Crystal Growth of Cu6(Ge,Si)6O18·6H2O and Assignment of UV-VIS Spectra in Comparison to Dehydrated Dioptase and Selected Cu(II) Oxo-Compounds Including Cuprates

Low-dimensional quantum spin systems with the Cu ²⁺ central ion are still in the focus of experimental and theoretical research. Here is reported on growth of mm-sized single-crystals of the low-dimensional S = 1/2 spin compound Cu ₆(Ge,Si) ₆O ₁₈ ·6H ₂O by a diffusion technique in aqueous solution. A route to form Si-rich crystals down to possible dioptase, the pure silicate, is discussed. Motivated by previously reported incorrect assignments of UV-VIS spectra, the assignment of dd excitations from such spectra of the hexahydrate and the fully dehydrated compound is proposed in comparison to dioptase and selected Cu(II) oxo-compounds using bond strength considerations. Non-doped cuprates as layer compounds show higher excitation energies than the title compound. However, when the antiferromagnetic interaction energy as J _z ·ln(2) is taken into account for cuprates, a single linear relationship between the Dq _e excitation energy and equatorial Cu(II)-O bond strength is confirmed for all compounds. A linear representation is also confirmed between ² A _1g energies and a function of axial and equatorial Cu-O bond distances if auxiliary axial bonds are used for four-coordinated compounds. The quotient Dt/ Ds of experimental orbital energies deviating from the general trend to smaller values indicates the existence of H ₂O respectively Cl ^− axial ligands in comparison to oxo-ligands, whereas larger Dt/ Dq _e values indicate missing axial bonds. The quotient of the excitation energy ² A _1g by 2 · ² E _g - ² B _2g allows checking for correctness of the assignment and to distinguish between axial oxo-ligands and others like H ₂O or Cl ^−.

• Dioptase
• Ge-Dioptase
• Copper(II) Compounds
• Cuprates
• Crystal Growth
• <i>UV-VIS</i> Spectroscopy
• <i>EPR</i>
• Color
• d-d Excitations
• Bond Strength
• Super-Exchange Interaction

1. Introduction

Low-dimensional quantum spin systems are of considerable theoretical and experimental interests together with some applications to which they may lead. In spite of the ability of the d⁹ transition metal ion Cu²⁺ to form, apart from 3D networks, chains, ladders and small clusters, copper compounds are among the most interesting phases. With equal electronegativity compared to silicon, but in contrast to its tetrahedral networks, Cu(II) mainly forms oxo-compounds with chains and networks of connected “octahedra”.

For instance, copper polygermanate, CuGeO₃, has a rather simple crystal structure of “einer” single chains of GeO₄ tetrahedra alongside S = 1/2 spin single chains of edge-sharing CuO₄₊₂ octahedra [1] [2] . It was the unique inorganic compound showing the Spin-Peierls-transition [3] [4] . As a quasi-one-dimen- sional system, it has been the subject of an intensive experimental and theoretical work for the past years. It was a great surprise, when Otto and Meibohm [5] [6] succeeded in the synthesis of pure copper polysilicate, CuSiO₃, by thermal decomposition of the mineral dioptase, Cu₆Si₆O₁₈・6H₂O. CuSiO₃ represents the example of a fully stretched silicate chain structure. It is isotypic to CuGeO₃, but does not show the spin-Peierls transition, instead an antiferromagnetic ordering below T_N = 7.9 K [7] [8] .

The rhombohedral title compound Cu₆(Ge,Si)₆O₁₈・6H₂O represents a hexacyclo-germanate (silicate) that contains copper-oxygen spiral chains along the c-axis, which are connected (intra-chain) by edge-sharing dimers (Figure 1).

Figure 1

Crystal structure of dioptase projected down [ 001 ]. A framework of copper oxide octahedra (yellow) screws around the c-axis with non-bonding axial water ligands (red) pointing towards empty channels. Six-membered silicate single rings are depicted in green

This structure is interesting because it allows for a quantum phase transition between an anti-ferromagnetically ordered state and a quantum spin liquid [9] . Large quantum fluctuations in green dioptase have been described [10] . Recently, also the germanate analogue, Cu₆Ge₆O₁₈・6H₂O [11] , has been the object of detailed magnetic and structural investigations [12] [13] .

If near the empty structural channels located water molecules are removed, a screwed framework of edge-sharing disphenoids rather than flat CuO₄ plaquettes remains in the dehydrated compound.

As part of a systematic study of transition metal germanates, silicates and arsenates we have undertaken syntheses of rare copper minerals and new copper compounds in view of its power as low dimensional S = 1/2 spin compounds allowing for interesting physical and physicochemical properties. First, the synthesis serves not to waste rare mineral specimens for research. There is also the possibility to study an improvement in the crystal growth by replacement of copper by other elements, apart from the chance of doping with electronically or magnetically interesting ones. For example, the replacement of copper by manganese was observed in natural samples of dioptase by EPR measurements [14] [15] .

Because the assignment of the dd excitations derived from the UV-VIS spectra of copper-bearing compounds are often found to be incorrect, this work contributed some simple tools that could lead to the right assignment. It is not the intent of this paper to review UV-VIS spectroscopy of Cu²⁺ compounds in general.

