XANES Reveals the Flexible Nature of Hydrated Strontium in Aqueous

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XANES Reveals the Flexible Nature of Hydrated Strontium in Aqueous Solution Paola D'Angelo, Valentina Migliorati, Francesco Sessa, Giordano Mancini, and Ingmar N Persson J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b01054 • Publication Date (Web): 11 Apr 2016 Downloaded from http://pubs.acs.org on April 17, 2016

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The Journal of Physical Chemistry

XANES Reveals the Flexible Nature of Hydrated Strontium in Aqueous Solution Paola D’Angelo,∗,† Valentina Migliorati,† Francesco Sessa,† Giordano Mancini,‡ and Ingmar Persson¶ Dipartimento di Chimica, “La Sapienza” Università di Roma, P.le Aldo Moro 5, 00185 Rome, Italy., Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy, and Department of Chemistry and Biotechnology, Swedish University of Agricultural Sciences (SLU), SE-750 07 Uppsala, Sweden. E-mail: [email protected]

Abstract

fold hydration complex with a Sr-O distance of 2.60 Å has been found to be compatible with the XANES data, in agreement with previous findings. However, the hydration shells of the strontium ions have been found to have a flexible nature with a fast ligand exchange rate between the first and second hydration shell occurring in the picosecond time scale.

X-ray absorption near-edge structure (XANES) spectroscopy has been used to determine the structure of the hydrated strontium in aqueous solution. The XANES analysis has been carried out using solid [Sr(H2 O)8 ](OH)2 as reference model. Classical and Car-Parrinello Molecular dynamics (MD) simulations have been carried out and in the former case two different sets of LennardJones parameters have been used for the Sr2+ ion. The best performing theoretical approach has been chosen on the basis of the experimental results. XANES spectra have been calculated starting from MD trajectories, without carrying out any minimization of the structural parameters. This procedure allowed us to properly account for thermal and structural fluctuations occurring in the aqueous solution in the analysis of the experimental spectrum. A deconvolution procedure has been applied to the raw absorption data thus increasing the sensitivity of XANES spectroscopy. One of the classical MD simulations has been found to provide a XANES theoretical spectrum in better agreement with the experimental data. An 8∗ To

Introduction Strontium is an alkaline earth element that has gained attention over the last years as 90 Sr has been produced on a large scale from tests of neclear weapons and it is one of the radioactive components of aqueous nuclear waste. This isotope is linked to bone cancer as calcium can be replaced by strontium during bone formation. 1,2 The solvation structure of the Sr2+ ion in aqueous solution is often used as a model for the interpretation of its complexation properties in different systems. Therefore, a detailed understanding of the hydration properties of Sr2+ is of great importance for diverse fields of chemistry, biology as well as for the development of efficient separation processes for the treatment of nuclear waste. Given this renewed interest for both fundamental and applicative reasons, questions about the structure and dynamics of the hydrated strontium ion in aqueous solution are still at the center of recent research. 3–7

whom correspondence should be addressed di Chimica, “La Sapienza” Università di

† Dipartimento

Roma. ‡ Scuola Normale Superiore ¶ Department of Chemistry, Swedish University of Agricultural Sciences (SLU)

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X-ray diffraction, 8,9 neutron scattering, 10 extended X-ray absorption fine structure (EXAFS), 11–17 Raman spectroscopy, 18 as well as classical, 3,19 QM/MM 20 and ab initio 7,21,22 Molecular Dynamics (MD) simulations and density functional theory (DFT) calculations 3,5,6 have been extensively used in the past to investigate Sr2+ in water, but unfortunately they showed widespread results concerning Sr-O distances (in the range 2.56 to 2.69 Å) as well as coordination numbers (in the range 6.7 to 10.3). Several EXAFS studies have been carried out on Sr2+ aqueous solutions but quite different coordination number values have been obtained due the presence of multielectron transition channels that lead to distortions of the EXAFS signal if not properly treated in the data analysis, and to the presence of a highly disordered first coordination shell. 11–17 In particular, anomalies in the Sr K-edge X-ray absorption cross section are present due to the simultaneous excitations of 1s4s, 1s3d, and 1s3p electrons. 12 These double electron shake-up processes give rise to discrete resonances and slope changes in the atomic background that have to be properly accounted for, to extract reliable structural parameters from the EXAFS spectra. Moreover, different starting models obtained from solid reference compounds or MD simulations have been used in the literature, and the structural results have been found to be strongly dependent on the model used for the analysis of the experimental data. The first EXAFS investigations of Sr2+ in water were carried out using the strontium oxide SrO with a six-coordinated strontium atom as reference compound, and coordination numbers of 7.3, 7.7 and 8.93 were obtained. 14,16,17 Persson et al. 11 and Moreau et al. 15 used solid [Sr(H2 O)8 ](OH)2 as reference compound and they obtained similar structural results with Sr-O distances of 2.61 and 2.60 Å, respectively, and a coordination number of 8. A different approach based on MD simulations was used by D’Angelo et al. 12 with the aim of properly characterize the multielectron transitions at the Sr Kedge. The initial MD cluster was taken from Spohr et al. 19 with a mean Sr-O distance of 2.63 Å and coordination number of 9.8. Starting from this model the EXAFS analysis provided an extremely high coordination number of 10.3.

