in the TIP3P model We performed two sets of TORQUE computations to investigate the extent of hydrogen bonding in phurcalite. In the first set, we orient the H 2 O molecules such that they match our X-ray observations as closely as possible. Slight adjustments are needed to account for deviations of d(O-H) and H-O-H angle between experiment and water model. More specifically, we place each water molecule in the corresponding experimental H 2 O plane, and adjust the bond geometry, such that the bisectors of the H-O-H angle coincide and place the two hydrogen atoms at AE52.26 o , from the bisector at the prescribed molecular O-H distance. With this placement of the H 2 O molecules the complete initial crystal structure of phurcalite is completely specified. Charges for ions in the structural unit are taken from bond-valence analysis (see below), and for H 2 O from the TIP3P model (Jorgensen et al., 1983). With this information, the torque on the H 2 O molecules is computed and the H 2 O molecules are rigidly rotated about their oxygen ions by a small increment. This torque compution/rigid rotation cycle is continued until the torque is vanishingly small and rotational equilibrium is reached (Ghazisaeed et al., 2018).
The results address stable and unstable water orientations in the X-ray derived hydrogen bond network. In the second set the H 2 O molecules are oriented randomly while preserving the molecular H 2 O geometry and addresses the (non)uniqueness of the identified rotational equilibria. We optimized 1000 random initial H 2 O orientations and statistically analyzed the similarities and differences of the obtained rotational equilibrium configurations, similar to our previous work (Ghazisaeed et al., 2018(Ghazisaeed et al., , 2020Steciuk et al., 2019). Moreover, we performed an additional TORQUE optimiza- Crystal structure of phurcalite. (a) Uranyl phosphate sheet of the phosphuranylite topology containing UO 2 2+ coordinated both as UO 7 (U1 and U2) and UO 8 bipyramids. (b) Stacking of the sheets perpendicular to b. Adjacent sheets are linked by an extensive hydrogen bonding network (bonds are omitted for clarity). Color scheme: U is yellow, P is pink, Ca is violet, O is red, H is gray; unit-cell edges are outlined as black solid lines. Table 2 Hydrogen-bond geometry as obtained from XRD data and TORQUE calculations.
Left: XRD; Right: TORQUE. For TORQUE, we list we list the highest probability joint seven-site model (17.5%). For details, see text.
tion where the H 2 O initial orientations are chosen as closely as possible to our X-ray refinements.

Crystal structure obtained from X-ray diffraction
The structure of phurcalite as obtained from the current structure determination by X-ray diffraction is in line with previous study done by Atencio et al. (1991). During the current study it was possible to reveal partially some of the positions of the H atoms in the structure and refine them to obtain a reasonable bonding geometry. The structure of phurcalite is based upon uranyl phosphate sheets [ Fig. 2(a)] of phosphuranylite topology (Burns, 2005;Lussier et al., 2016), with a ring symbol 6 1 5 2 4 2 3 2 (Krivovichev & Burns, 2007); with hexagons of the topology occupied by U 6+ . Unlike sheets of other members of the phosphuranylite group (Piret & Declercq, 1983;Piret et al., 1988;Demartin et al., 1991;Dal Bo et al., 2017), the sheet in phurcalite does not contain H atoms either as OH or as molecular H 2 O. The composition of the sheets are hydrogen free, [(UO 2 ) 3 O 2 (PO 4 ) 2 ] 4-, and stacked perpendicular to the [010] direction in phurcalite [ Fig. 2(b)]. Between adjacent sheets two independent Ca sites are located.

Hydrogen bonding as revealed from both X-rays and TORQUE
The stereochemical details of the hydrogen bonding as revealed from X-rays and TORQUE calculations are given in Table 2. There are seven independent O atoms corresponding to H 2 O groups in the structure of phurcalite: following the XRD structure determination, H 2 O is expected to belong to sites O16, O17, O19, O20, O21, O22, O23. However, the detailed orientation of O17 could not be resolved due to insufficiently resolved difference Fourier maxima from the X-ray data.