2. Experimental

2.1. Crystal Growth and Dehydration of the Samples

The method described below was used by the author many years earlier for the synthesis of rare minerals, for instance, the synthesis of Pb₃Ge(OH)₆(SO₄)₂・3H₂O, the piezoelectric Tsumeb mineral fleischerite [16] . For the synthesis of the title compound freshly precipitated gels of GeO₂ and Cu(OH)₂ were separately filled in 200 ml beaker glasses and thoroughly filled up with distilled water. Then a U-shaped glass pipe of 6 mm inner diameter, well annealed before use to reduce crystal nucleation frequency, was filled free of air bubbles with distilled water. This pipe is then used to connect the distinct solutions in the beakers. Finally, the water surface in the beakers is covered with a film of liquid paraffin to prevent water evaporation and entry of CO₂, respectively.

The desired slow diffusion of the distinct solutions into one another leads to the formation of Cu₆(Ge,Si)₆O₁₈・6H₂O seeds that grow up to 1 mm size of light blue crystals within 8 weeks. Interestingly, most individual crystals form double- crystals. The symmetry situation of this finding must be investigated further. The crystals of stocky prismatic, nearly spherical habit developed {110} and {021} forms (Figure 2).

One can extrapolate the time scale to get a crystal of about 2 mm diameter and calculate about 1 year of growing time. Trying to exchange Ge by Si by this method

Figure 2

The stocky prismatic habit of the as-grown Cu 6 (Ge,Si) 6 O 18 ・6H 2 O crystals, showing a combination of the {110} prism and the {021} rhombohedron

seems to be less efficient, only a slightly greenish sheen shows that a small exchange occurred.

The other method of co-precipitation of GeO₂, SiO₂ and Cu(OH)₂ gel and longer time vigorous stirring resulted in a vivid green colored polycrystalline material of about 12 at-% Si determined from lattice parameter changes [14] [17] . Also, the substitution of some B³⁺ for Ge⁴⁺ is possible, leading to a beautiful green color [17] . Stirring a longer period and in addition changing the pH to more acidic milieu gives at least about 15 at-% Si (a = 14.640 Å, c = 7.806 Å, this work). The effect is based on the different solubility of the Ge-compound in comparison to dioptase. Cu₆Ge₆O₁₈・6H₂O is easily decomposed by a dilute acetic acid, but dioptase does not dissolve. Recently we observed a deepening of color to dioptase green, when the Si-rich solution was exposed to ultrasonic waves, in this way superseding vigorous stirring. The energy that is released when voids implodes (super-cavitation) may be able to assemble more easily and faster the six-membered silicate rings within the cuprate framework of dioptase.

A proposed approach for a possible synthesis of pure polycrystalline dioptase results as follows. The first step will be the spontaneous formation of pure germanate and exchange of maximum Ge by Si through stirring or sonochemical treatment. Then pH, as well as temperature, is altered to increase the solubility of the still Ge-rich compound combined with a simultaneous offer of more Si to form a dioptase layer. A new core of silico-germanate can be grown epitaxially and subsequently transformed to dioptase. Repetition of this process may finally form pure dioptase in mm-sized crystals. An automated process would make sense. Nature has similar tools in the quiver such as rhythmic property changes (concentration, pH, temperature) of metal bearing ascending or descending solutions, apart from a lot of time.

A single-phase crystalline powder of synthetic Ge-dioptase for the UV-VIS spectroscopic investigation is best obtained from an aqueous solution of pH 5.5 at room temperature, formed by mixing and stirring equal amounts of 0.02 M cupric acetate with freshly produced 0.02 M GeO₂ solution. The initially formed gel settles as fully crystalline precipitate after an induction period of two days [10] .

Complete dehydration of synthetic Ge-dioptase was performed by annealing of the polycrystalline sample up to 920 K for 6 h, followed by cooling down to room temperature with a moderate cooling rate of 20 K/h. The chosen annealing temperature lies about 53 K below the temperature of decomposition to the orthorhombic spin-Peierls phase CuGeO₃ [10] .

A natural dioptase samples from the locality Altyn Tyube, Kazakhstan, was used as pure silicate sample. Its complete dehydration to “black” dioptase occurs at 660 K and should be controlled by X-ray powder diffraction analysis because decomposition into CuO (tenorite) and SiO₂ (partly quartz and cristobalite) starts only a few degrees higher at 673 K.

2.2. UV-VIS Spectroscopic Investigation

First results of UV-VIS spectroscopy on Cu₆(Ge,Si)₆O₁₈・6H₂O are given in the doctoral theses of my coworkers Brandt [17] and Meibohm [14] , respectively, whereas dioptase itself has been investigated earlier by different researchers [18] [19] [20] [21] .

Brandt [17] reported a color change from turquoise-green to blue on dehydration of dioptase-type copper germanate. In addition, the dehydrated compound showed thermochromic behavior on heating up to 500˚C with a reversible color change to vivid green similar to that of annealed CuGeO₃. The color persists when Cu₆Ge₆O₁₈ is rapidly cooled down to room temperature. A possible interpretation for this effect is according to [17] the low relaxation rate of the four oxygen ligands around copper. Remember that the equatorial coordination in dioptase is not planar but disphenoidic, and a change to a stiffer, more tetrahedral one may occur with raising the temperature.

A reinvestigation of the fully hydrated and dehydrated compounds is primarily undertaken in order to deconvolute and understand the broad UV-VIS spectrum of the synthetic color pigment litidionite, KNaCuSi₄O₁₀ [22] [23] , which shows similarity to that of dioptase.

The room temperature UV-VIS spectra of the samples were taken with the double-beam light scanning UV-2501PC CE spectrometer from Shimazu with selectable light sources (50W halogen lamp and D2 lamp). The powder sample was coated on a polished aluminum disk and measured in the reflection modus against a BaSO₄ standard in the wavelength range between 190 and 900 nm with a spectral bandwidth of 0.1 nm using a 50 nm/min scan and choosing 0.5 nm intervals. From the less structured absorbance profile, recalculated from the measured reflectance, the energy bands were fitted with Gaussian profile functions. The better resolved spectra of the dehydrated compounds were fitted first and then the results used as start parameters for the broad spectra of the hydrated compounds.