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All together these findings show that both the experimental techniques and the theoretical methods used thus far are not able to provide a unified picture of the hydration properties of the Sr2+ ion. We, therefore, decided to apply, for the first time, X-ray absorption near-edge structure (XANES) spectroscopy to gain new insights into the structure of Sr2+ hydration complexes. XANES is very useful to unveil the geometrical structure of ions in solution due to its sensitivity to geometrical and electronic properties of the photoabsorber. This is one of the few techniques that can be used for the structural investigation of liquid systems and it provides not only information on the radial distribution functions, as in the case of EXAFS or X-ray diffraction, but also on the three dimensional arrangement of the atoms surrounding the photoabsorber. In this work the sensitivity of XANES has been assessed using solid [Sr(H2 O)8 ](OH)2 as reference compound as in this crystal the Sr2+ ion has a first coordination sphere close to the one in solution. 11,15 At the same time MD simulations have been used to properly analyse the experimental data, as in the case of aqueous solutions the XANES signal originates from the average over all the possible configurations adopted by water molecules around the ion, and a single cluster cannot be used to correctly reproduce the XANES spectrum. This method is very powerful as disorder effects due to the dynamic distortions of the coordination shells are properly included in the calculation of the XANES theoretical spectrum. This combined approach exploiting both the ability of the XANES spectroscopy to provide detailed information on the geometric environment of the photoabsorber atom, and the dynamical description of the system provided by the MD calculations allowed us to find a robust hydration model for the strontium ion in aqueous solution.

Methods Chemicals Octaaquastrontium hydroxide[Sr(H2 O)8 ](OH)2 (Merck, analytical grade) was used as purchased. All water used was demineralized (18.2 M Ω cm, Millipore Direct-Q).


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XAS Data Collection

free path in solids. The numerical values of Es and As are derived at each computational step using a Monte Carlo fit. A Gaussian convolution is used to account for the experimental resolution. Solid [Sr(H2 O)8 ](OH)2 has been analysed starting from the X-ray structure including either the first, or both the first and higher distance coordination shells (up to a cut-off distance of 5.3 Å). 11 The hydrogen atoms have been considered in the analysis. 12 The XANES spectrum of Sr2+ in aqueous solution has been analyzed starting from the structural configurations derived from MD simulations. In particular trajectories containing the first shell water molecules have been extracted from the total simulations and 500 snapshots saved every 20 ps have been used to calculate the XANES signal associated with the instantaneous coordination geometries around the ion. The average spectrum has been obtained by summing all the theoretical spectra and dividing by the number of MD snapshots used. We have verified that 500 configurations are enough to reach convergence. Least-squares fits have been carried out by keeping fixed either the crystallogrphic or the MD structure and optimizing the nonstructural parameters using a residual function defined as:

X-ray absorption measurements on solid [Sr(H2 O)8 ](OH)2 and a 0.20 M aqueous solution of octaaquastrontium hydroxide were performed at the Sr K-edge (16105 eV). The solid was diluted with boron nitride, 29.1 mg of [Sr(H2 O)8 ](OH)2 in 36.6 mg BN, carefully grained in an agate mortar, and contained in 1.5 mm thick aluminum frames with Mylar tape covering the sample. The aqueous solution was contained in a liquid cell with 1.5 mm Teflon spacer and 6 micron thick polypropylene film hold with titanium frames. The data were collected at the wiggler beam line I811 at MAXlab, Lund University, which operated at 1.5 GeV with a maximum current of 220 mA. The experimental station was equipped with a Si[111] double crystal monochromator. Higher order harmonics were reduced by detuning the second monochromator crystal to reflect 70% of maximum intensity at the end of the scans. All measurements were performed simultaneously in transmission and fluorescence mode using gas filled ion chambers and a Passivated Implanted Planar Silicon detector. For each sample six 10 minute continuous scans were averaged.

XANES Data Analysis

exp 2 th ∑m i=1 wi (yi − yi ) Rsq = εi2 ∑m i=1 wi

The MXAN code has been used to carry out the XANES data analysis. 23 MXAN calculates the potential in the framework of the muffin tin (MT) approximation using a complex optical potential, based on the local density approximation of the excited photoelectron self-energy. The MT radii are 1.8 Å for strontium, 0.9 Å for oxygen and 0.2 Å for hydrogen. The self-energy is calculated in the framework of the Hedin-Lundqvist (HL) scheme using only the real part of the HL potential while inelastic losses are accounted for by convolution of the theoretical spectrum with a Lorentzian function having an energy-dependent width of the form Γtot (E)=Γc +Γm f p (E). The constant part, Γc includes the core-hole lifetime, while the energy-dependent term, Γm f p (E) represents all the intrinsic and extrinsic inelastic processes. The function Γm f p (E) is zero below an onset energy, Es , and begins to increase from a value, As , following the universal functional form of the mean

(1)

where m is the number of data points, yth i and yexp are the theoretical and experimental values of i absorption, respectively, εi is the individual error in the experimental data set, and wi is a statistical weight. Five nonstructural parameters have been optimized, namely the experimental resolution Γexp , the Fermi energy level EF , the threshold energy E0 , the energy and amplitude of the plasmon Es and As .

