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On the Hydration of Heavy Rare Earth Ions: Ho3+, Er3+, Tm3+, Yb3+ and Lu3+—A Raman Study

Raman spectra of aqueous Ho3+, Er3+, Tm3+, Yb3+, and Lu3+-perchlorate solutions were measured over a large wavenumber range from 50–4180 cm−1. In the low wavenumber range (terahertz region), strongly polarized Raman bands were detected at 387 cm−1, 389 cm−1, 391 cm−1, 394 cm−1, and 396 cm−1, respectively, which are fairly broad (full widths at half height at ~52 cm−1). These isotropic Raman bands were assigned to the breathing modes, ν1 Ln–O of the heavy rare earth (HRE) octaaqua ions, [Ln(H2O)8]3+. The strong polarization of these bands (depolarization degree ~0) reveals their totally symmetric character. The vibrational isotope effect was measured in Yb(ClO4)3 solutions in H2O and D2O and the shift of the ν1 mode in changing from H2O to D2O further supports the character of the band. The Ln–O bond distances of these HRE ions (Ho3+, Er3+, Tm3+, Yb3+, and Lu3+) follow the order of Ho–O > Er–O > Tm–O > Yb–O > Lu–O which correlates inversely with the band positions of the breathing modes of their corresponding octaaqua ions [Ln(OH2)8]3+. Furthermore, the force constants, kLn–O, were calculated for these symmetric stretching modes. Ytterbium perchlorate solutions were measured over a broad concentration range, from 0.240 mol·L−1 to 2.423 mol·L−1, and it was shown that with increasing solute concentration outer-sphere ion pairs and contact ion pairs were formed. At the dilute solution state (~0.3 mol·L−1), the fully hydrated ions [Yb(H2O)8]3+ exist, while at higher concentrations (CT > 2 mol·L−1), ion pairs are formed. The concentration behavior of Yb(ClO4)3 (aq) shows similar behavior to the one observed for La(ClO4)3(aq), Ce(ClO4)3(aq) and Lu(ClO4)3(aq) solutions. In ytterbium chloride solutions in water and heavy water, representative for the behavior of the other HRE ions, 1:1 chloro-complex formation was detected over the concentration range from 0.422–3.224 mol·L−1. The 1:1 chloro-complex in YbCl3(aq) is very weak, diminishing rapidly with dilution and vanishing at a concentration < 0.4 mol·L−1.


Introduction
In aqueous solution, the HRE ions of holmium, erbium, thulium, ytterbium, and lutetium exist in the tervalent state [1] and, with their high charge to radius ratio, are strongly hydrated [2,3]. The HRE ions possess eight water molecules arranged in a square antiprismatic geometry (S 8 symmetry) in their first coordination sphere. The hydration geometry of heavy rare earth ions in aqueous solution was determined by X-ray (XRD) and neutron diffraction (ND) [4][5][6] as well as extended X-ray absorption fine structure (EXAFS) [7][8][9][10] techniques. Computer simulations contributed to clarifying the details of the structure and dynamics of the waters in the first hydration sphere of the HRE ions [11][12][13] and their results confirmed the octahedral coordination.

Experimental Details and Data Analysis
Preparation of Solutions The rare earth ion concentrations of all solutions were analysed by complexometric titration [18]. The solution densities were determined pycnometrically at 22 • C and the molar ratios of water per salt calculated (R w -values). The solution pH values were measured with pH meter S220 using a pH electrode InLab Expert Pro-ISM (Mettler -Toledo GmbH, Deutschland, Giessen). For Raman spectroscopic measurements, the solutions were filtered through a fine sintered glass frit (1-1.6 µm pore size). The preparation of the lutetium perchlorate solutions at various concentrations were described earlier [17].
A 3.300 mol·L −1 YbCl 3 stock solution in D 2 O was used to prepare two dilute YbCl 3 solutions with heavy water (99.9 atom% D; Sigma-Aldrich) at 0.844 mol·L −1 and 0.422 mol·L −1 . The deuteration degree in the dilute solutions was determined at~96.5% D.
A Tm(ClO 4 ) 3 solution was prepared from Tm 2 O 3 (Sigma-Aldrich, 99.9%) which was dissolved with 6 mol·L −1 HClO 4 solution (Fisher Scientific GmbH, Schwerte, Deutschland until a clear solution was obtained. The solute concentration was determined at 1.897 mol·L −1 and two dilute solutions were prepared from the stock solution and triply distilled water by weight at 0.980 mol·L −1 and 0.315 mol·L −1 . These solutions contained a slight excess of HClO 4 . An Er(ClO 4 ) 3 stock solution was a commercial product from Alfa-Aesar (Thermo Fisher) (Kandel, Deutschland) at 50 wt%, Reagent Grade (99.9%) at 2.245 moL −1 . Two dilute solutions at 1.123 moL −1 and at 0.321 moL −1 were prepared by weight with ultrapure water. These solutions contained a slight excess of HClO 4 (pH value~1.5).
