Unraveling the Sc3+ Hydration Geometry: The Strange Case of the Far

Jun 14, 2016 - Unraveling the Sc3+ Hydration Geometry: The Strange Case of the. Far-Coordinated Water Molecule. Valentina Migliorati* and Paola D'Ange...
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Unraveling the Sc3+ Hydration Geometry: The Strange Case of the Far-Coordinated Water Molecule Valentina Migliorati* and Paola D’Angelo Dipartimento di Chimica, Università di Roma “La Sapienza”, P.le A. Moro 5, 00185 Roma, Italy ABSTRACT: The hydration structure and dynamics of Sc3+ in aqueous solution have been investigated using a combined approach based on quantum mechanical (QM) calculations, molecular dynamics (MD) simulations, and extended X-ray absorption fine structure (EXAFS) spectroscopy. An effective Sc−water two-body potential has been generated from QM calculations and then used in the MD simulation of Sc3+ in water, and the reliability of the entire procedure has been assessed by comparing the theoretical structural results with the EXAFS experimental data. The outstanding outcome of this work is that the Sc3+ ion forms a well-defined capped square antiprism (SAP) complex in aqueous solution, where the eight water molecules closest to the ion are located at the vertexes of a SAP polyhedron, while the ninth water molecule occupying the capping position is unusually found at a very long distance from the ion. This far-coordinated water molecule possesses a degree of structure comparable with the other first shell molecules surrounding the ion at much shorter distances, and its presence gave us the unique opportunity to easily identify the geometry of the Sc3+ coordination polyhedron. Despite very strong ion−water interactions, the Sc3+ hydration shell is very labile, as the far-coordinated ligand allows first shell water molecules to easily exchange their positions both inside the solvation shell and with the rest of the solvent molecules. for the Sc3+ aqua ion a coordination number intermediate between 6 and 9 would be expected purely on the basis of steric considerations. A great deal of effort has been made in the literature to unravel the Sc3+ hydration properties.7−17 However, the results of these works are surprisingly widespread, lacking a unified picture for the solvation of this ion. The Sc3+ ion has been proposed to be 6-coordinated in aqueous solution by theoretical studies on gas-phase clusters.7−9 On the other hand, investigations based on several experimental techniques including X-ray diffraction, extended X-ray absorption fine structure (EXAFS), and Raman spectroscopies have suggested that Sc3+ in water forms a first coordination shell consisting of seven water molecules.10−13 As far as the first shell geometry is concerned, three plausible geometries have been proposed on the basis of the Raman results, i.e., pentagonal bipyramid, monocapped octahedral, and monocapped trigonal prismatic, but a definite conclusion about the symmetry of the Sc3+ hydration complex could not be obtained from the Raman experimental data.12,13 A coordination number of 7, with the first shell water molecules forming a monocapped trigonal prismatic structure, has been also proposed by a QM/MM molecular dynamics investigation of Sc3+ in aqueous solution.14 At variance with these results, according to several EXAFS investigations, the Sc3+ ion in water is coordinated by eight water molecules.15−17 In the most recent study, in which the

1. INTRODUCTION Scandium is a very important element from an industrial point of view, and it is widely used in several areas such as electronic, nuclear energy, astronavigation, liquid−liquid extraction, catalysis, organic synthesis, and metallurgical industries.1,2 Due to the rapidly growing technological importance of this element, knowledge of its basic properties is of great importance. Moreover, scandium trifluoromethanesulfonate (triflate), Sc(CF3SO3)3, is an efficient Lewis acid able to catalyze many important organic reactions, such as the carbon− carbon bond-forming reaction.3 The great advantage of scandium triflate over traditional Lewis acids in organic synthesis is that while most Lewis acids are decomposed or deactivated in the presence of water, Sc(CF3SO3)3 is stable and works as a Lewis acid in aqueous solutions.3 An accurate description of the local structure around Sc3+ in water can be of great help to unravel the mechanisms by which scandium triflate carries out its catalytic activity. The coordination chemistry of scandium is one of the most challenging topics in inorganic chemistry.4 Scandium is often considered as part of the group of rare-earth elements as both scandium and lanthanoid ions have a stable trivalent state in solution, even if the chemical properties of scandium differ significantly from those of the other rare-earth elements. Sc3+ has an ionic radius (0.75 Å for 6-fold coordination) intermediate between that of Al3+ (0.54 Å) that is 6coordinated in aqueous solution4 and those of the lanthanoid(III) ions,5,6 that form in water 9-fold complexes for the early lanthanoids, and 8-fold complexes for the later ones. Therefore, © XXXX American Chemical Society

Received: April 18, 2016

A

DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

this procedure. The PES was constructed by 2676 points that were reduced to 2624 by imposing a threshold of 2500 kJ/mol for the interaction energy, thus leaving out from the PES the most repulsive configurations. The Sc3+−water ab initio interaction energies have then been fitted with the following function