Molecular Dynamics Simulations Classical MD simulations of the Sr2+ ion in aqueous solution have been performed using the GROMACS package 24 on a system composed by one Sr2+ ion and 819 water molecules placed in a cubic box with an edge length of 29.11 Å. The box dimension was chosen as to reproduce the experi-


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Berendsen method 28 with a coupling constant of 0.1 ps. The equations of motion were integrated with a 1 fs time step and the system was equilibrated for 5 ns before sampling. The production runs were 10 ns long.

mental density of the solution. Periodic boundary conditions were used to avoid edge effects. Nonbonded interactions were computed using the following equation: N

qi q j + ri j i> j " 6 # σi j 12 σi j − + 4εi j ri j ri j

V (r) =

∑f

(2)

where the summation is over all the system atoms (N), f is the electric conversion factor (138.935 kJ mol−1 nm e−2 ), ri j is the distance between atoms i and j, while qi and q j are the partial electrostatic charges of species i and j, respectively. The first Coulombic term describes the electrostatic interactions, while the second term is a LennardJones potential representing van der Waals interactions. The Lennard-Jones parameters σi j and εi j are the well depth and collision diameter for the interaction between atoms i and j. They are obtained using the Lorentz-Berthelot combination √ rules (εi j = εii ε j j , σi j = (σii + σ j j )/2) where εii and σii are determined for each atomic site in the system. The complete set of parameters used in the simulations are listed in Table 1. Two MD simulations have been carried out using the SPC/E water model, 25 and two different sets of Lennard-Jones parameters for the Sr2+ ion, the former developed by Åqvist 26 and the latter by Dang as reported in Ref. 14

Figure 1: Crystallographic structure of [Sr(H2 O)8 ](OH)2 . Strontium atoms are in blue, hydrogen atoms are in white while oxygen atoms are in red and purple for water molecules and hydroxide ions, respectively. The mean residence time of water molecules in the first solvation shell of the Sr2+ ion has been evaluated using the approach proposed by Impey et al. 29 Following previous studies 30–34 a t* value of 0.5 ps has been adopted in the Impey procedure.

Table 1: Lennard-Jones atomic parameters and partial charges used in the classical Molecular Dynamics simulations

Car-Parrinello Molecular Dynamics Simulation

atom model εii (kJ/mol) σii (nm) qi (e) Sr Åqvist 0.4947 0.3103 +2.0000 Sr Dang 0.4184 0.3314 +2.0000 O SPC/E 0.6500 0.3166 -0.8476 H SPC/E 0.0000 0.0000 +0.4238

The ab initio MD simulation of the Sr2+ ion in aqueous solution has been carried out using the Car-Parrinello approach 35 by means of the CPMD code package. 36 In this case the system is composed of 90 water molecules and 1 Sr2+ ion that is placed in a periodic cubic box with a 14 Å edge, chosen also in this case to reproduce the solution experimental density. Electronic calculations have been performed by use of the Kohn-Sham Density Functional Theory (DFT) approach, 37 with the revised Perdew-Burke-Ernzerhof (revPBE) exchange-correlation functional. 38,39 Van der

A cutoff of 9 Å was used to deal with non bonded interactions, with the Particle Mesh Ewald (PME) method to treat long range electrostatic effects. 27 A homogeneous background charge was utilized to compensate for the ion charge. The system was simulated in a NVT ensemble (T=300 K) using the


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Waals corrections to DFT are accounted for by using the Dispertion-Corrected Atom-Centered Pseudopotentials (DCACPs) developed by Rothlisberger et al. 40 to describe core electrons of oxygen and hydrogen atoms. Core electrons of the Sr2+ ion are treated with a Troullier-Martins pseudopotential. 41 The electronic degrees of freedom have an associated fictitious mass of 400 a.u. and the time step of the simulation is of 4 a.u. A 70 Ry energy cutoff has been used for the plane-wave basis set. A starting equilibration run has been performed for 2 ps in the NVT ensemble at 300 K, thermalizing the system by means of the NoséHoover thermostat with a coupling frequency of 1500 cm−1 . After a further equilibration in the NVE ensemble 2 ps long, a production run of 30 ps has then been carried out. A homogeneous background charge has been used to compensate for the charge of the Sr2+ ion. It should be noted that throughout the simulation no relevant drift of the fictitious electronic kinetic energy has been observed.

