Coordination and Thermodynamics of Trivalent Curium with Malonate

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Coordination and Thermodynamics of Trivalent Curium with Malonate at Increased Temperatures: A Spectroscopic and Quantum Chemical Study Andrej Skerencak-Frech,*,†,‡ Michael Trumm,‡ Daniel R. Fröhlich,† and Petra J. Panak†,‡ †

Physikalisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 253, D-69120 Heidelberg, Germany KITCampus Nord, Institut für Nukleare Entsorgung, P.O. Box 3640, 76021 Karlsruhe, Germany

‡

S Supporting Information *

ABSTRACT: The complexation of Cm(III) with malonate is studied by time-resolved laser fluorescence spectroscopy (TRLFS) in the temperature range from 25 to 90 °C. Three complexes ([Cm(Mal)n]3−2n, n = 1, 2, 3) are identified and their molar fractions are determined as a function of the ligand concentration, the ionic strength, and the temperature. A general shift of the chemical equilibrium toward higher complexes with increasing temperature is observed, with the [CmMal3]3− complex forming only at T > 40 °C. The conditional stability constants (log K′n(T)) are calculated and extrapolated to Im = 0 with the specific ion interaction theory (SIT). The log Kn0(T) values increase by 0.25 to 0.5 logarithmic unit in the studied temperature range. The temperature dependency of the log K°n(T) is fitted by the integrated Van’t Hoff equation, yielding the thermodynamic functions ΔrH°m and ΔrS°m. The results show positive reaction enthalpies and entropies for each complexation step. While the ΔrH°n values are constant within their error range, the ΔrS°n values decrease successively with each ligand added. To explain this effect, quantum chemical calculations of binding energies and bond lengths of the different Cm(III) malonate species are performed. The results show that malonate is capable of stabilizing its end-on coordination mode to some extent by forming hydrogen bonds to first-shell water molecules. As a result, an equilibrium between side-on and end-on coordinated malonate ligands is present, with the latter becoming more pronounced for the higher complexes due to steric reasons.

1. INTRODUCTION In the context of the disposal of high-level nuclear waste, deep geological formations are considered worldwide as the best option for long-term storage. Actinide elements are present in nuclear waste due to neutron capture reactions in the reactor and will determined its radiotoxicity over long time scales. A detailed knowledge of the geochemical reactions of the actinides is crucial to assess their migration behavior in a potential host rock. One of the major accident scenarios is the intrusion of groundwater into the repository. In such a scenario a broad range of chemical processes will occur, ranging from reactions at the solid−liquid interface (e.g., sorption to the host rock) to a rich aquatic chemistry of the actinides (e.g., complexation reactions). Organic ligands are abundant in numerous natural systems, involving small carboxylic acids as well as large macromolecular matter.1−3 Furthermore, organic polymers (superplasticizer) are widely used as additives for commercial concrete, which is considered as backfill and sealing material for a nuclear waste repository. Most of these large organic compounds contain carboxylic groups, and their decomposition will lead to the formation of a variety of small carboxylic ligands.4−6 These complexing agents may interact © XXXX American Chemical Society

with the actinides and affect their mobility in the geosphere.7−10 For long-term predictions on the impact of organic matter on the migration behavior of actinides in deep geological formations, a detailed thermodynamic description and an indepth knowledge of their complexation mechanisms on the molecular scale are required. The complexation of trivalent lanthanides and actinides with different carboxylic acids has been studied extensively in the past.9,11−16 However, the majority of these studies are limited to ambient temperatures. As a consequence of the radioactive decay of the stored nuclear waste, the temperature in the near field will increase significantly. This will have a distinct impact on the thermodynamics of the actinides and may even lead to the formation of new chemical species, which are not present at 25 °C. A comprehensive long-term safety analysis of a nuclear waste repository in deep geological formations requires therefore thermodynamic data at ambient conditions as well as at higher temperatures. Received: March 16, 2017

A

DOI: 10.1021/acs.inorgchem.7b00694 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry In the present work the complexation of Cm(III) with malonate is studied by fluorescence spectroscopy (TRLFS) and quantum chemical calculations. Cm(III) is chosen as a representative for trivalent actinides due to its outstanding spectroscopic properties.17 Malonate may be present in a repository as degradation product of different macromolecular organic compounds and may act as a complexing agent toward the actinides.18−20 Such macromolecular matter may be of natural origin (e.g., humic and fulvic acids which are present in the geosphere due to the degradation of dead organisms) and of anthropogenic origin (e.g., superplasticizers as additives in commercial concrete mixtures). Furthermore, the interaction of Cm(III) with malonate is of fundamental interest for a basic understanding of the coordination modes of dicarboxylic acids and the impact of the carbon chain length of the ligand.21,22 This will give an insightful understanding of the interaction of trivalent actinides with small organic molecules, which is important for the interpretation of the interaction of radionuclides with larger macromolecular ligands.

