Investigation of Astatine(III) Hydrolyzed Species: Experiments and

Article pubs.acs.org/JPCA

Investigation of Astatine(III) Hydrolyzed Species: Experiments and Relativistic Calculations Julie Champion,† Andréa Sabatié-Gogova,†,‡ Fadel Bassal,‡ Tahra Ayed,‡ Cyrille Alliot,§ Nicolas Galland,*,‡ and Gilles Montavon*,† †

SUBATECH, UMR CNRS 6457, IN2P3/Ecole des Mines de Nantes/LUNAM Université, 4 rue A. Kastler, 44307 Nantes Cedex, France ‡ CEISAM, UMR CNRS 6230, Université de Nantes, 2 rue de la Houssinière, 44322 Nantes Cedex 3, France § GIP ARRONAX, 1 rue Aronnax, 44817 Saint Herblain, France, and INSERM U892, IRTUN, 8 quai Moncousu, BP 70721 Saint Herblain, France ABSTRACT: This work aims to resolve some controversies about astatine(III) hydroxide species present in oxidant aqueous solution. AtO+ is the dominant species existing under oxidizing and acidic pH conditions. This is consistent with highperformance ion-exchange chromatography data showing the existence of one species holding one positive charge. A change in speciation occurs as the pH changes from 1 to 4, while remaining under oxidizing conditions. Dynamic experiments with ion-exchange resins evidence the existence of a neutral species witnessed by its elution in the void volume. Batch-experiments using a competition method show the exchange of one proton indicating the formation of the AtO(OH) species. The hydrolysis thermodynamic constant, extrapolated to zero ionic strength, was determined to be 10−1.9. This value is supported by two-component relativistic quantum calculations and therefore allows disclosing unambiguously the structure of the formed species.

1. INTRODUCTION Astatine (At) is a rare radioelement belonging to the halogen group. One of its isotopes, astatine-211 (211At) offers many potential advantages for targeted α-therapy.1,2 A carrier molecule should transport 211At to the cancer cells where αparticles emitted by the radionuclide would destroy the target. However, binding astatine to cancer selective carrier molecules remains a difficult task. On one hand, it is a rare element since it has only short half-life radioactive isotopes. Astatine-211 is produced in a cyclotron via the nuclear reaction 209Bi(α,2n)211At.3 On the other hand, it is an invisible element. The amount of 211At produced allows solely working at ultratrace concentrations (typically 10−11 to 10−15 M), and no spectroscopic tool can be used to evaluate astatine chemistry at the molecular level. These two major points limit the investigations of its chemistry and, consequently, the development of efficient labeling protocols for nuclear medicine. Similar to iodide labeling for disease-targeting carrier molecules, conventional labeling focuses on the formation of astatine− carbon bonds via a substitution reaction involving the halogen character of At. While some cases provide adequate in vivo stability to move into clinical studies, additional studies still need to be conducted to improve labeling approaches, particularly for systemic administration.4,5 In addition to the expected At− species and in the complement of experimental data published in the 1980s, we recently uncovered the existence of two stable metallic forms of At under acid and oxidizing conditions, i.e., At+ and AtO+.6,7 The use of these © 2013 American Chemical Society

metallic species for the binding of astatine to carrier molecules may be an efficient alternative.5 Several papers have shown the formation of complexes between AtO+ and simple organic and inorganic ligands.8,9 Some structural parameters were recently determined by (quasi) relativistic quantum calculations for the complexes AtOX and AtOX2−, with X = Cl, SCN, and Br.10 It has been shown by electromigration in noncomplexing medium (H/ NaClO4) that AtO+ reacts with water above pH 1.8,11−13 The mobility of the species decreases when the pH increases until it equals 0 above pH 6. Milanov and co-workers proposed the formation of a neutral hydrolyzed species AtO(OH) with an apparent hydrolysis constant of 10−1.5 M−1 (at ionic strength μ = 0.4 M) and 10−4.1 M−1 (at μ = 0.25 M).14,15 A constant of 10−5.23 M−1 (μ = 0.1 M) was also proposed by Schumann et al. for the pH range of 1−10 using migration data in the presence of nitrilotriacetic acid and nitroacetate.16 In conclusion, though authors agree with the formation of a hydrolysis species, significant discrepancies exist between the different constants obtained. This article aims at completing published data to provide indisputable evidence of AtO+ reactivity with water using a multidisciplinary chemical approach. The hydrolysis of AtO+ is described by the following equilibrium: Received: October 8, 2012 Revised: February 1, 2013 Published: February 2, 2013 1983