EXAFS spectroscopy has been combined with large-angle X-ray scattering, comparisons with crystalline reference compounds containing 6-, 7-, and 8-coordinated Sc3+ hydrated complexes have been used to evaluate the hydration structure of Sc3+ in water.17 From the similarity of the EXAFS spectra of the aqueous solution and solid [Sc(H2O)8](CF3SO3)3, it was suggested that the geometry of the Sc3+ hydration complex in water could be similar to that of the crystalline compound, i.e., an 8-fold distorted bicapped trigonal prism.17 In this structure, six water molecules are strongly bound to the ion with a mean Sc−O distance of 2.17 Å, while one capping position is located at 2.32 Å, and possibly another one at about 2.5 Å.17 This hypothesis has been formulated by the authors on the basis of steric requirements for the oxygen−oxygen distances inside the ion first coordination shell, and the authors themselves stress that the EXAFS and LAXS measurements cannot distinguish between one or two capping water molecules.17 Note that, as far as the solid state is concerned, coordination numbers of Sc3+ from 3 to 9 have been reported.18 It is clear that, despite an intense research activity aimed at unraveling the hydration properties of the Sc3+ ion, conflicting results are reported in the literature and the hydration number and coordination geometry of Sc3+ in aqueous solution are still a topic of intense debate. This is due to the fact that the study of disordered systems such as ionic solutions is a nontrivial task, and it is rather difficult to obtain reliable results by using a single method of investigation. During the last years, the synergic use of molecular dynamics (MD) simulations and the EXAFS experimental technique has been shown to be a powerful approach to unravel the solvation structure of ions in aqueous and nonaqueous solutions.19−27 Moreover, in the framework of classical MD, accurate interaction potentials to be used in the simulations can be developed by means of QM calculations.28 Here, we have undertaken an experimental and theoretical investigation of the Sc3+ ion in aqueous solution. In particular, we used a combination of QM calculations, classical MD simulations, and EXAFS spectroscopy, and this joint approach allowed us to shed light into the peculiar coordination properties of this ion in water.

V (r ) = f * +

qiqo rio

∑

+ f*

ih = ih1,ih2

Ao B C D + 6o + 8o + 12o + Eoe−Forio rio4 rio rio rio

qiqh rih

+

Ah B C D + 6h + 8h + 12h rih4 rih rih rih

(1) −1

−2

where f is the electric conversion factor (138.935 kJ mol nm e ), and rio, rih1, and ri2 are the ion−water distances, while qi, qo, and qh are the electrostatic charges of the cation (+3 au), and of the oxygen and hydrogen atoms in the water model used in the MD simulations, namely, the SPC/E,40 corresponding to −0.8476 and +0.4238 au, respectively. Ao, ..., Fo and Ah, ..., Dh are the parameters to be fitted. The fitting was performed with the Newton method by means of the statistic package SAS, and the obtained Sc3+−water parameters are reported in Table 1, together with their standard deviations. The

Table 1. Sc3+−Water Interaction Parameters and Relative Standard Deviations Obtained by the Fitting Procedure and Used in the MD Simulation of a Sc3+ Aqueous Solution param

value

Ao (kJ mol−1 nm4) Bo (kJ mol−1 nm6) Co (kJ mol−1 nm8) Do (kJ mol−1 nm12) Eo (kJ mol−1) Fo (nm−1) Ah (kJ mol−1 nm4) Bh (kJ mol−1 nm6) Ch (kJ mol−1 nm8) Dh (kJ mol−1 nm12)

5.302 × 10−1 −6.290 × 10−2 5.567 × 10−4 −1.503 × 10−8 9.064 × 10+5 3.764 × 10+1 −1.265 × 10−1 3.074 × 10−3 −1.657 × 10−5 1.348 × 10−10

std dev 3.49 4.31 5.80 2.73 3.15 3.59 2.45 5.60 3.65 4.10

× × × × × × × × × ×

10−2 10−3 10−5 10−9 10+4 10−1 10−3 10−5 10−7 10−12

differences between the energies computed using eq 1 and the original ab initio values have a standard deviation of 15 kJ mol−1, in agreement with previous results.30,31,33,34 The fitted Sc3+−water energy curve referring to an antidipole orientation of the solvent molecule with respect to the ion is shown in Figure 1. The minimum energy value is −440 kJ mol−1, and the corresponding Sc−O distance is found at 1.96 Å. It is important to stress that the Sc3+−water interaction energy is very high, due to the high charge density of the Sc3+ ion. Note for comparison that the minimum energy absolute values obtained with similar procedures for other first-row transition-metal ions forming very stable octahedral complexes in water, such as Zn2+, Co2+, and

2. METHODS 2.1. Computational Procedure. The MD simulation of the Sc3+ aqueous solution has been carried out using an effective two-body potential developed by fitting the parameters of an analytical function on an ab initio potential energy surface (PES). In particular, the effective Sc3+−water pair potential function (UScWat) has been calculated along the line of the method proposed by Floris et al.29 and previously applied to the study of several cations in aqueous28,30−32 and methanol33,34 solution. In this procedure, averaged many body effects due to the solvent molecules are included by means of the so-called conductor-like polarizable continuum model (CPCM). The cavity in which the Sc3+−water system is embedded has been modeled as a set of interlocking spheres centered on the atomic nuclei. Following previous studies,30,31 for the oxygen and hydrogen atoms of the water molecule sphere, radii of 1.68 and 1.44 Å have been used, while the Sc3+ cavity radius has been optimized on the basis of an internal consistency criterium, obtaining a value of 1.254 Å. Each sphere of the solute cavity has been subdivided into tesserae with constant average area of 0.05 Å2 without any charge compensation.35 QM calculations have been carried out with the Gaussian03 package, using the Hartree−Fock method and LANL2DZ effective core potential and valence basis set36−38 for Sc3+ and the cc-pVTZ basis set39 for the water molecule. The PES for the Sc3+−water system has been obtained by moving the Sc3+ ion around the water molecule, and the water geometry was kept fixed at the experimental one during

