Crystal structure and optical absorption spectra of LiCo(SO4)OH and its remarkable relationship to the Zn-Mn-silicate hodgkinsonite

Crystals of the compound LiCo(SO4)OH were synthesised at low-hydrothermal conditions, and the crystal structure was determined and refined from single crystal X-ray diffraction data. LiCo(SO4)OH crystallises monoclinic, space group P21/c, Z = 4, a = 9.586(2), b = 5.425(1), c = 7.317(1) Å, β = 109.65(1)°, V = 358.3 Å3, wR2 = 0.0485 (2215 unique reflections, 78 variables). The structure is built from chains of edge-sharing, quite strongly bond-length and -angle distorted Co(OH)3O3 octahedra (< Co–O > = 2.126 Å), which are further linked by common corners, hydrogen bonds, and by properly shaped SO4 tetrahedra (< S–O > = 1.476 Å) to sheets parallel (100). These sheets are connected to a three-dimensional framework by sharing corners with distorted LiO4 polyhedra (< Li–O > = 1.956 Å). Apart from the isotypic sulfates of Mn2+ and Fe2+, only the molybdate LiCd(MoO4)OH crystallises isostructural with LiCo(SO4)OH. However, a very close structural relationship exists with the rare mineral hodgkinsonite, Zn2Mn(SiO4)(OH)2, yielding crystal chemically very uncommon topological equivalents of Zn2+ ≡ S6+ and Si4+ ≡ Li+, aside from the expectable substitution Mn2+ ≡ Co2+. Polarised optical absorption spectra of LiCo(SO4)OH reveal that the dominating spin-allowed 4T1(P) band system of Co2+ (d7 configuration) is strongly split up and covers a prominent part (~ 15,500–24,500 cm−1) of the visible spectral range, in accordance with the significant distortion of the Co(OH)3O3 polyhedron. The spectra are interpreted in terms of the Superposition Model of crystal fields, yielding a new set of intrinsic and interelectronic repulsion parameters for Co2+.


Introduction
The crystal chemistry and spectroscopy of minerals and synthetic compounds with first-row transition metal cations in oxysalts of S, Se, or Te are long-lasting research topics at the authors' home institution, whereby well-defined synthetic phases can serve as model substances for the study of specific properties. In this respect, the new monoclinic compound LiCo(SO 4 )OH (space group P2 1 /c with b < c < a), prepared at low-hydrothermal conditions, provides several remarkable features (for a previous short note see Wildner et al. 2013a). Despite its rather simple composition, only very few isotypic compounds are known so far: These are, firstly, the respective compounds of Mn and Fe which have been studied together with the Co phase by powder diffraction techniques (Subban et al. 2013), LiFe(SO 4 )OH furthermore also by first principles calculations on the basis of density-functional theory (DFT) (Reshak and Khan 2014). The only other structurally characterised isotypic compound to date seems to be the molybdate LiCd(MoO 4 )OH (Kobtsev et al. 1968; Li and H atoms were not located directly); here, it has to be noted that the original description (Kobtsev et al. 1968) assigns it to space group P2 1 /a (correspondingly with b < a < c), but the given atomic coordinates obviously comply with cell setting P2 1 /c. From a crystal chemical point of view, however, the close structural relationship of the title compound with hodgkinsonite, Zn 2 Mn(SiO 4 )(OH) 2 (P2 1 /a, b < a < c; Rentzeperis 1963), a rare mineral found at the Franklin mine, New Jersey, USA, is even more remarkable, since it exemplifies the possibilities of some crystal chemically very uncommon topological equivalents. The crystal structure of LiCo(SO 4 )OH features rather strongly distorted Co(OH) 3 O 3 octahedra with bond lengths and cis-angles ranging between 2.04 to 2.22 Å and 80.1 to 104.5°, respectively. The distortion makes LiCo(SO 4 )OH an ideal candidate for the resolution of low-symmetry crystal field (CF) splittings of d-d electronic transitions of 3d 7 -configurated Co 2+ . In turn, this may allow to derive a reliable set of crystal field parameters (CFPs) for Co 2+ in terms of the semiempirical Superposition Model of crystal fields (SPM), originally mainly applied to f-element systems (Newman 1971;Newman andNg 1989, 2000), but increasingly also adopted for d-block cations (see, e.g., Andrut et al. 2004, or the recent review with extensive database by Rudowicz et al. 2019).

