Computational Study of Reduction Potentials of Th4+ Compounds and

Article pubs.acs.org/JPCA

Computational Study of Reduction Potentials of Th4+ Compounds and Hydrolysis of ThO2(H2O)n, n = 1, 2, 4 Anne E. V. Gorden and Michael L. McKee* Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States S Supporting Information *

ABSTRACT: The stability of Th4+ to reduction in water is studied by DFT methods. The standard reduction potential (SRP) of homoleptic complexes including Th(H2O)94+, Th(H2O)104+, Th(NO3)4, Th(NO2)62−, Th(NO3)62−, Th(COT)2, Th(acac)4, ThCp4, ThF4, and ThCl4 have been investigated. The values vary widely (from −3.50 V for Th(OH)4 to −0.62 V for Th(NO3)4 depending on whether the ligands are redox active (noninnocent) or not. Several additional topics of thorium chemistry are explored, including the hydrolysis mechanism of ThO2(H2O)n, n = 1, 2, 4, and the solution phase nonzero dipole moment of ThCp4. Dinuclear complexes are also characterized, including Th2O4, Th2O2(OH)4, Th2O2(H2O)8, Th2(OH)8(H2O)4, and Th 2 (OH) 2 (NO 3 ) 6 (H 2 O) 4 and condensed thorium complexes as [Th4(OH)6(H2O)12]10+ and [Th6(OH)14(H2O)12]10+. For the Th2(OH)2(NO3)6(H2O)4 dinuclear complex, the first SRP is −0.82 V and the second is 1.59 V. The first SRP corresponds to the reduction of the ligand NO3−, and the second SRP corresponds to dissociative electron transfer to the NO32− ligand. The calculated formation constant of Th(EDTA)(H2O)4 is in reasonable agreement with experiment. The different stereochemistries of the bidentate ligands NO2−, NO3−, and acetylacetonate (acac) around the thorium center have very similar stabilities.

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nuclear weapon.2,12 The fission products produced do not result in the quantities of Pu239 that could be used in weapons. There is an estimated 4-fold higher amount of thorium in the earth’s crust than uranium (8.1 ppm thorium in the earth’s crust versus 2.4 ppm for uranium), potentially making it more easily accessible and usable while limiting opportunities for nuclear weapons proliferation.13 In addition, the lanthanides that are needed for everything from magnets for cellular technology, wind turbines for wind energy production, and LCD and computer technology are often found codeposited with thorium.8,14 This thorium in the lanthanide ores as a contaminant greatly reduces the accessibility of the rare earths, because it complicates their isolation. Purification procedures are made much more complex by the need to consider limiting water or solvents, and thus, the volumes of radioactive wastes.15−18 As an early actinide element, the structural chemistry of thorium is varied, as documented by experimental19−24 and theoretical studies.25−29 Due to the potential importance of thorium as a future fuel, the solution chemistry has also been investigated.30−43 At pH 7.4 (near physiological pH), thorium salts hydrolyze to form colloidal particles of Th(OH)4. Thorium is a toxic heavy metal, and thorium ions or its hydroxides can react in vivo to form stable complexes with amino acids and proteins.44−47 In addition, because of its most

INTRODUCTION With the increasing energy dependence of our standard of living and quality of life, the environmental impacts of energy production weigh heavily on continued development. One proposal to reduce overall environmental atmospheric emissions and anthropogenic climate change is to increase the amount of civilian energy production based on nuclear fission; however, the extraction and use of nuclear fuels leads to many additional problems of storage, waste reduction, contamination, and remediation.1,2 A recent resurgence in environmentalism has led to an increase of interest in the solution and coordination behavior of the actinides.3−7 All of the actinide series are radioactive and have unique chemistry. Significant areas of fundamental research remain to be explored in actinide science and actinide coordination chemistry, in particular, if you compare the amount of research in this area to that of the early first row transition metals.8 The most common type of civilian fission reactors run on uranium containing material enriched in uranium 235 making it fissionable, but a reactor could also use plutonium or thorium fuels.9,10 In the United States, light water reactors operating for civilian power generation require an additional 200 metric tons of fissionable uranium each year,2 and the nuclear fuel cycle results in about 75 tons of plutonium as fuel waste.11 Recycling and recovery of uranium from these fuels is made problematic by this plutonium, which could be used in the production of nuclear weapons.1 Thorium has been used in the design of new modern reactors as it is also fissionable but, unlike uranium, is very difficult to make into material that could be used in a © XXXX American Chemical Society

Received: August 22, 2016 Revised: September 27, 2016

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DOI: 10.1021/acs.jpca.6b08472 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

culations (i.e., no frozen core approximation) were made to estimate the accuracy of the calculated DFT binding energies. When reduction potentials for thorium compounds (Th4+ → Th3+) are calculated, the product is a doublet, and the unpaired electron may reside on the thorium center, on the ligands, or on both. If the unpaired electron resides on thorium in a f or d orbital, the spin−orbit contribution is expected to be significant. An approximate correction is made for spin−orbit effects by including a correction that is the product of the unpaired spin density on thorium times 0.3 eV. Hay and coworkers have estimated a 0.30 V SO correction for the f1 configuration of U/Np/Pu.61 The Gaussian09 program system62 was used for all geometry optimizations, frequency and solvation calculations. MOLPRO63,64 was used for the larger CCSD(T) calculations. In CCSD(T) test calculations, Gaussian09 and MOLPRO produced the same energy to within 2.0 × 10−6 hartrees for the same structure. Charges were computed with natural bond orbital analysis.65,66

preferred +4 oxidation state, similar ionic radii, and relatively low specific radioactivity, Th4+ has at times been used as a model for plutonium in coordination and extraction studies.4,6,8,13,47−50 With this research, we seek to describe some of the interactions that must be occurring in thorium containing aqueous solutions.

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COMPUTATIONAL METHOD All structures were optimized at the M06 level28 with the Stuttgart small core scalar relativistic effective core potential (SDD) with the ECP60MWB basis set (contracted to 8s7p6d4f) for thorium52 and the 6-31+G(d) basis set for other elements. The M06 functional has been found51 to be competitive with high-level ab initio methods in the study of water exchange mechanism of the [UO2(H2O)5]2+ ion. The small size of the basis set allowed for studying larger systems and additional searching for the lowest energy structures. Vibrational frequencies were computed to determine the nature of the stationary points and to make zero-point, thermal, and entropy (298 K) corrections. Solvation free energies (ΔG(solv)) were computed using the SMD implicit solvation model53 with standard parameters as the difference between the gas-phase energy and the SMD energy. A 1.89 kcal/mol correction was added to all species to account for the change of state from 24.45 to 1 L/mol. A 2.38 kcal/mol correction was added to each free water to account for the change of state from aqueous to liquid. The SMD total energies of H3O+ and H2O were adjusted so that the experimental solvation free energies of H3O+ (−108.3 kcal/mol) and liquid water (−2.05 kcal/mol) were obtained. The aqueous free energy ΔG(aq,298 K) was computed from eq 1. ΔG(aq,298K) = ΔG(g,298K) + ΔG(solv)

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RESULTS AND DISCUSSION Benchmarking with CCSD(T). Table 1 compares H2O binding energies at the CCSD(T) and M06 levels for several Table 1. Comparison of Binding Energies (kcal/mol) for Water Molecules to Thorium Complexes by CCSD(T) and M06 Levels of Theorya

(1)