tra and applying a deconvolution procedure to reduce the effect of intrinsic and experimental broadening. 42–46 Intrinsic broadening highly affects XANES measurements at high energy and the experimental spectrum is the convolution of the ideal signal with a Lorentzian having full width at half-maximum (fwhm) of Γc . By applying the deconvolution procedure developed by Filipponi 45 it is possible to remove about twothirds of the lifetime broadening by using a Gaussian filter. We applied this method to the Sr Kedge XANES spectra and we deconvolved the entire core-hole width (Γc =3.25 eV) and we applied a Gaussian filter with full width at halfmaximum σ =1.5 eV. The σ value has been chosen by selecting the lowest value that did not give rise to ringing artifacts in the deconvolved spectrum. This procedure allowed us to convert the Lorentzian resonance into a much narrower Gaussian peak thus obtaining a spectrum with a resolution closer to that of the HERFD XAS spectrum. 4 The raw and deconvolved XANES spectra of solid [Sr(H2 O)8 ](OH)2 are shown in Figure 2A. Clearly, the structural features in the deconvolved spectrum are better resolved and the shoulder at about 16130 eV becomes a distinct peak. Note that this peak is also present in the HERFD XAS spectrum of [Sr(H2 O)8 ](OH)2 (see Figure 3 of Ref. 4 ) thus showing that the deconvolution procedure is able to properly extract the structural features from the experimental spectra. On the other hand no pre-edge features are present in the spectra and this is in agreement with HERFD XAS results showing that the pre-edge peaks are associated with quadrupolar excitation into d-states and their intensity is proportional to the deviation from centro-symmetry. 4 In the case of symmetric clusters, as in [Sr(H2 O)8 ](OH)2 , the pre-edge features are expected to be absent. Figure 2B shows the raw and deconvolved spectra of Sr2+ in water. In this case the deconvolution procedure increases the intensity of the white line but no additional structural features are observed. The comparisons between the XANES spectra of [Sr(H2 O)8 ](OH)2 and Sr2+ aqueous solution are reported in Figure 2C and D for the raw and deconvolved data, respectively. While the main structural oscillation is very similar in the two spectra, the solid reference compound contains a peak at

Results Crystalline Model Compound Crystalline [Sr(H2 O)8 ](OH)2 has been found to be the best reference compound to determine the coordination structure of Sr2+ in water as it crystallizes with eight water molecules coordinating the cation in a tetragonal antiprismatic configuration. 11 In this structure each water molecule is engaged in three hydrogen bonds while the hydroxide ions form chains of donor and acceptor bonds and they are not directly coordinated with the Sr2+ ion (see Figure 1). The mean Sr-O distance is 2.619 Å with two different sets of distances of 2.613 and 2.625 Å. 11 In a previous investigation high energyresolution fluorescence detection X-ray absorption (HERFD-XAS) was applied to investigate the local coordination of strontium in the same crystalline compound and some aqueous fluids at elevated temperature and pressure conditions. 4 HERFD-XAS provides XANES spectra with very high spectral resolution. Enanched resolution can be obtained also starting from standard XAS spec-


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B

1.5 Sr(H2O)8(OH)2

1

0.5

Raw Deconvolved

1.5

XANES (arb. units)

XANES (arb. units)

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2+

Sr

in water

1 Raw Deconvolved

0.5

0

0

16100 16125 16150 16175

16100 16125 16150 16175

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E (eV)

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1

2+

0.5

0

Sr in water Sr(H2O)8(OH)2

1.5

Deconvolved

1 2+

Sr in water Sr(H2O)8(OH)2

0.5

0 16100 16125 16150 16175

16100 16125 16150 16175

E (eV)

E (eV)

Figure 2: (A) Comparison between the raw Sr K-edge (red line) and deconvolved (green line) XANES spectra of solid [Sr(H2 O)8 ](OH)2 . (B) Comparison between the raw Sr K-edge (blue line) and deconvolved (purple line) XANES spectra of Sr2+ in aqueous solution. (C) Comparison between the Sr K-edge XANES spectra of solid [Sr(H2 O)8 ](OH)2 (red line) and Sr2+ in aqueous solution (blue line). (D) Comparison between the Sr K-edge deconvolved spectra of solid [Sr(H2 O)8 ](OH)2 (green line) and Sr2+ in aqueous solution (purple line). 16130 eV and additional small spectral features at higher energy that are not present in the aqueous solution spectrum. This difference is more evident in the deconvolved spectra shown in Figure 2D. These findings suggest that the 8-fold coordination of the reference compound is well suited to describe the geometry of the Sr2+ hydration complex, but in crystalline [Sr(H2 O)8 ](OH)2 there are some additional contributions that are not present in solution. In order to understand the origin of the additional features present in the XANES experimental signal of the crystalline compound, a quan-

titative analysis of the spectrum has been carried out. The XANES structure arises as multiple scattering contributions from a cluster of atoms surrounding the photoabsorber. 47–49 For this reason in the first step of the analysis a theoretical spectrum of solid [Sr(H2 O)8 ](OH)2 containing only the first coordination shell has been calculated. As previously mentioned the first coordination shell is formed by eight water molecules arranged in a slightly distorted antiprism with four Sr-O distances at 2.613 Å and four at 2.625 Å. During the fitting procedure the structural parameters have