dx.doi.org/10.1021/jp3099413 | J. Phys. Chem. A 2013, 117, 1983−1990

The Journal of Physical Chemistry A

Article

Khyd, m

AtO+ + mH 2O HoooooI AtO(OH)1m− m + mH+

with Khyd,m the hydrolysis constant. High-performance ionexchange chromatography (HPIEC) coupled to a gamma detector was first used to assess the charge of the species using the approaches followed by Khalkin et al. and some of us.14,16,17 Second, the competition method proposed by Champion et al.18 was used to define the nature of the species formed and to quantify its formation as well. Finally, the theoretical approach developed by some of us10 was used to evaluate the reliability of the experimental data.

2. EXPERIMENTAL METHODOLOGIES 211 At was produced via nuclear reaction of bismuth with αparticle accelerated to 28 MeV at the CEMTHI cyclotron (Orléans, France). Astatine was recovered from the targets by dry distillation and subsequent capture into methanol or by wet extraction into 1 M NaOH.18−20 Stock solutions of astatine-211 with a specific activity close to 100 MBq·mL−1 were used. The radionucleidic purity of 211At was monitored by γ-ray spectrometry with a high purity germanium (HPGe) detector. The activity of the stock astatine solution was measured on γrays at 687 keV from 211At, using a suitable geometry previously calibrated with standard gamma sources. Astatine solutions were then prepared by dilutions in the appropriate medium. At least two series of experiments with two different batches of astatine (i.e., from two distinct irradiations) were systematically done. Sodium-22 was provided by DAMRI (with a specific activity of 5.4 kBq·g−1 and a concentration of 10 μg·g−1 NaCl in 0.1 M HCl). For batch and dynamic experiments, 211At and 22 Na analysis were performed by liquid scintillation counting using a Packard 3170 TR/SL liquid scintillation analyzer using Ultima Gold LLT(Packard) scintillation mixture. All experiments used water produced by a Millipore system. All substrates were purchased from Sigma-Aldrich. Acids and organic solvents were of “pro analysis” quality and were used without further purification. All experiments were conducted in air-conditioned laboratories (25 ± 3 °C). Experiments realized above pH = 3 were done under N2 atmosphere for avoiding the presence of CO2 in the solution. Experimental conditions are schematically represented in Figure 1. This latter will be used throughout the article to help the reader to follow the experimental approach. Despite the method used, the pH and the potential (E) of the solutions were systematically measured at equilibrium. A Fisherbrand type electrode freshly calibrated against dilute standard pH buffers (pH 1−10, Merck) was used to determine the pH. The potential of aqueous solutions was measured using a Pt combined redox electrode (Metrohm type) calibrated against the redox buffer (Fe(SCN)63−/ Fe(SCN)64−, 215 mV/Pt/SCE Radiometer Analytical. 2.1. HPIEC Experiments. The high-pressure liquid chromatography (HPLC) device is a Dionex UltiMate3000 system consisting of a DGP-3600 MB pump, a TCC-3200B column oven, and a diode array DAD-3000 detector. The online γ-ray detector is a Raytest GabiStar, piloted by Gina Software. Count rate is 0−500 000 c/s. The detection energy window was set between 50 and 1630 keV. Experimental data were acquired and processed by Chromeleon 6.80 Chromatograph Software. The stationary phase used for anion exchange experiments was a Dionex AS20 anionic exchange column (0.2 cm diameter × 25 cm length), with an AG20 guard column being packed with a resin of proportionally lower capacity (0.2