Synthesis
Crystals of the new compound LiCo(SO 4 )OH were synthesized at low-hydrothermal conditions in Teflon-lined steel autoclaves (~ 5 cm 3 reaction volume, 10 days at 210 °C). A stoichiometric mixture of Co(OH) 2 and Li 2 CO 3 , dissolved in access of concentrated H 2 SO 4 , plus H 2 O were used as starting materials. The filling level of the reaction chamber was ≤ 25%. Reddish-pink, rhombus-shaped platy crystals up to 0.5 mm were obtained.

Single-crystal X-ray diffraction
The structure investigation was performed at room temperature on a Bruker-Nonius APEXII diffractometer equipped with a monocapillary optics collimator (graphite monochromatized Mo Kα radiation). Data were measured up to 80° 2θ full sphere (phi and omega scans, 2° scan width) at a crystaldetector distance of 35 mm. Absorption was corrected by evaluation of multi-scans. The structure was solved in space group P2 1 /c by direct methods and refined by full-matrix least-squares techniques on F 2 with the programs SHELXS and SHELXL, respectively (Sheldrick 2008(Sheldrick , 2015. Oxygen atoms were labelled according to the isotypic structure of LiCd(MoO 4 )OH with 'O5' changed to 'Oh' (Kobtsev et al. 1968; for details see the "Introduction" section). However, their specific atomic coordinates were selected to form direct bonds to S (O1 to O4) and Co (one Oh), respectively, and for all atoms to lie within the unit cell. Anisotropic displacement parameters (ADP) for all non-hydrogen atoms were applied. Information on crystal data, procedures of measurements and refinements are compiled in Table 1, final atomic parameters are listed in Table 2. Further details of the crystal structure investigation of LiCo(SO 4 )OH may be obtained from the joint CCDC/FIZ Karlsruhe online deposition service: https:// www. ccdc. cam. ac. uk/ struc tures/? by quoting the deposition number CSD 2215181.

Polarised optical absorption spectroscopy
Polarised optical absorption spectra of LiCo(SO 4 )OH in the spectral range 34,000-5000 cm −1 , i.e. covering the near ultraviolet (UV), the visible (Vis) and the near-infrared (NIR) range of the electromagnetic spectrum, were measured on (100) plates parallel to the b-and c-axes, and on a platy [~ (205 )] crystal fragment parallel to a*-axis, using a mirror-optics microscope IR-scopeII, attached to a Bruker IFS66v/S FTIR spectrometer. A quartz beam splitter, a calcite Glan-prism polariser, and appropriate combinations of light sources (Xenon or Tungsten lamp) and detectors (GaP-, Sior Ge-diodes) were used to cover the desired spectral range, using measuring spots between 100 and 165 µm in diameter. Hence, each full spectrum is combined from three partial spectra (34,000-20,500 cm −1 : spectral resolution 40 cm −1 , averaged from 1024 scans; 20,500-10,000 and 10,000-5000 cm −1 : spectral resolution 20 cm −1 , averaged from 512 and 256 scans, respectively), which were aligned in absorbance for perfect match, if necessary, and calculated to linear absorption coefficient α (cm −1 ). The transition energies observed in the optical spectra were extracted by visual inspection and subsequently used in the CF calculations.

