Hydration and Ion Pair Formation in Aqueous Lu³⁺- Solution

Abstract

Aqueous solutions of Lu³⁺- perchlorate, triflate and chloride were measured by Raman spectroscopy. A weak, isotropic mode at 396 cm⁻¹ (full width at half height (fwhh) at 50 cm⁻¹) was observed in perchlorate and triflate solutions. This mode was assigned to the totally symmetric stretching mode of [Lu(OH₂)₈]³⁺, ν₁LuO₈. In Lu(ClO₄)₃ solutions in heavy water, the ν₁LuO₈ symmetric stretch of [Lu(OD₂)₈]³⁺ appears at 376.5 cm⁻¹. The shift confirms the theoretical isotopic effect of this mode. In the anisotropic scattering of aqueous Lu(ClO₄)₃, five bands of very low intensity were observed at 113 cm⁻¹, 161.6 cm⁻¹, 231 cm⁻¹, 261.3 cm⁻¹ and 344 cm⁻¹. In LuCl₃ (aq) solutions measured over a concentration range from 0.105–3.199 mol·L⁻¹ a 1:1 chloro-complex was detected. Its equilibrium concentration, however, disappeared rapidly with dilution and vanished at a concentration < 0.5 mol·L⁻¹. Quantitative Raman spectroscopy allowed the detection of the fractions of [Lu(OH₂)₈]³⁺, the fully hydrated species and the mono-chloro complex, [Lu(OH₂)₇Cl]²⁺. In a ternary LuCl₃/HCl solution, a mixtrure of chloro-complex species of the type [Lu(OH₂)_8−nCl_n]⁺³⁻ⁿ (n = 1 and 2) were detected. DFT geometry optimization and frequency calculations are reported for Lu³⁺- water cluster in vacuo and with a polarizable dielectric continuum (PC) model including the bulk solvent implicitly. The bond distance and angle for [Lu(OH₂)₈]³⁺ within the PC are in good agreement with data from structural experiments. The DFT frequencies for the Lu-O modes of [Lu(OH₂)₈]³⁺ and its deuterated analog [Lu(OD₂)₈]³⁺ in a PC are in fair agreement with the experimental ones. The calculated hydration enthalpy of Lu³⁺ (aq) is slightly lower than the experimental value.

1. Introduction

The element lutetium (Lu), a silvery white metal with the atomic number 71, is the heaviest of the lanthanides and has a full f-electron shell with a configuration: [Xe] 4f¹⁴5d¹6s². With a crustal abundance of 0.32 ppm [1,2], it is one of the rarest of the lanthanides. Because of this rarity and accompanying high price, only a few applications of this metal are known to date. Lutetium is used as a catalyst for cracking hydrocarbons in oil refineries [3,4]. Lutetium aluminum garnet (LuAG, Lu₃Al₅O₁₂) is primarily known for its use in high-efficiency laser devices [5]. Lutetium oxyorthosilicat (LSO), a silicon oxygen compound of lutetium doped with cerium, is utilized as a detector for positron emission tomography [6]. Naturally occurring lutetium comprises two isotopes: ¹⁷⁵Lu and ¹⁷⁶Lu. ¹⁷⁶Lu is unstable with an extremely long half-life of 3.78 × 10¹⁰ years which makes it suitable for determining the age of meteorites [7]. A short lived radionuclide ¹⁷⁷Lu (half-life of 6.6430 days [8]) is used in the treatment of certain tumors, mainly neuroendocrine tumors [9].

In aqueous solution, lutetium exists exclusively in the trivalent state, Lu³⁺, and is strongly hydrated due to its high charge to radius ratio. Trivalent lutetium has the smallest ionic radius of all 15 lanthanides (Ln³⁺) across the series from lanthanum to lutetium known as the lanthanide contraction. Lu³⁺ hydrolyses most, i.e. shows a lesser basicity, than the preceding trivalent rare earth ions in aqueous solution. The difference in basicity is the basis for all separation methods of the individual rare earth ions [10]. The hydrolysis constant for the first monomeric species, β₁^o at 25 °C for LuOH²⁺ is 4.677 × 10⁻⁸, the largest across the series, while for LaOH²⁺, the lowest, it is 1.288 × 10⁻⁹ [11]. However, compared to other trivalent metal ions such as Al³⁺ or Fe³⁺, the hydrolysis is much less pronounced.

Light rare earth ions are nonahydrates while the heavy rare earth ions are octahydrates in aqueous solution with weakly complex forming anions. The crossover of the hydration number from 9 to 8 occurs in the middle of the series. This sudden change in hydration number, known as gadolinium break, was used to explain experimental data in aqueous solution [12,13,14,15]. Recent studies, however, concluded that no such break exists and that the hydration number of Ln³⁺ ions smoothly changes from 9 to 8 across the series [16,17,18] with the rare earth (RE) ions of the series having non-integer numbers between 9 and 8 in the middle of the series. This means that the water ligands in the nona-/octa- hydrates exchange rapidly with each another [19,20].

For the Lu³⁺ ion in aqueous solution, the local hydration structure was measured using extended X-ray absorption fine structure (EXAFS) spectroscopy [16,21,22,23,24] and X-ray diffraction [25,26]. The majority of studies agreed with the 8-fold coordination of water molecules grouped around Lu³⁺ in square antiprismatic (SAP) geometry. A combined study using molecular dynamics (MD) simulation and EXAFS measurement proved the SAP structure of the Lu³⁺- octahydrate and the Lu³⁺-O bond distance was given at 2.32 Å [21].

The reported Lu-O bond distances range from 2.282 Å to 2.35 Å. These variations may be due to the fact that XRD measured concentrated solutions while EXAFS used relatively dilute solutions [16,21]. However, such differences in concentration scale, pose a problem because ion pairs are likely to form in concentrated solutions [26,27,28,29]. Ion association studied on these solutions do not agree on the nature of the ion pairs/complex species formed. In addition to the detected complex species, there is no doubt that outer-sphere and outer-outer sphere ion pairs exist in rare earth solutions. A recent dielectric relaxation spectroscopy (DRS) study on chloride, nitrate and sulfate solutions of La³⁺ and Eu³⁺ claimed, exclusively, outer-sphere and outer-outer-sphere ion pairs in these solutions [30]. However, in a variety of studies applying a wide array of methods such as solvent extraction [31,32,33,34], ion exchange [35,36,37], fluorescence spectroscopy [38,39,40], ultrasound absorption [41,42,43,44] and NMR spectroscopy [45,46,47], it was convincingly shown that complex species also exist in aqueous solution contrary to the new DRS results [30] put forward.