Figure 1. Pourbaix diagram of astatine in noncomplexing medium in the pH range 1−7 based on previous studies by Champion et al.6 The experimental conditions explored in the present study are figured for HPIEC (gray arrow) and competition experiments (black arrow).

cm diameter × 5 cm length). The AS20 consisted of a hydrophilic polymer of divinylbenzene resin grafted with quaternary alkanol ammonium ions. The total capacity represented by both columns is 79 microequivalents. The cation exchange experiments were done using a homemade column (0.2 cm diameter × 15 cm length) with Dowex 50 × 8 sulfonated divinylbenzene resin (200−400 mesh) previously treated according to the protocol given by Tyung et al.21 Characteristics of the resin can be found elsewhere.22 The solutions and eluents were freshly prepared under argon atmosphere. Unless otherwise indicated, SO32−/S2O32− (10−4/ 10−3 M) and Cr2O42− (5.10−3 M) were used to maintain astatine at the oxidation states −I and +III, respectively, in the eluents throughout the experiments. The system pre-equilibration at the column’s outlet was controlled in terms of pH and E. The eluents were kept under argon flow during the proceedings. The solutions were injected into the column through a 50 μL sample loop injector. To follow the resins stability over time, I− and Tl+ (10−5 M) were used as internal standards. A characteristic retention at 11.2 ± 0.6 min (eluent, 0.1 M NaCl at 350 μL/min) using anionic exchange resin and 6.7 ± 0.7 min (eluent, 1 M HClO4 at 250 μL/min) using cation exchange resin were identified for I− and Tl+, respectively. Iodide and thallium cation were detected spectrophotometrically at 230 and 214 nm, respectively. Their concentrations, before injection and collected fractions from each run, were evaluated by using ICPMS and confirm a recovery yield in the range of 85−100%. The mean retention values are presented with errors corresponding to 2σ. Data are given as retention factors and given with respect to the UV detector position peak.17 For clarity, the results are quantified as retention factors k: t − tD k= R tD (1) with t R and t D being the retention and dead time (corresponding to the method of detection used), respectively. 2.2. Batch Experiments. The solid/liquid and liquid/liquid methods were used with Dowex 50 × 8 resin and toluene, respectively. A detailed description of the methodology can be 1984



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was first introduced in PHREEQC, and the associated parameters were adjusted to get the best visual agreement between the experiment and the modeling. The main equilibriums occurring in the experimental conditions were then considered to derive an analytical expression, which was then used to fit the data with Sigma Plot software using the Marquardt−Levenberg algorithm (version 2.0, Jandel Co.).24 Uncertainties associated with the fitting parameters were determined by the software. All the equilibrium constants in the database were extrapolated at zero ionic strength using the Truncated Davies theory.25

found elsewhere.18 A pretreatment and pre-equilibration of the system was systematically done before the addition of astatine. Kinetic measurements showed that the time required to reach equilibrium was less than 2 h. The distribution coefficient Kd for the solid/liquid experiments is defined as Kd =

A tot − A sol L × A sol S

(2)

where Atot, Asol, L, and S are the total activity in the suspension, the activity in solution, the volume of the liquid phase, and the dried mass of resin, respectively. The separation between solid and liquid phases was achieved by centrifugation (500g). Regarding the liquid/liquid extraction, the distribution coefficient D is calculated according to following relationship: D=