Table 1. Standard-State Thermodynamic Data Used for Speciation Calculations reaction

log β°

ref

ΔrH°

ref

2.83

24

−0.16

25

2H+ + Mal2 − ⇌ H 2Mal

8.52

24

4.93

25

Na + + Mal2 − ⇌ NaMal−

0.80

25

4.00

25

Na + + Cl− ⇌ NaCl

−0.30

26

8.00

26

H 2O ⇌ H+ + OH−

−14.00

26

−55.81

26

+

2−

H + Mal

−

⇌ HMal

analogous coefficients of the chemically similar oxalate species (Ox2−, HOx−) with the same charge were taken, as recommended by the NEA-TDB.16 The following ε(i,k) values were used for the calculation. ε(H+, Cl−) = 0.12 ± 0.01

ε(Na +, Mal2 −) ≈ ε(Na +, Ox 2 −) = −0.08 ± 0.01 ε(Na +, HMal−) ≈ ε(Na +, HOx −) = −0.07 ± 0.01 ε(Na +, NaMal−) ≈ ε(Na +, HOx −) = −0.07 ± 0.01

2. EXPERIMENTAL SECTION The molal concentration scale (mol/kg H2O, “m”) is used throughout this work to avoid changes of the concentrations due to changes of the density of the solutions with increasing ionic strength and/or temperature. 2.1. Sample Preparation. The concentration of Cm(III) in each sample was adjusted to 1 × 10−8 m by addition of defined aliquots of a Cm(III) stock solution with concentration of [Cm(III)]total = 10−7 m. The isotopic composition of the stock solution was 89.7% 248Cm, 9.4% 246 Cm, 25 °C were calculated with the integrated Van’t Hoff equation, assuming ΔrH°m = const and ΔrC°p,m = 0.27 The thermodynamic log β°n(T) values were extrapolated to the various ionic strengths according to the specific ion interaction theory approach (SIT), yielding the conditional log β′n(T) values.16 No binary ion−ion interaction coefficients of Mal2− and HMal− with Na+ are available in the literature. Thus, the

2.2. Time-Resolved Laser Fluorescence Spectroscopy. The TRLFS measurements were performed using a pulsed Nd:YAG (Surelite II, Continuum, USA) with a repetition rate of 10 Hz pumping a dye laser (NarrowScan, Radiant Dye Laser & Accessories GmbH, Germany) with a pulse energy between 2 and 4 mJ. Cm(III) was excited at a wavelength of 396.6 nm. The detector system consisted of an ICCD camera (iStar Gen II, Andor Technology PLC) and an imaging spectrograph with a 1200 line/mm grating and a spectral range of 580−620 nm (Shamrock SR-303i, Andor Technology PLC). The spectra were measured in time-gated detection mode with an initial delay of 1 μs and a pulse gate width of 1 ms. The temperature was controlled by a water bath thermostat (K6-mpc-NR, Peter Huber Kältemaschinen GmbH, Germany). 2.3. Quantum Chemical Calculations. Quantum chemical structure optimizations using density functional theory (DFT) with subsequent calculation of interaction energies on the MP2 level were employed to determine the molecular structure of the Cm(III) malonate complexes. The charges and static dipole polarizabilities of the malonate ion were calculated using the Hirshfeld method.28 For all possible combinations of side-on and end-on coordination of [Cm(H2O)9−2n(Mal)n]3−2n (n = 1, 2, 3) forming a 9-fold coordinated Cm(III) complex structure, optimizations have been carried out on the DFT/BH-LYP level of theory using basis sets of triple-ζ quality on all atoms.29 The BH-LYP functional was chosen as it provides good structural results as well as a very good self-consistent field convergence for complexes involving heavy ions.30 Within the optimizations the aqueous medium is modeled using the conductorlike screening model (COSMO).31 The COSMO cavity was constructed with standard radii for all C, O, and H atoms, as well as rCm = 1.72 Å. Subsequently, interaction energies were obtained on the MP2/aug-cc-pVTZ level of theory employing the resolution of the identity technique (RIMP2) as implemented in the TURBOMOLE software package.32,33 In all calculations, a small-core relativistic pseudopotential (ECP60MWB) is used for the Cm(III) ion.34 The interaction energies were corrected for basis-set superposition errors (BSSE) using the counterpoise method.35