The reduction free energy for thorium compounds (Th4+ → Th3+) was coupled with the standard oxidation reaction (eq 2) where the recommended value (4.28 eV) for use with the M06 method was used.54,55 1 H (g) → H+(aq) + e− 2 2

ΔG(aq,298K) = 4.28 eV (2)

Finally, the SRP (E°) was computed from ΔG(aq,298 K) = −nFE°, where n is the number of electrons transferred and F is the Faraday constant. For optimizing structures, the X-ray structure was used as a starting point when available. However, several alternative arrangements were also considered. A systematic (but not exhaustive) search for the lowest energy structure was made. If a structure with symmetry revealed an imaginary frequency, the structure was distorted and reoptimized until a structure with no imaginary frequencies was located. Single-point energy calculations were made to determine the effect of solvation. The structure giving the lowest aqueous free energy was chosen as the reference. In several cases, the reference structure was not the structure with the lowest electronic energy. Solvation effects tend to favor localized charge whereas electronic effects tend to favor more symmetric structures. To test the accuracy of the M06/6-31+G(d)/SDD(Th) level, a different ECP was used with a bigger basis set. The MCDHF/ DC+B effective core potential (MDF) was used with the ECP60MDF basis set (contracted to 10s9p5d4f3g) for thorium56−58 and the TZVP basis set for all other elements.59,60 In addition, CCSD(T)=FULL/6-311G(2d,p)/SDD(Th) cal-

product complex/ symmetry

no. of H2O’s

binding energy CCSD(T)

binding energy M06

Δ

Δ/ H2O

[Th(H2O)9]4+ D3 [Th(H2O)9]4+ C2 [Th(H2O)10]4+ D2 ThO2(H2O) C1 ThO2(H2O)2 Cs ThO2(H2O)2 C1 ThO2(H2O)4 C2 ThO(OH)2(H2O) C1 ThO(OH)2(H2O)3 Cs Th(OH)4(H2O)2 Ci Th(OH)4(H2O)2 Cs

3 3 4 1 2 2 4 1 3 2 2

−173.4 −173.3 −206.8 −28.4b −56.0 −56.2 −103.3 −24.6 −77.9 −38.9 −37.1

−163.4 −164.1 −195.2 −22.4 −44.0 −44.1 −86.6 −19.7 −63.9 −33.3 −33.2

10.0 9.2 11.6 6.0 12.0 12.1 16.7 4.9 14.0 5.6 3.9

3.3 3.1 2.9 6.0 6.0 6.0 4.2 4.9 4.7 2.8 2.0

a

Single-point CCSD(T)=FULL/6-311G(2d,p)/SDD(Th) and M06/ 6-31+G(d)/SDD(Th) calculations at optimized M06 geometries. b The CCSD(T) energy (−28.4 kcal/mol) can be compared to highlevel theory (ref 110), which has been adjusted to ΔE with M06 zeropoint and thermal corrections (−25.1 kcal/mol).

thorium complexes that will be further discussed below. The purpose is to determine how accurately the M06 method reproduces H2O binding energies. In each case, a thorium complex is compared to one with one or more additional waters. For example, the first three entries of Table 1 give the binding of three or four water molecules to [Th(H2O)6]4+ to form [Th(H2O)9]4+ or [Th(H2O)10]4+, respectively (eq 3 and 4) [Th(H 2O)6 ]4 + + 3H 2O → [Th(H 2O)9 ]4 +

(3)

[Th(H 2O)6 ]4 + + 4H 2O → [Th(H 2O)10 ]4 +

(4)

From Table 1, it can be estimated that the standard DFT method underestimates the binding energy of H2O by about 5.0 kcal/mol per molecule. For that reason, H2O DFT bindings B


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Table 2. Calculated Aqueous Free Energies (kcal/mol) for Water Association To Form Thorium Complexes at the M06/631+G(d)/SDD(Th) Level oxidized Form Th4+ product complex

a

[Th(H2O)9]4+ [Th(H2O)10]4+ ThO2(H2O) ThO2(H2O)2 ThO2(H2O)4 ThO2(H2O)5 ThO(OH)2(H2O) ThO(OH)2(H2O)3 Th(OH)4(H2O)2 Th(NO3)4(H2O)3 Th(NO3)4(H2O)4 Th(OH) (NO3)3(H2O)3 ThF4(H2O)4 ThCl4(H2O)4 Th2(OH)2(NO3)6(H2O)6 Th(EDTA)(H2O)4 [Th6(OH)15(H2O)12]9+ [Th6O8(H2O)18]10+

b

no. of H2O’s

corr

3 4 1 2 4 5 1 3 2 3 4 1 4 4 2 4 12 18

−15.0 −20.0 −5.0 −10.0 −20.0 −25.0 −5.0 −15.0 −10.0 −15.0 −20.0 −5.0 −20.0 −20.0 −10.0 −20.0 −60.0 −90.0

reduced Form Th3+

ΔG (aq,298 K)

best estimated ΔG

ΔG (aq,298 K)

best estimated ΔG

14.0 17.5 2.1 5.0 −1.7 2.7 −22.9 −22.2 6.2 8.2 23.7 3.1 22.5 −23.9 −0.1 10.7 88.4 153.5

−1.0 −2.5 −2.9 −5.0 −21.7 −22.3 −27.9 −37.2 −3.8 −6.8 3.7 −1.9 2.5 −43.9 −10.1 −9.3 28.4 63.5

20.8 18.7

5.8 −1.3

0.0 −1.7

−10.0 −21.7

6.5 8.1 20.0 5.0 32.0 −0.4

−3.5 −6.9 0.0 0.0 12.0 −20.4

a Oxidized form listed, the charge of the reduced form is more negative by one electron. Values refer to the most stable form of the oxidized Th4+ and reduced Th3+ product complexes. bA correction of −5 kcal/mol per H2O is made to M06 free energies to compensate for underestimation of binding energies based on calculated energy differences at the CCSD(T)=FULL/6-311G(2d,p)/SDD(Th) and M06/6-31+G(d)/SDD(Th) levels.

will be corrected by 5.0 kcal/mol per water in the discussion below. Water Association to Thorium complexes. Water is known to associate with many different thorium compounds.22,29,35 In addition, the associated waters may favor one oxidation state over another. It can be very difficult to determine the number of water molecules in the first coordination sphere of a thorium compound. The aqueous free energies of association of one or more water molecules to thorium compounds are collected into Table 2. Further discussion of individual complexes will be provided below. The first two entries give the free energy of association of 3 or 4 water molecules to [Th(H 2 O) 6 ] 4+ (aq) and to [Th(H2O)6]3+(aq). The coordination number of Th4+ in water has been investigated by a number of authors, both experimentally and computationally.21,38−43,67 The preferred number varies between 8 and 12 with 9 or 10 being the most common number. The present work considers [Th(H2O)6]4+/3+, [Th(H2O)9]4+/3+, and [Th(H2O)10]4+/3+. The highest symmetry for coordination number (CN) = 9 was a tricapped trigonal prism in D3/C2 point groups and a bicapped square antiprism for CN = 10 in D2/C2 point groups. The C2-symmetry strctures of [Th(H2O)9]4+ and [Th(H2O)10]4+ had the lowest free energy in solution (Figure 1). For the ten-coordinate complex with 3+ charge, structures of D2, C2, and C1 symmetry were located with 3, 2, and 0 imaginary frequencies; however, when solvation effects were included, the D2-symmetry structure was most stable. In the bicapped square antiprism, the two capping waters had larger Th−O distances (2.875 Å) with more localized positive charges. The experimental Th−O distance for Th4+ in water is 2.45 Å. The calculated average Th−O distance in [Th(H2O)9]4+ and [Th(H2O)10]4+ (Table 3) are much larger (2.532 and 2.578 Å, respectively).