3. COMPUTATIONAL METHODOLOGY Relativistic effects on the structure of molecules that contain heavy-elements, such as astatine, become as important as electron correlation effects. It is widely known that the inclusion of spin−orbit (SO) interactions as well as scalar relativistic effects are necessary for calculations on heavy pelements. The most accurate approach to incorporate relativity would be to perform four-component (4c) calculations based on the exact relativistic Hamiltonian, but this approach is computationally very demanding and several alternative twocomponent (2c) approximations have been proposed.26,27 The spin−orbit DFT (SODFT) method implemented in the NWChem programs package28 appears particularly attractive due to the computational expediency and the implicit inclusion of electron correlation effects. Using two-component relativistic effective core potentials (RECPs) and pseudopotentials (PPs), which contain scalar and spin-dependent potentials, significantly reduces the number of basis functions and simplifies the form of the Hamiltonian. The SODFT method has been successfully used to investigate relativistic effects on molecules containing halogen elements and notably astatine.6,10,29,30 Gas-phase properties (energy, geometry, and vibrational frequencies) of closed-shell AtOX species (X = OH, Cl, Br, and SCN) have been determined by B3LYP density functional31 calculations following the SODFT framework, while DFT calculations have been performed on X− species. We used the small-core ECPnMDF (n = 10 for Br and 60 for At) PPs generated by the Stuttgart/Cologne group.32 A modified augcc-pVDZ-PP (mAVDZ) basis set10,32 was used for At atom in conjunction with the aug-cc-pVDZ-PP basis set32 for Br atom and the aug-cc-pVDZ basis sets33−35 for O, H, Cl, C, N, and S atoms. Despite the fact that relatively small basis sets were selected, our computational methodology makes use of error cancellation approaches, and high-quality results are obtained.10 Complementary single-point ab initio energy calculations have been carried out. MP2 and two-component MP2 methods, using the resolution of the identity technique as implemented in the TURBOMOLE program package,36 were retained respectively for X− and AtOX species. The aug-cc-pVTZ-PP2c basis set37 was used for At atom in conjunction with the augcc-pVTZ-PP basis set32 for Br atom and the aug-cc-pVTZ basis sets33−35 for O, H, Cl, C, N, and S atoms. Note that the core electrons were frozen for all MP2 calculations (notably the 5s, 5p, and 5d inner cores of At and the 3s, 3p, and 3d inner cores of Br). For the sake of simplicity, Gibbs free energies calculated using (i) MP2 energies and (ii) B3LYP structural and vibrational properties will be referred to MP2//B3LYP throughout the text. In the case of species that exhibit several isomers, their Gibbs free energies have been evaluated using a Boltzmann distribution according to the relationship

Vaq × Aorg Vorg × A aq

(3)

where Vorg, Vaq, and Aorg and Aaq represent the volume of the organic phase, the volume of the aqueous phase, and the activities measured in the organic and aqueous phases, respectively. 2.3. Quantitative Analysis of Experimental Data. HPIEC and batch experiments were analyzed using the PHREEQC program.23 The thermodynamic database from the Lawrence Livermore National Laboratory supplemented with the redox reactions given by Champion et al.6 was used. In the case of the HPCEC experiments, the description of the model parametrization can be found elsewhere.17 Briefly, the affinity of a cation M+ (M+ = Na+, Tl+, AtO+) for the surface site S−X is described by: KX/M

S−X + M+ HooooI S−M + X +

(4)

where S is the exchange site. The selectivity coefficient KX/M is given by: KX/M =

{S−M} ·{X +} {S−X} ·{M+}

(5)

where square brackets indicate activities. The simplest model is used; i.e., the activity coefficients for the surface species are fixed to one or equal for all surface species, and the activity coefficients are equal for monocharged cations. The selectivity coefficients given in the article are relative to H+, i.e., KH/H = 1. The physical transport is considered advective and the system description necessary for the modeling (tube volume, pore water volume in the column, and number of sites) can be found in Figure 2.17 In the case of batch experiments, extraction/sorption processes were considered as a distribution. The equilibrium constants associated with the reactions were determined following a three-step procedure. The considered equilibrium

Figure 2. Parameters used for the modeling (1D). 1985



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Figure 3. Retention factor, k, on cationic exchange column as a function of the concentration of H+ and in different media. (A) Perchloric medium (0.5−2 M); AtO+, gray circle with presence of 5 × 10−3 M K2Cr2O7; Na+, black triangle with presence of 5 × 10−3 M K2Cr2O7 and black circle without; Tl+, white circle. (B) Na(H)ClO4 1 M and K2Cr2O7 5 × 10−3 M medium; same legends for AtO+, Na+, and Tl+. The modelings are represented with relative exchange selectivity coefficients of 100.16, 101.10, and 101.50 for AtO+, Na+, and Tl+, respectively. ° G{A} = −RT ln