2.3. EPR Data

Electron paramagnetic resonance spectroscopy (EPR) provides information about the electronic structure of transition metal ion complexes. For d^1,9 systems such as Cu²⁺ centered complexes with no fine structure the principal values of the g-tensor of the spin Hamiltonian H = β_eB・g・S, reflecting the symmetry of the ligand field, can be derived from the EPR spectrum, where B is the external magnetic field, S is the spin vector, and β_e = g_e・μ_B (Landé g-factor for the free electron, g_e = 2.0023, Bohr magneton μ_B). In this contribution g values for dioptase, Cu₆Si₆O₁₈・6H₂O, determined by Reddy et al. [19] , and data measured by Meibohm [14] for synthetic Cu₆Ge₆O₁₈・6H₂O were used as expressed in its principal axes system.

3. Results and Discussion

The Gaussian peak analysis of the UV-VIS spectra was performed with the aid of own Turbo-Basic programs using recast software modules once developed for X-ray powder profile analysis, supplemented by a program to provide an illustration of single Gaussian peaks besides the cumulative curve. Fortunately, the spectra of the dehydrated compounds are well-resolved and their reliably fitted profile data could serve as input for the less-resolved spectra of the as-grown respectively hydrated natural compounds, thereby applying variable constraints to parameters (mainly the band width) during successive refinement cycles. Results of a Gaussian deconvolution of the UV-VIS spectra for the hydrated and dehydrated compounds, respectively, are given in Table 1 and depicted in Figures 3(a)-(d). λ(nm) and Γ(nm) represent wavelength and the full width of the excitation peaks, and the wavenumber E(cm⁻¹) denotes the excitation energy. The

Table 1

Results of the Gaussian profile deconvolution of the UV-VIS spectra of the dioptase family

Cu6Si6O18・6H2O (dioptase)					Cu6Ge6O18・6H2O (Ge-dioptase)
P	λ(nm)	Γ(nm)	E(cm−1)	Assignment	P	λ(nm)	Γ(nm)	E(cm−1)	Assignment
329	935 ± 37	208	10,700	ΔA	1000	842 ± 30	198	11,884	ΔB + ΔA
815	869 ± 12	208	11,507	ΔB
1000	695 ± 7	194	14,400	ΔE	645	698 ± 24	166	14,321	ΔE
256	600	109	16,670	ZRS?	185	616	129	16,230	ZRS?
421	414	108	24,160	SPE?	271	462	147	21,650	SPE?
(554)	326	102	30,660	Eg	(531)	353	97	28,350	Eg
Cu6Si6O18 (dioptase dehydrated)					Cu6Ge6O18 (Ge-dioptase dehydrated)
P	λ(nm)	Γ(nm)	E(cm−1)	Assignment	P	λ (nm)	Γ(nm)	E(cm−1)	Assignment
1000	811 ± 14	158	12,330	ΔB	1000	827 ± 14	155	12,100	ΔB
866	668 ± 12	120	14,960	ΔE	843	679 ± 12	127	14,723	ΔE
492	558 ± 11	96	17,930	ΔA	450	565 ± 12	97	17,700	ΔA
235	441	100	22,680	SPE?	355	437	108	22,880	SPE?
(869)	330	120	30,300	Eg	(630)	357	102	28,000	Eg

P integrated band intensity (arbitrary units), Γ(nm) full band width at half f, E(cm⁻¹) band energy, SPE assumed simultaneous pair excitation, ZRS less intense band observed only in the hydrated compounds around 2 eV could correspond to a Zhang-Rice singlet excitation, E_g large energy gap.

Figure 3

UV-VIS spectra of (a) dioptase; (b) dioptase dehydrated; (c) Ge-dioptase; (d) Ge-dioptase dehydrated. Measured spectra red, calculated spectra blue. A mineral sample of dioptase from Altyn Tyube, Kazakhstan was used besides synthetic Ge-dioptase

remarkable integrated band intensity P (given in arbitrary units) is the consequence of non-zero dd transition probabilities due to the absence of symmetry elements on the Cu position with C₁ site symmetry and the disphenoidic (stocky tetrahedral) oxygen environment with 4 distinct equatorial bond lengths indicating Cu_3d-O_2p hybridization. The relative width Γ/λ of the bands of the dehydrated compounds is about 18%, whereas that of the hydrated ones suffer additional broadening to about 23% caused by a vibronic contribution of the water molecule rings and due to assumed peak overlapping according to the below presented assignment.

The steep increase of absorption at the badly resolved high energy limit of the UV-VIS spectra has been simulated by a Gaussian curve, too, and may be interpreted as absorption edge, the large gap between valence and conduction band of isolator compounds. The gap is determined around 3.80 eV for dioptase and shifts to 3.76 eV for Ge-dioptase, respectively. It is slightly lower for the dehydrated compounds, giving 3.52 and 3.47 eV, respectively (Table 1). For comparison, Rudko [24] observed an absorption edge near 3.5 eV for the charge transfer insulator CuGeO₃. The absorption structures at high energy just before the energy gap may be attributed to simultaneous ligand field transitions, involving both metal centers of the dimer at twice the monomer transition energy (SPE), because their oscillator strengths are too weak for charge transfer (CT) transitions. The position of a less intense absorption band observed only for the hydrated compounds around 2 eV (16,670 cm⁻¹, 16,230 cm⁻¹) would correspond to Zhang-Rice singlet excitations (ZRS), for instance, measured at this energy on CuO (tenorite) [25] and CuGeO₃, respectively [26] .