Raman spectroscopy probes the immediate environment of metal ions in solution and was frequently used to study hydrated metal ions and ion association. RE-ions, however, have only recently been measured at a sufficiently high quality in the low frequency region of the Raman spectrum. These spectra then allow the construction of the isotropic scattering profile from the measured data. A highly polarized band in the low frequency region of the Raman spectrum due to the symmetrical metal-oxygen mode of the hydrated cations is the most characteristic peak [26,27,28,29,48,49,50,51]. This mode is sensitive to possible ion pair formation. Occasionally, all the theoretically predicted bands of the metal-oxygen modes may be observed and used to support the assignment of the point group symmetry and the coordination number in these aqueous solutions. Raman scattering measurements on Lu³⁺ (aq) should allow, in principle, the characterization of the solution structure in greater detail. No systematic Raman studies on aqueous lutetium solutions exist but one study on a glassy LuCl₃ (aq) sample at high concentrations was reported [52].

The present study was undertaken to characterize the hydration and speciation in aqueous Lu³⁺ solutions and to this end Lu³⁺-salt solutions with common anions (ClO₄⁻, CF₃SO₃⁻ and Cl⁻) were considered over a broad concentration range and down to the low frequency region. Triflate (trifluoromethanesulfonate) and perchlorate are considered weakly-complex-forming anions and were, therefore, chosen to measure the Lu-O stretching modes in aqueous solution so as to identify and assign bands unique to the first hydration sphere of Lu³⁺ (aq). A Lu(ClO₄)₃ solution in heavy water was also measured to characterize the vibrational isotope effect by changing from [Lu(H₂O)₈]³⁺ to [Lu(D₂O)₈]³⁺. In a variety of di- and trivalent metal ion solutions with chloride as counterion, however, it has been shown that these anions readily form complexes [27,28,29] and the question arises as to whether chloro- complex species occur in Lu³⁺ (aq) solutions. A LuCl₃ solution series and a ternary solution of LuCl₃/HCl were studied in order to answer the question whether chloro-complex species exist and if possible to quantify the fraction of the chloro-complex species.

In addition, simulations on lutetium-water species with eight water molecules were considered by applying density functional theory (DFT) in the gas phase. Furthermore, the Lu³⁺- species with a polarizable dielectric continuum were also simulated in order to take into account the effects of the bulk solvent. Frequency calculations were carried out via the calculation of the second derivative of the energy with respect to the nuclear positions of the optimized Lu³⁺-water species. Furthermore, the hydration enthalpy of the Lu³⁺ ion at 25 °C was modeled.

2. Experimental Details; Data Analysis and DFT Calculations on Lu³⁺-Water Hydrates

2.1. Preparation of Solutions

Lutetium stock solutions were prepared and the lutetium concentrations of these solutions were analysed by complexometric titration [53]. The solution densities were determined with a pycnometer at 23 °C and the molar ratios of water per salt were calculated (R_w-values). For Raman spectroscopic measurements, the solutions were filtered through a fine sintered glass frit (1–1.6 µm pore size). The solutions showed no Tyndall effect and were “optically empty” [54].

Lutetium perchlorate solutions were prepared from Lu₂O₃ (99.9%, Merck KGaA, Darmstadt, Germany) and HClO₄ in a beaker until all oxide dissolved. A Lu(ClO₄)₃ stock solution was prepared at 2.233 mol·L⁻¹ (R_w = 19.01). The slightly acidified solution using HClO₄ had a pH value at ~1.0. From this stock solution, three dilute solutions were prepared: 1.132 mol·L⁻¹ (R_w = 42.77), 0.556 (R_w = 92.40), and 0.186 mol·L⁻¹ (R_w = 289.0). The solutions were analyzed for dissolved chloride with a 5% AgNO₃ solution. The absence of a white AgCl precipitate was proof that the stock solution was free of Cl⁻.

Two Lu(ClO₄)₃ solutions in heavy water were prepared from a deuterated Lu(ClO₄)₃ stock solution and with 99.9 atom % D (Sigma-Aldrich) at 1.398 mol·L⁻¹ and 0.439 mol·L⁻¹. The deuteration degree of the 0.439 mol·L⁻¹ Lu(ClO₄)₃ solution in D₂O was better than 97% D.

A 1.05 mol·L⁻¹ Lu(CF₃SO₃)₃ solution prepared from anhydrous Lu(CF₃SO₃)₃ (99.9%, Sigma-Aldrich,) and triply distilled water. The solution had a pH value at ~ 1.0.

A stock solution of LuCl₃ at 3.199 mol·L⁻¹ (R_w = 15.68) was prepared from Lu₂O₃ (99.9%, Sigma-Aldrich,) and HCl in a beaker covered with a glass lid until all oxide dissolved. The pH value of the stock solution was 0.85. The following solutions were prepared from the stock solution and triply distilled water by weight: 1.890 mol·L⁻¹ (R_w = 28.51), 0.935 mol·L⁻¹ (R_w = 59.00), 0.478 mol·L⁻¹ (R_w = 115.99), 0.241 mol·L⁻¹ (R_w = 229.86) and 0.105 mol·L⁻¹ (R_w = 528.65). Furthermore, a solution with an excess of HCl (37%, zur Analyse, Merck KGaA, Darmstadt, Germany) was prepared from the LuCl₃ stock solution and a 37% HCl solution (37%, zur Analyse, Merck, Darmstadt, Germany) by weight. The ternary solution contained 1.589 mol∙L⁻¹ LuCl₃ and 6.047 mol∙L⁻¹ HCl. An HCl solution was also prepared at 6.04 mol·L⁻¹ from a 37% HCl solution.