Figure 1. Fitted Sc3+−water potential energy curve referring to an antidipole orientation of the solvent molecule with respect to the ion. B

DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Ni2+, are in the range 245−300 kJ mol−1,30 while those for lanthanide ions such as Nd3+, Gd3+, Yb3+ have been found between 270 and 315 kJ mol−1.28 In order to carry out the MD simulation of the Sc3+ aqueous solution, we have included the newly developed Sc3+−water potential in the GROMACS package41 while using the SPC/E water model to describe water−water interactions, as it provides a very good description of the structural and dynamic properties of liquid water.40 The system was composed of 1 Sc3+ ion and 819 water molecules placed in a cubic box with an edge length of 29.11 Å, replicated using periodic boundary conditions. The simulation was performed in an NVT ensemble (T = 300 K) by means of the Berendsen method42 with a coupling constant of 0.1 ps. A cutoff of 9 Å has been adopted for the nonbonded interactions, and the particle mesh Ewald method was used to treat long-range electrostatic interactions.43 The simulations have been carried out for 10 ns, after an equilibration period of 3 ns, with a time step of 1 fs. 2.2. X-ray Absorption Measurements and EXAFS Data Analysis. A 0.2 M aqueous solution of scandium triflate was prepared by dissolving Sc(CF3SO3)3 in water, and trifluoromethanesulfonic acid was added to avoid hydrolysis. Sc K-edge X-ray absorption spectra of Sc3+ in aqueous solution were recorded at the bending magnet XAFS beamline of Elettra-Sincrotrone Trieste (Italy). The storage ring operated at 2.0 GeV in top-up mode with a current of 300 mA. The data were recorded at room temperature in transmission mode using ionization chambers filled with a N2 and He mixture in order to have 20% of absorption in the I0 and 80% in the I1. A Si(111) double-crystal monochromator was employed, and high order harmonics were rejected by using the cutoff of the reflectivity of a pair of silica mirrors placed at 7 mrad with respect to the direct beam downstream of the monochromator. E0 was assigned as the first inflection point of the rising edge of metallic scandium at 4492 eV. The sample consisted in a 1.5 μm thick cellulose membrane impregnated with the aqueous solution sealed between two 2.5 μm thick mylar windows. The sample was then enclosed in a chamber with 300 mbar of He overpressure. The EXAFS data analysis has been carried out with the GNXAS program starting from the MD Sc−O and Sc−H g(r)’s. For disordered systems the χ(k) signal is represented by the equation

χ (k) =

∫0

∞

dr 4πρr 2g (r )A(k , r )sin[2kr + ϕ(k , r )]

3. RESULTS To unravel the coordination properties of the Sc3+ ion in water we developed a Sc−water interaction potential by means of ab initio calculations and used it to carry out a MD simulation of Sc3+ in aqueous solution. All of the details of the computational procedure are reported in the Methods section. The Sc−O and Sc−H radial distribution functions g(r)’s calculated from the MD trajectory are shown in Figure 2, together with the

Figure 2. Sc−O (upper panel) and Sc−H (lower panel) radial distribution functions g(r)’s and corresponding running integration numbers N(r)’s calculated from the MD simulation. The inset shows a magnified view of the Sc−O g(r) for distances between 2.8 and 4.0 Å.

corresponding running integration numbers. The two g(r)’s show very sharp and separated first peaks, indicating the existence of a stable first solvation shell and of a preferential orientation of solvent molecules in the first coordination sphere. The positions of the Sc−O and Sc−H g(r) first maxima are found at 2.16 and 2.86 Å, respectively, while the first shell coordination number obtained by integration of the Sc−O g(r) up to the first minimum (2.90 Å) is 8.0. It is well-known that the ion−water g(r)’s in aqueous solution are usually non-Gaussian in shape, with the exception of some transition-metal ions, such as Zn2+, that form very stable hydration complexes.30,45,46 As in non-Gaussian g(r)’s the average first shell distance is usually longer than the position of the g(r) first maximum due to the shell asymmetry, it is useful to model the Sc−O g(r) with a gamma-like distribution (eq 3). The average distance R, coordination number N, Debye−Waller factor σ2, and asymmetry parameter β obtained from the fitting procedure are 2.19 Å, 8.0, 0.0082 Å2, and 0.72, respectively. As mentioned above, the results reported in the literature for the Sc3+ hydration properties are surprisingly widespread, due to the difficulties that are encountered when investigating disordered systems. However, the Sc−O first shell distance and coordination number obtained in the present work are within the range previously obtained by several experimental and theoretical techniques (R in the range 2.14−2.19 Å, and N between 6 and 87,10−15,17). As far as the Debye−Waller factor and asymmetry parameter are concerned, we can compare our results with those obtained in