The color of Cu²⁺ compounds with their Jahn-Teller distorted coordination polyhedra [27] is the conspicuously recognized property of this transition metal ion and is attributed to electronic excitations between its d-orbitals. The coordination polyhedron of copper in the d⁹ state with the unpaired electron in the x² − y² orbital is an elongated octahedron leading to splitting of formerly degenerated d-states. A recently found impressive example for a Jahn-Teller elongated octahedron is the new prototypic crystal structure of tetragonal CuO with a c > a rock salt structure [28] .

The transition energies ∆_n (cm⁻¹), derived from broad Gaussian-shaped absorption bands of UV-VIS spectra, are the energy differences between the

ground state and the, and ex- cited states and can be connected with crystal field splitting parameters repre- senting orbital energies. Bearing in mind the Cu²⁺ site symmetry of D_4h or lower, we are faced with an equatorial Dq_e splitting parameter and two radial Ds and Dt ones (Gerloch and Slade, [29] ). The crystal field theory (CFT) allows for the following relations:

Conversely, the D parameters can be recalculated as

Whereas ∆_E is always moderately larger than ∆_B, ∆_A ranges from about 8500 cm⁻¹ (<∆_B) for shortest axial bonds to at least 21,500 cm⁻¹ (>∆_E) for axially non- existent bonds (squared-planar coordination).

A more quantitative description of ligand field parameters using effective charges and bond lengths results in the following relations [29] :

where represents an effective ligand charge, R_e and R_a are equatorial and axial bond lengths in Å, and = 0.214 Å⁴ is the mean value of the fourth power of a 3d orbital radial distance from the nucleus, respectively = 0.294 Ų the mean of the second power of the radial distance. For the values calculated by Haverkort within the Hartree-Fock approximation are used [30] . Because is a measure proportional to the Cu(II) effective nuclear charge, one should multiply this value by a factor of 4 to give a realistic value of about 0.85 for the Scott charge, which would represent 42.5% ionicity of the Cu-O bond.

Quoting Gerloch and Slade [29] ones more, in the crystal-field theory with its point-charge formalism charges as well as bond lengths have to be considered as effective parameters that are not independent of each other. Therefore, cationic and ligand charges should be combined to common adaptable factors respectively.

For comparison of calculated band energies with experimental ones given in cm⁻¹ an energy conversion factor is applied.

Lebernegg et al. [31] found no general theoretical justification for R⁻⁵ dependence of ligand-field splitting. Nevertheless, one can use the inverse fifth power relationship Dq_e µ R⁻⁵ in order to calculate a linear regression curve of Dq_e (or D_B) values against the mean of the four equatorial copper-oxygen distances R_e(Å) according to Equation (7) for selected compounds with a reduced connectedness with respect to equatorial sharing, at the beginning excluding sheet structures as exemplified by cuprates.

The plot is depicted in Figure 4 and extrapolates well through the origin with, giving effective charge numbers of Q_e = ± 1.313 assumed to be evenly distributed over Cu²⁺ and ligands. The calculated Dq_e values deviate less than 1.6% from the experimental ones.

We chose compounds of the Egyptian Blue family (cuprorivaite, wesselite, effenbergite,) with isolated D_4h plaquettes, the dehydrated dioptase compounds with equatorially edge-shared dimers, further connected via water oxygen to

Figure 4

Calculated Dq energies versus experimental ones for dioptase and related compounds. In the right plot, an additional magnetic contribution of Dq calc for cuprates was considered

corner-shared spiral chains in the fully hydrated compounds, litidionite as characterized by pyramid-edge-shared dimers (cis-arrangement), in contrast to lammerite with infinite chains of such units and with two distinct Cu sites, further azurite with “octahedral” chains (two distinct sites), and finally conichalcite and CuGeO₃ showing infinite single chains with equatorially edge-shared “octahedra”. One may learn more about the structural hierarchy of special copper oxy-salt minerals from Eby and Hawthorne [32] . Selected crystal data as well as UV-VIS data were summarized in the Table 2 and Table 3 with references.

Table 2

Coordination numbers CN, bond length and bond valence sums s for selected Cu(II) compounds. s e equatorial sum, s a axial sum, Ss overall sum (particularly striking values in red)