2.2. Spectroscopic Measurements:

Raman spectra were measured in the macro chamber of the T 64000 Raman spectrometer from Jobin Yvon in a 90° scattering geometry at 23 °C. These measurements have been described elsewhere [49,55]. A quartz cuvette from Hellma Analytics (Müllheim, Germany) with 10 mm path length and a volume 1000 µL was used. Briefly, the spectra were excited with the 487.987 line of an Ar⁺ laser at a power level of 1100 mW at the sample. After passing the spectrometer in subtractive mode, with gratings of 1800 grooves/mm, the scattered light was detected with a cooled CCD detector. The scattering geometries I_VV = (X[ZZ]Y) and I_VH = (X[ZX]Y) are defined as follows: the propagation (wave vector direction) of the exciting laser beam is in X direction and the propagation of the observed scattered light is in Y direction, the 90° geometry. The polarisation (electrical field vector) of the laser beam is fixed in Z direction (vertical) and the polarisation of the observed scattered light is observed in Z direction (vertical) for the I_VV scattering geometry. For I_VH the fixed electric field vector of the exciting laser beam in Z direction (vertical) and the observed scattering light is polarized in the X direction (horizontal). Thus, for the two scattering geometries it follows:

I_VV = I(X[ZZ]Y) = 45α′²+ 4γ′²

(1)

I_VH = I(X[ZX]Y) = 3γ′²

(2)

The symboles ${\overline{\alpha }}^{\prime }$ and γ′ are the isotropic and the anisotropic invariant of the Raman polarizability tensor, respectively [49,55]. The isotropic spectrum, I_iso was constructed according to Equation (3):

I_iso = I_VV − 4/3 × I_VH

(3)

The polarization degree of the Raman bands, ρ (ρ = I_VH/I_VV) was determined using an analyzer and adjusted, if necessary, before each measuring cycle using CCl₄. A detailed account of this procedure may be found in ref [49,55].

In order to characterize the spectral features in the low wavenumber region, the Raman spectra in I-format were reduced and the R-spectra obtained. The R- spectra have been constructed according to the procedure previously described [49]. The I-spectra were corrected for the scattering factor (ν_L-$\overline{v}$)³ and further corrected for the Bose-Einstein temperature factor, B = [1 − exp(−h$\overline{v}$c/kT)] and the frequency factor, $\overline{v}$, to give the so called reduced or R($\overline{v}$) spectrum. The isotropic spectrum in R-format arise from the corrected R_VV and R_VH spectra according to Equation (4):

R (v)_iso = R(v)_VV − 4/3R(v)_VH.

(4)

In the low wavenumber region, the I($\overline{v}$) and R($\overline{v}$) spectra are significantly different and only the spectra in R-format are presented. It should be noted that one of the advantages of using isotropic R-spectra is that the baseline is almost flat in the 50–700 cm⁻¹ wavenumber region allowing relatively unperturbed observation of the presence of any weak modes [49,51].

2.3. Quantitative Raman Measurements

The quantitative relationship between the band intensity and the solute concentration by Raman measurements is the simple equation: I_i = J_i × C_T, where I_i is the integrated band intensity of band i of the molecular species as a function of the scattering coefficient J_i multiplied by the solute concentration, C_T in mol·L⁻¹. The perchlorate band in these solutions served as the internal standard. The result of the functional relationship between the integrated band intensity of the ν₁LuO₈ mode in Lu(ClO₄)₃ (aq) and the concentration of Lu³⁺ (aq) is given by Equation (5):

I₃₉₆ = 1148.3 × C_T

(5)

The coefficient of determination, R² is 0.99. The relationship holds if Lu(ClO₄)₃ (aq) is completely dissociated into its ions and C_T is equal to the concentration of Lu³⁺. The linearity of the integrated band intensity I₃₉₆ versus solute concentration of Lu(ClO₄)₃ up to a concentration at ~3 mol·L⁻¹ proves this point. The LuCl₃ solutions were then measured under the same conditions as the Lu(ClO₄)₃ solutions and the integrated band intensities for the ν₁LuO₈ mode could be determined and compared to the one in the perchlorate solution. The accuracy of the band intensities in these solutions was estimated to be ± 5%.

2.4. DFT Calculations

The calculations were executed using the Gaussian03 package [56] employing the B3LYP functional [57]. The Stuttgart/Dresden (SDD) basis set was used which adequately reproduces the geometrical parameters, in particular the experimentally observed Lu–O distance. SDD uses a relativistic effective core potential (ECP) for Lu³⁺. All electrons for the other atoms are described by Dunning/Huzinaga valence double-zeta (D95V) functions. Placing the octa-hydrate in a solvent continuum employing the Polarized Continuum Model (PCM) which takes into account the solvation effect of bulk water gave significantly better results compared with the experimental frequencies. The PCM used was the version described in ref. [58] where the solvent is modelled as an isotropic and homogeneous continuum, characterized by its dielectric properties. The cavity is defined as a set of interlocking spheres attached to the solute atoms. The electrostatic solute-solution interaction is calculated introducing an apparent charge distribution spread over the cavity surface.

Geometries of gas phase hydrates and within the PC framework with 8 water molecules surrounding the Lu³⁺ ion were optimized. The aqua ion with S₈ symmetry was the only structure, which led to an energy minimum without imaginary frequencies. The geometrical data and the frequency of the breathing mode of the [Lu(H₂O)₈]³⁺ ion will be discussed below. Furthermore, the hydration enthalpy of Lu³⁺ was simulated applying the DFT method and this procedure is presented in App. A.

3. Results

3.1. The [Lu(OH₂)₈]³⁺ (aq) Ion

Lu³⁺ is strongly hydrated in aqueous solution as revealed by its large standard molar enthalpy of hydration (ΔH^ϴ_hyd) at −3640 kJ·mol⁻¹. However, the ΔH^ϴ_hyd —values reported in the literature scatter from −3530 to −3695 kJ·mol⁻¹ [59,60,61]. Our DFT value for ΔH^ϴ_hyd at −3847.7 kJ·mol⁻¹ is slightly smaller than the thermodynamic value (calculation procedure see Appendix A). The DFT optimized [Lu(H₂O)₈]³⁺ geometry in the gas phase and also with a polarizable continuum (PC) model gave a square antiprismatic coordination polyhedron with symmetry S₈ (Figure 1). Figure 1 shows both the hydrated ion and its LuO₈ skeleton. Furthermore, the [Lu(H₂O)₈]³⁺ aqua ion and its deuterated analog, [Lu(D₂O)₈]³⁺, imbedded in a PC were successfully simulated. The calculated Lu-O bond distance of the [Lu(H₂O)₈]³⁺ ion with a solvation sphere (taking into account the influence of the bulk water) is in good agreement with the experimental value (

Table 1. Geometrical parameters such as bond distances and angles of [Lu(H₂O)₈]³⁺ imbedded in a polarizable dielectric continuum. Comparison of our DFT results (B3LYP/LANL2DZ) with published MD simulation and experimental results.