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Figure 3: Comparison between the raw Sr K-edge XANES spectrum (blue dotted line) (A) and deconvolved spectrum (blue dotted line) (B) of solid Sr(H2 O)8 ](OH)2 and the best-fit theoretical spectra (red solid line) calculated including the first coordination shell, only. Comparison between the raw Sr Kedge XANES spectrum (blue dotted line) (A) and deconvolved spectrum (blue dotted line) (B) of solid Sr(H2 O)8 ](OH)2 and the best-fit theoretical spectra (red solid line) calculated including all the atoms within a distance cut-off of 5.3 Å. The atomic clusters used in the calculations are also depicted where strontium atoms are in blue, hydrogen atoms are in white while oxygen atoms are in red and purple for water molecules and hydroxide ions, respectively. are shown in Figure 3A, B for the raw and deconvolved spectra, respectively, while the molecular cluster used in the calculations is shown at left. In both cases the agreement between the theoretical and experimental curves is not good in the low energy region and the peak at about 20 eV above the edge is not reproduced. The Rsq values obtained from the fit were 1.8 and 2.4 for the raw and deconvolved spectra, respectively. In the second step of the analysis a theoretical spectrum with a distance cutoff of 5.3 Å has been calculated including more water molecules and the closest hydroxide ions. We have verified that the calculations as a function of the cluster size con-

been kept fixed while the nonstructural parameters have been optimized to obtain the best agreement with the experimental data. The XANES data analysis has been carried out both on the raw spectrum and on the deconvolved data. In the former case Γc was set to 3.25 eV and the Γexp bestfit value was 1.5 eV, while in the latter case Γc was equal zero and Γexp was 3.0 eV. Note that when dealing with deconvolved spectra no physical meaning can be ascribed to the Γexp parameter as it is used to reproduce the amplitude of spectrum that is mainly dependent on the width of the Gaussian filter used in the deconvolution procedure. The results of the minimization procedures


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A

verge at this cutoff distance. Also in this case the structural parameters have been kept fixed while the nonstructural parameters were refined, obtaining the same values reported above. Comparisons of the experimental and theoretical spectra are presented in Figures 3C, D for the raw and deconvolved data, respectively, while the corresponding atomic cluster is depicted at left in Figure 3. It can be seen that all the features visible in the experimental spectra are perfectly reproduced in the theoretical calculations, and a very good agreement has been obtained with Rsq =1.2 and 1.3 for the raw and deconvolved spectra, respectively. This analysis demonstrates that the peak at 16130 eV and the additional small features that are evident in the experimental spectrum of solid [Sr(H2 O)8 ](OH)2 are due to single and multiple scattering contributions associated with the water molecules and hydroxide ions belonging to the higher distance coordination shells. On the other hand when only the first coordination shell is included in the calculations, the theoretical spectrum closely resembles that of Sr2+ in aqueous solution. Moreover, the excellent agreement between the theoretical and experimental spectra suggests that the XANES spectroscopy can be very efficient to provide accurate structural information on coordination properties and this approach can be profitably used to investigate the Sr2+ hydration structure. Finally, by deconvolving the Sr K-edge raw spectra it is possible to extract additional structural features thus increasing the sensitivity of the XANES technique to the local symmetry around the absorbing atom and to the higher distance coordination shells.

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Sr-O

g(r)

10

Dang Åqvist CarPar

5

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2

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6

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B 5

Sr-H 4

g(r)

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Dang Åqvist CarPar

3 2 1 0

2

4

6

r (Å) Figure 4: Sr-O (A) and Sr-H (B) radial distribution functions for Sr2+ in aqueous solution obtained from classical MD simulations using Dang (blue line) or Åqvist (red line) potentials, and calculated from the Car-Parrinello (CarPar) MD simulation (green line). is not much influenced by the water model used in the simulations. 3 The Sr-O and Sr-H g(r)’s are shown in Figure 4 for the three simulations. They all reveal well defined first and second coordination shells and the use of different theoretical approaches strongly affects the first-shell positions. In order to provide a quantitative determination of the Sr2+ hydration sphere, the Sr-O g(r) first shell peaks have been modelled with gamma-like distribution curves with mean distance R, coordination number N, standard deviation σ , and asymmetry index β (see Ref. 50 for details). The full list of structural parameters obtained for the three simulations is reported in Table 2. As far as the classical MD simulations are concerned, the Sr-O first shell distances are 2.60 and 2.68 Å for the Åqvist and Dang potentials, respectively, and they are both within the range distance of previous determinations (2.56-2.69 Å).