Compound	CN	d(Cu-O) (Å)	Bond strength			Reference
			se	sa	Ss
Ca0.5Sr0.5CuO4	4	1.945	1.913	-	1.913	[41]
CaCuO2		1.928	2.004	-	2.004	[33]
BaCuSi4O10 Effenbergite		1.925	2.022	-	2.022	[42]
SrCuSi4O10 Wesselite		1.925	2.022	-	2.022	[43]
CaCuSi4O10 Cuprorivaite		1.929	1.998	-	1.998	[44]
Cu6Si6O18	4 + (1)	1.9250 1.9294 1.9354 1.9466 3.3153	1.969	0.023	1.992	[20]
Cu6Ge6O18		1.9043 1.9284 1.9380 1.9979 3.3841	1.954	-	1.954	[17]
Y2BaCuO5	2 + 2 + 1	1.985 1.988 2.206	1.692	0.232	1.923	[45]
CuGeO3	4 + 2	1.941 2.926	1.941	0.093	2.022	[1] [2] [3]
Cu6Si6O18・6H2O	6	1.952 1.952 1.959 1.983 2.502 2.648	1.818	0.195	2.014	[46]
Cu6Ge5.4Si0.6O18・6H2O	6					[17]
Cu6Ge6O18・6H2O	6	1.9037 1.9486 1.9547 1.9884 2.6364 2.6696	1.894	0.159	2.053	[11]
Cu3(CO3)2(OH)2 Azurite	2 + 2 + 2 Cu(1) site	1.9387 1.9455 2.9840	1.953	0.083	2.036	[47]
	6 Cu(2) site	1.9385 1.9388 1.9675 1.9947 2.3608 2.7578	1.830	0.223	2.053
CuSO4 ・5H2O Chalcanthite	2+2+2 Cu(1) site	1.9748 1.9770 2.3858	1.769	0.250	2.019	[48]
	2+2+2 Cu(2) site	1.9447 1.9696 2.4400	1.739	0.293	2.033
KNaCuSi4O10 Litidionite	6	1.9220 1.9434 1.9683 1.9799 2.6238 3.4024	1.863	0.109	1.972	[22] ; this work
Cu3(AsO4)2 Lammerite	2 + 2 + 2 Cu(1) site	1.933 1.974 2.923	1.864	0.093	1.957	[49]
	6 Cu(2) site	1.941 1.947 1.972 2.028 2.282 2.782	1.772	0.254	2.026
CaCuAsO4OH Conichalcite	6	1.8850 1.8855 2.0666 2.0688 2.2976 2.3882	1.811	0.332	2.143	[50] ; this work
La2CuO4	4 + 2	1.9043 2.4145	2.151	0.278	2.439	[51]
Sr2CuO2Cl2	4 + 2	1.9864 2.860	1.687	0.292	1.979	[52]

Table 3

Collection of some properties and data for selected Cu(II) oxo-compounds. , , , energies in cm −1 . Other transitions: CT charge transfer, SPE simultaneous pair excitation, ZRS? Zhang Rice excitation, E g energy gap

Compound	Color	Cu site symmetry	ΔB	ΔE	ΔA	Other Transition	Reference
CaCuO2 (infinite layer)	dark-grey	D4h	13,230	15,730	21,370	-	[33]
Tenorite CuO	brownish	Ci	12,170	12,930 15,530	16,670	many	[53] **
Conichalcite synth. CaCuAsO4OH	light green	C1	10,575	12,500	8585	15,313 ZRS? 31,370 (Eg)	[54]
Lammerite synth. Cu3(AsO4)2	dark green	C1 Ci	11,530	12,400 14,050	10,200 14,050	23,260 CuO 31,250 (Eg)	[22] ; this work*
Y2BaCuO5	vivid green	D4h	12,500		14,700	25,970 CT	[55] **
			10,700	13,200
Azurite Cu3(CO3)2(OH)2	blue	Ci C1	11,806 11,806	16,484 11,806	16,484 11,806	19,793 17,952	[56] ** T = 80 K
Chalcanthite CuSO4・5H2O	deep blue	C1 C1	11,407 11,860	13,308 13,488	9699 9735	15,234 ZRS? 15,567	[57]
Litidionite synth. KNaCuSi4O10	light blue	Ci	11,723	14,700	13,900	21,400 SPE 31,600 (Eg)	[22] [23] ; this work
Cu6Ge6O18	dirty blue	C1	12,100	14,723	17,700	22,880 SPE	[17] ; this work
Cu6Ge6O18・6H2O	bluish-green	C1	11,880	14,320	11,880	16,230 ZRS? 21,650 CT 30,300 (Eg)	[17] ; this work
Cu6Ge5.4Si0.6O18・6H2O	dark green	C1	13,300		19,400	23,900 CT	[17]
CuGeO3	turquoise	D2h	12,570	13,970	12,920	15,733 ZRS? 15,800	[24] ; this work
BaCuSi4O10 synth. (Effenbergite)	deep blue	D4h	12,200	15,950	18,520	-	[58]
SrCuSi4O10 synth. (Wesselite)			12,480	16,050	18,520	-	[58]
CaCuSi4O10 synth. (Cuprorivaite)			12,590 12,740	15760 16130	18,530 18,520	-	[44] [59]
Dioptase dehydrated Dioptase partly dehydrated	black dark blue	C1	12,330 12,500	14,960 14,500	17,930 17,600	22,680 SPE -	This work; [19]
Dioptase Cu6Si6O18・6H2O	emerald green	C1	11,500 12,495	14,500 15,010	17,000 10,200		[18] [19]
			11,507	14,400	10,700	16,670 ZRS? 24,160 CT 30,660 (Eg)	This work

*synthetic lammerite with an amount of CuO; **for this work a different assignment as given in the reference was used.

Recently, the energy and symmetry of dd excitations of some undoped layered cuprates have been measured by CuL₃ resonant X-ray scattering [33] . The well- assigned dd excitations of these compounds with high connectedness were found to be higher than the energies of the compounds described before. Multiferroic CuO as limiting case can be added to this group with due allowance. Applying Equation (a), a steeper slope with results, representing higher excitation energies and effective charges (Q_e ± 1.35) than for the dioptase group.

The different connectedness of cuprates in comparison to the dioptase group is manifested in a larger contribution of the principal magnetic super-exchange interaction J_z to the optical excitation energies. In Figure 5, this contribution is depicted versus the Cu-O-Cu bond angle Φ, a representation first used by Rocquefelte et al. [34] , and here applied in an extended form, illustrating both dioptase group compounds and cuprate ones. A data fit resulted in the relation

with an exponent near 5/3, explained by chemical pressure (Rocquefelte et al., 2012) [34] [35] . Adding J_z(Φ)・ln(2) as bond angle dependent contribution to the bond length dependent one, a surprisingly good agreement is achieved between the two groups of compounds, now giving, respectively Q_e = 1.312. It should be noticed that for the dioptase group an antiferromagnetic contribution is not included because T_N is lower than room temperature_, at which the optical spectra are taken.