(2)

where A(k, r) and ϕ(k, r) are the amplitude and phase functions, respectively, and ρ is the density of the scattering atoms. Phase shifts, A(k, r) and ϕ(k, r), have been calculated starting from one of the MD configurations, by using muffin-tin potentials and advanced models for the exchange-correlation self-energy (Hedin−Lundqvist). The values of the muffin-tin radii are 0.2, 0.9, and 1.6 Å, for hydrogen, oxygen, and scandium, respectively. The Sc−O and Sc−H g(r)’s obtained from the MD simulation have been used to calculate the single scattering first shell χ(k) theoretical signal, as the ion−hydrogen interactions have been found to provide a detectable contribution to the EXAFS spectra of metal ions in water,22,44 without optimization of the structural parameters. As far as the nonstructural parameters are concerned, the energy difference between the experimental and theoretical scale (E0) and the amplitude correction factor S20 have been optimized. To quantitatively extract the structural parameters related to the Sc3+ first hydration shell, the Sc−O g(r) obtained from the MD simulation has been modeled with gamma-like distribution curves with mean distance R, standard deviation σ, and asymmetry index (third cumulant divided by σ3) β = 2p−1/2 . The general expression is

g (r ) = N

p−1 p1/2 ⎡ ⎛ r − R ⎞ 1/2 ⎤ ⎟p × ⎥ ⎢⎣p + ⎜⎝ ⎦ σ Γ(p) σ ⎠

⎡ ⎛ r − R ⎞ 1/2 ⎤ ⎟p exp⎢− p − ⎜ ⎥⎦ ⎝ σ ⎠ ⎣

(3)

where Γ(p) is the Euler’s gamma function for the parameter p, and N is the coordination number providing the correct normalization. C

DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry an EXAFS investigation of Sc3+ in water.17 In such a study, Sc K-edge EXAFS spectra have been measured for three different Sc3+ aqueous solutions: scandium triflate in dilute trifluoromethanesulfonic acid at two different salt concentration (0.35 and 0.11 M) and scandium perchlorate in dilute perchloric acid (0.98 M).17 Least-squares refinements of the EXAFS data have been carried out for the three samples with both FEFF7 and GNXAS codes, by using a single asymmetric shell around the Sc3+ ion composed of eight water molecules. In this way, σ2 and third cumulant C3 values have been obtained in the range 0.0062−0.0121 Å2 and 2.5 × 10−4 to 7.6 × 10−4 Å3, respectively. By converting our β value in C3 (C3 = βσ3 = 5.3 × 10−4 Å3), it is clear that the σ2 and C3 values obtained in the present study are within the range obtained by Lindqvist-Reis et al. in ref 17. A very peculiar feature that can be observed in the Sc−O g(r) reported in Figure 2 is an anomalous trend in the distance region between 3 and 4 Å. This characteristic can be better appreciated by looking at the inset of Figure 2, where the presence of a peak is clearly visible that, at long distances, is partly overlapping the second shell one. Before getting additional insights into this peculiar behavior, we have assessed the validity of the structural results obtained from the MD simulation by comparing them with the EXAFS experimental data collected at the Sc K-edge for a Sc3+ aqueous solution. χ(k) theoretical signals have been calculated starting from the MD Sc−O and Sc−H g(r)’s using eq 2. In order to directly compare the first coordination shell structure obtained from the simulation with the experimental data, the structural parameters derived from the simulation were kept fixed during the EXAFS analysis, while the nonstructural parameters have been optimized by least-squares fits carried out in the k-range 5.4−12.9 Å−1. From the minimization procedure E0 was found 2.7 ± 0.2 eV above the first inflection point of the spectrum while S20 was 0.9 ± 0.1. The upper panel of Figure 3 shows the comparison between the experimental EXAFS spectrum and the theoretical curve obtained from the MD simulation. The first two curves from the top are the Sc−O and Sc−H contributions calculated from the MD g(r)’s without any adjustable parameter, while the reminder of the figure shows the total theoretical signal compared with the experimental spectrum and the residual curve. A very good agreement is found between the EXAFS theoretical and experimental signals, showing that the structural information derived from the MD simulation is basically correct. This finding is reinforced by the Fourier transform (FT) moduli of the EXAFS χ(k) theoretical and experimental signals shown in the lower panel of Figure 3. The FTs have been calculated in the k-range 5.4−12.0 Å−1 with no phase shift correction applied. Once the validity of our computational procedure has been assessed on the basis of the experimental data, additional insights into the Sc3+ hydration properties can be gained by the analysis of the MD trajectory. To understand the origin of the peak between 3 and 4 Å in the Sc−O g(r), it is useful to separately calculate the g(r)’s of water molecules ranked by their distance from the Sc3+ ion (see Figure 4). In this analysis all of the g(r)’s have been normalized to give ∫ 4πρr2g(r) dr = 1, where ρ is the average number density of the oxygen atoms. Moreover, a single g(r) for the first six neighbors has been calculated for the sake of clarity. The results show that, as expected, the 1st−6th, 7th, and 8th neighbors belong to the first solvation shell of the ion, as testified by three well-defined peaks below 2.90 Å (peak maximum positions at 2.16, 2.26, and

Figure 3. Upper panel: fit of the Sc K-edge EXAFS spectrum of Sc3+ in aqueous solution using a theoretical model obtained from the MD g(r)’s. From top to bottom the following curves are reported: the Sc− O contribution, the Sc−H contribution, the total theoretical signal (full blue line) compared with the experimental spectrum (dotted red line), and the residual curve. Lower panel: non-phase-shift-corrected Fourier transforms of the experimental data (dotted red line) and of the total theoretical signal (full blue line) reported in the upper panel.