3. RESULTS AND DISCUSSION 3.1. Emission Spectra. The fluorescence spectra of the Cm(III) ion resulting from the 5D′7/2 → 8S′7/2 transition is recorded as a function of the total malonate concentration, the ionic strength, and the temperature. The temperature-dependent spectra show a general decrease of the emission intensity by about 30% independent of the ionic strength and ligand concentration. This effect is attributed B


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Inorganic Chemistry

Figure 1. (a) Emission spectra of Cm(III) as a function of the total malonate concentration. T = 20 °C, [H+]tot = 8 × 10−3 m. (b) Emission spectra of Cm(III) as a function of the temperature. [Mal2−]tot = 10−2 m, Im = 2.0 (NaCl), and [H+]tot = 8 × 10−3 m.

Figure 2. Single component spectra of the [Cm(Mal)n]3−2n (n = 0, 1, 2, 3) complexes at (a) T = 25 °C and (b) T = 90 °C, and deconvoluted experimental spectra at (c) [Mal2−]tot = 10−2 m, Im = 2.0, T = 25 °C and (d) [Mal2−]tot = 1.5 × 10−2 m, Im = 2.0, T = 90 °C.

increasing ligand concentration the emission band shifts successively to longer wavelengths, resulting in a broad emission band at λ = 600.6 nm at [Mal2−]tot = 2.0 × 10−2 m. This shift is due to the increasing formation of higher Cm(III) complexes with malonate. The exchange of water molecules by malonate ligands in the inner coordination sphere of Cm(III) results in a strengthening of the ligand field, which leads to a stronger splitting of the four levels (A1−4) of the first excited

to a thermal population of higher energetic states of Cm(III) and a subsequent nonradiative relaxation.36 To enhance comparability, the emission spectra are normalized to equal peak area. The evolution of the normalized emission spectra at room temperature with increasing ligand concentration is given in Figure 1a. Without addition of ligand, a single emission band is observed at λmax = 593.8 nm. This band is attributed to the [Cm(H2O)9]3+ aquoion.17 With C


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Inorganic Chemistry

Figure 3. Linear slope analysis of the stepwise formation of the Cm(III) malonate complexes: (a) T = 25 °C; (b) T = 90 °C.

state (6D′7/2). This results in a lowering of the energy gap between the ground state and the A1 level of the first excited state of the metal ion, and the fluorescence transition occurs at lower energies. The normalized emission spectra of Cm(III) as a function of the temperature at a fixed total malonate concentration are given in Figure 1b. With increasing temperature a bathochromic shift toward 600 nm is observed. This is comparable to the shift of the spectra observed for increasing malonate concentration at 25 °C and is also attributed to the formation of Cm(III) malonate complexes. This shows that the chemical equilibrium shifts toward the complexed species with increasing temperature, indicating endothermic reaction enthalpies. 3.2. Peak Deconvolution and Identification of the Ligand Species. In order to deconvolute the fluorescence spectra these are treated as a linear combination of the pure emission bands of the individual Cm(III) species in solution with respect to their molar fractions and quantum yields. The pure emission bands are introduced as so-called single component spectra. The quantum yields of the different Cm(III) species are accounted for by their relative fluorescence intensity factors (FI factors). The FI factors of the different Cm(III) species are derived by monitoring of the total fluorescence intensity of Cm(III) with increasing malonate concentration at a constant temperature. In the present work no systematic change of the total fluorescence intensity with the malonate concentration is observed at any temperature. Thus, differences in the FI factors of the Cm(III) malonate complexes are negligible and they are treated as unity in the following data evaluation. Besides the Cm(III) aquoion at 593.8 nm, three Cm(III) malonate complexes are identified. The single component spectra at 25 and 90 °C are given in Figures 2a and 2b. The emission bands are located at 597.4, 600.7, and 603.3 nm. This is in good agreement with literature data of analogous Cm(III) oxalate and succinate systems.21,22 This indicates that the Cm(III) emission bands correspond to the complexes [Cm(Mal)]+, [Cm(Mal)2]−, and [Cm(Mal)3]3−. An additional emission band at higher wavelengths, which would correspond to an additional [Cm(Mal)4]5− complex, was not observed under the present experimental conditions. Such a species was observed for oxalate, indicating that malonate is a weaker ligand. Furthermore, Cm(OH)n3−n complexes can be excluded due to the low pH range of the samples (pH ≈ 2−4). The presence of Cm(Cl)n3−n complexes can as well be neglected at