Data collection and refinement
Unique data 2215 Variables 78

The superposition model of crystal fields -background theory and calculations for LiCo(SO 4 )OH
Crystal field calculations were performed in the framework of the semiempirical Superposition Model of crystal fields, originally developed by Newman (1971) to separate the geometrical and physical information contained in crystal field parameters, taking into account the exact geometry of the coordination polyhedra in the respective phases. The SPM is based on the assumption that the CF can be expressed as the sum of axially symmetric contributions of all i nearest neighbour ligands of the transition metal cation. The CFPs B kq in Wybourne notation are then obtained from where B k are the 'intrinsic' parameters (related to a reference metal-ligand distance R 0 ), t k are the power-law exponent parameters, both for each rank k of the CFPs, R i are the individual metal-ligand distances, and K kq (Θ i ,Φ i ) are the coordination factors calculated from the angular polar coordinates of the ligands. For details and comprehensive reviews on the SPM refer to Newman (1971), Newman andNg (1989, 2000), Rudowicz et al. (2019), and (with geoscientific focus) Andrut et al. (2004); for a review on the explicit forms of low-symmetry CF Hamiltonians the reader is referred to Rudowicz et al. (2011). The actual CF calculations were done using the HCFLDN2 module of the computer program by Yau-yuen Yeung (Rudowicz et al. 1992;Chang et al. 1994;Yang et al. 2004), which includes imaginary CF terms and is thus applicable to arbitrary low symmetries of all 3d N electron systems. A suite of supplementary programs (Manfred Wildner, unpublished) was used to manage the input and output of the HCFLDN2 program, in particular (i) for the transformation of atomic to polyhedral polar coordinates; (ii) for the systematic variation of intrinsic and power-law SPM parameters, as well as of the Racah parameters B and C; (iii) for the SPM calculation itself, giving the actual values of the CFPs B kq 's; (iv) for the corresponding communication with a slightly modified version of the HCFLDN2 program (Yau-yuen Yeung, personal communication); and (v) for the interpretation and evaluation of the HCFLDN2 output results in terms of a reliability index for the agreement of calculated and observed transition energies.
In the case of the triclinic point symmetry group 1 (C 1 ) of the Co(OH) 3 O 3 polyhedron in LiCo(SO 4 )OH, symmetrically unrestricted SPM calculations including all 14 B kq CFPs (with rank k = 2 and 4) were performed; however, to reduce the number of variables (accompanied by reduced CPU time) and to improve the transferability of intrinsic B k parameters, the power-law exponent parameters t k were fixed at their ideal electrostatic values of t 4 = 5 and t 2 = 3. The reference metal-ligand distance R 0 for Co 2+ was set to 2.1115 Å, i.e. the overall mean Co-O bond length in six-fold coordination (Wildner 1992). For comparison with classical CFPs, a Dq cub value (representing the strength of CF acting on a metal ion within an ideal octahedron) was calculated from the B kq 's via the rotational invariant s 4 (Leavitt 1982), i.e. Dq cub = s 4 /(2√21). Note that the intrinsic B k parameters (and if refined also the power-law exponents t k ) can be directly compared with the results of SPM analyses carried out by others. However, the comparison of SPM calculations of orthorhombic, monoclinic, and triclinic B kq CFPs with respective sets from other sources would require rotations to obtain the standardized parameter sets (see, e.g. Newman and Ng 2000;Rudowicz and Jian 2002;Gnutek and Rudowicz 2008, and references in these papers). The pertinent standardization calculations for Co 2+ ions in LiCo(SO 4 )OH are, however, beyond the scope of the present study.  (7) 0.0023(6) -0.0013(7) O1 0.09572 (7)