A Ho(ClO 4 ) 3 stock solution was prepared from Ho 2 O 3 (Sigma-Aldrich, 99.9%) which was dissolved with 6 mol·L −1 HClO 4 (Riedel-de Haen, 70 wt%) until a clear solution was obtained. The solute concentration was determined at 1.675 mol·L −1 . Two dilute solutions at 0.838 mol·L −1 and 0.240 mol·L −1 were prepared by weight from the stock solution with ultrapure water. The solutions contained a slight excess of HClO 4 (pH value~1.75).
Raman spectroscopic measurements have been reported in detail elsewhere, so only a brief summary is given [19,20]. Raman spectra were measured in the macro chamber of the T 64000 Raman spectrometer from Jobin Yvon in a 90 • scattering geometry at 22 • C. A quartz cuvette was used (Hellma Analytics, Müllheim, Germany) with a 10 mm path length and a volume at 1000 µL. The spectra were excited with the 487.987 nm or the 514.532 nm line of an Ar + laser at a power level of 1100 mW at the sample. The Yb 3+ -perchlorate and -chloride solutions have no visible absorption bands and therefore, both excitation wavelengths may be used. Tm(ClO 4 ) 3 solutions were measured with the 514.532 nm Ar + line. Er(ClO 4 ) 3 solutions were excited with the 487.987 nm Ar + line and only the most dilute solution could be measured reliably because the concentrated ones were strongly absorbing at the absorption gap at~488 nm of its UV-vis spectrum. Ho(ClO 4 ) 3 solutions were excited with the 514.532 nm Ar + line and only the most dilute solution could be reliably measured.
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 electric field vector of the exciting laser beam is in Z direction (vertical) and the observed scattering light is polarized in the X direction (horizontal). Thus, for the two scattering geometries it follows: The symbols α and γ' are the isotropic and the anisotropic invariant of the Raman polarizability tensor, respectively [19]. The isotropic spectrum (I iso ) was constructed according to Equation (3): The polarization degree of the Raman bands, ( = I VH /I VV ) was determined using an analyzer and adjusted, if necessary, before each measuring cycle using CCl 4 [19].
The calibration of the Raman spectra has been carried out using plasma lines [19]. The accuracy of the peak positions for the perchlorate deformation modes were not better than ±0.5 cm −1 and for the much narrower ν 1 (a 1 )ClO 4 − band ±0.2 cm −1 . The peak positions of the bands were determined by fitting the baseline corrected bands with a Gauss-Lorenz product function (see ref. [20]). The accuracy of the weak and much broader ν 1 Ln-OH 2 /OD 2 bands was ±1 cm −1 using the perchlorate band at 461 cm −1 as an internal reference band. In order to characterize the spectral features in the low wave number region, the Raman spectra in I-format were reduced and the R-spectra obtained. The R( ν) spectra are independent of the excitation wavenumber ν L and the measured Stokes intensity is further corrected for the scattering factor (ν L -ν) 3 . (The scattering factor must be to the power of 3 when applying counting methods [21].) The spectra were further corrected for the Bose-Einstein temperature factor, B = [1-exp(-h νc/kT)] and the frequency factor, ν, to give the so-called reduced spectrum, R( ν) (detailed in earlier publications [19,20]). The isotropic spectrum in R-format, R iso , is calculated according to equation 3 but substituting the spectra in I-format, I VV and I VH with R VV and R VH . In the low wavenumber region, the I(v) and R(v) spectra are significantly different and only the spectra in R-format are presented. An advantage in applying isotropic R-spectra is the almost flat baseline in the terahertz region allowing relatively unperturbed observation of any weak modes present.