Bond Distances (Å) and Angels (°)	DFT Data/Gas Phase Cluster	DFT Data/Cluster + PC Model	ref. [25]	ref. [16]	ref. [24]	ref. [21]
Lu-O	2.350	2.311	2.338	2.307	2.37	2.32
O-H	0.981	0.982	-	-	-	-
H-O-H	109.29	110.45	-	-	-	-

). The discussion of the DFT frequencies of the cluster will be given below.

The vibrational analysis of the [Lu(OH₂)₈]³⁺ (S₈ symmetry) with its 69 normal modes (n.m.s) leads to the irreducible representation: Γ_v(S₈) = 8a(Ra) + 9b(i.r.) + 18e₁(Ra, i.r.) + 18e₂(n.a.) + 16e₃(n.a.) (Ra as Raman, i.r. as infrared and n.a. as not active). The modes with character a and e₁ are Raman active and those with character b and e₃ are i.r. allowed. The vibrations can be divided into 24 internal and 24 external vibrational modes of the coordinated water molecules plus 21 n.m.s of the LuO₈ skeleton (a similar procedure has been given in ref. [62]).

The internal and external vibrations of the coordinated water may be considered separate from those of the LuO₈ skeleton with the ligated water molecules seen as point masses. The LuO₈ skeleton possesses D_4d symmetry and with its 9 atoms leads to 21 n.m.s and the irreducible representation is as follows: Γ_v(D_4d) = 2a₁(Ra) + b₁(i.a.) + 2b₂(i.r.) + 3e₁(i.r.) + 3e₂(Ra) + 2e₃(Ra). Although the LuO₈ skeleton possesses no symmetry centre, the mutual exclusion rule is nevertheless effective. Seven modes with the character a₁, e₂ and e₃ are Raman active while six modes with the character b₁, b₂ and e₁ are i.r. allowed. The symmetric Lu-O stretch, the breathing mode, is only Raman active and appears strongly polarized in the Raman spectrum as the strongest band of the LuO₈ skeleton spectrum. Two additional depolarized Raman active stretching modes are expected (character e₂ and e₃) as well as four other Raman deformation modes (character a₁, e₂ and e₃). In I.R., two stretching modes (character b₂ and e₁) are expected and the remaining are deformations. In reality, however, the skeleton modes may not always be easily detected because they appear quite broad, weak and even obscured by the water background in solution.

Considering the coordinated water molecules of the [Lu(OH₂)₈]³⁺- ion, the internal and external n.m.s of the water molecules may be divided into 24 internal and 24 external vibrations. These vibrations are derived from the rotational- and translational degrees of freedom of the isolated water molecule. The n.m.s of these water molecules, the external modes, are librational modes such as wag, twist, and rock [49,62]. In aqueous solutions, however, the librational modes are strongly overlapped with the librations of the bulk water and therefore not easily detected. They appear as weak, very broad modes below 1200 cm⁻¹ [62]. In addition to these librational modes, internal water modes are observed, the deformation mode, ν₂(H₂O) and two stretching OH modes, ν₁ and ν₃. The deformation mode in liquid water is found at 1640 cm⁻¹ and the stretching modes at ~3400 cm⁻¹ appear as a very broad structured band of H-bonded water molecules. The water modes are modified when coordinated to metal ions such as Lu³⁺ but are difficult to separate from the contributions of the librational and internal water modes of the bulk phase. In neat liquid water, the H-bonded water molecules show broad and weak librational modes and internal water modes, the deformation band, δ H-O-H, and the stretching O-H bands [29,62]. Spectra of liquid water and heavy water, bands and band assignments are given elsewhere [62].

The hydration sphere of Lu³⁺ (aq) is somewhat labile and a water-exchange rate constant k_ex at 25 °C was given at 6 × 10⁷ s⁻¹ (from H₂O-SO₄²⁻ interchange rates [42,43]) with a water residence time τ = 16.7 ns and is slightly more labile than for instance [Y(OH₂)₈]³⁺ (aq) with τ = 50 ns [29]. On the other hand, it has a more rigid hydration sphere than [La(OH₂)₉]³⁺ with τ = 5 ns (aq). [27]. (The vibrational duration for the Lu-O breathing mode is 0.084 ps, short enough to allow ~ 199,000 vibrations before the cluster experiences a water exchange. In other words, Raman spectroscopy probes an average hydration structure of rapidly exchanging water molecules in the direct vicinity of the Lu³⁺ ion.).

3.2. Lu(ClO₄)₃ and Lu(CF₃SO₃)₃ Solutions in Water and Heavy Water

Lu(ClO₄)₃ solution spectra: A Raman spectrum in the low frequency range of a 0.186 mol·L⁻¹ Lu(ClO₄)₃ solution (water to salt ratio at 289.0) is presented in Figure 2. Additionally, Raman spectra of two more concentrated Lu(ClO₄)₃ solutions at 2.233 mol·L⁻¹ (R_w = 19.01) and at 0.556 mol·L⁻¹ (R_w = 92.37) are presented in Figures S1 and S2. The perchlorate ion has been chosen as a counterion because it is known as a weakly complex-forming ion. A high frequency band at 3542 cm⁻¹ (fwhh = 90 cm⁻¹), in the O-H stretching band region of H₂O, is observed in Lu(ClO₄)₃ solutions which is attributed to an O-H band of weakly hydrated perchlorate ion (Figure S3 A/B). (In addition to the stretching mode ν(O-H···ClO₄⁻) at 3542 cm⁻¹ a very weak, broad mode appears in the terahertz region at ~165 cm⁻¹ in Lu(ClO₄)₃ solutions (R_iso). The latter mode has an equivalent in pure water at ~175 cm⁻¹ where it is moderately intense and slightly polarized. It is the restricted translational mode of the H- bonded water molecules (O···O-H)). In concentrated Lu(ClO₄)₃ solutions other H-bonds are important, namely OH···OClO₃^- and the intensity of the band due to HOH··· OClO₃⁻ is extremely weak in the isotropic Raman spectrum [27,28,29]). For a detailed discussion on the influence of ClO₄⁻ on the stretching band on water in, for instance, La(ClO₄)₃ (aq) and Ce(ClO₄)₃ (aq) see [27,28].