the studied chloride concentration. Due to the very small stability constants of these complexes, their formation requires chloride concentrations well above [Cl−] = 3.0 m.37 As examples two deconvoluted spectra at 25 and 90 °C are given in Figures 2c and 2d. The experimental spectra are well described by considering only the Cm(III) aquoion and the Cm(III) malonate complexes as no additional spectroscopic features are visible in the residues, which also shows the good quality of the fit. The uncertainty of this method is about 0.05 in the total molar fraction of the species. The single component spectra show a slight broadening and small bathochromic shift with increasing temperature. This is in good agreement with the literature and is attributed to the equilibrium of a 9- and 8-fold coordinated Cm(III) which is shifted toward the latter with the temperature.38 Due to this effect an individual set of single component species is required for the deconvolution of the experimental spectra at each temperature. The assignment of the emission bands is further validated by linear slope analysis. The method of linear slope analysis is based on the logarithmic law of mass action (eq 1). Cm 3 + + n Lm − ⇌ Cm(L)n3 − n·m

⎛ [Cm(L) 3 − n·m ] ⎞ m ⎟ log K ′ + n·log([Lm −]eq ) = log⎜ [Cm 3 +] ⎝ ⎠

(1)

The reactive ligand species and the stoichiometry of the formed complexes are identified by a double logarithmic plot of the equilibrium concentrations of the different potential ligand species (Mal2−, HMal−, NaMal−) versus ([Cm(L)n3−n·m]/ [Cm(L)n−13−(n−1)·m]) and linear regression analysis. This requires that the activity coefficients of all reactive species do not change with increasing ligand concentration. This is achieved by using a high concentration of an inert background electrolyte. In this case the change of the ionic strength by added ligand is negligible and the activity coefficients are determined only by the background electrolyte. Two plots of log [Mal2−]eq versus log([Cm(Mal)n3−2n]/ [Cm(Mal)n−13−2(n−1)] at 25 and 90 °C are displayed in Figure 3. Data points with at least one species below 10% are not considered in the plot due to their large errors. The results show that only the plots with the fully deprotonated Mal2− as ligand species yield a linear correlation of the data with slopes of 1.0. Plotting of the other potential ligand species HMal− and NaMal− on the abscissa yields no linear correlation of the data D


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Inorganic Chemistry

Figure 4. Cm(III) speciation at Im = 2.0 (NaCl) as a function of the temperature at (a) [Mal2−]tot = 0.01 m and (b) [Mal2−]tot = 0.015 m and as a function of the total malonate concentration at (c) T = 25 °C and (d) T = 90 °C.

4c and 4d. At 25 °C the speciation consists mainly of the Cm3+ aquoion and the [Cm(Mal)]+ and [Cm(Mal)2]− complexes. The [Cm(Mal)3]3− species is only present as a minor fraction at the highest studied ligand concentration. At 90 °C the chemical equilibrium is shifted distinctively toward the higher complex species. Especially the formation of the [Cm(Mal)3]3− complex is pronounced at [Mal2−]tot > 10−2 m. Using the experimentally determined speciation and the calculated free ligand concentration, the conditional stepwise stability constants (log K′n(T)) are calculated at various temperatures according to the law of mass action (eq 2).

points. This proves that only the fully deprotonated malonate acts as complexing ligand toward the Cm(III) ion under the applied experimental conditions. 3.3. Thermodynamic Data. The entire set of emission spectra is deconvoluted with the temperature-dependent single component spectra, yielding the fractions of the different Cm(III) species as a function of the malonate concentration, the ionic strength, and the temperature. As an example the change of the chemical speciation with the temperature at two different total malonate concentrations ([Mal]tot = 1 × 10−2 m and 1.5 × 10−2 m) is displayed in Figures 4a and 4b. At lower ligand concentration and ambient temperature the speciation is mainly determined by the Cm3+ aquoion and the [Cm(Mal)]+ complex. The [Cm(Mal)2]− complex is present only as a minor species, whereas no [Cm(Mal)3]3− is observable. As the temperature increases, the complexation is shifted visibly toward higher complexes. The [Cm(Mal)2]− complex becomes the dominant species, and also the fraction of the [Cm(Mal)3]3− complex increases successively. An analogous effect is observed at higher [Mal2−]tot. Due to the increased ligand concentration the speciation is shifted toward higher complexes. Already at room temperature the speciation is determined by [Cm(Mal)]+ and [Cm(Mal)2]−, whereas the Cm3+ aquoion and the [Cm(Mal)3]3− complex are present only in minor fractions. With increasing temperature the fraction of [Cm(Mal)3]3− increases and becomes the dominant species at 90 °C. Furthermore, the speciation of the Cm(III) malonate system as a function of the total ligand concentration at two constant temperatures (25 and 90 °C) is displayed in Figures