Crystal structure description
The crystal structure of LiCo(SO 4 )OH is built from chains of edge-sharing Co(OH) 3 O 3 polyhedra which are linked by sharing corners among each other and with SO 4 tetrahedra to sheets parallel (100) (Fig. 1). These sheets are further connected to a three-dimensional structure by sharing corners with LiO 4 polyhedra (Fig. 2a). The oxygen atom (Oh) which is shared by three CoO 6 polyhedra acts as donor of a hydroxyl group, while the oxygen atom linking one S and one Li atom (O2) is acceptor of a moderately strong, intra-sheet hydrogen bond (Oh···O2 = 2.831 Å), in agreement with its slightly reduced bond valence sum (1.82 v.u. in Table 3). All atoms are located on general positions and each cation forms one crystallographically distinct type of polyhedron. Selected crystal chemical data and bond valences are compiled in Table 3. The CoO 6 polyhedron (Fig. 3) exhibits considerable distortion with three shorter Co-O bonds to OH groups (Co-Oh = 2.045 -2.097 Å) and three longer bonds to oxygen atoms of SO 4 tetrahedra (Co-O = 2.166 -2.216 Å). Cis-bond angles range from 80.1 -104.5°; the two longest bonds are trans-located, thus forming a roughly pseudo-tetragonally elongated octahedron. The extents of the octahedral bond length and especially bond angle distortion (Table 3) per se are not unusual for CoO 6 polyhedra (Wildner 1992), but both combined in one polyhedron are less common. The mean Co-O bond length of 2.126 Å is above average (2.1115 Å; Wildner 1992), thus complying with the distortion theorem by Brown and Shannon (1973). Similarly, the LiO 4 polyhedron is strongly distorted (Table 3), especially concerning its angular and related edge-length distortion; in fact, it ranges among the strongest combined bond-length/edge-length distortions found for LiO 4 tetrahedra without shared edges, as compiled by Wenger and Armbruster (1991). In contrast, the sulfate tetrahedron adopts a much more regular shape, especially in terms of its small angular distortion.
A comparison of LiCo(SO 4 )OH with the structures of LiM (SO 4 )OH (M 2+ = Mn, Fe, Co) obtained from powder diffraction  (Subban et al. 2013), and in case of the Fe-compound also by DFT calculations (Reshak and Khan 2014), shows a basic agreement, e.g. in that the three shorter octahedral bonds are formed with the OH groups, but an advanced analysis is hardly useful considering the inherent deficiencies in the powder (and DFT) data vs. the present single crystal data. In isotypic LiCd(MoO 4 )OH (Kobtsev et al. 1968) the Li and H atoms could not be located, but a (topologically basically correct) position for Li was postulated. Anyway, the Li-polyhedra in both compounds can hardly be compared (e.g., Kobtsev et al. 1968 claim Li-O distances of 1.92 -2.07 Å, but a recalculation in the corrected setting -see Introduction -gives 1.57 Å as lower limit). Also the fundamental differences of respective central atoms in the M 2+ O 6 and X 6+ O 4 polyhedra prevent a useful comparison; e.g., the MoO 4 group is strongly distorted compared to the quite regular SO 4 tetrahedron in the title compound.
Anyway, Kobtsev et al. (1968) pointed out that LiCd(MoO 4 ) OH -and hence also LiCo(SO 4 )OH -is structurally related to the rare mineral hodgkinsonite, Zn 2 Mn(SiO 4 )(OH) 2 (Rentzeperis 1963). The structure of hodgkinsonite (a = 8.171 Å, b = 5.316 Å, c = 11.761 Å, β = 95.15º, V = 508.7 Å 3 , space group P2 1 /c) shown in Fig. 2b contains octahedral-tetrahedral sheets which are topologically identical to those shown in Fig. 1 for LiCo(SO 4 )OH, but composed of MnO(OH) 5 octahedra and Zn(2)O 4 tetrahedra. A comparison of Figs. 2a and b reveals that in hodgkinsonite the roles of the inter-sheet-linking LiO 4 tetrahedra in LiCo(SO 4 )OH are somewhat surprisingly taken by SiO 4 tetrahedra, as well as by a second type of ZnO 4 tetrahedra, i.e. Zn(1)O 4 , without topological equivalence in LiCo(SO 4 )OH. These Zn(1)O 4 tetrahedra are inserted between adjacent sheets in hodgkinsonite and form their sole direct linkage. Hence, perpendicular to the structural sheets the lattice expands at a higher rate than caused solely by the larger ionic radii of Mn and Si in hodgkinsonite relative to Co and S, respectively, in LiCo(SO 4 )OH (radius Zn 2+ ≈ Li + ), and the cell angle β is reduced by nearly 14°. The layout of the hydrogen bonding scheme in hodgkinsonite is not as clear-cut as in LiCo(SO 4 )OH. The MnO(OH) 5 octahedron includes two crystallographically different donor oxygen atoms of hydroxyl groups. According to Rentzeperis (1963), one of them (O6-H2 ≡ Oh-H···O2 in the title compound) forms no hydrogen bond (the Table 3 Selected interatomic bond lengths (Å), angles or angular ranges (°), bond strengths ν (v.u.; calculated -without H atoms -according to Brese and O'Keeffe 1991), and polyhedral distortion parameters (Δ oct : Brown and Shannon 1973; σ oct 2 and σ tetr 2 : Robinson et al. 1971;BLDP and ELDP: Griffen and Ribbe 1979;BLD and ELD: Renner and Lehmann 1986)   corresponding bridge O6···O1 = 3.10 Å with already overbonded O1); the other one (O5-H1 ≡ the 'plain' O4 in the title compound) forms a weak intra-sheet hydrogen bond in hodgkinsonite (to O2 ≡ O3; a recalculation of bond valences from the structure data of Rentzeperis 1963 also supports this assignment). Irrespective of any uncertainties regarding possible hydrogen bond acceptor oxygens, the formation of inter-sheet hydrogen bonds can be excluded.