It is noteworthy to mention that the stretching band of O-H···OClO₃⁻ is slightly cation dependent because of the different charge to radius ratios (polarizing power) of these ions. In Lu(ClO₄)₃ (aq), the band appears at 3542 cm⁻¹, slightly lower than in La(ClO₄)₃ (aq) where it appears at 3550 cm⁻¹ [27].

The Raman spectrum of ClO₄⁻ (aq) (T_d symmetry) has been discussed in detail elsewhere so only a brief discussion shall be given [27,28,29]. The ClO₄⁻ ion possesses nine vibrational degrees of freedom and its internal vibrations span the representation Γ_vib(T_d) = a₁(Ra) + e(Ra) + 2f₂(Ra, i.r.). All four n.m.s are Raman active, but in i.r. only the f₂ modes are allowed. In dilute solution, the symmetric Cl-O stretch, ν₁(a₁) ClO₄⁻ appears at 931.5 cm⁻¹ and is totally polarized (ρ = 0.005) (fwhh = 7.1 cm⁻¹) and is the strongest mode in the Raman spectrum. The antisymmetric stretch, ν₃(f₂) ClO₄⁻ centred at 1105 cm⁻¹ and the deformation modes ν₄(f₂) ClO₄⁻ at 629 cm⁻¹ and ν₂(e) ClO₄⁻ at 458 cm⁻¹ are depolarized.

In a Lu(ClO₄)₃ solution at 0.186 mol·L⁻¹, the ν₁(a₁) ClO₄⁻ band appears at 931.8 cm⁻¹ (fwhh = 7.4 cm⁻¹). In a concentrated solution (2.233 mol·L⁻¹) the ν₁(a₁) ClO₄⁻ band shifts to 934.2 cm⁻¹ and broadens (fwhh = 12.0 cm⁻¹). At the same time, the antisymmetric stretch, ν₃(f₂) ClO₄⁻ shifts to slightly higher wavenumbers and broadens.

The Raman spectra of Lu(ClO₄)₃ (aq) reveal, in addition to the perchlorate-bands, weak bands in the low frequency region (50 to 400 cm⁻¹) which are connected to Lu³⁺ (aq) species. In the isotropic scattering, a band appears at 396 cm⁻¹ which does not exist in ClO₄⁻ (aq). The band must stem from vibrations connected to the LuO₈ skeleton. This isotropic band at 396 cm⁻¹ has a symmetrical profile with fwhh at 50 cm⁻¹. In the totally symmetric stretching mode of the LuO₈ skeleton, the Lu³⁺ ion remains stationary while the oxygen atoms vibrate without changing the symmetry of the LuO₈ unit. (It is strongly polarized with a depolarization degree at 0.005). An example for the Raman spectrum of a 0.186 mol·L⁻¹ Lu(ClO₄)₃ solution is given in Figure 2. In the anisotropic scattering, broad and very weak bands appear at 113 cm⁻¹, 161.6 cm⁻¹, 231 cm⁻¹, 261.3 cm⁻¹ and 344 cm⁻¹. Figure 3 shows the weak anisotropic modes for a concentrated Lu(ClO₄)₃ (aq) solution. Out of the seven theoretically predicted Raman modes only six could be observed. The second polarized LuO₈ mode could not be observed. It is known that for hydrated metal ions in aqueous solution not all skeleton modes may be detected. In reality, the bands may be too broad and weak to be observed. The totally symmetric stretch, also called breathing mode of LuO₈ is accompanied by a change in the polarizability ellipsoid but not in the dipole moment itself. This type of vibration which takes place with the conservation of all symmetry properties is thus called totally symmetric and has a depolarization degree ~ 0.

Replacing water with heavy water leads to an isotope shift to lower wavenumbers by a factor of ~0.948 in Lu(ClO₄)₃(D₂O). The effect of deuteration on the LuO₈ breathing mode was measured in Lu(ClO₄)₃- D₂O solutions and a band at 376.5 cm⁻¹ was observed (Figure S4). The theoretical shift of ν₁ on deuteration (H₂O/D₂O considered as point masses) is given according to:

ν₁′ = ν₁[m(H₂O)/m(D₂O)]^1/2 = (396 cm⁻¹) × 0.948 = 375.6 cm⁻¹

(6)

(The simple formula for calculating the isotopic shift of the ν₁ mode is applicable because of the totally symmetric character of the normal mode of the LuO₈ skeleton where Lu³⁺ remains stationary and only the oxygen atoms vibrate; the observed and theoretical depolarization degree is ~0.)

The agreement between the measured ν₁ symmetric stretch of the [Lu(D₂O)₈]³⁺ species and the calculated one is excellent. Furthermore, the DFT result calculated for [Lu(D₂O)₈]³⁺ with S₈ symmetry imbedded in a PC leads to ν₁ = 356.3 cm⁻¹. If the DFT value at 376.3 cm⁻¹ for [Lu(H₂O)₈]³⁺ is used to calculate the breathing mode for [Lu(D₂O)₈]³⁺, according to Equation (5), a value at 356.9 cm⁻¹ follows. This agreement reinforces the assignment of this normal mode as a totally symmetric stretch with only insignificant contributions of the librations from heavy water.

Relative intensity measurements confirm that the scattering intensity of the ν₁Lu-O mode is very weak with a scattering coefficient, S_h = 0.0024. The S_h values, defined as the R-corrected relative scattering efficiency of the M-O bands, were published for a variety of stretching modes of aqua metal ions in solution [27,28,29]. For Y³⁺, for instance, which resembles properties of the heavy rare earths, its ν₁ breathing mode for [Y(H₂O)₈]³⁺ appears at 384 cm⁻¹ [29] and also possesses a small relative intensity of 0.0025. Both ions, Lu³⁺ and Y³⁺, have a low polarizability and are classified as hard cations according to Pearson’s HSAB concept [63].