∑ i ∈ {A}

°

monocharged cation used in the literature as a model ion for AtO+.21 The determination of selectivity coefficients requires modeling the equilibrium at all stages of the column. In our dynamic system, the principle of local equilibrium was assumed, i.e., the rate of reactions was more rapid than the rate of solute transport. If this principle is generally valid, it must be checked for astatine considering the low amount of solute injected (about 3.8 × 108 atoms corresponding to a concentration at the outlet of the column of 10−13 M). Experiments were first realized on cationic column as a function of H+ concentration in HClO4 media to identify AtO+ and quantify the exchange process; in the range of H + concentration chosen (0.5−2 M), AtO+ species is supposed to not react with water.6 Experimental data are presented in Figure 3A. As expected by the ion-exchange principle, the lower the concentration of H+, the greater the retention. Data could be described considering an exchange of one proton in agreement with the existence of monocharged cations. The selectivity coefficients obtained were 100.13, 100.76, and 100.96 for Na+, Tl+, and AtO+, respectively. The coefficient for Na+ is in good agreement with the one tabulated in the literature for the studied resin; this indicates a good parametrization of the system.44 AtO+ retention is higher than Tl+, in agreement with the work of Tyung et al.18 It is worth noting that Rössler et al. showed a lower retention for astatine species than thallium species in similar conditions (0.1 M HNO3, 5 × 10−3 M K2Cr2O7, strong cation exchanger Aminex A7).45 On the basis of size aspects, they concluded that the species was At+ rather than AtO+. In a second series of experiment, the ionic strength was fixed (μ = 1 M) while the concentration of H+ was varied between 1 and 10−4 M to assess the change of speciation previously observed by electromoblity (Figure 3B). For the nonreactive species Na+ and Tl+ (i.e., no reaction with H2O is expected), the quantitative analysis of the experimental data against the previously determined selectivity coefficients appears relatively good. The underestimation yielded by the modeling at pH = 4 for Tl+ is certainly explained by a change in the selectivity

e−Gi / RT (6)

where {A} emphasizes calculation over the population of all isomers of A. Gibbs free energies of aqueous solvation were computed for the closed-shell ground state of the species using the polarizable continuum model (PCM) implemented in the Gaussian03 program package.38 We selected the conductor-like formulation, CPCM,39,40 since this model used in conjunction with the UAHF cavity model yields accurate solvation free energies at a very low computational cost.41 The UAHF cavities were built up using the united atom topological model applied on atomic spheres optimized for the HF/6-31G(d) level of theory.42 The spheres’ radii depend on the nature of the element and its molecular environment (basically hybridization, formal charge, and first neighbor inductive effect). However, at present no parameters for astatine are included in these cavity models. Recently, we proposed to use for At a basic radius (R°) of 2.41 Å, consistent with the rest of the radii included in the UAHF model, and a charge factor (γq) of −0.87 Å for an astatine atom bearing a positive charge.6,10 Note that, in the CPCM model, the solvation free energy is partitioned in different terms. The most important one is the electrostatic term. Some other terms are usually negligible,41 while the dispersion and repulsion terms are unavailable for astatine. Furthermore, the sum of nonelectrostatic terms is generally weak with respect to the electrostatic term, especially for charged species, due to the cancellation of different contributions.43 Hence, for all studied species, we only retained the electrostatic term in CPCM computations. The solvation free energies were determined at HF level of theory using the above-mentioned double-ζ basis sets and PPs. Geometries of the species were optimized both in the gas-phase and in the presence of solvent.