K ′n =

[Cm(Mal)n3 − 2n ] [Cm(Mal)n − 13 − 2(n − 1)]· [Mal2 −]

(2)

The log K′n(T) values are extrapolated to zero ionic strength using the SIT approach as recommended by the NEA-TDB, yielding the thermodynamic log K°n(T) values (eq 3).16 log K °n (T ) − Δεn(T ) ·Im = log K ′n (T ) − Δz 2·D(T ) (3)

Hereby, Im is the molal ionic strength, z is the ion charge, and Δz2 = ∑z2(products) − ∑z2(educts). The temperaturedependent Debye−Hückel term D(T) is defined as D(T) = (A(T)·(Im)0.5·(1 + B(T)aj·(Im)0.5)−1. The temperature-dependent Debye−Hückel parameters A(T) and B(T) are tabulated in the literature.16 Δεn(T) is defined as the difference between the binary ion−ion interaction coefficients of the products and educts (Δεn(T) = ∑ε(products) − ∑ε(educts)). The NEAE


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Inorganic Chemistry

Figure 5. Linear SIT regression analysis for the first (a) and second (b) complexation reactions at T = 25 °C.

TDB recommends to set the term B(T)aj to 1.5 kg1/2·mol−1/2 in order to reduce possible variations of the ε(i,k) parameters with the increasing ionic strength and temperature. This recommendation is followed in the present work. Equation 3 shows that, by plotting log K′n(T) − Δz2D(T) versus Im and linear regression analysis, the log K°n(T) and Δεn(T) values are obtained from the slope and the y-axis intercept. Two examples of SIT regression analyses are given in Figure 5. The log K°n(T) values are summarized in Table 2. The log K°3(T) was determined at temperatures >40 °C due to the low fraction of the [Cm(Mal)3]3− complex at lower temperatures.

to Im = 0 with the extended Debye−Hückel equation. Degischer et al. studied the complexation of different trivalent lanthanides with malonate in 0.1 and 1.0 M NaClO4 solution using potentiometry and calorimetry.11 The determined log K°1 (Eu(Mal)+) = 5.93 and log K°2 (Eu(Mal)2−) = 3.46 at 25 °C are higher compared to the present results. This is explained by the fact that methods like potentiometry do not distinguish between inner and outer sphere complexes and thus generally yield higher stability constants compared to spectroscopic methods. Niu et al. also applied potentiometric measurements to study the complexation of Gd(III) with malonate in 0.1 M NaClO4 solution.13 The log K°1 (Gd(Mal)+) = 5.76 at 25 °C is also slightly higher compared to the present results, whereas the log K°2 (Gd(Mal)2−) = 3.16 at 25 °C is in good agreement. However, due to the above-mentioned differences in potentiometric and spectroscopic methods, this agreement shall not be overinterpreted. In addition, the complexation of Eu(III) was studied by Wang et al. using luminescence and absorption spectroscopy.15 They determined log K°1 (Eu(Mal)+) = 5.49 ± 0.01 and log K°2 (Eu(Mal)2−) = 2.98 ± 0.01 at 25 °C, which also agree with the present values within the error range. The Δεn(T) values for the formation of the [Cm(Mal)n]3−2n complexes are given in Table 3 as a function of the temperature. Due to the lack of data for the [Cm(Mal)3]3− complex at lower temperatures, the Δε3(T) are limited to T ≥ 40 °C. The Δε1(T) decreases by approximately 0.3 unit in the studied temperature range, whereas the Δε2(T) and Δε3(T) show no clear temperature dependency. The SIT-specific binary ion−ion interaction parameters ε(i,k) of the different Cm(III) malonate complexes are calculated using the following

Table 2. Thermodynamic Stability Constants of the Stepwise Formation of the [Cm(Mal)n]3−2n Complexes (n = 1, 2, 3) as a Function of the Temperature Cm3+ + Mal2− ⇌ CmMal+