Perchlorate (Figure 2; Figures S1, S2 and S3A) was chosen as the counter ion because it is known as a weakly complex forming anion that does not substitute water in the first hydration sphere of the metal ions such as Lu³⁺. However, in a Lu(ClO₄)₃ (aq) at 2.233 mol·L⁻¹, the mole ratio solute to water is 19.01. This water content is barely enough to completely hydrate the Lu³⁺ ion while the remaining 11.1 water molecules hydrate the three ClO₄⁻ ions. In such a concentrated solution outer sphere ion pairs, [Lu(OH₂)₈]³⁺·ClO₄⁻ form and this explains the slight concentration dependence of the peak position appearing at 394 cm⁻¹ and the broadening of the band [27,28,29]. In a 0.189 mol·L⁻¹ Lu(ClO₄)₃ solution, however, the ν₁LuO₈ band occurs as a symmetrical band at 396 cm⁻¹ (fwhh at 50 cm⁻¹). A hydrolysis effect which might have been the cause of the changes of these bands can be ruled out in these acidic solutions. In a recent La(ClO₄)₃ study on the influence of additional HClO₄ in ternary solutions of La(ClO₄)₃ plus HClO₄, measured in the low frequency region, the hydrolysis effect did not play a role at all [27,28,29].

To summarize: the Raman spectroscopy data clearly shows that in dilute Lu(ClO₄)₃ (aq) an isotropic mode appears at 396 cm⁻¹ with fwhh = 50 cm⁻¹ which represents the breathing mode of the LuO₈ skeleton. Furthermore, five additional weak and broad bands, depolarized in character, could be found in concentrated Lu(ClO₄)₃ (aq).

DFT frequencies and assignments of the LuO₈ modes: The DFT frequencies for the LuO₈ skeleton modes for [Lu(H₂O)₈]³⁺ imbedded in a polarizable dielectric continuum simulating the bulk water phase are given in Table S1. The totally symmetric stretch of the LuO₈ skeleton ν₁ LuO₈ gave the wavenumber position at 376.3 cm⁻¹ in satisfactory agreement with the measured value (Table S1). The remaining 6 Raman active modes are in fair agreement with the measured ones considering the simple model used. One theoretical mode could not be detected. Table S1 presents and describes the theoretical LuO₈ skeleton modes for [Lu(H₂O)₈]³⁺ and its deuterated analog. Furthermore, the character of the ν₁LuO₈ mode as a totally symmetric stretch with a depolarization degree zero was also verified. In contrast to the frequency in the condensed phase, the breathing mode for the [Lu(OH₂)₈]³⁺ in the gas phase gave a frequency value at 347.1 cm⁻¹. The totally symmetric LuO₈ stretch is called the breathing mode because while vibrating, the geometry of the cluster does not change its shape, the symmetry remains and therefore this mode is not allowed in i.r. The DFT frequency for ν₁LuO₈ in vacuo is much smaller than the one calculated with a polarizable continuum because the latter method takes into account the influence of the bulk water molecules. It is important to estimate the accuracy of the DFT method and such a brief discussion is given in Appendix B.

The hypothetical nonahydrate [Lu(OH₂)₉]³⁺ in vacuo with its tricapped trigonal prism (TTP) structure gave a much lower value for the symmetric stretching mode namely at 329 cm⁻¹ compared to 347.1 cm⁻¹ for the in vacuo frequency of [Lu(OH₂)₈]³⁺. Furthermore, the Lu-O bond distances are much larger at 2.448 Å (three capping water molecules) and at 2.379 Å (6 prism water molecules). This is an additional and significant result for the existence of the octahydrate with its SAP structure.

To summarize, embedding the [Lu(H₂O)₈]³⁺ species in a polarizable continuum, taking into account the effect of the bulk water, gave a reasonable agreement with the experimental frequencies found in Lu(ClO₄)₃ (aq). Table S1 shows the results of all theoretical LuO₈ modes for [Lu(H₂O)₈]³⁺ and its deuterated analog. The DFT value for the Lu-O bond distance of the [Lu(H₂O)₈]³⁺ at 2.31 Å is in good agreement with the experimental structural data (Table 1).

3.3. Lu³⁺- Trifluorosulfonate in Aqueous Solution

In Lu(CF₃SO₃)₃ (aq), the Lu-O band is slightly overlapped with a polarized triflate band at 319 cm⁻¹ and appears at 396.5 cm⁻¹. The Raman spectrum is shown in Figure S5. A band separation resulted in two bands with the first band component at 319 cm⁻¹ and the second band at 396.5 cm⁻¹ (fwhh = 48 cm⁻¹). The first band, a polarized band, stems from CF₃SO₃⁻ (aq) but the second, much weaker one, strongly polarized, represents the LuO₈ breathing mode of [Lu(H₂O)₈]³⁺. The triflate in aqueous solution acts as a non-complexing anion and is suited, therefore, to study metal ion hydration. Band parameters and assignments of CF₃SO₃⁻ (aq) modes are given in ref. [29].