Figures 1B and C show the scattering profiles of aqueous Yb(ClO4)3 solutions at 0.240 mol·L −1 (Rw = 226.6) and, in comparison, a solution at 2.423 mol·L −1 (RW = 16.86) respectively. The Raman scattering profiles of the 0.240 mol·L −1 aqueous Yb(ClO4)3 solution ( Figure 1B) from 40-750 cm −1 shows two ClO4 − (aq) bands at 461 cm −1 and 629 cm −1 and a broad, weak polarized mode (isotropic scattering) at 394 cm −1 which does not occur in NaClO4(aq). Therefore, the band at 394 cm −1 has to be assigned to the ν1 YbO8 breathing mode of the [Yb(H2O)8] 3+ species. In the at 2.423 mol·L −1 (RW = 16.86) Yb(ClO4)3 solution ( Figure C), however, the ν1 YbO8 breathing mode is shifted by 4 cm −1 to lower wavenumbers compared to the dilute solution ( Figure 1B). An overview Raman spectrum of the 2.423 mol·L −1 Yb(ClO4)3 solution is given in Figure S2 Figure 1B). An overview Raman spectrum of the 2.423 mol·L −1 Yb(ClO 4 ) 3 solution is given in Figure S2 (top panel) from 80-1400 cm −1 which displays all four perchlorate bands and the weak isotropic mode at 390 cm −1 assigned to the ν 1 YbO 8 breathing mode. The vibrational bands in the anisotropic scattering could only be detected in the concentrated Yb(ClO 4 ) 3 solution at 2.423 mol·L −1 because of their very weak and broad nature. These anisotropic bands are even weaker than the already weak ν 1 YbO 8 breathing mode with an integrated band intensity at 3161. The band fit results for the anisotropic scattering are given in Table S1 and presented in Figure 2 Five bands appear at 88.5 cm −1 (fwhh = 119), 158.7 cm −1 (fwhh = 97.6.9 cm −1 ), 229.4 cm −1 (fwhh = 75.7 cm −1 ), 260.0 cm −1 (fwhh = 68cm −1 ) and 333.2 cm −1 (fwhh = 85.3) in the anisotropic scattering in the 2.423 mol·L −1 Yb(ClO 4 ) 3 (aq) solution. These weak, broad bands stem from the YbO 8 skeleton fundamentals of the [Yb(OH 2 ) 8 ] 3+ species and break the symmetry of the YbO 8 skeleton. Therefore, they appear only in the anisotropic scattering, but not in the isotropic profile. From group theoretical considerations we expect 7 Raman active modes for the YbO 8 skeleton (ligated water molecules seen as point masses) and a brief group theoretical discussion shall be given. The YbO 8 skeleton (D 4d symmetry) with its 9 atoms leads to 21 normal modes and the irreducible representation follows as: . (The YbO 8 skeleton possesses no symmetry centre but the mutual exclusion rule nevertheless applies.) Seven modes with the character a 1 , e 2 and e 3 are Raman allowed while six modes with the character b 1 , b 2 and e 1 are i.r. active. The totally symmetric Yb-O stretch, the breathing mode, is only Raman active and appears strongly polarized in the Raman spectrum as the strongest band of the YbO 8 skeleton. Two additional depolarized Raman stretching modes are expected (character e 2 and e 3 ) as well as four other Raman deformation modes (character a 1 , e 2 and e 3 ). In infrared, two stretching modes (character b 2 and e 1 ) are expected and the remaining are deformations. In reality, however, we observe only six skeleton modes with one unaccounted mode (see also [17]). From our Raman spectroscopic results, it follows directly that the Yb 3+ -OH 2 hydration shell cannot constitute a hexa-hydrate (T h symmetry) which has been, for instance, characterized for [Al(OH 2 ) 6 ] 3+ (aq) [22,23]. Group theoretical considerations expect only three skeleton modes in Raman for [Al(OH 2 ) 6 ] 3+ ; one of which should be totally polarized (breathing mode for the AlO 6 skeleton) and the remaining two depolarized. All of these bands were detected in the Raman spectrum of an Al(ClO 4 ) 3 (aq) solution with the symmetric stretching mode of [Al(OH 2 ) 6 ] 3+ at 525 cm −1 strongly polarized and two bands at 438 cm −1 and 332 cm −1 which are depolarized [22,23].
