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Oct 14, 2016 - ABSTRACT: The water exchange reaction of the americyl(VI) aqua ... electron correlation, near-degeneracy, and spin−orbit coupling, ar...
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Quantum Chemical Study of the Water Exchange Mechanism of the Americyl(VI) Aqua Ion Alberto Fabrizio and François P. Rotzinger* Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 6, CH-1015 Lausanne, Switzerland S Supporting Information *

ABSTRACT: The water exchange reaction of the americyl(VI) aqua ion was investigated with quantum chemical methods, density functional theory (DFT), and wave function theory (WFT). Associative and dissociative substitution mechanisms were studied, whereby DFT produced inaccurate results for the associative mechanism in contrast to WFT. The Gibbs activation energies (ΔG‡) for the dissociative (D) and the associative interchange (Ia) mechanisms, computed with WFT taking into account static and dynamic electron correlation, near-degeneracy, and spin−orbit coupling, are equal within the error limits of the calculations. ΔG‡ for the water exchange of americyl(VI) via the dissociative mechanism is considerably lower than those for uranyl(VI) and plutonyl(VI) (for which the Ia mechanism is preferred) due to ligand-field effects. On the basis of the present computations, it is not possible to distinguish the Ia from the D mechanism for americyl(VI). In contrast to two other theoretical studies, the dissociative mechanism cannot be ruled out.

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INTRODUCTION The water exchange reaction of the uranyl(VI) and plutonyl(VI) aqua ions, reaction 1, proceeds via an associative mechanism, most likely the concerted associative interchange one (Ia).1−4

The americyl(VI) aqua ions involved in the water exchange reaction (reaction 1) exhibit a 5f 3 electron configuration, fδ2fϕ1, with a degenerate or near-degenerate ground state. Furthermore, the two states with a fδ1fϕ2 electron configuration lie close. Hence, in addition to static (and dynamic) correlation, near-degeneracy effects have to be considered as well. The two near-degenerate states furthermore give rise to non-negligible SO coupling. The energies of these four near-degenerate states are close. In such cases, single-state methods might be inappropriate. Instead, multistate techniques should be used as for genuine degenerate states. Pressure-dependent 17O NMR measurements on radioactive compounds are demanding and have not been reported thus far. Hence, experimental data are not available for the water exchange reaction of the americyl(VI) aqua ion, but two theoretical studies.6,7 In a quantum chemical investigation by Vallet et al.,6 the associative (A) mechanism was found to be favored by about 45 kJ mol−1 over the dissociative (D) one. This conclusion was based on the energies of the intermediates AmO2(OH2)42+ and AmO2(OH2)62+ for the D and the A mechanisms, respectively, whose relative energies might differ from those of the respective transition states. They optimized the geometries with Hartree−Fock (HF) in the gas phase, and calculated the energies with MP2, also in the gas phase. Static electron correlation, near-degeneracy, and SO effects as well as hydration were neglected, whereby the authors stated that SO contributions were negligible. In classical molecular dynamics

AnO2 (OH 2)52 + + H 2O → AnO2 (OH 2)4 OH 2 2 + + H 2O (An = U, Pu, Am)

(1)

For the uranyl(VI) ion it was shown that a proper treatment of static electron correlation is necessary to obtain a Gibbs activation energy (ΔG‡) agreeing with experiment,2,4 since, with density functional theory (DFT), an accurate ΔG‡ value could not be obtained.4 In fact, this is not surprising, since the adjustable parameters of functionals are optimized using databases, which do not contain actinides (and other heavy elements). Static electron correlation arises from configurations exhibiting larger CI coefficients than those involved in dynamic correlation. They give rise to natural orbital occupations deviating more strongly from 0 and 2 as shown in Figures 1 and 2 of ref 5. Their energies are high, and near-degeneracy is absent.5 For the uranyl(VI) and plutonyl(VI) ions, ΔG‡ calculated for the dissociative pathways (D or Id) is higher by more than 15 kJ mol−1 (compared to the associative mechanism).4 The 5f shell of these two ions is occupied by 0 and 2 electrons. Thus, for the species participating in reaction 1, the two degenerate or neardegenerate fδ molecular orbitals (MO) are empty for uranyl(VI) or half-filled for plutonyl(VI). This is the reason why spin−orbit (SO) effects are negligible.4 © XXXX American Chemical Society