Figure 4. Sc−O distance distributions calculated for water molecules ranked by their distance from the Sc3+ ion: 1st−6th (black line), 7th (red line), 8th (blue line), 9th (magenta line), 10th (violet line), and 11th (cyan line). A magnified view of the distributions in the distance range 2.4−4.4 Å is shown in the inset.

2.31 Å), while the 10th and 11th water molecules are found in the second coordination sphere (peak maximum positions at 4.00 and 4.09 Å). Conversely, a broad peak is found for the 9th water molecule ranging from 2.60 to 4.20 Å. From the magnified view shown in the inset of Figure 4 it is evident that this is the superposition of two peaks, with the former centered at 3.49 Å, and the latter at 3.88 Å. The two peaks are not separable, but by integration of the former one up to the shoulder at 3.80 Å, a coordination number of 0.73 is obtained. This result shows that the 9th water molecule has two different behaviors: most of the simulation time (73%) it is found in a distance region between the first and second hydration sphere, while for the remaining time it behaves like a second shell molecule. A hypothesis that can be formulated on the basis of D

DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry this result is that the Sc3+ ion, besides forming an inner 8-fold first shell complex, is able to coordinate an additional water molecule at very long distances as compared to the first shell ones. In order to corroborate this hypothesis, it is necessary to check if the 9th water molecule possesses a degree of structuring somehow comparable with the other first shell molecules. Before addressing this issue, it is interesting to understand if the 9th water molecule provides a detectable contribution to the EXAFS signal of Sc3+ in aqueous solution. To this end we have separately calculated the EXAFS theoretical signals associated either with the first peak of the Sc−O g(r) up to 2.9 Å or to the tail of the distribution. The EXAFS theoretical signal associated with the 8-fold first solvation shell has been found to be identical to the total theoretical signal shown in Figure 3, while the EXAFS signal associated with the oxygen atoms at distances longer than 2.9 Å has been found to have a negligible amplitude. As a consequence no information can be gained on the structure of the far-coordinated water molecule from the EXAFS spectroscopy. A useful analysis to determine the geometry of the first shell complexes formed by ions in aqueous solution is the angular distribution function (adf) of the O−Sc−O angle (labeled as ψ). ψ is between two Sc−O vectors, where Sc is the angle vertex, while O indicates two different oxygen atoms belonging to the ion first shell water molecules, or molecules inside a certain cutoff distance from the ion. The adf has been calculated by selecting all of the water molecules up to a Sc−O cutoff distance of 2.9 Å, which corresponds to the first minimum of the Sc−O g(r) (see Figure 5). The ψ distribution shows three

corresponding to the angles of an ideal SAP symmetry. Note that the number of angles contributing to the three different peaks should instead be 17, 1, and 10 for an ideal BTP configuration. However, as the ideal symmetries describing 8coordinated configurations are close to each other and quite difficult to discriminate, special attention has to be paid when trying to define the geometry of an ion solvation complex in solution, and the analysis of the ψ angle adf alone is not always adequate to definitely establish the first shell symmetry. The presence of a 9th water molecules coordinated at longer distances by the Sc3+ ion could point to the existence of either a capped SAP or of a tricapped trigonal prism (TTP) geometry of the nine water molecules nearest to the ion. If a TTP arrangement were present, the ψ angle adf calculated only for the capping water molecules should feature a single peak centered at 120°. Generally in the ψ angle analysis of a TTP hydration complex it is very difficult to separate the different contributions coming from prismatic and capping water molecules. By ordering the water molecules on the basis of their distance from the ion, usually one cannot be sure that the three farthest water molecules are the capped ones in every single time instant, as instantaneous distortion of the first shell polyhedron can occur, due to the intrinsic disorder of ionic aqueous solutions, and to the high mobility of solvent molecules. However, in the present case the 9th water molecule can be easily separated from the others as its distance is significantly longer. In order to calculate a ψ angle adf in a restricted region where water molecules are likely to behave as the 9th and the 8th water molecule in an ideal polyhedron, we have included in the analysis solvent molecules with a Sc−O distance between 2.5 and 3.2 Å. Looking at the g(r)’s shown in the inset of Figure 4, the upper cutoff has been chosen in order to include the 9th water molecule and to leave out the 10th, while the lower cutoff includes only the long distance tail of the Sc−O g(r) calculated for the 8th molecule, in an attempt to possibly exclude from the calculation prismatic water molecules. As can be clearly seen in Figure 5, the obtained adf shows a single peak at 120°. This result suggests that the 9th water molecule is strongly structured by the Sc3+ ion, even if it is very far away from it. However, the angle obtained is compatible with the presence of either a capped SAP or a TTP symmetry for the nine water molecules around the Sc3+ ion. In order to shed light on this issue, a strategy to identify the Sc3+ first solvation shell geometry has to be developed. Additional information on the mutual arrangement of the 8th and 9th water molecule can be gained by calculating radialangular combined distribution functions (CDFs). In this analysis, the values of the two variables (one angle and one distance) are regarded as a 2-tuple, so that they are connected and related to each other as they stem from the same configuration, and the 2-tuple is plotted in a two-dimensional histogram. The left panel of Figure 6 shows the CDF obtained combining the g(r) between the Sc3+ ion and the oxygen atom of the 8th water molecule nearest to the ion (RSc−O8), and the distribution function of the ψ angle calculated between the 8th and 9th water molecule. Note that in this and in the following analyses we have used only those simulation frames in which the 9th water molecule is located inside a cutoff distance of 3.80 Å from the ion, in order to select only configurations where the 9th water molecule does not behave like a “standard” second shell molecule. As it can be seen, two well-defined peaks are found centered at 60° and 120°. The low angle peak is related