(The YbO8 skeleton possesses no symmetry centre but the mutual exclusion rule nevertheless applies.) Seven modes with the character a1, e2 and e3 are Raman allowed while six modes with the character b1, b2 and e1 are i.r. active. The totally symmetric Yb-O stretch, the breathing mode, is only Raman active and appears strongly polarized in the Raman spectrum as the strongest band of the YbO8 skeleton. Two additional depolarized Raman stretching modes are expected (character e2 and e3) as well as four other Raman deformation modes (character a1, e2 and e3). In infrared, two stretching modes (character b2 and e1) are expected and the remaining are deformations. In reality, however, we observe only six skeleton modes with one unaccounted mode (see also [17]). From our Raman spectroscopic results, it follows directly that the Yb 3+ -OH2 hydration shell cannot constitute a hexa-hydrate (Th symmetry) which has been, for instance, characterized for [Al(OH2)6] 3+ (aq) [22,23]. Group theoretical considerations expect only three skeleton modes in Raman for [Al(OH2)6] 3+ ; one of which should be totally polarized (breathing mode for the AlO6 skeleton) and the remaining two depolarized. All of these bands were detected in the Raman spectrum of an Al(ClO4)3(aq) solution with the symmetric stretching mode of [Al(OH2)6] 3+ at 525 cm −1 strongly polarized and two bands at 438 cm −1 and 332 cm −1 which are depolarized [22,23]. The concentration dependence of the band parameters (peak positions, full width at half height (fwhh) and integrated band areas) of the ν 1 YbO 8 breathing mode for Yb(ClO 4 ) 3 solutions allows the determination of the change of these band parameters as a function of concentration. The band profiles of the ν 1 YbO 8 breathing mode are given in Figure 3 at concentrations 0.240 mol·L −1 (R W = 268.74), 0.603 mol·L −1 (R W = 85.17), 0.808 mol·L −1 (R W = 62.13), 1.217 mol·L −1 (R W = 16.86) and finally at 2.423 mol·L −1 (R W = 16.86). The ν 1 Yb-O breathing mode appears at 394 cm −1 at the lowest concentrations and shifts~4 cm −1 to lower wavenumbers at the highest concentration. Furthermore, the bandwidths also increase with increasing solute concentration from 52 cm −1 for the 0.240 mol·L −1 solution to 59 cm −1 for the 2.423 mol·L −1 solution ( Figure 3). This slight change in band parameters of ν 1 YbO 8 breathing mode with increasing solute concentration may be due to ion pair formation in concentrated solutions (The ion pairing effect in perchlorate solutions is discussed in detail in [15,17]). The integrated band intensity of the ν 1 YbO 8 breathing mode, A 394 , rises linearly with the solution concentration. The dependence of the integrated band intensity of the ν 1 YbO 8 breathing mode of [Yb(OH 2 ) 8 ] 3+ as a function of the Yb(ClO 4 ) 3 concentration is given in Figure S3 and for the linear relationship follows: A 394 = 1303.7·C Yb(ClO4)3 (R 2 = 99.9). the band fit and the band components. Underneath is the residue curve, which is the difference of the measured spectrum and the sum curve.
The concentration dependence of the band parameters (peak positions, full width at half height (fwhh) and integrated band areas) of the ν1 YbO8 breathing mode for Yb(ClO4)3 solutions allows the determination of the change of these band parameters as a function of concentration. The band profiles of the ν1 YbO8 breathing mode are given in Figure 3 at concentrations 0.240 mol·L −1 (RW = 268.74), 0.603 mol·L −1 (RW = 85.17), 0.808 mol·L −1 (RW = 62.13), 1.217 mol·L −1 (RW = 16.86) and finally at 2.423 mol·L −1 (RW = 16.86). The ν1Yb-O breathing mode appears at 394 cm −1 at the lowest concentrations and shifts ~4 cm −1 to lower wavenumbers at the highest concentration. Furthermore, the bandwidths also increase with increasing solute concentration from 52 cm −1 for the 0.240 mol·L −1 solution to 59 cm −1 for the 2.423 mol·L −1 solution (Figure 3). This slight change in band parameters of ν1 YbO8 breathing mode with increasing solute concentration may be due to ion pair formation in concentrated solutions (The ion pairing effect in perchlorate solutions is discussed in detail in [15,17]). The integrated band intensity of the ν1YbO8 breathing mode, A394, rises linearly with the solution concentration. The dependence of the integrated band intensity of the ν1 YbO8 breathing mode of [Yb(OH2)8] 3+ as a function of the Yb(ClO4)3 concentration is given in Figure S3 and for the linear relationship follows: A394 = 1303.7·CYb(ClO4)3 (R 2 = 99.9). In addition to the ν1YbO8 of [Yb(OH2)8] 3+ an extremely weak and broad band centered at 170 ± 10 cm −1 appears isotropic Raman scattering in of aqueous Yb(ClO4)3 solution (see Figure S2, top panel). This isotropic band is assigned to a restricted translational mode of the weakly H-bonded water molecules (O-H····OClO3 − ). The mode is strongly anion and concentration-dependent [14][15][16]. The influence of the ClO4 − on the water spectrum has been discussed in recent studies on aqueous Ln(ClO4)3 solutions [14][15][16][17]. In addition to the ν 1 YbO 8 of [Yb(OH 2 ) 8 ] 3+ an extremely weak and broad band centered at 170 ± 10 cm −1 appears isotropic Raman scattering in of aqueous Yb(ClO 4 ) 3 solution (see Figure S2, top panel). This isotropic band is assigned to a restricted translational mode of the weakly H-bonded water molecules (O-H····OClO 3 − ). The mode is strongly anion and concentration-dependent [14][15][16].
The influence of the ClO 4 − on the water spectrum has been discussed in recent studies on aqueous  Figure S2, bottom panel, and for details see [14][15][16].