CmMal+ + Mal2− ⇌ CmMal2−

CmMal2− + Mal2− ⇌ CmMal33−

T/°C

log K°1(T)

Δ

log K°2(T)

Δ

log K°3(T)

Δ

25 30 40 50 60 70 80 90

5.26 5.28 5.31 5.33 5.37 5.38 5.53 5.50

0.22 0.19 0.18 0.18 0.11 0.09 0.13 0.09

3.12 3.21 3.38 3.37 3.36 3.36 3.43 3.48

0.17 0.13 0.12 0.14 0.21 0.28 0.23 0.24

1.15 1.26 1.34 1.44 1.36 1.52

0.35 0.31 0.24 0.25 0.15 0.19

All stability constants increase with increasing temperature. The log K°1(25 °C) = 5.26 ± 0.22 increases by approximately 0.25 and log K°2(25 °C) = 3.12 ± 0.17 by 0.4 logarithmic unit in the studied temperature range. Furthermore, the log K°3(T) values increases by 0.5 logarithmic unit from 40 to 90 °C. Only a few literature data on binary complexes of trivalent actinides with malonate at increased temperature are available. Thakur et al. studied the complexation of Eu(III), Cm(III), and Am(III) using luminescence spectroscopy.39 Unfortunately, the studies were performed in 6.60 M NaClO4 solution. Thus, the SIT cannot be applied to calculate the standard-state stability constants from the given conditional data to compare them with the data of the present work. More data are available for trivalent lanthanides at room temperature. However, most of the given stability constants are conditional values valid only for a specific ionic matrix. Thus, in order to enable a comparison with the present results, the literature values were extrapolated

Table 3. Δεn(T) Values for the Stepwise Formation of the [Cm(Mal)n]3−2n Complexes T [°C] 25 30 40 50 60 70 80 90 F

Δε1(T) −0.204 −0.197 −0.275 −0.320 −0.327 −0.264 −0.393 −0.495

± ± ± ± ± ± ± ±

0.023 0.051 0.126 0.097 0.060 0.097 0.053 0.067

Δε2(T) −0.207 −0.178 −0.135 −0.137 −0.170 −0.188 −0.129 −0.147

± ± ± ± ± ± ± ±

0.014 0.030 0.100 0.020 0.025 0.018 0.034 0.034

Δε3(T)

−0.030 −0.033 −0.021 0.004 −0.061 0.021

± ± ± ± ± ±

0.126 0.053 0.017 0.025 0.042 0.029


Article

Inorganic Chemistry data given by the NEA-TDB:16 ε(Cm3+,Cl−) ≈ ε(Am3+,Cl−) = 0.23 ± 0.02, ε(Na+,Mal2−) ≈ ε(Na+,Ox2−) = −0.08 ± 0.01. Since no temperature-dependent ε(i,k) are available in the literature, the values for the Cm(III) malonate complexes are calculated only at 25 °C ([Cm(Mal)]+, [Cm(Mal)2]−) or 40 °C ([Cm(Mal)3]3−). The calculated ε(i,k) values are given in Table 4 together with literature data on analogous oxalate and succinate complexes.

variation of the reaction enthalpies of the first two complexations steps (ΔrH′1 = 13.52 ± 0.38 kJ·mol−1, ΔrH′2 = 7.83 ± 0.30 kJ·mol−1) and a rather strong decrease of the reaction entropies (ΔrS′1 = 133.6 ± 1.7 J·mol−1·K−1, ΔrS′2 = 84.2 ± 1.3 J·mol−1·K−1). Regarding the complexation of Ln(III) and An(III) with malonate, no reaction enthalpies or entropies valid for zero ionic strength are available in the literature. The thermodynamic functions determined in the present work indicate that the degree of chelating complexation mode of the ligands reduces with each added ligand malonate molecule. 3.4. Quantum Chemical Calculations. In order to resolve the geometry and structure of the different Cm(III) malonate complexes and to investigate the origin of the decreasing reaction entropies of the higher complexes (see section 3.3), quantum chemical structure optimizations are performed using density functional theory. The charges and polarizabilities of malonate which are calculated according to the Hirshfeld method are shown in Table 6 together with the data for oxalate and succinate.