Received: July 25, 2016

A

DOI: 10.1021/acs.inorgchem.6b01793 Inorg. Chem. XXXX, XXX, XXX−XXX

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to eliminate rotational and translational contaminants.23 Because of the presence of static correlation, the geometries and frequencies were also calculated with single-state and four-state multiconfiguration selfconsistent-field (MCSCF) methods (including CPCM16−18 hydration) based on the occupationally restricted multiple active space (ORMAS)24 technique with an active space composed of three subspaces. For single-state MCSCF, the two σ(AmO) and the four π(AmO) MOs formed the first active space, the lowest three 5f MOs (two fδ and one fϕ) formed the second active space, and the two σ*(AmO) and the four π*(AmO) MOs formed the third active space. Between all three subspaces, singles−doubles excitations were allowed. These calculations are abbreviated as MCSCF(10−12/6,1− 5/3,0−2/6,15), whereby 15 is the number of electrons in the active space.12 Since the ground states are degenerate or near-degenerate, and two excited states lie close to the ground state, four-state MCSCF geometry optimizations were also performed, whereby the second active space involved four 5f MOs (two fδ and two fϕ), abbreviated as 4st-MCSCF(10−12/6,1−5/4,0−2/6,15). For the four-state computations, the gradients had to be computed numerically and, therefore, frequency computations were prohibitive. Because of the similar MCSCF and 4st-MCSCF geometries and electronic energies (see below), the thermal corrections (for 25 °C) were based on the singlestate MCSCF vibrational frequencies. For all of the geometries, DFT, MCSCF, and 4st-MCSCF, the electronic energies were calculated using the extended general multiconfiguration quasi-degenerate second-order perturbation theory (XGMC-QDPT2),25−29 at the four-state level, 4st-XGMC-QDPT2(10−12/6,1−5/4,0−2/6,15), whereby the 6s and 6p MOs of Am were included in the PT2 treatment. The SO energy was evaluated based on the 4st-MCSCF wave function using SO configuration interaction (SO-CI) with a (3/4) active space (the three 5f electrons in the two fδ and two fϕ MOs) involving four quartet and six doublet states. The hydration energy was calculated using the conductor polarizable continuum model (CPCM).16−18 The CPCM cavity was constructed based on Batsanov’s30 van der Waals radii, whereby, for Am, the same value as for U and Pu was taken. A finer tessalation than the default was used (ntsall = 960, the default is 60). At the WFT level, the hydration energy was computed with 4st-MCSCF(10−12/6,1−5/ 4,0−2/6,15)-CPCM. In the calculation of the thermal corrections to the Gibbs energy (G or G‡), the energy difference (Δε) between the first and the second state of the near-degenerate ground state was taken into account using eq 2, whereby qel is the electronic partition function, g0 is the degeneracy (spin-multiplicity) of the ground state, g is that of the first excited state, kB is Boltzmann’s constant, T is the absolute temperature, and R is the gas constant.

(MD) simulations of the actinyl(VI) and actinyl(V) aqua ions, Tiwari et al.7 suggested an associative mechanism for the water exchange of the former and a dissociative one for the latter ions. It should be noted that ΔG‡ for uranyl(VI) was underestimated by more than 10 kJ mol−1 and that for americyl(VI) ΔG‡ was calculated as 29.7 kJ mol−1. The question whether classical MD simulations are suitable for the treatment of asymmetrically occupied shells with fδ1 and fδ2fϕ1 electron configurations and near-degenerate energies remained open. In the present study, reaction 1 of the americyl(VI) ion was investigated with DFT and wave function theory (WFT), taking into account static and dynamic correlation, degeneracy or near-degeneracy, SO coupling, and hydration.