The triflate ion (trifluoromethanesulfonate) in aqueous solution acts as an even weaker complex forming anion and is suited, therefore, for studying metal ion hydration. In aqueous solution, however, the weak ν 1 band of [Yb(OH 2 ) 8 ] 3+ at~394 cm −1 is overlapped by a strongly polarized triflate band at 319 cm −1 and so band fit analysis was applied. The isotropic Raman spectrum of Yb(CF 3 SO 3 ) 3 (aq) at 1.25 mol·L −1 is shown in Figure S4 and the band fit analysis gave two bands with the first band component at 319 cm −1 and the second band at 394 cm −1 (fwhh = 50 cm −1 ). The first band, a polarized band, stems from CF 3 SO 3 − (aq) but the second band is the ν 1 YbO 8 breathing mode of [Yb(H 2 O) 8 ] 3+ .
Band parameters and assignments of CF 3 SO 3 − (aq) modes are given in [16]. In the Raman spectra of the Tm(ClO 4 ) 3 , Er(ClO 4 ) 3 and Ho(ClO 4 ) 3 solutions appear also as strongly polarized bands and were observed at 391, 389 cm −1 , and 387 cm −1 respectively. These isotropic bands are unique in these HRE ion solutions and cannot be found in the hydrated ClO 4 − (aq) spectrum.
Molecules 2019, 24, x FOR PEER REVIEW 9 of 18 region of H2O and its bending mode of a Yb(ClO4)3 solution at 2.423 mol·L −1 and their peak positions are given in Figure S2, bottom panel, and for details see [14][15][16]. The triflate ion (trifluoromethanesulfonate) in aqueous solution acts as an even weaker complex forming anion and is suited, therefore, for studying metal ion hydration. In aqueous solution, however, the weak ν1 band of [Yb(OH2)8] 3+ at ~394 cm −1 is overlapped by a strongly polarized triflate band at 319 cm −1 and so band fit analysis was applied. The isotropic Raman spectrum of Yb(CF3SO3)3(aq) at 1.25 mol·L −1 is shown in Figure S4 and the band fit analysis gave two bands with the first band component at 319 cm −1 and the second band at 394 cm −1 (fwhh = 50 cm −1 ). The first band, a polarized band, stems from CF3SO3 − (aq) but the second band is the ν1 YbO8 breathing mode of [Yb(H2O)8] 3+ . Band parameters and assignments of CF3SO3 -(aq) modes are given in [16].
The In the Raman spectra of the Tm(ClO4)3, Er(ClO4)3 and Ho(ClO4)3 solutions appear also as strongly polarized bands and were observed at 391, 389 cm −1 , and 387 cm −1 respectively. These isotropic bands are unique in these HRE ion solutions and cannot be found in the hydrated ClO4 − (aq) spectrum. The weak band at 375 cm −1 is assigned to the Yb-OD2 mode of the YbO8 skeleton which is shifted due to the isotope effect by changing from H2O to D2O (see also Figure 1B). Note the band at 1204 cm −1 which is due to the deformation mode of D2O.
The representative Raman spectra of Tm(ClO4)3, Er(ClO4)3 and Ho(ClO4)3 solutions are given in Figures S6-S8 (4): with c, the velocity of light, ν i the wavenumber of the mode i, N the Avogadro constant and A L the molecular weight of the ligand, in our case water. The force constants, k Ln-O , calculated for the measured ν 1 breathing modes are given in Table 1 Figure S9). a) Ref. [24]; − data at 25 • C. b) Ref. [7]; EXAFS data from L 3 edge (one shell fit) on aqueous trifluoromethansulfonate solutions.