Figure 1. Optimized geometries of [Th(H2O)9]4+ and [Th(H2O)10]4+. The experimental structure (X-ray) is a bicapped square-antiprism for Th(H2O)10Br4 from ref 48.

Table 3. Average Th−O Distance in [Th(H2O)n]4+/3+, n = 6, 9, 10

a

n

+4(calc)

+4(exptl)a

+3(calc)

6 9 10

2.421 2.532 2.578

2.301 2.451 2.501

2.543 2.633 2.700

See ref 99 and Table 4.

It is interesting to note that addition of 3 or 4 waters to [Th(H2O)6]4+ is not predicted to be spontaneous until the 5 kcal/mol per water correction is included. It should be remembered that [Th(H2O)6]4+(aq), [Th(H2O)9]4+(aq), and [Th(H2O)10]4+(aq) are gas-phase clusters with implicit (SMD) solvation and are all models of Th4+(aq). Thus, the predicted spontaneous addition of water molecules indicates thorium− water clusters that have enhanced stability. As a cautionary note, SMD optimization of [Th(H2O)10]4+ produced an C


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The Journal of Physical Chemistry A Table 4. Computed Standard Reduction Potentials (V) of Some Thorium Compounds Relative to SHE 4+

[Th(H2O)6] [Th(H2O)9]4+ [Th(H2O)10]4+ Th(NO3)4 DOD(mmmm) D2da Th(NO3)4 CUB(ssss) D2da [Th(NO2)6]2− [Th(NO3)6]2− Th(NO3)4(H2O)3 Th(NO3)4(H2O)4 ThCp4 ThO2 ThO2(H2O)2 ThO2(H2O)4 Th(OH)4 Th(OH)4(H2O)2 Th2(OH)8(H2O)4 Th(OH)(NO3)3(H2O)2 Th2-μ-(OH)2(NO3)6(H2O)4 Th(OH)(NO3)3(H2O)3 Th(EDTA)(H2O)4 [Th2-μ-(OH)2(NO3)6(H2O)4]− ThF4 ThCl4 ThF4(H2O)4 ThCl4(H2O)4 Th(COT)2 Th(acac)4 D2 Th(acac)4 S4

unpaired spin (Th)b

SRP (V)

SO correctedc

0.99 1.04 1.09 0.44d/0.08 0.37d/0.09 0.54 0.38 0.12 0.13 1.14 0.81 0.89 0.88 0.70 0.67 0.27, 0.27 0.08 0.12, 0.00 0.13 0.92 0.28e 1.03 0.85 0.72 1.05 1.49 0.06 0.08

−2.36 −2.56 −2.09 −1.23d/-0.78 −1.08d/-0.65 −2.24 −2.11 −0.78 −0.63 −2.82 −3.55 −3.36 −3.56 −3.70 −3.80 −3.74 −1.08 −0.86 −0.78 −3.58 1.63 −3.43 −1.58 −3.72 −2.68 −2.68 −2.19 −2.00

−2.06 −2.25 −1.76 −1.10d/-0.76 −0.97d/-0.62 −2.08 −2.00 −0.74 −0.59 −2.48 −3.31 −3.09 −3.30 −3.50 −3.60 −3.58 −1.06 −0.82 −0.74 −3.30 1.59 −3.12 −1.33 −3.50 −2.36 −2.23 −2.17 −1.98

a

Two isomers of Th(NO3)4, both have D2d symmetry. See text. bUnpaired spin density on the reduced form (formally Th3+) at the M06/631+G(d)/SDD(Th) level. cSpin−orbit correction of the reduced form is taken as 0.30 V times unpaired spin density on thorium. dThe first value refers to the reduced formed with D2d symmetry where a nitrate ligand has not become pyramidal. eThe unpaired spin density is for the oxidized form (formally, Th3+/Th4+).

isolated Th4+ cation and ten distant water molecules. It appears that overestimation of SMD solvation of a bare Th4+ cation distorts the solvation-corrected potential energy surface of [Th(H2O)10]4+. As a reminder, all comparisons in the present study are for structures optimized in the gas phase with singlepoint solvation corrections. In comparing [Th(H2O)9]4+ and [Th(H2O)10]4+, water is predicted to spontaneously add to [Th(H2O)9]4+ by −1.5 kcal/ mol, thus suggesting a coordination number of ten for Th4+(aq). If Th4+(aq) is reduced to Th3+(aq), the tenth water is predicted to add spontaneously to [Th(H2O)9]3+ by −7.1 kcal/mol. The best explanation for the greater stability of [Th(H2O)10]3+ versus [Th(H2O)10]4+ (relative to the ninecoordinated species) can be seen in Table 3. The average Th− O distance in [Th(H2O)10]3+ is longer than in [Th(H2O)10]4+ (2.700 vs 2.578 Å), which means the waters will experience less interligand repulsion. It is interesting to point out that the X-ray structure of Th(NO3)4(H2O)n is known with three24 and with four68 water molecules coordinated to the thorium center. However, in a water−acetone mixture, a proton magnetic resonance study resulted in a hydration number of 2.9 for Th(NO3)4(H2O)n.69 From Table 2, it can be seen that the association of the fourth water to Th(NO3)4(H2O)3 is unfavorable (free energy) by 10.5 kcal/mol. The free energies of water association to two larger charged thorium complexes are considered (Table 2) in the

[Th6(OH)15(H2O)12]9+ and [Th6O8(H2O)18]8+ complexes where 12 and 18 water molecules are coordinated, respectively. The free energies of reaction are 28.4 and 63.5 kcal/mol, respectively, which indicates that either (1) the correction of 5 kcal/mol per water is not enough or (2) the full number of water molecules are not spontaneously bound in water at 298 K. For both complexes, the electronic binding energy of water association is quite negative (−63.2 and −64.2 kcal/mol per water, respectively). It should be noted that small errors in the computed very large solvation free energies of the charged complexes (ΔG(solv) = −3319.5 and −3219.5 kcal/mol for [Th6(OH)15]9+ and [Th6O8]8+, respectively) could affect the reliability of the calculated free energies of association. Standard Reduction Potential of Thorium Compunds. The most stable oxidation state of thorium is 4+, where the thorium center is 5f06d0. Th3+ is expected to have a 5f1 or perhaps a 6d1 configuration unless the attached ligands are involved in the reduction process, in which case the ligands are considered noninnocent. Though the spin−orbit correction for Th4+ is expected to be small, the correction for the reduced form with a 5f1 or 6d1 configuration may be much larger. Although the present calculations cannot claim quantitative accuracy, some accounting for spin−orbit correction should be made. That said, if the ligands (rather than thorium) are involved in the reduction process, the correction will be much different. Therefore, a correction will be made on the basis of the unpaired spin density on thorium in the reduced form. The D