Table 4. Binary Ion−Ion Interaction Coefficients ε(i,k) for the [Cm(Mal)n]3−2n Complexes at T = 25 °C ε(Cm(Mal)+,Cl−) ε(Cm(Mal)2−,Na+) ε(Cm(Mal)33−,Na+) ε(Cm(Ox)+,Cl−) ε(Cm(Ox)2−,Na+) ε(Cm(Ox)33−,Na+) ε(Cm(Succ)+,Cl−) ε(Cm(Succ)2−,Na+) ε(Cm(Succ)33−,Na+)

−0.05 −0.34 −0.45 −0.06 −0.26 −0.40 −0.08 −0.23 −0.37

± ± ± ± ± ± ± ± ±

0.06 0.10 0.24 0.04 0.06 0.10 0.03 0.07 0.08

this study this study this study 21 21 21 22 22 22

Table 6. Calculated Oxygen Charges and Polarizabilities for Oxalate, Malonate, and Succinate Using the Hirshfeld Method

The results show that the data for Cm(III) malonate is in excellent agreement with those of other structurally comparable dicarboxylic ligands. Also, the here determined value of ε(Cm(Mal)2−,Na+) is in excellent agreement with the analogous value of ε(Am(Ox)2−,Na+) = −0.21 ± 0.08 recommended by the SIT.16 The standard-state stability constants of the Cm(III) malonate complexes are linearly correlated with the reciprocal temperature. Thus, the reaction enthalpies are considered as constant and the temperature dependence of the log K°n(T) values is fitted by the integrated Van’t Hoff equation (eq 4). log K °n (T ) = log K °n (T0) +

Δr H °n(T0) ⎛ 1 1⎞ ⎜ − ⎟ R ·ln 10 ⎝ T0 T⎠

q0 (e) α0 (Å3)

T0 is the reference temperature, which is 25 °C in the present work. The thermodynamic functions ΔrH°n and ΔrS°n for the stepwise complexation reactions are summarized in Table 5. Due to the lack of data for the formation of [Cm(Mal)3]3− at T < 40 °C the thermodynamic functions are derived from a smaller data set showing higher errors.

ΔrS°n [J·mol−1·K−1]

n=1 n=2 n=3

8.69 ± 1.62 9.82 ± 2.71 12.50 ± 4.08

129.05 ± 4.74 94.28 ± 8.56 62.64 ± 11.83

succinate22

−0.50 2.10

−0.51 2.14

−0.49 2.14

Table 7. Binding Energies (BE) and Cm(III) Oxygen Distances to the Inner-Sphere Water Molecules (OH2O) and Malonate Ligands in Side-On (Os) and End-On (Oe) Coordination Modea

Table 5. Standard-State Reaction Enthalpies (ΔrH°n) and Reaction Entropies (ΔrS°n) for the Stepwise Formation of the [Cm(Mal)n]3−2n (n = 1, 2, 3) Complexes ΔrH°n [kJ·mol−1]

malonate

Both properties are almost independent of the carbon chain length within the accuracy of the method. Accordingly, very similar coordination modes of the dicarboxylic ligands oxalate, malonate, and succinate to Cm(III) are expected, apart from steric differences. The former and latter ligands both prefer side-on coordination as confirmed in recent studies.21,22 The Cm(III)−O bond distances and interaction energies of the different Cm(III) malonate complexes for all combinations of side-on and end-on coordination are given in Table 7. The

(4)

Cm(Mal)n3−2n + Mal2− ⇌ Cm(Mal)n+13−2(n + 1)

oxalate21

[Cm(H2O)7Mals]+ [Cm(H2O)7Male]+ [Cm(H2O)5Mal2s]− [Cm(H2O)5MalsMale]− [Cm(H2O)5Mal2e]− [Cm(H2O)3Mal3s]3− [Cm(H2O)3Mal2sMale]3− [Cm(H2O)3MalsMal2e]3− [Cm(H2O)3Mal3e]3−

The results show that all complexation steps are endothermic with positive reaction entropies. The ΔrH°n increases slightly, however, this effect is not significant and is within the error range of the data. Contrary to this, the ΔrS°n values decrease considerably with each complexation step. A similar effect was observed by Degischer et al. for the formation of Eu(III) malonate complexes.11 Although this data is conditional and only valid for a 0.1 M NaClO4 solution, the trend of the thermodynamic functions is comparable to the results of the present work. The data given by Degischer et al. shows a small

a

BE [kJ·mol−1]

d(Cm− OH2O) [Å]

−4448 −4342 −6332 −6251 −6205 −8009 −7992 −7963 −7813

2.54 2.51 2.58 2.54 2.51 2.61 2.60 2.55 2.51

d(Cm− Oe) [Å]

d(Cm− Os) [Å] 2.36

2.46 2.53 2.47 2.57 2.53 2.50

2.42 2.39 2.41 2.43 2.41

s: side-on coordination. e: end-on coordination.