Polarised optical absorption spectra and crystal field calculations
The strong and irregular bond-length and -angle distortion of the CoO 6 polyhedron with point symmetry group 1 (C 1 ) (Fig. 3) makes LiCo(SO 4 )OH a promising candidate for the resolution of low-symmetry absorption band splittings of the generally broad spin-allowed absorption bands of Co 2+ with cubic quartet ground state 4 T 1 (F). In fact, as evident in Fig. 4, the intense spin-allowed 4 T 1 (P) band system is strongly split up and covers a prominent part (approx. 15,500 -24,500 cm −1 ) of the visible spectral range. In contrast, the weaker spin-allowed 4 T 2 (F) band in the NIR region (centred around 7500 cm −1 ) shows only weak splitting, and the spin-allowed but electronically forbidden 4 A 2 (F) band (at ~ 14,800 cm −1 ) does not split up since the 4 A 2 (F) state is a non-degenerate orbital singlet. As a consequence of the strong splitting and broadening of the intense 4 T 1 (P) state in LiCo(SO 4 )OH, generally weak spin-forbidden doublet levels (arising from the doublet 2 G, 2 P and 2 H terms) are now located at the onset or within the 4 T 1 (P) band system and can'steal' significant intensity (i.e. partly gain quartet character) from the spin-allowed bands due to spin-orbit coupling. In particular, sharp features assigned to the more or less field-independent levels 2 T 1,2 (G) at 16,110 cm −1 and especially 2 T 1 (P) at 19,990 and 20,540 cm −1 exhibit strong intensity stealing. Since for transition metal ions at triclinic symmetry sites -as Co 2+ at point symmetry group 1 (C 1 ) in the present case -all CF levels split completely and hence their states become orbital singlets, which transform as A-states, and the above-mentioned vague pseudotetragonal elongation is not pronounced enough, a meaningful analysis of the polarisation behaviour is not feasible. At least it Fig. 4 Polarised optical absorption spectra of LiCo(SO 4 )OH with assignments of CF levels for cubic symmetry (spin-allowed states in bold, spin-forbidden in normal narrow letters). Tick marks indicate observed and calculated energy levels for triclinic symmetry can be stated that the transition intensity seems to be enhanced when the electric vector lies within the octahedral sheet, i.e. parallel to the b-and c-axes (Fig. 4).
Results of the SPM calculations (for details see the section on background theory above) for LiCo(SO 4 )OH are listed in Table 4, and corresponding calculated energy levels are indicated in Fig. 4. Compared to previous SPM analyses of Co 2+ compounds (see, e.g., Andrut et al. 2004;Brik and Yeung 2008), the order of the intrinsic parameters B 2 > > B 4 is rather surprising. Generally, B 2 > > B 4 is expected from theory (Newman and Ng 1989), but in case of 3d N transition ions this sequence is often not observed, sometimes even B 2 < B 4 is found Wildner et al. 2013b), especially if spin-allowed and spin-forbidden levels are fitted to the same respective set of SPM parameters. In terms of classical CF and interelectronic repulsion parameters, the obtained parameters Racah B (815 cm −1 ) and C as well as and the average CF strength parameter Dq cub (786 cm −1 , calculated from the triclinic B kq 's) fit well in the expected range for Co 2+ in octahedral coordination in oxysalts (as compiled, e.g., by Wildner et al. 2004); only the ratio Racah C/B is somewhat above average. Overall, the remarkable magnitude of low-symmetry band splittings in the spectra of LiCo(SO 4 )OH, especially of the 4 T 1 (P) system, allows to extract well defined transition energies. Hence, the various spectroscopic parameters listed in Table 4 are assumed to be very reliable, and may thus serve as starting values in CF calculations of other Co 2+ -bearing inorganic compounds.

Conclusions
Despite its rather simple composition and well-defined crystal structure, the new synthetic compound LiCo(SO 4 )OH exhibits some remarkable chemical and spectroscopic features. While up to date only a very limited number of isotypic phases has been identified, LiCo(SO 4 )OH is closely related to the mineral hodgkinsonite, Zn 2 Mn(SiO 4 )(OH) 2 , revealing surprising topological equivalences of tetrahedral Zn 2+ ≡ S 6+ and Si 4+ ≡ Li + , as well as of octahedral MnO(OH) 5 ≡ Co(OH) 3 O 3 . The Co(OH) 3 O 3 polyhedron shows strong combined bond-length and angular distortions, allowing to properly resolve lowsymmetry absorption band splittings in the optical absorption spectra of LiCo(SO4)OH. This enables deriving reliable CF parameters as well as interelectronic repulsion ones for Co 2+ ions in LiCo(SO 4 )OH.

Supplementary Information
The online version contains supplementary material available at https:// doi. org/ 10. 1007/ s00710-022-00807-w. Table 4 Summary of refined SPM (intrinsic B k ) and interelectronic repulsion parameters (Racah B, C), as well as of calculated (real and imaginary B kq CFPs in Wybourne notation and rotational invariants s k ), derived (cubic CF strength Dq cub and 'covalency indicator' β = B/B 0 ), or fixed (power-law exponents t k ) parameters for Co 2+