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band reported by Klapötke and Schulz73 as the f → d transition for Th3+. If the SRP of HN3 (HN3 + 3H+ + 2e− → N2(g) + NH4+) is taken as E° = 2.079 V,75 the nonstandard reduction potential at pH = 3.5 would be 1.77 V. The present calculations would suggest that HN3 is (barely) a strong enough reducing agent to reduce [Th(H2O)10]4+ to [Th(H2O)10]3+ (E° = −1.76 V). The most negative calculated SRPs are associated with negatively charged, redox inactive ligands such as OH− and O2−, and EDTA4− where the values are more negative than −3.0 V. Ligands like H2O and Cp (C5H5−) produce values between −3.0 and −2.0 V. The fluoride and chloride thorium complexes, ThF4 and ThCl4,76,77 have surprisingly different SRP values of −3.12 and −1.33 V, respectively. A large contribution to the difference is differential solvation. The solvation free energy of [ThF4]− is −7.8 kcal/mol more negative than ThF4, whereas the solvation free energy of [ThCl4]− is −26.6 kcal/mol more negative than ThCl4. The increase of negative NPA charge65,66 of the halide upon reduction is much smaller for ThF4 compared to ThCl4 (−0.03 e− and −0.15 e−, respectively). The complexes [ThF 4 (H 2 O) 4 ] n , n = 0, 1−, and [ThCl4(H2O)4]n, n = 0, 1−, were also computed. The coordination of four waters to ThF4 is not sponantous (Table 2, ΔG(aq,298K) = 2.5 kcal/mol) but is quite spontaneous for ThCl4 (Table 2, ΔG(aq,298K) = −43.9 kcal/mol). Upon reduction, the coordination of four waters becomes less favorable for both [ThF4]− and [ThCl4]−. Similarly, the SRP for [ThF4(H2O)4] and [ThCl4(H2O)4] become more negative compared to the unhydrated complex (Table 4, ThF4, −3.12 → −3.50 V and ThCl4, −1.33 → −2.36 V). Redox active ligands such as NO2− and NO3− 78−81 give values between roughly −0.6 and −2.0 V. In systems where the ligands are redox active,82,83 the unpaired spin density on thorium is less than about 0.2 e−. The homoleptic complexes [Th(NO2)6]2− and [Th(NO3)6]2− display very different behavior from Th(NO3)4. In the hexacoordinated complexes, the nitrogen centers of the ligands remain essentially planar. In Th(NO3)4, on the contrary, one nitrate group becomes nonplanar and has significant unpaired spin density. Thus, the NO3− ligand is reduced to produce a NO32− ligand. The calculated redox potential of the isolated couple NO3−/NO32− has been reported to be about −1.1 V vs NHE,79 which suggests that the NO3− ligand in thorium nitrate complexes might be reduced before the thorium metal center. For the [Th(NO2)6]3− complex, 0.54 unpaired electron resides on thorium with the rest equally distributed on the six nitrite ligands. The acetylacetonate (acac) and 1,3,5,7-cyclooctatetraene (COT) ligands, Th(acac)484,85 and Th(COT)2,86−90 are expected to be somewhat noninnocent because each ligand contains empty π* orbitals which are capable of receiving an electron. Both SRP values are close to −2.0 V (−1.96 and −2.23 V, respectively). In the Th(acac)4 reduced complex, there is very little unpaired spin density on thorium (0.06 e−). In contrast, the unpaired spin density on the reduced form of Th(COT)2 is 1.49 e− on thorium, which is due to the fact that the two reduced COT ligands (COT)25− are both capable of donating electron density into the empty thorium orbitals. The NPA charge on thorium of Th(COT)2 decreases from 1.59 to 1.11 e− upon reduction, whereas the NBO population in the valence orbitals (8s/7p/6d/5f) shows an increase in the s and d

correction of 0.30 V times Th(unpaired spin) will be used to adjust the calculated SRP. The SRP of thorium (Th4+(aq)) has been estimated to be between −3.0 and −3.7 V.70−73 The computed SRP values for [Th(H2O)n]4+, n = 6, 9, 10, are tabulated in Table 4. The optimized structures of four Th4+ complexes are shown in Figure 2.

Figure 2. Optimized geometries of several thorium complexes and selected geometric parameters from available X-ray structures: ThCp4 (ref 99), ThEDTA(H2O)4 (ref 96), Th(NO3)4(H2O)3 (ref 15), and Th(NO3)4(H2O)4 (ref 49).

The calculated standard reduction potential (SRP) for [Th(H2O)n]4+(aq) varies from −2.25 to −1.76 V. The unpaired spin density on thorium is close to one electron (Table 4, 0.99−1.09 e−). The calculated SRP for Th4+ is significantly smaller than the estimated value in the literature of −3.7 V.70−73 The unpaired spin density on Th(H2O)n3+, n = 6, 9, 10, is largely localized in an f-orbital with 0.94, 0.79, and 1.00 electrons, respectively. The NPA charge on thorium in Th(H2O)n3+, n = 6, 9, 10, decreases as the number of water molecules increases: +2.27, +1.81, and +1.78, respectively. For comparison, the NPA charges on thorium in [Th(H2O)n]4+, n = 6, 9, 10, are +2.72, +2.15, and +2.06, respectively. Klapötke and Schulz73 used HN3 to reduce an aqueous solution of ThCl4 under N2 at pH = 3.5. The broad band centered at 460 nm in the UV/vis spectra was interpreted as the f → d transition for a trivalent Th complex (i.e., Th3+(aq)). Ionova et al.72 adopted a different interpretation of the 460 nm peak on the basis of their assumption that the SRP of Th4+ was too negative to be reduced by HN3 in aqueous solution. To shed light on the possibility of Th3+ in aqueous solution,74 the excited states [Th(H2O)9]3+ were calculated using TD-DFT28 at the M06/6-31+G(d)/SDD(Th) level. Two excitations were found at 475 and 474 nm with oscillator strengths of f = 0.012 which correspond to f → d transitions. Although the calculated excitations for [Th(H2O)10]3+ were not as definitive as the [Th(H2O)9]3+ results, both were consistent with the broad E


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The Journal of Physical Chemistry A populations upon reduction (0.13/0.24/1.34/0.44 → 0.29/ 0.21/1.81/0.36). An experimental reduction potential of −2.55 V versus Ag/AgClO4 has been reported for Th(acac)4.85 Stereochemistry. Different isomers arise in homoleptic complexes due to the different arrangement of the bidentate ligands around the metal center.20,91 For [Th(NO3)4]n, n = 0, 1−, the different isomers can be described by which vertexes are coordinated by the bidentate ligands in a dodecahedron (DOD), square antiprism (SAP), or cube (CUB). Three lower energy isomers were considered (Figures 3 and 4), one based