bond lengths of Cm(III) to the oxygen atoms of malonate are shorter compared to the coordinating oxygen atoms of water molecules. This is in excellent agreement with the literature.21,22 Furthermore, the side-on coordination (indicated by the superscript s) of malonate provides shorter Cm(III)−Os bond lengths (2.36 to 2.43 Å), compared to the end-on G


Article

Inorganic Chemistry

Figure 6. Molecular structures of the [Cm(Mal)3]3− complex: (a) all ligands in side-on coordination; (b) two side-on and one end-on coordinated ligands.

increasing temperature in the range of 0.25 to 0.5 logarithmic unit. Their temperature dependency is fitted according to the integrated Van’t Hoff equation, yielding the standard-state thermodynamic functions (ΔrH°n and ΔrS°n). The results show that all complexation steps are endothermic and driven solely by positive reaction entropies. While the ΔrH°n values are almost constant for the different complexation steps, the ΔrS°n values decrease with each ligand added. This effect is explained by quantum chemical calculations of the complex structures. The results show that malonate is able to form hydrogen bonds to inner-sphere water molecules while in end-on coordination mode. This lowers the binding energy of this coordination mode, resulting in an equilibrium with the chelating side-on coordination mode. Furthermore, this equilibrium is shifted toward end-on coordination with each additional ligand due to steric reasons. The present work provides detailed insight in the complexation of malonate with Cm(III) in aqueous solution at increased temperatures on the molecular level and leads to a better understanding of the interaction of aliphatic dicarboxylic ligands with trivalent actinides. It shows how the length of the carbon chain strongly affects the complexation modes and the resulting thermodynamic constants. Due to the potential presence of dicarboxylic ligands in nuclear waste repositories in deep geological formations, the present data are a valuable prerequisite to model the migration behavior of trivalent actinides under repository conditions in the context of a longterm safety analysis.

coordination (indicated by the superscript e) with bond lengths Cm(III)−Oe of 2.46 to 2.57 Å. For all calculated complexes the lowest interaction energies are found for the structures with only side-on coordinated ligands. This shows that malonate prefers a chelating binding mode to Cm(III) via two oxygen atoms, one of each carboxylic group. This is in good agreement with results for other dicarboxylic ligands like oxalate and succinate.21,22 In contrast to oxalate and succinate, however, the differences of the binding energies of the all side-on structures and the mixed structures with one ligand in end-on coordination are quite small. For example, for the 1:3 complexes this difference is only 17 kJ·mol−1 for malonate compared to 99 kJ·mol−1 for oxalate and 137 kJ·mol−1 for succinate. This effect can be explained by analyzing the structural properties of the different complexes: Due to the carbon-chain length, the malonate ligand has the ability to form hydrogen bonds to inner-sphere water molecules when bound in end-on coordination (see Figure 6). These hydrogen bonds stabilize the end-on coordination of malonate to some extent and lower the binding energies. The carbon chains of oxalate and succinate are either too short or too long to form such hydrogen bonds. Furthermore, for the higher complexes the Coulombic repulsion between the ligands increases due to steric reasons, which favors more and more the sterically less demanding endon coordination mode. Whereas oxalate and succinate coordinate exclusively in side-on coordination mode, an increasing contribution of end-on coordination is expected with increasing number of malonate ligands present in the inner coordination sphere. This is in excellent agreement with the observed decrease of the reaction entropies given in Table 5.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00694. log K′n(T) for the stepwise formation of complexes (PDF)

4. SUMMARY AND CONCLUSION In the present work the thermodynamic and structural properties of Cm(III) malonate complexes at T = 25−90 °C are studied in detail by spectroscopic and theoretical methods. Three different complex species [Cm(Mal)]+, [Cm(Mal)2]−, and [Cm(Mal)3]3− are identified. The stepwise standard-state stability constants log K°n(T) and the binary ion−ion interaction parameters ε(Cm(Mal)n3−2n,Na+/Cl−) were determined from 25 to 90 °C (n = 1, 2) and 40 to 90 °C (n = 3) by the SIT approach. All log K°n(T) show an increase with

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +49 (0)721 608 23907. Phone: +49 (0)721 608 26024. H


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Andrej Skerencak-Frech: 0000-0003-2177-4462 Daniel R. Fröhlich: 0000-0001-8380-8598 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially funded by the German Federal Ministry of Economics and Technology (BMWi) under Contract No. 02E11415H.

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