Figure 5. Distribution functions of the O−Sc−O angle (ψ) calculated by selecting either the water molecules up to a Sc−O cutoff distance of 2.9 Å (red line), or the water molecules with a Sc−O distance between 2.5 and 3.2 Å (blue line).

well-defined peaks at ψ values of 74°, 120°, and 142°. As mentioned above the first shell coordination number obtained by integration of the Sc−O g(r) up to 2.9 Å is 8.0. In general, 8fold complexes can be described by several geometries, such as trigonal dodecahedron, cubic, square antiprism (SAP), and bicapped trigonal prism (BTP).47 When looking at the adf obtained here, an SAP arrangement of the eight nearest water molecules sourrounding the Sc3+ ion seems the most probable configuration. The total number of ψ angles for 8-fold structures is 28, and it is possible to calculate the number of angles that contribute to the three peaks, by integration of the adf function over the three peak ranges: 1 − cos(ψ) = 0.00− 1.08, 1 − cos(ψ) = 1.08−1.65, and 1 − cos(ψ) = 1.65−2.00. In this way we have obtained a number of angles contributing to the first, second, and third peak of 16, 4, and 8, respectively, E

DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 6. Left panel: combined distribution function (CDF) obtained combining the g(r) between the Sc3+ ion and the oxygen atom of the 8th water molecule nearest to the ion (RSc−O8), and the distribution function of the O−Sc−O (ψ) angle calculated between the 8th and 9th water molecules. Right panel: CDF obtained combining the g(r) between the oxygen atoms of the 8th and 9th water molecule in order of distance from the ion (RO8−O9), and the distribution function of the O−Sc−O (ψ) angle calculated between the 8th and 9th water molecule.

to Sc−O8 distances up to 2.45 Å, while the tail of the peak at 120° extends over a much longer distance range (up to 2.80 Å). Therefore, when the 8th water molecule is close to the ion it can form with the 9th one either low or high angles, while when its distance is longer than 2.45 Å, the ψ angle is always above 100°. We have then calculated another CDF using the same angle (ψ) and the distance between the 8th and 9th water molecule (RO8−O9) (right panel of Figure 6). Also in this case two separated peaks are found showing that when RO8−O9 is shorter than 4.0 Å the ψ angle is below 80°, while for RO8−O9 distances longer than 4.5 Å, angles larger than 100° are formed. Bearing in mind these results, we have resorted to build an internal reference system based on the instantaneous positions of the 8th and 9th water molecule. We have thus calculated a spatial distribution function (SDF) of the oxygen atoms around Sc3+ in this internal reference system. In particular, two unit vectors have been defined, the former along the direction between the ion and the oxygen atom of the 8th water molecule, and the latter along the same direction involving the 9th molecule. Also, for this analysis, we have considered only simulation frames in which the 9th water molecule is located inside a cutoff distance of 3.80 Å from the ion. Moreover, an additional condition has been imposed to select the MD configurations, i.e., that the RO8−O9 distance was longer than 4.50 Å, to include only the frames where the 8th water molecule is on the opposite side of the 9th water molecule with respect to the central ion. Note that about 50% of simulation frames simultaneously satisfy these two conditions. Three different orientations of the obtained SDF are reported in Figure 7, and the existence of a well-defined geometry of water molecules around the Sc3+ ion can be clearly observed. These results unambiguously indicate that the 9th water molecule is strongly coordinated by the ion and possesses a degree of structuring comparable with that of the other first shell molecules that are located at much shorter distances. The distribution clearly shows the existence of a capped SAP geometry for the water molecules around the Sc3+ ion, with the 9th water molecule in the capping position at a very long distance from the ion. The obtained structure is compatible with the ψ angle values calculated between the 8th and 9th water molecules in the CDF analysis. Indeed, the 9th water molecule forms an angle of about 60° with the water molecules of the adjacent square face, and an angle of about 120° with the

Figure 7. Spatial distribution functions of the oxygen atoms of water molecules (red) around the Sc3+ ion (violet) calculated in an internal reference system based on the instantaneous positions of the 8th and 9th water molecule.