Relative scattering intensities, S h , for the ν 1 Ln-O breathing modes are also given in Table 1 and for the definitions of the S h see ref. [20]. The small scattering intensity values at 0.0156 to 0.0165 for the ν 1 Ln-O modes of the HRE octahydrates reflect the fact that the Ln-OH 2 bonds possess low polarizability and are hard cations [25]. The accuracy of the scattering coefficient is not better than ± 0.0004 due to the low scattering intensity, the broadness of the modes and the uncertainties in subtracting the baseline. (Note that the S h value for the totally symmetric stretching mode, ν 1 Lu-O is 0.0156 ± 0.0004 and the value reported in [17] is too small.) From ab initio quantum mechanical charge field molecular dynamics studies, the mean Ln-O bond distances (Ln = Ho 3+ , Er 3+ , Tm 3+ , Yb 3+ and Lu 3+) of the octahydrates, [Ln(OH 2 ) 8 ] 3+ , average coordination numbers, vibrational frequencies and the corresponding force constants were presented [13]. The authors claimed an "excellent agreement with experimental results" [13] of the computed frequencies with the measured ones in the glassy state [26]. The theoretical force constants for the ν 1 breathing modes in [13] deviate considerably from our data in Table 1and do not follow the expected trend given in Figure S9 in going from holmium to lutetium. This trend reflects the steady increase of the force constants of the Ln-O breathing modes with decreasing Ln-O bond distances in going from holmium to lutetium (Table 1; Figure S9). The force constant for ν 1 Er-OH 2 breathing mode in [13] was given 360 cm −1 equal to the one for the ν 1 La-OH 2 breathing mode of [LaOH 2 ) 9 ] 3+ . However, our recently published datum for the ν 1 La-OH 2 breathing mode [14,15] is with 343 cm −1 much smaller. The calculations in [13] are based on the simplified model of a heteronuclear diatomic species but such an assumption may not be correct. The character of the symmetrical normal mode ν 1 of the LnO 8 skeleton of the corresponding [Ln(OH 2 ) 8 ] 3+ species reveals that the central cations remain stationary and only the water molecules are involved in the breathing motion without disturbing the symmetry and therefore these normal modes are totally polarized. It is known from kinetic studies [24,27,28] that the water exchange reactions of the [Ln(OH 2 ) 8 ] 3+ species for the octahydrates are very fast and these ions are known to be labile. From the rate constants, kex at 25 • C, given in Table 1, follow the water residence times, the time the water molecules reside at these cations. The water residence times are in the range of several nanoseconds (see Table 1) which shows that these ions are indeed quite labile. From the vibration periods of the ν 1 Lu-O modes which are at 0.086 to 0.084 ps in going from holmium(III) to lutetium(III) it follows that these species vibrate several hundred thousand times [17] before one water exchange occurs. Although the HRE ions are labile structures, Raman spectroscopy probes the actual structure of these octahydrate species. (It is worth mentioning that the intramolecular bond exchange rate is only a few picoseconds, much faster than the water exchange reaction, therefore for such labile structures for instance [Cu(OH 2 ) 5 ] 2+ [27], Raman observes an average structure and, so, a single broad mode appears as a result and at higher peak positions than for comparable divalent metal ions.)
The ν 1 Yb-OH 2 stretching mode in the 3.224 mol·L −1 YbCl 3 (aq) solution, with a mole ratio of solute to water at 1 to 15.64 appears at 389 cm −1 and shifts with dilution to higher frequencies (see Figure 5). In a 0.400 mol·L −1 (R w = 136.98) YbCl 3 (aq) solution the ν 1 Yb-OH 2 breathing mode appears at 394 cm −1 with a fwhh at 52 cm −1 and these band parameters are comparable to the ones in a dilute Yb(ClO 4 ) 3 (aq) solution in which the fully hydrated [Yb(OH 2 ) 8 ] 3+ exists.
A broad isotropic component at 206 cm −1 and a broad feature at 256 cm −1 are also observed. The band at 256 cm −1 is due to the partially hydrated water molecules of the [Yb(OH 2 ) 7 Cl] 2+ species. A Yb-Cl stretching mode should appear at much higher frequencies, namely at~500 cm −1 , but may be very broad and weak and could not be observed (see spectroscopic and DFT results on ZnCl 2 (aq) [33]). The isotropic component at 206 cm −1 is assigned to the restricted translation band of water of its O-H···O/Cl − units. These findings are evidence that Cl − substitutes water from the first hydration shell of Yb 3+ and a partially hydrated Yb 3+ -chloro-complex formulated as [Yb(OH 2 ) 7 Cl] 2+ is formed.