3.4. LuCl₃ (aq)

A Raman spectrum in R-format of two LuCl₃ solutions, one at 3.199 mol·L⁻¹ (R_w = 15.68) and a more dilute one at 0.478 mol·L⁻¹ (R_w = 166) are presented in Figure 4A,B, respectively, in the wavenumber range from 50–1300 cm⁻¹. The Lu-O stretching mode in the concentrated solution is down shifted and appears at 390 cm⁻¹ and an additional very broad isotropic component at 205 cm⁻¹ with a shoulder at ~254 cm⁻¹ was observed. This finding is clear evidence that Cl⁻ substituted a water molecule in the first hydration shell of Lu³⁺. The second isotropic band is due to the restricted translation mode of water and water/Cl⁻ at 205 cm⁻¹ (Figure 4A) while the broad band at 254 cm⁻¹ appearing as a shoulder has been assigned to a Lu(OH₂)₇³⁺Cl⁻ stretching mode of a 1:1 Lu³⁺-chloro-complex, [Lu(OH₂)₇Cl]²⁺. The concentration of the 1:1 chloro-complex species is in equilibrium with the fully hydrated species, [Lu(OH₂)₈]³⁺. In contrast to concentrated LuCl₃ solutions, the Lu-O stretching mode appears in dilute solutions (< 0.478 mol·L⁻¹) at 396 cm⁻¹ identical to the peak position in Lu(ClO₄)₃ (aq). A dilution series presented in Figure 5 shows the shift of the Lu-O stretching mode to higher wavenumbers from 390 cm⁻¹ to 396 cm⁻¹. In a 3.199 mol·L⁻¹ solution with a mole ratio solute to water at 1 to 15.68, the peak appears at 390 cm⁻¹, shifts to 394 cm⁻¹ for a solution at 1.890 mol·L⁻¹ (R_w = 28.51) and to 395 cm⁻¹ for a 0.935 mol·L⁻¹ (R_w = 59.00) solution and then remains constant at 396 cm⁻¹ for solutions < 0.478 mol·L⁻¹ (R_w = 115.99). This frequency shift is $\mathrm{Geben}\mathrm{Sie}\mathrm{hier}\mathrm{eine}\mathrm{Formel}\mathrm{ein}.$ accompanied by a change of the fwhh which becomes smaller with dilution and in solutions < 0.478 mol·L⁻¹ remains constant at 50 cm⁻¹. This shows that with dilution the chloro-complex species disappears quickly and extrapolation of the Raman data show that in LuCl₃ (aq)$\le$ 0.5 mol·L⁻¹ the Lu³⁺ cation is fully hydrated. Furthermore, the intensity of ν₁LuO₈ band as a function of concentration does not increase linearly in the LuCl₃ solutions. However, the intensity increases less with concentration in contrast to the linear concentration dependence in Lu(ClO₄)₃ (aq). Such a linear increase in band intensity would be expected if the octahydrated Lu³⁺ species remained the only stable species. This shows, clearly, that a chloro–complex species must have formed in higher concentrated solutions at the expense of the fully hydrated Lu³⁺, [Lu(H₂O)₈]³⁺ ion (Figure 5). Quantitative Raman analysis revealed the species concentrations of fully hydrated Lu³⁺ (aq) and the 1:1 chloro-complex. The relationship between the integrated band intensity of ν₁ LuO₈, I₃₉₆ and the solute concentration of Lu(ClO₄)₃ is a linear one (see Equation (1); Experimental Sect.). The measured integrated band intensity of LuO₈ in LuCl₃ (aq), I₃₉₆, follows the given linear relationship between I₃₉₆ and C_T established in Lu(ClO₄)₃ (aq) up to ~0.5 mol·L⁻¹ but then levels off noticeably at higher LuCl₃ concentrations (Figure S6). Obviously, above 0.5 mol·L⁻¹ LuCl₃ fractions of the fully hydrated Lu³⁺ (aq) are converted to a 1:1 Lu³⁺ chloro-complex species. The existence of higher chloro complexes than 1:1 can be convincingly ruled out taking into account the results of earlier anion exchange studies on aqueous rare earth chloride systems [37].

The mole fractions of both species are plotted in Figure 6. The fraction of the chloro-complex at 32%, in the most concentrated solution, is rather small and the fully hydrated species at 68% is still dominant. With dilution, the fraction of the chloro-complex species disappears quickly and at 0.5 mol·L⁻¹ it has vanished. It should be pointed out that the chloro-complex species is the only species detectable by Raman spectroscopy in agreement with the majority of the solution chemistry studies put forward [31,32,33,34,35,36,37]. The formation of the 1:1 chloro-complex may be formulated according to Equation (7):

[Lu(OH₂)₈]³⁺ + Cl⁻ ⇄ [Lu(OH₂)₇Cl]²⁺ + H₂O

(7)

and the formation constant for the 1:1 Lu³⁺- chloro-complex formation, K₁, is according to Equation (8):

$${\mathrm{K}}_1=\frac{\left[{\mathrm{LuCl}}^{2+}\right]}{\left[{\mathrm{Lu}}^{3+}\right]\left[{\mathrm{Cl}}^{-}\right]}\times \frac{{\mathrm{f}}_{{\mathrm{LuCl}}_2^{2+}}}{{\mathrm{f}}_{{\mathrm{Lu}}^{3+}}\times {\mathrm{f}}_{{\mathrm{Cl}}^{-}}}$$

(8)

33 and with K₁’ the “concentration quotient” we get:

$${\mathrm{K}}_1={\mathrm{K}}_1^{\prime }\times \frac{{\mathrm{f}}_{{\mathrm{LuCl}}_2^{2+}}}{{\mathrm{f}}_{{\mathrm{Lu}}^{3+}}\times {\mathrm{f}}_{{\mathrm{Cl}}^{-}}}.$$

(9)

The concentration quotient can be measured by Raman spectroscopy according to Equation (10):

$${\mathrm{K}}_1^{\prime }=\frac{({\mathrm{C}}_{\mathrm{T}}-[{\mathrm{Lu}}^{3+}])}{[{\mathrm{Lu}}^{3+}]\times [{\mathrm{Cl}}^{-}]}$$

(10)

where C_T is the total LuCl₃ concentration and the concentrations in brackets denote the equilibrium concentrations of the fully hydrated Lu³⁺ and Cl⁻. The equilibrium concentration of Lu³⁺ can be measured by Raman according to Equation (1) and thus we obtain ${\mathrm{K}}_1^{\prime }$.

The logK₁′ value measured by Raman spectroscopy is −0.62 (I = 5.61 mol·L⁻¹) and reveals the weak nature of the chloro-complex in LuCl₃ (aq) at 23 °C. Literature values for logK₁ for rare earth chlorides were compiled by Wood [31] and our logK₁^′ fits reasonably well with the literature data given in ref. [31] Applying the specific ion interaction theory [64] in order to extrapolate logK₁^′ to zero concentration, a logK₁ value at ~ −1.3 is obtained. The nature of observed chloro-complex species has been controversially discussed. While NMR- and fluorescence spectroscopy [38,39,40,41,42,43] as well as the Raman effect detect chloro-complex species where chloride substitutes a water in the first hydration sphere, other methods such as ultrasound absorption [44,45,46,47] and DRS [30] may detect all 1:1 species, namely ion pairs where Cl⁻ is in the outer-sphere, in the outer-outer-sphere and also contact ion pairs/complex species. (DRS has however a considerable drawback in detecting complex species because symmetric complex species for which the dipole moment is zero cannot be probed.)