Sr2+ Aqueous Solution MD Radial Distribution Functions The structural properties of the Sr2+ ion in aqueous solution have been investigated using both ab initio and classical MD simulations. In the latter case two simulations have been carried out using two different sets of Lennard-Jones parameters for the Sr2+ ion, the former developed by Åqvist 26 and the latter by Dang. 14 Conversely, only the SPC/E water model has been used in the calculations as in a previous investigation it has been shown that the hydration structure of the Sr2+ ion


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Table 2: Sr-O coordination number N, mean distance R1 , Debye-Waller factor σ 2 and asymmetry parameter β obtained from the Åqvist, Dang and Car-Parrinello (CarPar) MD simulations for the Sr2+ first hydration shell. R2 is the position of the maxima of the second hydration shell. N R1 (Å) σ 2 (Å2 ) Åqvist 8.0 2.60 0.010 Dang 8.2 2.68 0.010 CarPar 7.5 2.72 0.017

β R2 (Å) 0.63 4.78 0.67 4.86 0.75 4.92

Both simulations provide a coordination number close to the expected 8-fold coordination, even if the Sr-O g(r) obtained by the Dang potential is slightly longer and more crowded as compared to the Åqvist one. Moreover, the high values of the β parameters indicate the existence of a quite asymmetric first hydration shell and this result is in accordance with previous QM/MM and EXAFS findings. 15,20 In particular, the first shell asymmetry is due to the simultaneous presence of hydration complexes with different symmetries and varying bond distances. For the Sr-O g(r)’s the maxima of the second shell are located at 4.78 and 4.86 Å for the Åqvist and Dang potentials, respectively. The former value is in perfect agreement with the results obtained from a large angle Xray scattering (LAXS) investigation where the SrO second shell was found to be very diffuse with a maximum at 4.78 Å. 11 The Sr-O distance and coordination number obtained form the ab initio simulation are 2.72 Å and 7.5, respectuvely. As evident also from Figure 4 the CarPar Sr-O g(r) is shifted towards longer distances as compared with the classical simulations, and the Sr-O first peak distance is outside the values previously reported in the literature. Three DFT-based simulations have been previously published, 7,21,22 providing Sr-O distances of 2.60, 2.60 and 2.65 Å and coordination numbers of 7.6, 6.7, and 8.0. The most recent one was carried out by including a DFT-D2 type dispersion correction, 7 at variance with the previous two simulations where no corrections were used for dispersion interactions. 21,22

Figure 5: Comparison of the theoretical XANES spectrum of Sr2+ in aqueous solution obtained from the MD average including only the first hydration shell (red dotted line) and several spectra associated with individual MD configurations (black lines) for the Åqvist (panel A) and Dang (panel B) potential and for the Car-Parrinello simulation (panel C). XANES Data Analysis Several cluster models have been used in the past to describe the coordination of Sr2+ in water and among them 8-fold coordination seems to be the most suited to interpret the experimental data. The same conclusion can be drawn from the comparison of the XANES spectra of Sr2+ in aqueous so-


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lution and solid [Sr(H2 O)8 ](OH)2 reported in Figure 2. Overall, the two spectra show a similar pattern and this can be explained by the fact that XANES is inherently a short-range order technique that is dominated by first-shell contributions that are similar in the two systems. This finding is in perfect agreement with the EXAFS results obtained by Moreau et al. 15 showing that the Sr2+ local environment is similar in water and in the solid octahydrated hydroxide. From the EXAFS analysis they found that the Debye Waller factor of the aqua ion in solution is larger than in solid [Sr(H2 O)8 ](OH)2 indicating the existence of a disordered first shell. The temperature factor coefficients of the first and second hydration shell of the hydrated strontium ion are unusually large indicating a significant disorder for both hydration shells, especially the second one. This result is confirmed by the present MD calculations as previously discussed. The disordered nature of the aqueous solution has to be considered in the analysis of the XANES data that cannot be correctly carried out using a static cluster model as it is usually done to interpret the EXAFS spectra. For this reason we performed a quantitative analysis of the XANES spectra starting from the microscopic description derived from the MD simulations. Comparison between the XANES spectra of solid [Sr(H2 O)8 ](OH)2 and Sr2+ in water suggests a substantial insensitivity of the latter toward the second coordination sphere as no high frequency structural features arising from higher distance shells are visible in the spectrum. Therefore, we decided to focus our attention on the first hydration shell, and three theoretical XANES spectra have been calculated starting from the classical MD trajectories using the Dang or Åqvist potentials, and from the Car-Parrinello simulation. Panels A, B and C of Figure 5 show the averaged theoretical spectra obtained from 500 snapshots (not including intrinsic and extrinsic inelastic process) associated with the first hydration shell of the Sr2+ ion, together with several individual instantaneous structures, for the classical and QM simulations. In all cases, the XANES spectra calculated from each MD snapshot present noticeable differences in all the energy range, showing the sensitivity of XANES to geometrical changes of the first hydra-