4. RESULTS AND DISCUSSION 4.1. HPIEC Experiments. Experiments by HPIEC were done for AtO+, Na+ (present in the medium), and Tl+, a 1986



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retention factor of 9. Elution of samples without the redox buffer (E = 380 mV/SHE) from the eluent leads to the appearance of an additional peak characterized by a retention time of 5 min, indicating the formation of a new species eluted near void volume. This change in redox potential leads also to a drastic decrease of the recovery yield (from 100% to 40%). This latter species becomes predominant when the potential is imposed with the chromate ions, as it was the case for the cationic column experiments. In conclusion, the HPIEC results show the passage of a species holding one positive charge (i.e., AtO+) to a neutral species as the pH varies from 0.5 to 7.4. 4.2. Batch Experiments. This work was focused on determining the number of protons exchanged during the AtO+ hydrolysis reaction (hence the speciation of the formed species) and to measure the associated equilibrium constant accurately. The kinetic studies of AtO+’s distribution for the two biphasic systems and different pH (Figure 5A) show that the equilibrium is achieved after 40 min. In agreement with HPIEC data, the competition experiments realized in the liquid/liquid and liquid/solid systems demonstrate a clear change in speciation with pH increase, as evidenced by the change in D/Kd values (Figure 5A). At equilibrium, AtO+ and the hydrolyzed species are characterized by D/Kd values of 292/126 and 57/32.6, respectively (Table 1 and Figure 5B). It is worth noting that, while the species formed at pH higher than 4 are not sorbed on the column (HPIEC experiments), a slight but significant sorption is observed in liquid/solid batch experiments although a similar resin is used. This difference is explained by the resin treatment which was more complete for the column than for the batch experiments. Furthermore, we can observe a difference in D value of the biphasic system according to the method of astatine production/purification method; a higher extraction is observed when the wet method is used. As it was shown by Champion et al., small impurities may lead to not expected behavior; this is related to the use of ultratrace concentrations of astatine.18 However, these parasitic perturbations do not alter the quantitative treatment of the data as they have no influence on the inflection point and the slope

coefficient, which is known to be strongly dependent on the nature of the exchange (H+ vs Na+ cations). For AtO+, a good prediction is observed in the H+ range 0.5−1 M where no change of speciation is expected (Figure 3B). Below 0.5 M concentration, a drastic decrease of retention is observed, which ends close to 0 at pH = 4. This result evidences the reaction of AtO+ species with water to form a neutral or anionic species. To obtain further information about the charge of the species, complementary experiments were done at pH around 7.4 on the anionic exchanger Dionex AS20 (Figure 4). In this

Figure 4. γ-Chromatogram of astatine (0.1 M NaCl, 10−3 M of PBS) using anionic exchange resin with the presence (gray spectrum) or absence (black spectrum) of redox buffer (10−4/10−3 M SO32−/ S2O32−).

case, the nonretained species on the cation exchanger dominates astatine speciation. The sample was first eluted under reducing conditions (0.1 M NaCl, 10−3 M of PBS buffer, and 10−4/10−3 M SO32−/S2O32− redox buffer, E = 250 mV/ SHE) where At− exists. This latter species is characterized by a

Figure 5. (A) Kinetic studies at different pH of the distribution of AtO+ in a biphasic systems: aqueous/toluene system (white symbol) and aqueous/solid system (black symbol). (B) Distribution studies of AtO+ between biphasic systems: aqueous/toluene (white symbol) and aqueous/ solid (black symbol). D and Kd are plotted as a function of pH in the aqueous solution. The line corresponds to the modeling performed with PHREEQC. 1987



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Table 1. Experimental Values of Astatine Distribution and log Khyd,1 from Liquid/Liquid and Solid/Liquid Systems, and Weighted Average Value of log Khyd,1 AtO+ distribution

AtO(OH) distribution

Khyd,1 (10−2)