water molecules of the opposite one. Moreover, it is interesting to observe that the presence of the 9th molecule in the capping position forces the water molecules in the near square face to be closer to the ion, as shown by the CDF results reported in Figure 6. As a last analysis, we have evaluated the residence time of water molecules in the Sc3+ first hydration shell by means of the Impey method.48 In this method a solvent molecule is considered as having left a shell only if it remains outside the shell itself for a continuous period longer than a threshold time (t*). Following previous studies, a t* value of 0.5 ps has been used.33,49,50 In a conventional residence time calculation the ion first hydration shell would be defined by including the water molecules up to a Sc−O cutoff distance corresponding to the Sc−O g(r) first minimum. However, as explained above, in the F

DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry case of the Sc3+ ion a peculiar result has been found, i.e., that on average an additional solvent molecule is coordinated at a very long distance from the ion, resulting in a capped SAP geometry around the Sc3+ ion. For this reason, in order to include this farcoordinated molecule in the first shell, we have used a Sc−O cutoff distance of 3.80 Å, obtaining a residence time of 188 ± 10 ps. It is interesting to point out that, by using a Sc−O cutoff distance of 2.90 Å in the calculation, a slightly lower residence time of 149 ± 10 ps is obtained. This result can be explained by the fact that the water molecules, after leaving the internal SAP polyhedron, spend some time in the region between 2.90 and 3.80 Å from the central ion, by occupying the capped position of the capped SAP geometry. A detailed description of the selfexchange mechanisms is given below. Note that in the previously published QM/MM simulation of Sc3+ in water no exchange processes involving water molecules in the ion first coordination shell have been observed, but this could be due to the very short time of the QM/MM trajectory (10 ps).14 Moreover, it is noteworthy that, during such simulation, two water molecules approached the Sc3+ ion, and this event has been interpreted by the authors as an unsuccessful water exchange attempt in the first hydration shell of the ion.14 As far as our MD simulation is concerned, several water exchange events have been observed in which a 10th water molecule enters inside the cutoff distance of 3.80 Å, leading to the formation of transient 10-coordinated clusters. The selfexchange mechanism can be defined as concerted associative (of the type 9-10-9): when a water molecule enters the shell, another one leaves it, and for a very short time the incoming and leaving molecules are simultaneously inside the shell. The exchange process involves the water molecule in the capping position of the Sc3+ first shell polyhedron, that can be easily replaced by two different exchange mechanisms. A schematic representation of the two exchange processes is shown in Figure 8. In the former, the 10th water molecule approaches the ion on the same side of the capped one, finally pushing it out and replacing it in the capping position. In the latter, which is the most probable process, the 10th water molecule enters the shell by occupying the other capping position at the opposite side with respect to the 9th molecule. In this process, a transient bicapped SAP structure is formed, leading to a new capped SAP geometry when the original capped molecule finally leaves the shell. On the basis of these results, the rapidity of the water exchange events in the Sc3+ aqueous solution can be explained by the fact that the two structures with either one capping position occupied or the other are equally favored from an energetic point of view, so that the Sc3+ ion can easily pass from one configuration to the other. Besides these processes, also the eight water molecules belonging to the internal SAP prism rapidly change identity in the course of the simulation. The capped water molecule can indeed replace one water molecule in a prismatic position, and simultaneously a prismatic molecule becomes the capped one. These internal rearrangements of the Sc3+ hydration shell pass through the formation of a temporary TTP geometry of the water molecules surrounding the ion. Figure 9 shows a schematic picture of this process that can be described as follows: the 9th water molecule in the capping position approaches the ion; the square face near to the capped molecule is pushed toward the ion by the repulsion with the 9th water molecule; simultaneously the square face on the opposite side distorts itself in such a way that two water molecules move toward the C4 axis of the SAP geometry; two parallel triangular

Figure 8. Self-exchange mechanisms (of the type 9-10-9) by which the water molecule in the capping position of the Sc3+ first shell polyhedron is replaced by a new water molecule. In the former exchange mechanism (upper panel), the 10th water molecule approaches the ion on the same side of the capped one, finally pushing it out and replacing it in the capping position. In the latter (lower panel), the 10th water molecule enters the shell by occupying the other capping position at the opposite side with respect to the 9th molecule. Only the oxygen atoms of water molecules are shown for clarity. The incoming and leaving water molecules are colored cyan and pink, respectively, while the Sc3+ ion is colored in violet, and the oxygen atoms of all the other first shell water molecules are red.

Figure 9. Self-exchange mechanism by which the 9th water molecule in the capping position (pink) enters the internal SAP polyhedron around the Sc3+ ion (violet) while a water molecule belonging to the internal SAP cluster becomes the new capped ligand (cyan). Only the oxygen atoms of water molecules are shown for clarity. The exchange process leads to the formation of a TTP transient structure, and then it relaxes toward a new capped SAP geometry. To guide the eyes the oxygen atoms of molecules belonging to either the top or the bottom square face of the initial SAP polyhedron have been colored blue and green, respectively.

faces are thus formed by each of these molecules and two water molecules on the other side, resulting in a trigonal prismatic geometry; the other two water molecules of the lower square place are instead pushed away from the ion and become, together with the 9th water molecule, the three capping ligands of a TTP transient polyhedron; finally the structure relaxes G

DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Sc3+ ion, which is significantly smaller than the last lanthanoid ion, Lu3+, coordinates the nearest water molecules at shorter distances, forming an inner 8-coordinated complex with an SAP symmetry. However, the high charge density of Sc3+ allows it to coordinate an additional water molecule at very long distances, so that the overall Sc3+ hydration shell corresponds to a 9-fold complex with a capped SAP geometry. Anyhow, the very long distance of the 9th water molecule cannot be explained by simple considerations about the repulsion among the water oxygen atoms. Maybe the peculiar Sc3+ hydration properties can be rationalized only taking into account the important role of the 9th water molecule in both the water exchange process between the first and second coordination spheres and the internal rearrangements of the first shell hydration polyhedron. Indeed, the presence of the far-coordinated water molecule makes the Sc3+ coordination complex very labile, by allowing the first shell water molecules to easily exchange their positions inside the solvation shell and to easily exchange also with the rest of the solvent. From a dynamic point of view, the 9th water molecule can be seen like a “bridge” between the inner SAP cluster and the second coordination sphere, by means of which solvent molecules can effortlessly and rapidly pass from one side to the other. Therefore, even if the small and highly charged Sc3+ ion is able to form very strong interactions with the surrounding molecules, the Sc3+ hydration shell is characterized by a high mobility and by the tendency to frequent changes of the coordinated ligands. The structural and dynamic properties of the Sc3+ aqua ion found in this work could explain the high catalytic activity that several Sc3+ compounds show when used as Lewis acids for catalyzing many types of organic reactions.3 The Sc3+ salts have a higher efficiency than lanthanoid-based compounds, and this high efficiency could be due to the ability of the Sc3+ ion to form complexes with a very distant coordinated ligand, as the donor atoms of the substrate molecules in an organic reactions would be able to compete favorably with the far-coordinated ligands and to easily bind the Sc3+ ion in the capping position. Indeed, the flexible nature of the Sc3+ coordination cluster increases the accessibility of the ligands to the ion, and therefore the ion effectiveness as a Lewis acid.

toward a new capped SAP geometry in which the C4 axis is rotated of about 120° with respect to the original one.

4. DISCUSSION AND CONCLUSIONS In this work the coordination properties of the Sc3+ ion in water have been investigated by combining QM calculations, MD simulations, and EXAFS spectroscopy. The outstanding outcome of this investigation is that the Sc3+ ion forms a well-defined capped SAP complex in aqueous solution. In particular, the eight water molecules closest to the ion are located at the vertexes of a SAP polyhedron, while the ninth water molecule occupying the capping position is found at a very long distance from the ion. This far-coordinated water molecule possesses a degree of structuring comparable with the other first shell molecules surrounding the ion at much shorter distances. To the best of our knowledge, this is the first time that an aqua ion has shown such a peculiar behavior. The presence of a ninth far-coordinated water molecule has given us the unique opportunity to easily identify the geometry of the Sc3+ coordination polyhedron. Generally, with the exception of some cases where very stable hydration complexes are formed,51,52 it is very difficult to single out the mean hydration structure of aqua ions due to the strong disorder of the first shell, and because of the high mobility of water molecules surrounding the ion. As far as TTP and SAP geometries are concerned, several procedures have been adopted in the literature to identify these structures from MD simulations of lanthanoid aqueous solutions. Kowall et. al for example calculated “dot plots” of the ion first shell after identification and superposition of the MD configurations with the underlying regular polyhedra.53 Conversely, to distinguish between TTP and capped SAP geometries, Floris et al. introduced a method based on the diagonalization of the inertia tensor for a polyhedron formed by the oxygens of water molecules belonging to the lanthanoid first hydration shell.28 An approximate classification of the structures was then made using a similarity index whose sign defined the shape of the complex.28 At variance with these rather complex procedures, in this work the presence of a 9th water molecule coordinated at very long distances allowed us to easily separate it from the others and to build an internal reference system based on its position. By using this internal reference system the identification of the Sc3+ coordination polyhedron has been very straightforward. The hydration properties of Sc3+ have many similarities with those found for the lanthanoid(III) aqua ions that form very crowded coordination spheres in aqueous solution. For these ions, a change of the coordination number from 9 to 8 takes place in the middle of the series, and the lighter ions were shown to be 9-coordinated in TTP fashion.54−58 Conversely, the heavier ions are 8-coordinated, and according to some investigations the first shell polyhedron is a SAP,54 while according to others heavier lanthanoid ions retain a TTP geometry, and along the series two of the three capping water molecules become less and less strongly bound, and finally one of them leaves the hydration cluster.55 The geometries of these coordination polyhedra derive from the balance between the maximization of electrostatic forces and the minimization of the repulsion among the solvent molecules. Across the lanthanoid series, the ion−water first shell distance decreases as a consequence of the lanthanoid contraction, so that the heaviest lanthanoids are not able to retain a 9th water molecule, resulting in a 8-fold first shell cluster. In this framework, the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the University of Rome “La Sapienza” (Progetti Ateneo 2015 C26N159PNB and C26H159F5B) and by the CINECA supercomputing centers through Grant IscrC_DIWA (HP10C2Q0F3).

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DOI: 10.1021/acs.inorgchem.6b00962 Inorg. Chem. XXXX, XXX, XXX−XXX