four bidentate ligands with either D2d or D4h symmetry. The Th(NO3)4 DOD(mmmm) D2d isomer and the CUB(ssss) D2d isomer have been observed for a complex of Plutonium using the bidentate ligand L = 3-hydroxy-2-methylpyran-4-one).93 The third Th(NO3)4 isomer with D4h symmetry has been observed by Smith and Raymond94 for a complex of thorium with L = i-PrN(O)C(O)-t-Bu.95 The CUB(ssss) D4h arrangement is less common, but examples are known for the actinides Th, U, and Pu, which may be due to the more favorable alignment of the ligand orbitals in CUB(ssss) with f-orbitals. Electronically, the DOD(mmmm) isomer is favored over the two CUB(ssss) isomers (D2d and D4h, Table 5). However, the aqueous free energy of the CUB(ssss) D4h isomer is only 0.5 kcal/mol less stable than the DOD(mmmm) D2d isomer. If the isolated Th4+ centers in the three Th(NO3)4 isomers are considered to have 5f06d0 occupation, then the ligands donate about 0.5 electrons into the 5f orbitals and between 0.84 to 0.95 electrons into the 6d orbitals. The 7s and 7p orbitals accept between 0.20 and 0.26 electrons, respectively. Electronically, the reduced form favors the DOD(mmmm) D2d isomer, but solvation effects strongly favor the CUB(ssss) D4h isomer. Presumably, the solvent-accessible surface above and below the molecular plane of the D4h isomer favors the greater solvation. The SRPs have been computed (Table 4) for each isomer type (Th(NO3)4 → [Th(NO3)4]−). However, the actual reduction may start with the DOD(mmmm) D2d isomer as the oxidized form and end with the CUB(ssss) D4h isomer as the reduced form which would make the SRP more positive by 0.09 V. For [ML6]2− isomers with bidentate ligands such as L = NO2− and NO3−, the two lowest energy isomers are referred to as Type I (Th symmetry) and Type II (D3 symmetry).96,97 The electronic energies and solution free energies of [Th(NO2)6]n, n = 2−, 3− (Table 5), are very similar for the two isomers. The free energy in solution favors the Type I isomer of [Th(NO2)6]2− by −2.4 kcal/mol, whereas the Type II isomer is favored for the reduced form ([Th(NO2)6]3−). Experimentally, both forms (Types I and II) can be found in the X-ray structure of [Th(NO2)6]2− with Th−O, N−O, and O−N−O parameters of 2.57 Å, 1.25 Å, and 114°. The calculated average distances for both isomers are 2.62 Å and 1.26 Å, and the angle is 113.0°. Very strong IR bands are calculated (gas phase) at 1367 cm−1 (Type I) and 1367−1384 cm−1 (Type II), which can be compared to observed bands96 for [Th(NO2)6]2− in acetonitrile at 1212 and 1305 cm−1. For [Th(NO3)6]n, n = 2−, 3−, the oxidized form favors Type I by ΔG(aq,298K) = −2.1 kcal/mol, and the reduced form favors the Type II isomer. It is interesting to note that that the O−N−O angle in the nitrate ligand is 115.6°, 2.6° larger than the corresponding angle in the nitrite complex. Experimentally, the increase is 2°.96 The Th(acac)4 complex84,85 also displayed two stereochemistries with similar energies. The D2-symmetry structure is −0.9 kcal/mol more stable than the S4-symmetry structure in energy, and the free energy difference in aqueous solution increases to −5.1 kcal/mol. The D2-symmetry structure is consistent with the published X-ray structure of [Th(C5H7O2)4]2·C6H5NH2 by Reeves and Smith.84 ThO2(H2O)n, n = 1, 2, 4, Reaction. The hydrolysis of actinide oxides has been of interest.30−34 The thorium oxide ThO2(H2O)4 can be converted into Th(OH)4(H2O)2 and condensed complexes98−100 such as Th2(OH)8(H2O)4 (or the protonated form [Th2(OH)2(H2O)10)]6+) as well as more condensed forms101−103 containing Th4 and Th6 cores (such as

Figure 3. Scheme showing three possible arrangements of four bidentate ligands around a metal center.

Figure 4. Optimized geometries of isomeric pairs: Th(NO3)4, [Th(NO2)6]2−, [Th(NO3)6]2−, and Th(acac)4. The experimental structure (X-ray) for Th(acac)4 is from ref 84.

on a dodecahedron (DOD(mmmm)) and two based on a cube (CUB(ssss)) where the naming convention used by Hay et al.92 is used. The latter two isomers differ in the arrangements of the F


Article

The Journal of Physical Chemistry A Table 5. Comparison of Relative Energies of Th(NO3)4,a [Th(NO2)6]2−, and [Th(NO3)6]2− Th(NO3)4 DOD(mmmm) D2d Th(NO3)4 CUB(ssss) D2d Th(NO3)4 CUB(ssss) D4h [Th(NO2)6]2− Th [Th(NO2)6]2− D3 [Th(NO3)6]2− Th [Th(NO3)6]2− D3 Th(acac)4 S4 Th(acac)4 D2

Th4+

Th3+ b

Th3+/NO3 pyc

0.0(0.0) 5.2(3.7) 2.6(0.5) 0.0(0.0) −0.1(2.4) 0.0(0.0) 0.0(2.1) 0.0(0.0) −0.9(−5.1)

0.0(0.0) 4.1(0.3) 6.8(−2.0) 0.0(0.0) 0.0(−0.2) 0.0(0.0) −0.8(−3.3) 0.0(0.0)e 0.1(0.9)e

0.0(0.0) 5.2(0.7) d

The first value is the relative electronic energy at M06/6-31+G(d)/Th(SDD) and the value in parentheses is the relative aqueous free energy at 298 K. bReduced form where all nitrito/nitrato ligands are planar. cReduced form where a single nitrato ligand has become pyramidal. The distortion of [Th(NO3)4]− reduces the electronic energy of DOD(mmmm) by −6.9 kcal/mol (D2d → Cs) and of CUB(ssss) by −5.8 kcal/mol (D2d → C1) d Rearranges to [Th(NO3)4]− DOD(mmmm) Cs with one pyramidal NO32− ligand. eThe reference structure for the reduced form of Th(acac)4 has C1 symmetry. a

[Th4(OH)6(H2O)12)]10+) and [Th6(OH)14(H2O)12)]10+). Theoretical calculations have played an important role.104−109 Very recently, Dixon and co-workers110 have studied (among other actinide oxides) the conversion of ThO2(H2O) to ThO(OH)2 using a variety of high-level theoretical methods (Figure 5a). In Table 6, the values are compared for the

thermal corrections from M06 are applied to the reported ΔH(298K) results, then the agreement with the present results is quite good. The M06 geometries of ThO2(H2O) and Th(OH)2 were also compared with the CCSD(T) geometry of Dixon and co-workers.110 The Th−O distances were within 0.05 Å, and the O−Th−O angles were within 0.2°. The NBO charge on thorium and the 5f and 6d populations at the PW91 level109 for ThO2(H2O) (2.04, 0.69, 1.32) and ThO(OH)2 (2.30, 0.59, 1.17) agrees well with the M06 results (ThO2(H2O) 2.06, 0.68, 1.26; ThO(OH)2 2.33, 0.52, 1.13). The good agreement suggests that the M06 level with a modest basis set can generate reasonable charge distributions. The hydrolysis of ThO2(H2O)2 follows a similar path, but now two transition states are required to reach the Th(OH)4 product (Table 6 and Figure 5b, TS2 and TS3). The two protonmigrating steps both have low activation barriers. In ThO2(H2O)4, two of the waters are tightly coordinated (Th−O, 2.609 Å) and two waters are coordinated to the tight water and to the oxo ligands (Figure 5c). In the first mechanism, the uncoordinated water becomes bound to the thorium center as a proton is transferred to an oxo ligand. This is called the “direct” mechanism. In the second mechanism, an uncoordinated water remains uncoordinated and transfers a proton to an oxo ligand while accepting a proton from a tight water. This is the “relay” mechanism. The “direct” mechanism is about 1 kcal/mol lower in free energy. Several ThO(OH)2(H2O)3 structures were optimized. The lowest freeenergy structure has Cs symmetry and is characterized by two tight waters and one loose water. The loose water is hydrogen bonded to the oxo ligand (O--H, 1.623 Å) and to two highly coordinated waters (O--H, 1.870 Å). For the second step, two “direct” transition states and one “relay” transition state (TS5ac) were located. In the first two “direct” transition states, the uncoordinated water approaches the thorium center with short O--H distances (1.278 Å, TS5a; 1.261 Å, TS5b). The stability order between TS5a and TS5b changes when entropy and solvation effects are included. The most favorable transition state is TS5c (“relay”), which is 5.5 kcal/mol lower than TS5b in free energy. The Cs-symmetry transition state appears to be forming the [Th(OH)3(H2O)2][OH] ion pair. However, after the transition state, the nascent hydroxyl anion abstracts a proton from water to form Th(OH)4(H2O)2. It would be difficult to distinguish between the two mechanisms by experiment. Both mechanisms have low barriers indicating that hydrolysis should be facile.