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tion shell, and the importance of making a proper sampling of the configurational space. A similar behaviour was previously found for other metal ions in water and organic solvents. 51–54 Moreover, the three averaged spectra present a different main oscillation frequency due to the different Sr-O first shell distances. To shed light on which of the three simulations provides the best structural model we compared the averaged theoretical spectra with the experimental data. In particular, both the raw and deconvolved spectra have been compared with the calculated signals, and inelastic processes and experimental resolution have been accounted for by convoluting the theoretical averaged spectra with broadening Lorentzian and Gaussian functions, respectively. In panels A, B and C of Figure 6, the raw experimental XANES spectrum of the Sr2+ ion in water is compared with the averaged theoretical spectra including the first shell cluster as derived from the classical and QM simulations. In all cases Γc was set to 3.25 eV and the best-fit value of Γexp was 1.5 eV. The agreement between the experimental and theoretical curves is very good in the case of the Åqvist potential (Rsq =1.1) while it is quite poor for the Dang potential and for the QM simulation (Rsq =2.6 and 4.2, respectively). In the latter cases a clear mismatch of the main frequency can be observed and this is due to the long values of the average Sr-O first shell distance as compared to the experimental results. This is confirmed by the analysis of the deconvolved data reported in panels D, E and F of Figure 6, where the agreement between the theoretical and deconvolved curves is very good for the Åqvist model (Rsq =1.3) while a clear disagreement can be observed for the Dang and QM simulations (Rsq =3.2 and 6.8, respectively). In all cases the best-fit value of Γexp was 3.0 eV while the Γc was equal zero. Taken together these findings indicate that the Åqvist potential is better suited to describe the Sr2+ -water interactions and thus the structural results obtained from the Åqvist simulation are more reliable. Moreover, the good agreement between the experimental spectrum and the theoretical curve including the first shell cluster only shows that the second hydration shell provides a negligible contribution to the XANES spectrum at variance with solid [Sr(H2 O)8 ](OH)2 . This finding corroborates the idea that the second coordination


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Figure 6: Comparison between the raw Sr K-edge XANES spectrum (blue dotted line) of Sr2+ in water and the best-fit theoretical spectra (red solid line) calculated from the classical MD simulations carried out with the Dang (A) or Åqvist potential (B), and from the Car-Parrinello MD simulation (C). Comparison between the deconvolved Sr K-edge XANES spectrum (blue dotted line) of Sr2+ in water and the best-fit theoretical spectra (red solid line) calculated from the classical MD simulations carried out with the Dang (A) or Åqvist potential (B), and from the Car-Parrinello MD simulation (C). sphere around the Sr2+ ion in aqueous solution is very diffuse, as previously shown from LAXS experimental data. 11 Our findings show that the Car-Parrinello simulation provides a structural organization of the Sr2+ local environment that is not able to reproduce the XANES experimental data. As previously mentioned, three DFT-based MD simulations have been reported in the literature, 7,21,22 and quite different structural results have been obtained. In particular, in the present QM simulation we tried to improve the theoretical scheme by using state-of-the-art DCACP pseudopotentials for water but even if the number of water molecules coordinating the Sr2+ ion is quite correct, the first shell distance is too long. On the other hand, the

Sr2+ hydration sphere obtained from the QM/MM simulation by Hofer et al. 20 is too crowded and too long (Sr-O distance and coordination number are 2.69 Å and 9, respectively) as compared to all the previous QM simulations. Note that the comparison with experimental data is the only reliable way to prove the validity of a MD simulation, regardless the level of theory used, and it may happen that a classical MD calculation provides a better structural description of ion hydration than QM approaches. This result is not surprising as in previous combined DFT-based MD and EXAFS studies of Co2+ and I− ions in aqueous solution, the classical MD simulations were in better agreement with the experimental data as compared to the QM ones. 55,56 These shortcomings of DFT-


11


based MD are due to the fact that even if quantum effects are included in the description of the system, many approximations are used and the outcome of the simulations is very dependent on the choice of the functional, pseudopotential and basis set. Moreover, a major advantage of classical over DFT-based MD is that in the former case it is possible to extend the simulation time to the ns time scale, thus allowing one to obtain a proper sampling of the structural and dynamic properties of the investigated systems. On the other hand, if one is interested in determining specific properties related to the electronic wave function, the use of ab initio MD simulations is mandatory. 57 A last remark we would like to make concerns the effect of multielectron excitations on the analysis of the XANES data. Double electron excitations have been found to increase the error in the determination of the structural parameters from the EXAFS data analysis thus hampering a reproducible extraction of the fitting parameters. 12 This is one of the main reasons of the scattered results obtained from the EXAFS analysis of Sr2+ aqueous solutions. Conversely, multielectron excitations do not affect the XANES region at the Sr K-edge and this allows a more reliable extraction of the structural parameters from the experimental data.