In a recent DRS study [30] the existence of outer-outer sphere ion pairs with two interposed water molecules was claimed to exist exclusively in LaCl₃ solutions but no (direct ion pair) chloro-complex species could be detected. It is clear that different methods show different sensitivities probing species in aqueous solution. The sensitivity of DRS towards the different types of ion pairs is greatest for outer-outer sphere ion pairs less so for outer-sphere ion pairs and the least for complex species. Raman spectroscopy on the other hand fails to detect the outer-outer-sphere ion pairs but detects outer-sphere ion pairs and complex species/direct ion pairs. A Raman study taking into account the DRS data showed the different sensitivities for the detected species and this applies that different methods show different sensitivities toward the individual species [65]. For complete ion association models speciation data from different methods should be taken into account.

The weak chloro-complex species detected in LuCl₃ (aq) could be also found in similar systems such as LaCl₃ (aq), CeCl₃ (aq) and YCl₃ (aq) [27,28,29]. However, in AlCl₃ solutions even at high concentrations, Cl⁻ does not substitute water of the first hydration shell of Al³⁺ [44,62] but forms outer-sphere ion pairs instead. The hydration shell of [Al(OH₂)₆]³⁺ is inert towards chloride substitution. Further experimental support for Lu³⁺- chloride complex formation stems from a recent THz FTIR study on a similar system, YbCl₃ (aq) and YbBr₃ (aq). While in YbCl₃ (aq) chloro-complex species albeit weak are formed no such species exist in the bromide system [66].

To further verify chloro-complex formation in LuCl₃ (aq), HCl was added. A ternary LuCl₃-HCl solution composed of 1.589 mol·L⁻¹ LuCl₃ plus 6.047 mol·L⁻¹ HCl was measured and from its isotropic scattering profile the isotropic scattering contribution of a 6.02 mol·L⁻¹ HCl solution was subtracted. This difference spectrum reveals a band at 386 cm⁻¹, a prominent and broad, slightly asymmetric component at 230 cm⁻¹ and a small scattering contribution at 110 cm⁻¹ (Figure 7). Clearly, chloro-complex species are formed in these solutions and the common ion effect results in the formation of a second chloro-complex, a 1:2 complex species in addition to the 1:1 complex. Results of anion exchange experiments of metal ions in aqueous HCl solutions including Lu³⁺ showed that lutetium has a negligible adsorption [31,37]. Therefore, higher Lu³⁺- chloro-complexes (complex anions) with n ≥ 3 can be ruled out. The formation of a second complex cation, the di-chloro-complex is formed according to Equation (11):

[Lu(OH₂)₇Cl]²⁺ + Cl⁻ ⇄ [Lu(OH₂)₆Cl₂]⁺ + H₂O

(11)

To summarize, a 1:1 chloro-complex species, [Lu(OH₂)₇Cl]²⁺ was detected in concentrated LuCl₃ (aq) solution in equilibrium with the fully hydrated [Lu(OH₂)₈]³⁺ ion. The bands in the low frequency range assigned to the chloro-complex species could be characterized. A dilution series of LuCl₃ solutions was studied by quantitative Raman spectroscopy and it could be shown that the chloro–complex dissociates completely to the [Lu(OH₂)₈]³⁺ (aq) and Cl⁻ (aq) (c < 0.5 mol·L⁻¹). In other words the chloro-complex, [Lu(OH₂)₇Cl]²⁺, is very weak and dissociates rapidly with dilution (increasing water activity).

4. Conclusions

Raman spectra of aqueous Lu³⁺ perchlorate, triflate and chloride solutions were measured over a concentration range from 0.105 mol·L⁻¹ to 3.199 mol·L⁻¹. The weak, isotropic mode at 396 cm⁻¹ (fwhh = 50 cm⁻¹) was assigned to ν₁ Lu-O of the LuO₈ skeleton. In deuterated Lu(ClO₄)₃ solutions, a mode at 376 cm⁻¹ was assigned to the breathing mode, ν₁ Lu-O of [Lu(OD₂)₈]³⁺. In the anisotropic scattering of aqueous Lu(ClO₄)₃, five bands of very low intensity were observed at 113 cm⁻¹, 161.6 cm⁻¹, 231 cm⁻¹, 261.3 cm⁻¹ and 344 cm⁻¹. Raman spectroscopic data suggest that perchlorate and triflate do not substitute water molecules in the first hydration sphere and the [Lu(OH₂)₈]³⁺ ion is stable in these solutions. Perchlorate and triflate are weakly complex forming anions. Although, no inner-sphere complex species could be detected in these solution, outer-sphere ion pairs of the type [Lu(OH₂)₈]³⁺·ClO₄⁻ may be formed in concentrated Lu(ClO₄)₃ (aq). DFT frequency calculations of a [Lu(OH₂)₈]³⁺ imbedded in a polarizable dielectric continuum gave a ν₁ Lu-O equal to 376.3 cm⁻¹ in fair agreement with the experiment. The bond distances and angles of the [Lu(OH₂)₈]³⁺ imbedded in a polarizable dielectric continuum were also presented. The hydration enthalpy for Lu³⁺ (aq) could be simulated by DFT and ΔH_hyd(l) = −3847.7 kJ/mol was obtained in fair agreement with experimental values.

In LuCl₃ solutions, in addition to the breathing mode, ν₁ Lu-O of [Lu(OH₂)₈]³⁺, a second isotropic mode at 254 cm⁻¹ was be verified. This new mode has been assigned to a Lu³⁺-chloro-complex species. A chloride ion, thereby, substitutes a water molecule of the first hydration sphere of Lu³⁺ (aq) forming a 1:1 chloro-complex. This is proof of the lability of the first hydration sphere of Lu³⁺ (aq). The Raman spectroscopic characterization of a 1:1 chloro-complex confirms recent results applying neutron- and X-ray scattering as well as EXAFS [12,20]. Quantitative Raman measurements allowed the determination of the fraction of the 1:1 chloro-complex and the fully hydrated species in concentrated LuCl₃ solutions down to ~ 0.5 mol·L⁻¹ where the chloro-complex vanishes.