Figure 5. Aqueous free energy diagram for reactions of (a) ThO2(H2O), (b) ThO2(H2O)2, and (c) ThO2(H2O)4.

hydrolysis of ThO2(H2O)n, n = 1, 2, 4. The activation energies (ΔE) for the ThO2(H2O) reaction at the CCSD(T), MO6/ TZVP/MDF(Th), and M06/6-31+G(d)/SDD(Th) levels are very similar (5.2, 5.4, and 8.0 kcal/mol, respectively. The CCSD(T) values for ThO2(H2O) can be compared with the results of Dixon and co-workers.110 If the zero-point and G


Article

The Journal of Physical Chemistry A Table 6. Comparison of Thermodynamic Values for the Hydrolysis Reactions of ThO2(H2O)n, n = 1, 2, 4 CCSD(T) 6-311G(2d,p)/SDD(Th)

M06/TZVP/MDF(Th)

ΔE

ΔE

ΔE

ΔH(298K)

ΔG(aq,298K)

0.0 5.4 −34.1

0.0 8.0 −31.1 0.1 0.0 6.4 −29.1 −22.3 −63.5 0.0 0.4 6.7 7.9 −30.7 −23.1 −21.5 −28.1 −54.2

0.0 4.5 −32.5 −1.0 0.0 3.1 −30.5 −27.5 −67.1 0.0 0.0 3.2 2.9 −32.4 −28.0 −26.6 −33.3 −57.1

0.0 1.0 −25.2 3.4 0.0 0.1 −24.9 −19.4 −38.5 0.0 0.7 4.8 5.6 −17.3 −8.8 −11.6 −17.1 −30.8

n ThO2(H2O) TS1 ThO(OH)2 ThO2(H2O)2 C2 ThO2(H2O)2 Cs TS2 ThO(OH)2(H2O) TS3 Th(OH)4 ThO2(H2O)4 C2 ThO2(H2O)4 Cs TS4a direct TS4b relay ThO(OH)2(H2O)3 TS5a direct TS5b direct TS5c relay Th(OH)4(H2O)2

1 1 1 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4

a

0.0 5.2a −38.5a 0.2 0.0 4.3 −35.2 −33.4 −81.0 0.0

0.0 −32.0 −71.6 0.0

−41.5

−33.9

−71.0

−60.8

M06/6-31+G(d)/SDD(Th)

The ΔH(298K) values at high-level theory by Dixon and co-workers (ref 110) at the CCSD(T)/CBS(aw-CVnXZ/PW91+SO+ECP correction are 0.0, +1.8, and −38.4 kcal/mol. If corrected to ΔE using the M06 vibrational frequencies, the values become 0.0, +5.3, and −36.9 kcal/mol, respectively. a

Table 7. Aqueous Free Energies (kcal/mol at 298 K) of Reaction for Hydrolysis plus Condensation Reactionsa corr + nonstandard [H+]c pH = 0

pH = 3

pH = 7

pH = 11

hydrolysis reaction

ΔG(aq)

corrb

ΔG(aq)

ΔG(aq)

ΔG(aq)

ΔG(aq)

[Th(H2O)10]4+ → Th(OH)4(H2O)2 + 4H3O+ 2[Th(H2O)10]4+ → [Th2(OH)2(H2O)10]6+ + 2H3O+ + 6H2O 3[Th(H2O)10]4+ → [Th3(OH)6(H2O)9]6+ + 6H3O+ + 9H2O 3[Th(H2O)10]4+ → [Th3O(OH)4(H2O)9]6+ + 6H3O+ + 10H2O 4[Th(H2O)10]4+ → [Th4(OH)6(H2O)12]10+ + 6H3O+ + 16H2O 4[Th(H2O)10]4+ → [Th4(OH)8(H2O)12]8+ + 8H3O+ + 12H2O 6[Th(H2O)10]4+ → [Th6O4(OH)4(H2O)18]12+ + 12H3O+ + 22H2O 6[Th(H2O)10]4+ → [Th6(OH)14(H2O)12]10+ + 14H3O+ + 20H2O 6[Th(H2O)10]4+ → [Th6(OH)15(H2O)12]9+ + 15H3O+ + 18H2O 6[Th(H2O)10]4+ → [Th6O8(H2O)18]8+ + 16H3O+ + 18H2O

45.7 −13.2 −1.7 11.2 −56.3 −8.9 19.1 69.3 82.6 73.5

0.0 30.0 45.0 50.0 80.0 60.0 110.0 100.0 90.0 90.0

45.7 16.8 43.3 61.2 23.7 51.1 129.1 169.3 172.6 163.5

29.3 8.6 18.8 39.3 −0.8 18.4 80.0 112.1 111.3 98.1

7.5 −2.3 −13.9 4.7 −33.5 −25.2 14.6 35.7 29.5 10.8

−14.3 −13.2 −46.7 −28.8 −66.3 −68.9 −50.9 −40.7 −52.3 −76.5

a Free energies in water at the M06/6-31+G(d)/SDD(Th) level. bCorrection of 5.0 kcal/mol per uncoordinated water applied to product. cAqueous free energies after correction due to number of water molecules not coordinated in reactants plus nonstandard [H+].

The overall hydrolysis reactions involving [Th(H2O)10]4+ are given in Table 7. The free energies of reaction are too low (too spontaneous) due to the underestimation of the Th−water interaction at the M06 level. A correction of 5.0 kcal/mol for each uncoordinated water is made in Table 7. At pH = 0 (standard [H+]), all reactions are nonspontaneous. If a correction is made to the free energy for nonstandard H+ concentrations, the free energies become more spontaneous as the pH increases. At pH = 7, most of the reactions are spontaneous, and at pH = 11 all of the reactions are spontaneous. Two [Th4(OH)6(H2O)12]10+ complexes are optimized, one with Td symmetry and one with T symmetry, 26.7 kcal/mol lower in energy. Solvation effects are very large (>3500 kcal/ mol) and differential solvation favors the Td structure, which becomes 18.8 kcal/mol lower in aqueous free energy. The Th− Th, bridging Th−OH, and Th−water distances for the Tdsymmetry structure are 4.880, 2.516, and 2.435 Å, respectively. The largest condensation complexes studied are the hexamers