15.2 ± 2.7 292 ± 51 126 ± 18

2.96 ± 0.62 57 ± 32 32.6 ± 3.4

1.9 ± 1.3 1.6 ± 1.8 1.02 ± 0.64

liquid/liquid separation D; dry extraction liquid/liquid separation D; wet extraction solid/liquid Kd separation weighted average value47

log Khyd,1 −1.7 −1.8 −2.0 −1.9

± ± ± ±

0.4 0.5 0.3 0.2

Table 2. Computed Values of log Kexc and log KOH− at Different Levels of Theory

of the curve when passing from AtO+ to the hydrolyzed species. The three series of data can thus be explained considering one proton exchange in the reaction process (solid lines in the Figure 5B). In agreement with the assumptions made in the literature and taking into account the demonstrated neutral charge of the hydrolyzed species, this result indicates the formation of AtO(OH). The corresponding hydrolysis constants are close (Table 1). The weighted average value obtained in this work, 10−1.9 (μ=0 M), appears in fairly good agreement with the one determined by Milanov et al. (10−1.5 M−1, μ=0.4 M) but much higher than those proposed by Schumann et al. (10−5.23 M−1, μ=0.1 M) and Hung et al. (10−4.1 M−1, μ=0.25 M).14−16 4.3. Quantum Calculations. The hypothesis that an AtO(OH) species is formed through the hydrolysis of AtO+ was theoretically investigated using quantum chemistry calculations. In the experimental conditions, the relevant reaction is

experimenta

B3LYP + CPCMUAHFb

MP2//B3LYP + CPCM-UAHFc

X− species

log KX−

log Kexc

log KOH−

log Kexc

log KOH−

Cl− Br− SCN−

2.5 ± 0.2 2.7 ± 0.2 2.8 ± 0.2

9.7 9.0 8.9

12.2 ± 0.2 11.7 ± 0.2 11.7 ± 0.2

10.4 10.4 10.9

12.9 ± 0.2 13.1 ± 0.2 13.7 ± 0.2

a Ref 10. bThe free energies of the exchange reactions, ΔΔGs*, are calculated using ΔΔG°g values computed with B3LYP method and * , based on CPCM-UAHF calculations. solvation free energies, ΔGsol c The free energies of the exchange reactions, ΔΔG*s , are calculated using ΔΔGg° values computed at MP2//B3LYP level of theory and solvation free energies, ΔG*sol, based on CPCM-UAHF calculations.

Khyd,1

AtO+ (aq) + H 2O(1) HooooI AtO(OH)(aq) + H+(aq)

(7)

which can be recasted as follows: K OH−

AtO+ (aq) + OH−(aq) HooooI AtO(OH)(aq)

Figure 6. Computed structure of AtO(OH) using two-component B3LYP method (distances in angstroms, angles in degrees).

(8)

The equilibrium constant of reaction 7, Khyd,1, is related to the complexation constant of reaction 8, KOH−, between AtO+ and OH− via eq 9: log K OH− = log Khyd,1 − log K w

K exc

AtOX(aq) + OH−(aq) HoooI AtO(OH)(aq) + X−(aq) (10)

(9)

The associated constant, Kexc, is related to KOH and the complexation constant between AtO+ and X−, KX−: −

where Kw is the ionization constant of water (log Kw = −13.995 at 298 K).46 According to the value of log Khyd,1 determined from this experimental work, −1.9 ± 0.2, we obtain log KOH− = 12.1 ± 0.2. The reliability of this value was verified by theoretical calculations.

log K OH− = log Kexc − log K X−

(11)

Therefore, KOH− can be estimated via the computation of Kexc if the value of KX− is known (with accuracy). Experimental values of the complexation constants KCl−, KBr−, and KSCN− are indeed available (Table 2), which can valuably be used to estimate KOH−. Kexc is calculated from the computed standard free energy change of reaction 10 in solution, ΔΔGs*. As Scheme 1 shows, ΔΔGs* can be calculated from its components by introducing a thermodynamic cycle:

Scheme 1. Thermodynamic Cycle Used to Calculate the Free Energy of Reaction 10 from Its Components

* (AtO(OH)) + ΔGsol * (X−) ΔΔGs* = ΔΔGg° + ΔGsol * (AtOX) − ΔGsol * (OH−) − ΔGsol