Discussion -hydrogen bonding
X-ray structure refinements and results from TORQUE provide strong evidence for extensive hydrogen bonding in phurcalite. In contrast to the results of our X-ray diffraction refinements, TORQUE successfully identified reasonable H 2 O hydrogen bond arrays for all seven water sites, including O17 (Table 2).
Bond-valence analysis shows that calculated sums of bondvalence at the sites are within a few percent of expected oxidation states of all elements in phurcalite (Table 3). Therefore, we chose the corresponding formal charges for all non-H 2 O toms for the TORQUE simulations. We obtained rotational equilibria for 1000 randomly initialized configurations. In order to compare more directly to X-ray data, we identified structures as equivalent, if the closest acceptor for all seven H 2 O sites for two configurations is the same. We TORQUE-optimized 1000 randomly chosen initial H 2 O orientations and found 53 geometrically distinct O-HÁ Á ÁA environments (H 2 O rotational equilibrium orientations), with occurrences that range from 0.1% to 17.5% (see Fig. 3). However, only six of the seven-site H 2 O environments are predicted to have an occurrence probability of 6% or higher (with a joint probability of 52.3%, Fig. 3). This observation suggests that a comparatively small number of O-HÁ Á ÁA environments likely capture a significant fraction of the stereochemical variability, at least in phurcalite. The stereochemical results for the average seven-site model for the highest probability O-HÁ Á ÁA environment (17.5%) are shown in Table 2, the TORQUE predicted hydrogen acceptor sites are listed in Table 4, and the corresponding hydrogen positions are listed in Table 5. The reported standard deviations were obtained from the analysis of the TORQUEpredicted equilibrium orientations that belong to an equivalent set. For example, for the highest probability configuration, 175 equilibrium orientations were averaged, and the corresponding standard deviations were computed. If we analyze the probability of orientations for each site, we find that all seven water orientations appear either with the highest or second highest probability (Table 4). This observation that not every site belongs to the highest probability orientations demonstrates that local and global rotational equilibrium do Probabilities for the 53 non-equivalent TORQUE identified H 2 O equilibrium orientations in phurcalite.