[Th(OH)15(H2O)12]9+ with C3h symmetry and [Th6(OH)14(H2O)12]10+ with S6 symmetry (Figure 6). The structure of the [Th(OH)15(H2O)12]9+ complex is based on a hexagonal prism of thorium atoms with bridging OH groups and one terminal and two waters coordinated at each metal center. The structure of the [Th6(OH)14(H2O)12]10+ complex is characterized with eight μ3 (capping) hydroxides and six terminal hydroxides with Th−O distances of 2.699 Å (average) and 2.014 Å, respectively. The 12 Th−water distances are 2.491 Å, and the 12 Th−Th distances are 4.516 Å. In addition, the [Th6O4(OH)4(H2O)18]12+ complex was computed because a very similar cluster Th6O4(OH)4(H2O)6(HCOO)12·nH2O is known.108,109 Dinuclear Complexes. Because dimerization free energy changes will be considered below, benchmarking dimerization is appropriate (Table 8). Examples of two thorium centers bound by two oxygen atoms and two hydroxyl groups (dioxo and dihydroxyl) are known. The dimerzation 2ThO(OH)2 → Th2-μ-(OH)2(O)2(OH)2 is underestimated by about 12.0 kcal/ H


Article


In the discussion below, a correction will be added to the DFT results in light of the CCSD(T) calculations. Specifically, dimerization reactions where a dihydroxyl linkage is formed will be made more exothermic by 12.0 kcal/mol and dimerization reactions where a dioxo linkage is formed will be made more exothermic by 24.0 kcal/mol. Two dimerization reactions are given in eqs 5 and 6 (Figure 7). Equation 6 forms the dimer Th2-μ-(OH)2(NO3)6(H2O)6, 2Th(OH)(NO3)3 (H 2O)2 → Th 2‐μ‐(OH)2 (NO3)6 (H 2O)4 (5)

2Th(OH)(NO3)3 (H 2O)3 → Th 2‐μ‐(OH)2 (NO3)6 (H 2O)6 (6)

a known compound,111 which is calculated to be spontaneous by only −1.2 kcal/mol in water. When the correction is added (Table 8), the reaction becomes spontaneous by −13.2 kcal/ mol, which is more reasonable. The stepwise two-electron reduction of Th 2 -μ(OH)2(NO3)6(H2O)4112 produces a pyramidal nitrate ligand in the first step with substantial unpaired electron density on one oxygen atom (Figure 8). In that sense, it resembles a Th4+/ Th4+ complex with a NO32− dianion rather than a Th4+/Th3+ dinuclear complex with a NO3− ligand. Reducing this complex in the second step causes the NO32− ligand to undergo dissociative electron transfer.113,114 The elongated N−O bond of the NO32− ligand is broken (eq 7) to produce a nitrite ligand NO2− NO32 − + e− → NO2− + O2 − Figure 6. Optimized geometries of hydrolysis condensation products: [Th(OH)(H2O)5]3+, [Th2(OH)2(H2O)10]6+, [Th2(OH)3(H2O)6]5+, [Th4(OH)6(H2O)12]10+, [Th3(OH)7(H2O)6]5+, [Th6(OH)14(H2O)12]10+, and [Th6(OH)15(H2O)12]9+.

(7)

2−

and an oxo ligand O . The triplet product of two stepwise reductions [Th2-μ-(OH)2(NO3)6(H2O)4]2− (67.3 kcal/mol higher in aqueous free energy than the singlet state) resembles a Th3+/Th3+ complex with substantial unpaired spin density on both thorium centers. Overall, the sum of the first and second reduction potentials of Th2-μ-(OH)2(NO3)6(H2O)4 (−0.82 and +1.59 V, Table 4) indicates a favorable process. EDTA Formation Constant. The hexadentate ethylenediaminetetraactetate (EDTA4−) is an excellent coordinating ligand. The experimental formation constant (log K) for Th(EDTA)115−118 (see Figure 2 for the optimized structure

mol. For the 2ThO2 → Th2O4 dimerization, two dioxo products were considered, trans (C2h symmetry) and cis (C2v symmetry). DFT and CCSD(T) agree that the trans product is slightly more stable by 1.0 and 0.5 kcal/mol, respectively. However, the CCSD(T) results indicate that the reaction is much more exothermic compared to DFT results.

Table 8. Calculated Free Energy Changes ΔG(aq,298K) for Dimerization of some Thorium Compounds dimerization reaction/symmetry of product

CCSD(T)a

M06a

2ThO2 → Th2O4 C2h 2ThO2 → Th2O4 C2v 2ThO(OH)2 → Th2(O)2(OH)4 D2h 2ThO(OH)2 → Th2(OH)2(O)2(OH)2 Ci 2ThO(OH)2 → Th2(OH)2(O)2(OH)2 C2 2Th(OH) (NO3)3(H2O)2 → Th2(OH)2(NO3)6(H2O)4 Ci 2Th(OH) (NO3)3(H2O)3 → Th2(OH)2(NO3)6(H2O)6 Ci 2Th(OH)4(H2O)2 → Th2(OH)8(H2O)4d C2 2ThO2(H2O)4 → Th2O4(H2O)8 Ci [Th(OH)2(NO3)3(H2O)2]0,− → [Th2(OH)2(NO3)6(H2O)4]− C1 2[Th(OH)(H2O)5]3+ → [Th2(OH)2(H2O)10]6+ D2 2[Th2(OH)3(H2O)6]5+ → [Th4(OH)6(H2O)12]10+ Td 2[Th3(OH)7(H2O)6]5+ → [Th6(OH)14(H2O)12]10+ S6

−113.8 −108.6 −114.5 −59.9 −60.9

−90.4 −86.1 −86.7 −48.8 −49.3

e

Δ

ΔG(aq,298K)

corr

best estimate ΔG

23.4 22.5 27.8 11.1 11.6

−26.5 −23.0 −17.0 −0.9 −0.6 5.1 −1.2 −6.1 −12.3 0.0 6.5 −21.0 33.0

−24.0 −24.0b −24.0b −12.0c −12.0c −12.0c −12.0c −12.0c −12.0c −12.0c b

−50.5 −47.0 −41.0 −12.9 −12.6 −6.9 −13.2 −18.1 −24.3 −12.0

a

Single-point CCSD(T)=FULL/6-311G(2d,p)/SDD(Th) and M06/6-31+G(d)/SDD(Th) calculations at optimized M06 geometries. bCorrection for association of two ThO units to form a Th2O2 unit based on comparisons of M06 results with the CCSD(T) level calculation. cCorrection for association of two Th(OH) units to form a Th2(OH)2 unit based on comparisons of M06 results with the CCSD(T) level calculation. dThe Th2(OH)8(H2O)4 dimer in C1 symmetry has been reported in ref 33. eThe calculated enthalpy of reaction at 298 K has been reported to be −100.8 kcal/mol (ref 104). I


Article


Figure 7. Monomers and dimer of Th(OH)(NO3)3(H2O)2 and Th(OH)(NO 3 ) 3 (H 2 O) 3 are shown. The X-ray structure of Th2(OH)2(NO3)6(H2O)4 is from ref 89. The X-ray structure of Th2(OH)2(NO3)6(H2O)6 is from ref 90.

Figure 8. Singly reduced dinuclear complex [Th2(OH)2(NO3)6(H2O)44]− (top), and doubly reduced dinuclear complex [Th2(OH)2(NO3)6(H2O)4]2− as a singlet (middle) and triplet (bottom).

of ThEDTA(H2O)4 and ref 118 for the X-ray structure) is 25.3, which gives ΔG = −34.5 kcal/mol using ΔG(aq,298K) = −RT ln K. Three reactions are considered where the protonation state of the complex is altered. In reaction eq 8a, the H4EDTA ligand is neutral, in reaction eq 8b, the H2EDTA2− ligand is zwitterionic with the two nitrogen centers protonated and the four carboxyl groups unprotonated; in reaction 8c, the ligand is a tetra-anion. In reactions 8a and 8b, the free energy is corrected for nonstandard conditions of H3O+ by assuming pH = 7. This leads to a correction of −38.2 kcal/mol for eq 8a and −19.1 kcal/mol for eq 8b. The experimental pKa’s found for H4EDTA are 1.99, 2.67, 6.16, and 10.26.