The integrated band intensities of ν 1 YbO 8 band of the fully hydrated species, [Yb(OH 2 ) 8 ] 3+ , as a function of concentration was determined from quantitative Raman analysis and it turned out that the integrated band intensity, A 394 , does not increase linearly with the total YbCl 3 concentration (C T ). However, a linear increase in band intensity would be expected if the Yb 3+ -octahydrate is the only stable species in YbCl 3 solution and such a linear relationship was observed in Yb(ClO 4 ) 3 (aq) solutions (see Figure S3). The measured integrated band intensity of the ν 1 YbO 8 band in YbCl 3 (aq), A 394 , follows a linear relationship between A 394 and C T up to~0.4 mol·L −1 but then levels off noticeably at higher YbCl 3 concentrations ( Figure S11). Obviously, above~0.4 mol·L −1 YbCl 3 fractions of the fully hydrated Yb 3+ (aq) are converted to a 1:1 Yb 3+ 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 [32]. The mole fractions of both species are plotted in Figure 7. The fraction of the chloro-complex at 29%, in the most concentrated solution, is rather small and the fully hydrated species at 71% is still dominant. With dilution, the fraction of the chloro-complex species diminishes quickly and at~0.4 mol·L −1 it is zero. Shown ( Figure 5) is the ν 1 YbO 8 symmetric stretching mode at 394 cm −1 in a 0.802 mol·L −1 solution compared to the one at 389 cm −1 in a 3.224 mol·L −1 solution. An additional isotropic band appears at 256 cm −1 in the 3.224 mol·L −1 solution which is due to the stretching mode of the chloro-complex species, [Yb(OH 2 ) 7 Cl] 2+ (details in R iso scattering in the terahertz region see Figure 6). The remaining bands in both panels are due to the water being strongly influenced by the solute at the most concentrated solution. First, in the terahertz region (R VV scattering), weak, broad bands appear at 186 cm −1 in the 0.802 mol·L −1 solution and at 202 cm −1 in the 3.224 mol·L −1 solution assigned to the restricted translational band of water of the O-H···O/Cl − units. Second, very broad bands (R VV scattering) with peak maxima which appear at 712 cm −1 (0.802 mol·L −1 ) and 684 cm −1 (3.224 mol·L −1 ) are due to the librational bands of water. Third, the band at 1272 (0.802 mol·L −1 ) and 1204 cm −1 (3.224 mol·L −1 ) are due to overtones of water librations. Finally, the bands at 1645 and 1647 cm −1 respectively are due to the deformation mode of water, ν 2 H 2 O. The formation of a 1:1 complex with Cl − at higher YbCl 3 concentrations may be written as: The formation constant for the 1:1 Yb 3+ -chloro-complex, K 1 , may be formulated according to Equation (6): with K 1 the "concentration quotient" we get: The concentration quotient can be measured by Raman spectroscopy according to equation (7): where C T is the total YbCl 3 concentration and the concentrations in brackets denote the equilibrium concentrations of the fully hydrated Yb 3+ and Cl − . The equilibrium concentration of Yb 3+ determined by Raman spectroscopy allows us to calculate K 1 . The formation of a 1:1 complex with Clat higher YbCl3 concentrations may be written as: The formation constant for the 1:1 Yb 3+ -chloro-complex, K1, may be formulated according to equation (6): with K1′ the "concentration quotient" we get: The concentration quotient can be measured by Raman spectroscopy according to equation (7): where CT is the total YbCl3 concentration and the concentrations in brackets denote the equilibrium concentrations of the fully hydrated Yb 3+ and Cl − . The equilibrium concentration of Yb 3+ determined by Raman spectroscopy allows us to calculate .
The estimated K1 value for chloro complex formation in YbCl3(aq) from (see ref [17]for details) equal to ca. 0.06 ± 0.015 and a logK1 value at ca. −1.22 follows at 22 °C. (Quantitative Raman spectroscopy applied to these solution spectra with weak and broad low frequency bands is not very precise and therefore a higher uncertainty results.) Data from thermodynamic and spectroscopic studies on YbCl3(aq) solutions confirm the weak nature of the complex species [29][30][31][32]. The results on aqueous LuCl3 solutions and similar rare earth systems [17,[29][30][31][32]  The estimated K 1 value for chloro complex formation in YbCl 3 (aq) from K 1 (see ref [17] for details) equal to ca. 0.06 ± 0.015 and a logK 1 value at ca. −1.22 follows at 22 • C. (Quantitative Raman spectroscopy applied to these solution spectra with weak and broad low frequency bands is not very precise and therefore a higher uncertainty results.) Data from thermodynamic and spectroscopic studies on YbCl 3 (aq) solutions confirm the weak nature of the complex species [29][30][31][32]. The results on aqueous LuCl 3 solutions and similar rare earth systems [17,[29][30][31][32] confirm our findings on YbCl 3 solutions. The chloride ion substitutes a water molecule from the flexible first hydration shell of Lu 3+ and Yb 3+ . With dilution, the weak chloro-complex species dissociates and fully hydrated Yb 3+ (aq) ions detected. This is in contrast to AlCl 3 (aq) solutions, even in concentrated AlCl 3 (aq), Cl − does not substitute water in the first hydration shell of Al 3+ and it is known that the hydration shell of [Al(OH 2 ) 6 ] 3+ is quite inert [22,23].