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COMPUTATIONAL DETAILS

The calculations were performed with the GAMESS programs.8,9 For Am, Karlsruhe def-TZVP basis sets10 without g function, and the corresponding small-core effective core potentials (ECP)11 with Z = 60 were used. Since GAMESS does not support ECP h functions, a modified4 version thereof (Supporting Information) was used. For O and H, modified12 Karlsruhe def2-TZVP basis sets13,14 were taken. Figures 1 and 2 were generated with MacMolPlt.15

Figure 1. Antibonding fϕ MO of the reactant AmO2(OH2)52+ (LCBOP-LRD).

qel = go + g e−Δε / kBT Gel = − RT ln qel

(2)

Δε was computed at the 4st-XGMC-QDPT2(10−12/6,1−5/4,0−2/ 6,15)/SO-CI(3/4) level. The corresponding correction to ΔG or ΔG‡ amounted to less than 0.5 kJ mol−1. The transition states (TS) were located by maximizing the energy along the reaction coordinate (the imaginary mode) via eigenmode following. They exhibited a single imaginary frequency. Reactants, products, and intermediates were obtained via computation of the intrinsic reaction coordinate. All of their computed vibrational frequencies were real. The coordinates of the geometries optimized at the MCSCF or 4st-MCSCF level are given in Tables S1−S6 (Supporting Information).

Figure 2. Antibonding fϕ MO of the TS AmO2(OH2)4···OH22+‡ (LCBOP-LRD).

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The geometries and vibrational frequencies were computed with spin-unrestricted DFT and CPCM16−18 hydration. A grid finer than the default was used (nrad = 120, nleb = 770 for LC-BOP-LRD,19,20 and nrad =160, nleb = 974 for ωB97X;21,22 the respective defaults are 96 and 302). The Hessians were calculated numerically (based on analytical gradients) using the double-difference method and projected

RESULTS AND DISCUSSION

Water Exchange Mechanisms and Models for Their Treatment. The water exchange reaction (reaction 1) may follow a dissociative or an associative substitution mechanism.31−33 The former can proceed in a concerted process, in which the dominating An−O(H2) bond breaking (An = U, Pu, B

DOI: 10.1021/acs.inorgchem.6b01793 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 1. Computed Bond Lengths of all Am(VI) Complexes Participating in Reactions 3−8a AmO2(OH2)52+

AmO2(OH2)4···OH22+‡

AmO2(OH2)4·OH22+

AmO2(OH2)42+

AmO2(OH2)5·OH22+

AmO2(OH2)5···OH22+‡ AmO2(OH2)4···(OH2)22+‡ AmO2(OH2)62+ a

geometry

d(AmO)av

d(Am−O)av

LC-BOP-LRD ωB97X MCSCF 4st-MCSCF LC-BOP-LRD ωB97X MCSCF 4st-MCSCF LC-BOP-LRD ωB97X MCSCF 4st-MCSCF LC-BOP-LRD ωB97X MCSCF 4st-MCSCF LC-BOP-LRD ωB97X MCSCF 4st-MCSCF LC-BOP-LRD ωB97X MCSCF 4st-MCSCF LC-BOP-LRD ωB97X

1.668 1.683 1.674 1.674 1.666 1.681 1.672 1.672 1.667 1.682 1.672 1.672 1.666 1.680 1.672 1.672 1.669 1.685 1.675 1.675 1.668 1.683 1.672 1.672 1.668 1.684

2.414 2.439 2.473 2.474 2.359 2.379 2.419 2.419 2.353 2.372 2.415 2.415 2.353 2.371 2.413 2.414 2.415 2.438 2.473 2.473 2.468 2.483 2.506 2.506 2.508 2.530

d(Am···O)

3.239 3.258 3.396 3.398

2.783 2.867 2.708, 2.765 2.708, 2.764

Units: Å.