[Th(NO2 )6 ]2 − + 6NO3− → [Th(NO3)6 ]2 − + 6NO2− ΔG(aq) = 23.8 kcal/mol Th(OH)4 (H 2O)2 + 4H3O+ + 4NO3− → Th(NO3)4 (H 2O)3 + 7H 2O

Equations 9−11 involve the nitrate and/or nitrite ligands. Experimentally, it is known that nitrates of thorium can be formed by dissolving Th(OH)4 in nitric acid (eq 11). Nonzero Dipole Moment of ThCp 4 . The ThCp 4 complex119−123 has a permanent electric dipole moment at 20 °C in benzene of 1.18 ± 0.05 D, which is inconsistent with the calculated molecular structure of S4 symmetry.121 To investigate the origin of the nonzero dipole moment, a series of constrained optimizations were made where the five Th−C distances to one ring were fixed to 2.90, 3.00, 3.10, 3.20, and 3.30 Å, and all other geometric parameters were optimized. The average Th−C distance in the S4-symmetry structure is 2.885 Å, but the Th−C distances are not all the same. For that reason, the constrained structure with all Th−C distances of one ring fixed to 2.90 Å is taken as the reference. Solvation effects in benzene and water are computed for each optimized structure. The results are displayed in Figure 9 and Table 9. As seen in Table 9, the electronic energy increases as one ring moves away

ΔG(aq) = −37.8 kcal/mol (8a)

[Th(H 2O)10 ]4 + + H 2EDTA2 − → Th(EDTA)(H 2O)4 + 4H 2O + 2H3O+

ΔG(aq) = −24.1 kcal/mol (8b)

4+

[Th(H 2O)10 ] + 6H 2O

4−

+ EDTA → Th(EDTA)(H 2O)4 ΔG(aq) = −43.7 kcal/mol

(8c)

[Th(H 2O)10 ]4 + + 4NO3− → Th(NO3)4 (H 2O)3 + 7H 2O ΔG(aq) = 12.3 kcal/mol

ΔG(aq) = −33.4 kcal/mol (11)

[Th(H 2O)10 ]4 + + H4EDTA → Th(EDTA)(H 2O)4 + 2H 2O + 4H3O+

(10)

(9) J


Article


on the Cp rings, the bonding can be described as substantial donation from the Cp rings into the empty valence orbitals of thorium, which is supported by the NPA charge on thorium (+1.19). The NBO analysis indicates that the rather than one electron in a thorium d or f orbital, the unpaired spin density is spread into the s, p, d, and f valence orbitals, which suggests that the empty valence orbitals on thorium are acting as acceptor orbitals for electron density.

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CONCLUSION

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ASSOCIATED CONTENT

The aqueous redox chemistry of thorium 4+ has been explored. In addition, the hydrolysis of ThO2(H2O)n, n = 1, 2, 4, and the nonzero dipole moment of ThCp4 in benzene have been studied. The economical M06/6-31+G(d)/SDD(Th) method is able to rationalize a wide range of thorium properties. The standard reduction potential of Th4+(aq) is predicted to be about −2.0 V, which is much smaller than previous estimates. The DFT method predicts very similar stability for different arrangements of ligands in the homoleptic complexes Th(NO3)4, Th(NO2)62−, Th(NO3)62−, and Th(acac)4. The value of the reduction potential depends strongly on whether the ligands are noninnocent or not. The structures of several condensed thorium hydroxides are calculated to quite stable in basic solution. The structure of the [Th6(OH)15]9+ complex, a known prominent condensed species, is predicted to have a trigonal prism core with 12 waters of hydration (i.e., [Th6(OH)15(H2O)12]9+). In conclusion, carefully calibrated DFT calculations on aqueous thorium complexes can provide useful information.

Figure 9. Plot of free energy in benzene and water of ThCp4 as a function of the Th−C distances to one ring. All other geometric parameters are optimized.

from thorium. In benzene, at a fixed Th−C distance of 3.00 Å, the dipole moment is 1.12 D, and the free energy is 0.7 kcal/ mol lower than the reference. For Th−C fixed distances in the range 3.10−3.30 Å, the increase in the energy of distortion is not compensated by the increase in solvation in benzene. In water, the solvation effect is greater and compensates for the distortion even at Th−C distances of 3.30 Å, where the dipole moment in water is predicted to be 5.55 D. The free energy for loss of one C5H5− ring is calculated to be −8.3 kcal/mol. The stability of the fourth ring of ThCp4 in water may be underestimated because the M06 method underestimates Th−water binding by about 5 kcal/mol. The dipole moment of ThCp4 is known to be temperaturedependent. The computed entropy increases as the thorium− ring distance increases (Table 9). This suggests that the −TΔS contribution to the free energy may explain the temperature dependence of the dipole moment. There is 1.14 e− unpaired spin density on thorium in ThCp4−. The breakdown of the unpaired spin density is 0.14s, 0.19p, 0.28d, and 0.53f. Because there is substantial spin density

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b08472. Complete refs 62 and 64, point groups, electronic states, total energies, zero-point energies, imaginary frequencies, thermal corrections to 298 K, entropies, and solvation free energies (Table S1) at the M06/6-31+G(d)/ SDD(Th) level, energies of thorium compounds at the CCSD(T)=FULL/6-311G(2d,p)/SDD(Th) level (Table S2), Cartesian coordinates of relevant species (Table S3) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*M. L. McKee. Phone: +1 334-844-6985. E-mail: mckeeml@ auburn.edu.

Table 9. Geometry Parameters and Thermal Dynamic Properties of ThCp4 Where the Th−C Distances to One Ring Is Fixed Th−Cp fixeda

Th−Cp av optb

ΔEc

entropyd

ΔG(benzene,298K)

DM

ΔG(water,298K)

DM

S4 2.885 2.90 3.00 3.10 3.20 3.30 ThCp3+/Cp−

2.885 2.885 2.870 2.859 2.849 2.839 2.771

−0.2 0.0 1.3 3.9 7.5 11.6 151.7

141.51 143.24 145.11 146.27 143.98e 146.16e 188.62

−0.2 0.0 −0.7 0.6 1.9 3.5 63.4

0.00 0.14 1.12 2.12 3.13 4.11

−2.6 0.0 −3.4 −4.8 −7.1 −9.7 −8.3

0.00 0.20 1.54 2.89 4.25 5.55

The minimum ThCp4 structure has S4 symmetry. For the other entries, the Th−C distances to one ring are fixed. bThe average Th−C distance to the other three rings. cEnergies at the M06/6-31+G(d)/SDD(Th) level. dUnits of cal/(mol·K). eOne calculated imaginary frequency. a

K


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The Journal of Physical Chemistry A Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding for this project was provided in part by Auburn University Department of Chemistry and Biochemistry and was supported by the Defense Threat Reduction Agency, Basic Research Award No. HDTRA1-11-1-0044, to Auburn University. The authors are grateful for computer time provided by the Alabama Supercomputer Center.

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