The results of an extensive EXAFS study by Allen and co-workers [34] on 0.1 and 0.01 mol·L −1 Lu 3+ -, Yb 3+ and Tm 3+ -solutions in 0.20 mol·L −1 HCl and with 14 mol·L −1 LiCl are worthwhile to consider. It could be shown that in solutions with low chloride concentrations, the Ln-O bond distance for Yb 3+ is consistent with the fully hydrated Yb 3+ . In solutions with an excess of LiCl, it was demonstrated that inner sphere chloro-complexation takes place together with a loss of water [34]. Furthermore, a current study in the terahertz frequency range of YbCl 3 solutions using FT-IR spectroscopy [35] confirmed weak contact ion pairs as do our recent Raman results on LuCl 3 (aq) [17]. Choppin and Unrein [36] claimed that only outer-sphere ions pairs exist in lanthanide chloride solutions, but such a view has been questioned [17,[29][30][31][32].
To summarize, the [Yb(OH 2 ) 7 Cl] 2+ modes in chloride solutions could be detected and formation of weak chloro-complexes with Yb 3+ verified. In dilute solutions (C T < 0.4 mol·L −1 ) the chloro-complex species disappeared upon dilution and [Yb(OH 2 ) 8 ] 3+ and Cl − (aq) formed. The chloro-complex formation may be one reason for the data scatter of the recently published Yb-O bond distances and coordination numbers presented for Yb 3+ (aq) and other rare earth chloride systems [35,36]. In recent experimental structural studies, it was observed that inner-sphere chloro-complex species are formed in aqueous LnCl 3 solution (Ln = Lu and Yb) with high chloride concentrations while in dilute solutions, fully hydrated ions exist [17,34,35].

Conclusions
Raman measurements on dilute aqueous Lu(ClO 4 ) 3  As a representative example for the lanthanide perchlorate solutions, higher concentrated aqueous Yb(ClO 4 ) 3 solutions were studied and in solutions > 2 mol·L −1 a small fraction of contact ion pairs between Yb 3+ and ClO 4 − were detected. This is supported by the parameters of ClO 4 − -bands (peak position, half width, band shapes) as well as changes of the band parameters of the ν 1 Yb-O breathing mode. In YbCl 3 solutions, Cl − penetrates into the first hydration sphere of Yb 3+ (aq) by pushing out a water molecule, and a weak 1:1 chloro-complex species forms. However, the fraction of the chloro-complex diminishes rapidly upon dilution and at a concentration < 0.4 mol·L −1 , the chloro-complex species vanished. Our Raman spectroscopic findings were substantiated by recently published EXAFS and terahertz FT-IR and results [34,35].
Supplementary Materials: The following are available online. Table S1. Band fit data on of the anisotropic spectrum of an aqueous 2.423 mol·L −1 Yb(ClO 4 ) 3 solution in the terahertz region. Five YbO 8 skeleton modes of [Yb(H 2 O) 8 ] 3+ (aq) were detected. In addition to isotropic band at 390 cm −1 (fwhh = 59 cm −1 ) was observed with an integrated band intensity = 3160. Figure S1. Raman scattering profiles (I VV (black), I VH (blue) and I iso (red)) of a 3.800 mol·L −1 NaClO 4 (aq) solution. The depolarized modes, ν 2 (e) at 461 cm −1 and ν 2 (f 2 ) at 629 cm −1 are the deformation modes of perchlorate, ClO 4 − (aq). The strongly polarized mode, ν 1 (a 1 ) at 933 cm −1 is the Cl-O symmetric stretching mode and the depolarized band, ν 3 (f 2 ) at 1110 cm −1 is due to the antisymmetric stretching mode of ClO 4 − (aq). The broad mode at 1634 cm −1 is due to the deformation mode of H 2 O. Figure Figure  S3. Integrated band intensity, A 394 , of the symmetric stretching mode ν 1 YbO 8 in arbitrary units as a function of the Yb(ClO 4 ) 3 solution concentration. Figure S4. Isotropic Raman scattering profile (R-format) of a 1.25 mol·L −1 Yb(CF 3 SO 3 ) 3 solution. In addition to the strong triflate band at 319.5 cm −1 a very weak and relatively broad band appears at 394 cm −1 which is assigned to the totally symmetric stretching mode of YbO 8 . Figure S5. Raman scattering profiles of a 1.276 mol·L −1 Yb(ClO 4 ) 3 solution in heavy water in order to observe the isotope effect on the symmetric stretching mode of the hydrate respectively deuterated species by changing from [Yb(H 2 O) 8 8 ] 3+ (D 2 O). Shown are the isotropic scattering profile (red), the anisotropic one (blue) and the polarized scattering (black). Figure S6. Tm(ClO 4 ) 3 solution at 0.315 mol·L −1 (R w = 226.6) in R-format (spectra from top to bottom: R VV , R VH and R iso ). The inset shows the R iso spectrum in greater detail. Note the broad and weak ν 1 TmO 8 stretching mode at 391 cm −1 (fwhh = 53 cm −1 ) of the [Tm(OH 2 ) 8 ] 3+ species. The much larger, depolarized