The R⁻⁵ inverse power of Cu-O bond lengths is nearly a measure for the bond strength. Therefore, the reliability of the fit can be enhanced applying the empirical Cu-O bond strength relation s = Σ(R/R₀)^−N [36] by choosing only the

Figure 5

Principal superexchange interaction J z versus Cu-O-Cu bond angle Φ [ 34 ] [ 35 ]

bond strength sum s_e of the four equatorial bonds. New values R₀ = 1.713(9) Å, N = 5.76(16) were re-calculated for this work [37] . Results of a double-regression yielded for the cuprate group

respectively (12b)

for both the dioptase group and cuprates. Δ_B of the last mentioned group is corrected by a bond angle dependent (magnetic) contribution (Figure 6). It is recommended to extend the analytic bond strength-bond length expression by a magnetic (angle dependent) contribution. In contrast to this result, the quoted authors [33] fitted their cuprate data with a lower slope of N = 4.2. On the other hand, the selection of compounds for such fit is not convincing, because an influence of some equatorial O⁻ ions in La₂CuO₄ (high bond strength, see Table 2) on the excitation energies can be expected. In addition, the epitaxially grown infinite-layer structure of Ca_0.5Sr_0.5CuO₂ is obviously strained.

Turning now to the calculation of splitting parameters Ds (Equation (9)) and Dt (Equation (10)) involving axial ligands one has to distinguish according to the Nephelauxetic Effect between pure oxo-ligands and such ones as H₂O or Cl⁻ with increased cationic charge and assumed higher Dq_a values [29] . H₂O (as equatorial ligands) are found in chalcanthite, and hydroxyl groups in azurite and conichalcite. The last compound has the most distorted “octahedron” and should show a pronounced splitting of the ²E_g term, which is not considered here.

Figure 6

A linear relation between Dq (cm −1 ) and the equatorial bond strength s e , in case of cuprates (red curve) corrected by a bond angle dependent (magnetic) contribution to show a single linear plot (green curve) with dioptase group compounds (yellow) besides cuprates (now green)

In the case of square-planar environment it is useful to limit the extent of the orbital with “long” auxiliary axial bonds. Dehydrated dioptase and the germanate analogue already have some far distant oxygen ions (see Table 2) within the orbital sphere of influence. For the group of M²⁺CuO₂ layered cuprates the limit is given by the layer separation down c of about 3.3 Å. Again the results differ somewhat for the two groups of compounds with slightly different effective charges. From the fitted values for Ds and Dt the Δ_E (Equation (2)) and Δ_A (Equation (3)) energies have been calculated as well as ²E_g and ²A_1g. Results are summarized in Table 4.

In order to check the correct assignment one can use a relation between experimental B_2g, E_g and A_1g values of form, which results from Equations (1) to (3). Obviously, this relation holds only for shortest axial bonds and more octahedral ligand environment, such fulfilling the precondition for the underlying ionic model. For non-existent axial bonds the value for the quotient is close to unity. The values listed in Table 4 indicate clearly bond length dependence. An empirical function may serve as a correction giving quotients f(Δ)/f(R) near unity when using α₁ = 0.59 for dioptase group compounds respectively 0.70 for cuprates. Compounds with axial water ligands or Cl⁻ can clearly be identified by relatively small values. Another possibility here published the first time ever is to use the linear relation

, where, (13)

with a R_a/R_e ratio including well adapted auxiliary R_a bonds for compounds of coordination number 4, but different ε values for the dioptase group () and cuprates () to guide the regression line well through the origin (Figure 7 and Table 5).

It should be stressed with respect to the use of mean bond distances in Equation (13) that also in the Equations (7) to (10) the mean of corresponding bond distances is taken first and then their inverse fifth power is calculated to yield the convincing results of Table 4.

An additional scaling between 1.7 and 2.0 (Equation (10)) is needed to fit the Dt values of compounds with H₂O respectively Cl⁻ as axial bonds. Also, La₂CuO₄ needs such correction () possibly caused by some O^- expected as axial ligands. Applied scaling factors were summarized as supplemented material in the Table 7.

Indeed, the connectedness of copper-ligand units, representing the number of shared copper-oxygen polyhedra, should be important for the dd excitation energy. Therefore, besides the equatorial ligand sums that are calculated as fit coordinate, we used the bond valence sums to check for inconsistent structural details and signs for mixed valences. Copper polygermanate in the Pbmm prototypic structure [1] [2] shows too high a sum with Σs = 2.08. There is evidence from EPR [38] , X-ray diffraction [39] and NQR measurements [40] that copper is statistically out of center of the CuO₂ plaquette, in this way the copper bond

Table 4

Comparison of experimental and calculated excitation energies and orbital ones in cm −1 . Δ B is sorted from high values to low ones down the table; , . Experimental and calculated Δ values are arranged one above the other