Table 4
Summary of all site occurrences among the 1000 configurations.
Nearest oxygen acceptor sites for the two hydrogens are shown in parenthesis. Bold and underlined are TORQUE-predicted sites that agree with our X-ray diffraction experiment. Detailed hydrogen positions for the random TORQUE seven-site model (probability 17.5%), and EXP + TORQUE model are given in Table 5 and Table 6 not necessarily coincide, and correlated changes in the water array must be taken into account during data analysis. A comparison of the stereochemistry of the water positions determined by X-ray diffraction and the 53 equilibrium H 2 O orientations shows no simultaneous match for all seven sites. Complete O20 and O22 stereochemistry matches occur in our library with probabilities of 4.2% and 38.5%, respectively (Table 4). Partial matches exist for O17, O19, O21 and O23, and no match is found for O16. This result suggests that the X-ray derived water stereochemistry does not correspond to a rotational equilibrium state. In order to explore whether this conclusion is due to sampling, we initialized TORQUE close to our X-ray-derived H 2 O positions (while preserving the predefined H 2 O geometry of the TIP3P water model, see method section for details on hydrogen placement); we find again significant re-bonding of hydrogen, partial matches can be found for O19, O21, O22 and O23, while complete rebonding is predicted for O16, O17 and O20 (Table 4, optimized hydrogen positions are listed in Table 6. However, in contrast to the X-ray derived H 2 O array we find a simultaneous match for all seven water sites among the 53 equilibrium orientations with a probability of 3.8%, ranked #6 among the 53 distinct rotational equilibrium orientations (Fig. 3). Therefore, it is unlikely that the X-ray hydrogen positions correspond to an accidentally unsampled rotational equilibrium state, and uncertainties can be more likely attributed to simultaneous rotations of several H 2 O molecules. The X-ray O16 water site has no match among the TORQUE determined 53 equilibrium H 2 O orientations, while all other sites at least show a partial match. For O16, the X-ray observations suggest (Table 2) hydrogen bonding to O19 (water) and O20 (water). In contrast, TORQUE predicts bonding to O10 (U3) and O23 (water). The driving force for re-bonding is H32 which is only 1.87 Å from Ca2 in the refined X-ray data, closer than any of its oxygen ligands. The corresponding Ca-H electrostatic repulsion provides a driving torque for water re-orientation, and in rotational equilibrium we find d(H32-Ca2) = 3.02 Å , an increase of $60%. Therefore, the X-ray O16 stereochemistry is predicted to be unstable, and we note that the TORQUE-optimized O16 water orientation appears in our library with a probability of 8.8% (Table 4).
X-ray diffraction was unable to identify reasonable hydrogen bonding for O17. The origin of this inability may be explained by TORQUE-predicted re-bonding, the X-ray observations suggest hydrogen bonding (Table 2) with O19 (water) and O23 (water). However, we find hydrogen atoms only $1.5 Å from O17H1 and O17H2, distances comparable to the intramolecular H-H distance. Therefore, H-H repulsion induces water rotation and a new stereochemistry to O7(U2) and O10(U3), which we find for the TORQUE-optimized X-ray orientations, as well as for the highest probability model in our library and corresponds to the highest probability O17 orientation (66.3%, Tables 2 and 4 Table 5 TORQUE-predicted average fractional positions and standard deviations for the TORQUE-optimized X-ray hydrogen bond scheme for the highest probability seven-site model (17.5%).
A standard deviation of (0) signifies that is smaller than the last displayed digit.  successfully describes a rotational equilibrium state for O17, that could not be resolved from our X-ray diffraction results. The discussion of possible hydrogen-bonding arrangements in phurcalite has been used in the theoretical bond-valence studies (Schindler & Hawthorne, 2008) focused on interactions between anionic (i.e. Lewis bases) and cationic (i.e. Lewis acids) parts of the structures of hydrated oxysalts. Their conclusions, which they found on the basis of the bond-valence theory (Brown, 2002(Brown, , 2009Hawthorne, 2012Hawthorne, , 2015,  (Schindler & Hawthorne, 2008). Our study advances the understanding of H 2 O complexes and their interactions with the surrounding crystal framework in phurcalite. From the scheme given in Fig. 4 it is possible to simply read off that there are five transformer H 2 O groups (with corresponding O atom being three-coordinated); one bonded to Ca1 atom (O22) three others bonded to Ca2 atom (O16, O19, O21) and an additional one, O23, which is not linked to the metal cation (see below). Furthermore, there are two non-transformer H 2 O groups (with corresponding O atom being four-coordinated). First one, O17, is linked to Ca1 site, nevertheless accepts also one weak hydrogen bond from H1 O19 . Second one, O20, is shared between Ca1 and Ca2 atoms. Finally, the O23 atom belongs to the transformer H 2 O group, with no linkage to any metal cation; O23 receives one hydrogen bond from H1 O22 and transform it into two hydrogen bonds, via H1 O23 and H2 O23 , therefore the O23 is three-coordinated. The magnitude of strength of two corresponding hydrogen-bonds (H1 O23 + H2 O23 = 0.13 vu) match the initial strength of the hydrogenbond accepted by O23 (0.14 vu). To summarize, the interstitial complex in phurcalite can be expressed as

Conclusions
The structure of the mineral phurcalite (calcium uranyl phosphate heptahydrate) is stabilized by an extensive network of hydrogen bonds. Phurcalite is unique among uranyl phosphates in that it shows a high Ca:U ratio (2:3) (for instance mineral autunite has 1:2) and its structure displays an unusual hydrogen bonding scheme. Structure data obtained from a XRD experiment and theoretical calculations (TORQUE) indicate that the structure of phurcalite contains a rare functional type of H 2 O group in the interlayer which is not linked to any metal cation directly, as it accepts one hydrogen bond from an adjacent H 2 O group. This H 2 O group thus splits the incident bond-strength (represented by one incoming hydrogen bond) into two weaker hydrogen bonds. Therefore it is a transformer H 2 O group with a three-coordinated O atom.
Our study advances our understanding of hydrogen bonding in complex uranyl minerals and shows the synergy of experiment and theory provides new insights into the complex hydrogen bonding in uranyl phosphates and the role of H 2 O groups in complex oxysalt minerals. In summary, it is likely that the rare hydrogen bonding topology in phurcalite is responsible for its low abundance in nature.