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Sr2+ First Shell Structure and Dynamics

Figure 8: O-Sr-O (ψ) angular distribution (a.d.f.) calculated from the Åqvist MD simulation.

Once the reliability of the Åqvist potential has been assessed we carried out additional analyses on the Åqvist MD simulation in order to provide a more complete description of the structural and dynamical properties of the Sr2+ hydration complexes. As previously mentioned both the comparison with the solid reference compound and the results of the MD simulations indicate the existence of an 8-fold hydration complex for the Sr2+ ion. A deeper insight can be gained by defining an instantaneous coordination number N, as the number of oxygen atoms at a distance shorter than the Sr-O g(r) first minimum, and analyzing its variation along the simulation. The coordination number distribution is reported in Figure 7. Eightfold coordination dominates and it occurs with 91 % probability. Configuration with coordination num-

bers of 9 and 7 are also present, and their probability is 8 and 1 %, respectively. These findings indicate the existence of a quite stable structure and the very low percentage of the 7-fold coordination points toward an associative pathway for the first shell ligand exchange reaction. These results are quite different from those obtained from a recent QM/MM simulation where a 9-fold complex was obtained for the Sr2+ ion, 20 while they are is in perfect agreement with the most reliable EXAFS and LAXS results. 11,15 Additional insights into the geometry of the first hydration shell cluster can be gained looking at the geometrical arrangement of the water molecules around the Sr2+ ion obtained from the angular distribution functions (a.d.f.). Figure 8 displays the


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distribution of the O-Sr-O ψ angle within the first hydration shell. The a.d.f. shows two peaks at ψ=72◦ and 142◦ . The two peaks are quite broad thus indicating the existence of a high degree of internal motions of the first shell water molecules. Moreover, these ψ values are compatible both with a bicapped trigonal prism (BTP) and a square antiprism (SAP) geometry, and hence it can be concluded that the hydration structure of the Sr2+ ion can be better described using a dynamical picture in which the 8-fold first coordination shell transits between a SAP and BPT geometry. The flexible and unstructured nature of the Sr2+ first hydration shell is reflected on its dynamical behavior. Several water exchange events have been observed between the first and the second hydration shell, and the rate of the water exchange processes has been calculated using the Impey method. A t* value of 0.5 ps has been employed as it corresponds to the average lifetime of a waterwater hydrogen bond. The calculated mean residence time is 227 ps and this value is quite longer than the one obtained by Hofer et al. 20 from a QM/MM simulation, even if it is in the same order of magnitude.

The presence of strong thermal and structural disorder explains the lack of high-frequency structures in the XANES spectrum of the aqueous solution at variance with solid [Sr(H2 O)8 ](OH)2 where structural features associated with higher distance shells are clearly detectable in the XANES data. The flexible nature of the Sr2+ hydration complex can explain the capability of this element to substitute Ca2+ during bone formation. The hydration structure of Ca2+ has been studied by EXAFS, XRD and MD investigations and all these experimental techniques displayed a wide distribution of the Ca-O first shell distances, thus causing a high asymmetry in the Ca2+ first hydration shell. 58,59 The flexible nature of the Ca2+ hydration sphere makes this ion suitable for the control of conformational changes occurring in metallo proteins during their biochemical activity. Therefore, this is a mandatory prerequisite for any cation that can substitute Ca2+ in biological media. Mercury and cadmium, that are two of the most toxic elements, have the ability to replace biological metals such as zinc and calcium in enzymes, proteins and nucleic acids. Also in this case the ability of these two cations to mimic ions adopting different coordination geometries in biological media has been explained by the flexible nature of their hydration complexes. 52,60–64 The results of the present investigation suggest that this may be a general characteristic of toxic metals. In conclusion, the results presented here demonstrate the potential of XANES in providing a quantitative determination of the coordination structure of alkaline cations in solution, and this technique can be used to eliminate some ambiguities present in the literature.

Discussion and Conclusions XANES spectroscopy has been used, for the first time, to unveil the structural properties of Sr2+ in aqueous solution. By applying a deconvolution procedure to the raw absorption data it was possible to increase the sensitivity of XANES thus allowing a conclusive determination of the structural parameters of the Sr2+ ion in water. By using MD simulations and solid [Sr(H2 O)8 ](OH)2 as model compound it was possible to prove that the Sr2+ ion in water forms a quite flexible 8-fold hydration complex with an average Sr-O distance of 2.60 Å, in agreement with previous EXAFS determinations. 11,15 The combined XANES-MD analysis shows that the Sr2+ first hydration sphere has to be described as an ensemble of structures fluctuating between SAP and BPT geometries. This leads to a considerable asymmetry of the first shell. Both the first and second hydration shells are quite disordered and the ligand exchange rate between the two shells occurs in the picosecond time scale.

Acknowledgement This work was supported by the University of Rome “La Sapienza” (Progetto ateneo 2015, n.C26H159F5B).

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XANES Reveals the Flexible Nature of Hydrated Strontium in Aqueous

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