Isolated CuO plaquettes, clusters and chains: Calculation with, , , ,
Phase	ΔB	ΔE		ΔA	Ds	Dq	Dt	Dt/Dq	Dt/Ds	f(Δ)		f(Δ)/f(R)	Ligands
													equat.	axial
Cuprorivaite	12,590 12,501	15,760 15,446		18,530 18,414	3100 3051	1259 1250	1226 1241	0.974	0.395	0.979		0.956	oxygen	no
CuGeO3	12,570 12,439	13,970 14,209		13,970 14,324	2196 2299	1257 1244	1037 1026	0.825	0.472	0.909		1.081	oxygen	oxygen
Effenbergite	12,500 12,566	15,950 15,895		18,520 18,591	3139 3132	1250 1257	1139 1213	0.955	0.380	0.955		0.930	oxygen	no
Wesselite	12,480 12,566	16,050 15,895		18,520 18,591	3156 3132	1248 1257	1179 1213	0.945	0.374	0.944		0.920	oxygen	no
Dioptase black	12,330 12,324	14,960 15,057		17,930 17,850	2937 2940	1233 1232	1236 1218	1.003	0.421	1.019		1.013	oxygen	no
Cu6Ge6O18	12,100 12,123	14,723 14,845		17,700 17,606	2903 2904	1210 1212	1217 1198	1.006	0.419	1.020		1.017	oxygen	no
Ge-Dioptase	11,884 11,929	14,321 14,434		11,884 12,084	2046 2084	1188 1193	740 750	0.623	0.362	0.709		0.866	oxygen	H2O
Azurite (1)	11,806 12,070	16,484 14,162		16,484 15,014	− 2444	1181 1207	− 1048	0.770	0.317	0.809		1.024	OH−/ oxygen	oxygen
Azurite (2)	11,550 11,589	12,770 12,924		11,300 11,669	1789 1858	1155 1159	829 848	0.718	0.464	0.808		1.067	OH−/ oxygen	oxygen
Litidionite	11,723 11,794	14,700 14,465		13,900 13,917	2411 2397	1172 1179	851 866	0.726	0.353	0.786		0.915	oxygen	oxygen
Lammerite (1)	11,780 11,735	13,744 13,744		14,356 14,357	2331 2328	1178 1174	1006 1000	0.854	0.432	0.914		0.914	oxygen	oxygen
Lammerite (2)	11,280 11,231	12,400 12,425		10,200 10,279	1617 1639	1128 1123	746 745	0.662	0.461	0.754		1.023	oxygen	oxygen
Chalcanthite (1)	11,407 11,135	12,600 12,302		8900 8828	1442 1428	1141 1113	627 623	0.549	0.435	0.645		0.906	H2O	oxygen
Chalcanthite (2)	11,860 11,678	13,488 13,369		9735 98,108	1623 1643	1186 1168	648 648	0.547	0.399	0.644		0.875	H2O	oxygen
Dioptase green	11,508 11,491	14,398 14,094		10,700 10,325	1940 1847	1151 1149	588 587	0.511	0.303	0.619		0.801	oxygen	H2O
Conichalcite	11,400 11,119	12,195 11,922		8585 8449	1340 1339	1140 1141	645 658	0.566	0.481	0.661		0.940	OH−	oxygen
Y2BaCuO5	10,700 13,200*)			14,700 14,571	2457 2435	1070 1073	974 966	0.911	0.397	0.936		0.904	oxygen	oxygen
	10,732		13,205
Cuprates (undoped): Calculation with, , , ,
Phase	ΔB	ΔE		ΔA	Ds	Dq	Dt	Dt/Dq	Dt/Ds	f(Δ)	f(Δ)/f(R)		Ligands
													equat.	axial
La2CuO4	14,516 14,308	17,097 16,833		13,710 13,664	2327 2313	1452 1431	880 883	0.606	0.378	0.697	0.788		oxygen	O−?
CaCuO2	13,226 13,322	15,726 15,982		21,370 21,671	3410 3476	1323 1332	1546 1554	1.169	0.453	1.173	0.994		oxygen	no
Sr0.5Ca0.5CuO2	12,581 12,744	15,565 15,494		21,452 21,026	3491 3397	1258 1274	1498 1488	1.190	0.429	1.157	0.976		oxygen	no
NdBa2Cu3O6	12,258 12,372	14,113 13,741		15,968 15,940	2546 2473	1226 1237	1157 1210	0.944	0.454	1.000	1.072		oxygen	oxygen
CuO (tenorite)	12,170 12,254	14,230 14,520		16,670 16,878	2676 2735	1217 1225	1193 1188	0.981	0.446	1.023	1.027		oxygen	oxygen
Sr2CuO2Cl2	12,097 11,838	14,839 14,756		15,887 16,021	2661 2706	1210 1184	1048 1040	0.867	0.394	0.904	0.897		oxygen	Cl−

*) The broad band at 12,500 cm⁻¹ is proven to split into two bands at about 10,700 cm⁻¹ and 13,200 cm⁻¹, respectively.

Table 5

Experimental ∆ A energies versus calculated ones using the relation: ∆ A = 17,892・( ) (cm −1 ), for dioptase group and for cuprates. Auxiliary bonds introduced in case of compounds with coordination number CN = [ 4 ] are underlined