(12)

where ΔΔGg° is the change of free energy in the gas-phase; ΔG*sol(AtO(OH)), ΔG*sol(AtOX), ΔG*sol(OH−), and ΔG*sol(Y−) are, respectively, the solvation free energies of AtO(OH), AtOX, OH−, and X− species in water. Therefore, the prediction of ΔΔGs* could benefit from (1) bond-by-bond errors in electron correlation/relativistic contributions, which partially cancel in the computed gas-phase free energy, ΔΔG°g , and (2) cancellation of systematic errors (including the neglect of nonelectrostatic and SO contributions) associated with the

Recently, some of us have proposed a computational methodology designed to study astatine chemistry in aqueous solution.10 While this methodology is not designed to perform direct computation of complexation constants, it allows reliable prediction of equilibrium constants corresponding to an exchange of ligands as in the reaction between OH− and X−: 1988



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Table 3. Values of log Khyd,1 for Various Monocharged Cations species

AtO+

log Khyd,1

−1.9

Tl+ −13.21

Li+ 48

−13.64

48

calculations of solvation free energies, ΔG*sol, for ionic species and for neutral species. Table 2 reports calculated values of log Kexc corresponding to an exchange between OH− and X− (X = Cl, Br, and SCN) and the resulting values of log KOH−. Let us consider first the results based on ΔΔGg° computed using B3LYP method and the modeling of solvent effects through CPCM-UAHF calculations. Note that this methodology was found previously to predict log Kexc values with a mean signed error of −0.4.10 The three predicted values of log KOH− are very close. The average value, 11.9 ± 0.2, is in fairly good agreement with the one obtained from the experiments, 12.1 ± 0.2. The results based on ΔΔG°g computed at MP2//B3LYP level of theory and the modeling of solvent effects through CPCM-UAHF calculations, are in lesser agreement. Nevertheless, compared to the value obtained from the liquid/liquid separation experiments (dry extraction), the predicted values of log KOH− corresponding to the exchange reactions with Cl− and Br− (12.9 ± 0.2 and 13.1 ± 0.2, respectively) deviate on average by only 1.0 kcal mol−1 on the free energy scale. Results obtained from the exchange reaction with SCN− are less reliable at MP2//B3LYP level of theory as the wave function of the AtO(SCN) species has a some multiconfigurational character. Therefore, the quantum calculations corroborate the measured values of the hydrolysis constant of AtO+ and in the same time allow unambiguously the identification of the formed species as AtO(OH) (Figure 6). On the basis of our experience of computations on astatine species and on the relative short distance between At and the O atom of the OH moiety, 2.176 Å, we predict a partly covalent bond between these two atoms. This may explain the large value measured for the AtO+ hydrolysis constant.

PuO2+

MeHg+

Et3Sn+

−9.10

−9.90

−4.65

−6.3448

48

48

■

ACKNOWLEDGMENTS

■

REFERENCES

48

We would like to thank the French National Research Agency (ANR 2010-BLAN-0807-01) and the “Region Pays de la Loire” (NUCSAN project) for financial support, and CEMTHI for the production of 211-At. We are also grateful to Dr. Florian A. Bischoff for the astatine basis sets needed for RI approximation and helpful discussions. This work was performed using HPC resources from GENCI-CINES/IDRIS (Grant 2011c2011085117) and CCIPL (Centre de Calcul Intensif des Pays de la Loire).

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5. CONCLUSIONS The presented experiments show that the AtO+ species reacts with water to form the AtO(OH) species with a hydrolysis constant of 10−1.9 (μ = 0 M). In oxidant aqueous solution, this hydrolyzed species appears to dominate astatine speciation above pH 2. This is rather surprising if we compare this result with published data for other monocharged cations (Table 3). For spherical cations such as Tl+ and Li+, the reported constants are very weak. This notably excludes the existence of At+ because we would expect a similar constant than the one published for Tl+. In agreement with this statement, higher Khyd are found with molecular ions, the highest constant being for MeHg+. However, the constants remain still lower than the one observed for AtO+. This high constant appears as a peculiarity of this cation and is supported by quasirelativistic quantum calculations.

■

NpO2+

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (N.G.); montavon@ subatech.in2p3.fr (G.M.). Notes

The authors declare no competing financial interest. 1989



Article

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