Phase	CN	e> (Å)	a> (Å)	ΔA (exp.)	ΔA (calc.)
Cuprorivaite	[4]	1.9307	3.35	18,530	18,393
CuGeO3	[4 + 2]	1.9326	2.7549	12,920	12,854
Effenbergite	[4]	1.9265	3.35	18,520	18,460
Wesselite	[4]	1.9265	3.35	18,520	18,460
Dioptase black	[4]	1.9340	3.30	17,930	17,874
Cu6Ge6O18	[4]	1.9404	3.30	17,700	17,777
Ge-Dioptase	[4 + 2]	1.9474	2.6622	11,884	11,808
Azurite (1)	[4 + 2]	1.9434	2.9840	16,488 (?)	14,821
Azurite (2)	[4 + 1 + 1]	1.9593	2.5143	11,806	10,309
Litidionite	[4 + 2]	1.9525	2.8434	13,900	13,404
Lammerite (1)	[4 + 2]	1.9529	2.9230	14,350	14,128
Lammerite (2)	[4 + 1 + 1]	1.9703	2.4609	10,200	9695
Chalcanthite (1)	[4 + 2]	1.9759	2.3858	8900	8952
Chalcanthite (2)	[4 + 2]	1.9569	2.4400	9735	9657
Dioptase green	[4 + 2]	1.9613	2.5688	10,700	10,735
Conichalcite	[2 + 2 + 2]	1.9640	2.3403	8585	8668
Y2BaCuO5	[4 + 1]	1.9899	2.196 + 3.90	14,700	14,754
La2CuO4	[4 + 2]	1.9043	2.4045	13,710	13,646
CaCuO2	[4]	1.9281	3.26	21,370	21,306
Sr0.5Ca0.5CuO2	[4]	1.9440	3.30	21,452	21,426
NdBa2Cu3O7-δ	[4 + 1]	1.9609	2.275 + 3.25	15,968	16,260
CuO (tenorite)	[4 + 2]	1.9558	2.7842	16,670	16,524
Sr2CuO2Cl2	[4 + 2]	1.9864	2.8600	15,887	16,841

strength is reduced towards the net charge of 2+. Even large thermal displacement ellipsoids indicate structural features that require a careful evaluation. Bond lengths should be corrected for “thermal” displacement because not less than their inverse fifth power is used in calculations (see for instance [51] ).

4. EPR Analysis

Finally, the assignment of the dd excitations can be compared with results of EPR measurements. For 3d⁹ ions in (nearly) tetragonal ligand symmetry one can apply the following two formulas for the principal components g_|| and g_﬩, if the ground state is ²B_1g:

Figure 7

Δ A excitation energies (cm −1 ) depicted versus a function of axial to equatorial bond distances. Again the cuprate group excitations (in red) must be corrected by a (magnetic) contribution to reliably represent all data in a single regression line. Auxiliary axial bonds (see the yellow field) were introduced in case of compounds with really missing axial bonds (coordination number 4)

where g_e = 2.0023 is the g-value for the free electron, and λ is the spin-orbital coupling parameter, which yields for the free Cu²⁺ ion λ_o = 829 cm⁻¹ [60] .

The k values are the spin orbital reduction factors used to scale the coupling parameters to the free Cu²⁺ ion value, k = λ/λ_o. This parameter reduction is attributed to covalence effects. Table 6 compares the results for dioptase and Ge- dioptase, respectively. Not surprisingly, the found covalence reduction effect is markedly smaller for the copper germanate than for the copper silicate, in accordance with crystal-chemical experience, confirming higher ionicity of the germanate (Table 6). Unfortunately, EPR data for the dehydrated compounds were not available.

Table 6

EPR analysis of dioptase related compounds

Notation	Dioptase	Ge-Dioptase
ΔB	11,508	11,884
ΔE	14,395	14,321
ΔA	10,700	11,884
g||	2.3601	2.3780
g﬩	2.0511	2.0970
λ||	−504.08	−545.53
k||	0.608	0.658
λ ﬩	−346.91	−662.63
k﬩	0.418	0.799

5. Conclusion

As shown, a comparative reappraisal of Cu²⁺ UV-VIS spectra benefits from a special consideration of crystal-chemically similar groups of compounds, com- paring exemplarily the dioptase group, covering minerals as well as synthetic samples, with cuprates. The assignment of dd excitations and their representa- tion each on a single curve is possible by attributing a magnetic (bond angle de- pendent) contribution to the cuprate group. It is recommended to extend the bond strength-bond length relation by a bond angle dependent (magnetic) con- tribution. Deviations of the linear representation of orbital excitation energies may be helpful to discriminate results of compounds with peculiar orbital features from those with normal behavior. Fortunately, the first done assignment of well-resolved spectra of dehydrated dioptase Cu₆(Ge,Si)₆O₁₈ served as input data to deconvolute the badly resolved spectra of as-grown Cu₆(Ge,Si)₆O₁₈・6H₂O samples. At present, the deconvolution of superposed spectra resulting from different Cu sites of a structure is inadequate. However, a pre-calculation of the expected energy levels can serve as input for fitting the experimental spectra. This has been successfully applied to lammerite. It is recommended to take a series of UV-VIS spectra step by step over the entire temperature range from hydrated to fully dehydrated dioptase as a didactic tool to follow the energy levels and their correct assignment, thereby simultaneously controlling the crystal water content by IR spectroscopy with a device that offers both analytical possibilities. Especially it should be investigated whether a Zhang-Rice excitation like that observed for CuGeO₃ can be confirmed for the hydrated compounds of the dioptase family, too. In addition, the proposed assignment of the dd excitations of the green phase YBa₂CuO₅ should be supported by a CuL₃ resonant X-ray scattering investigation.

Acknowledgements

The author would like to thank colleague Prof. Bernd Lehmann for supporting this work by the donation of wonderful dioptase pieces from Altyn-Tyube, Kazakhstan. Also my teacher, the late Prof. Hugo Strunz, donated dioptase pieces from the Tsumeb mine, Namibia.

Conflict of Interest

The author declares no conflict of interest.

Supplemented Material

Table 7

Comparison of scaling factors used for Cuprates in comparison to dioptase group compounds

Scaling factor notation	Cuprates	Dioptase group	Ratio
	1.755	1.733	1.013
	0.936	0.761	1.230	1.243
	1.587	1.276	1.244
	2.180	1.738	1.254

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