“·OH2” water is in the second coordination sphere,36−38 or by formulating the reaction, (eq 4), with the participation of a water molecule from the bulk solution (WB).4 The exchange process is completed by the reaction of the intermediate with another H2O from the second coordination sphere or the bulk solution via the reverse reaction (reaction 3 or 4).

and Am) of the leaving water ligand is concerted with the formation of a new An−O(H2) bond of the entering water ligand. This mechanism, denoted as a dissociative interchange (Id) pathway, proceeds via the TS AnO2(OH2)4···(OH2)22+‡, exhibiting two weak An···O(H2) bonds. Alternatively, bondbreaking and bond-formation may proceed in two distinct steps, involving first the severance of an An−O(H2) bond leading to an intermediate with a reduced coordination number, AnO2(OH2)42+, which subsequently reacts with a water molecule from the bulk solution to form AnO2(OH2)52+. This process involving two TSs with a weakened An···O(H2) bond, AnO2(OH2)4···OH22+‡, is referred to as the dissociative mechanism (D). Likewise, for associative activations, the dominating bond formation process involving the TS AnO2(OH2)4···(OH2)22+‡ (with shorter bonds than for the Id mechanism34−36) may be concerted with the loss of one water ligand, or it may proceed in two steps via an intermediate with an increased coordination number, AnO2(OH2)62+, which subsequently loses a water ligand to form AnO2(OH2)52+. The latter pathway involves the two TSs AnO2(OH2)5··· OH22+‡. These two mechanisms are denoted as the associative interchange (Ia) or the associative (A) pathway. In cases where the energy difference between intermediate and TS is small, with the lifetime of the intermediate being shorter than the duration of the vibration leading to the reactant or product, it is preferable to attribute an interchange mechanism, Id or Ia, to the substitution reaction.2,36 In the interchange (I) mechanism, bond-formation and bond-breaking are fully concerted. In the formation of the intermediate AnO2(OH2)42+ for the D mechanism, a water ligand is transferred to the bulk solution. This process (eq 3) can be modeled using the water-adduct (WA) of the intermediate, AnO2(OH2)4·OH22+, where the

AnO2 (OH 2)52 + → AnO2 (OH 2)4 ···OH 2 2 +‡ → AnO2 (OH 2)4 ·OH 2 2 + (D, WA)

(3)

AnO2 (OH 2)52 + → AnO2 (OH 2)4 ···OH 2 2 +‡ → AnO2 (OH 2)4 2 + + H 2O (D, WB)

(4)

In the latter case, appropriate corrections for the standard states (25 °C, 1 M, 55.35 M for H2O)4,39 have to be made. The Ia, I, Id, and A mechanisms, represented by eqs 5−8, can be treated analogously using the WA or WB model. AnO2 (OH 2)5 ·OH 2 2 + → AnO2 (OH 2)4 ···(OH 2)2 2 +‡ → AnO2 (OH 2)5 ·OH 2 2 + (Ia , I, Id , WA)

(5)

AnO2 (OH 2)52 + + H 2O → AnO2 (OH 2)4 ···(OH 2)2 2 +‡ → AnO2 (OH 2)52 + + H 2O (Ia , I, Id , WB)

(6)

AnO2 (OH 2)5 ·OH 2 2 + → AnO2 (OH 2)5 ···OH 2 2 +‡ → AnO2 (OH 2)6 2 + → AnO2 (OH 2)5 ···OH 2 2 +‡ → AnO2 (OH 2)5 ·OH 2 2 + (A, WA) C

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DOI: 10.1021/acs.inorgchem.6b01793 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 2. Calculated Gibbs Activation (ΔG‡) and Reaction (ΔG) Energies for the Water Exchange Reaction of the Americyl(VI) Aqua Iona

AnO2 (OH 2)52 + + H 2O → AnO2 (OH 2)5 ···OH 2 2 +‡ → AnO2 (OH 2)6 2 + → AnO2 (OH 2)5 ···OH 2 2 +‡ → AnO2 (OH 2)5 + H 2O2 + (A, WB)

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DFT geometry

The interchange (I) and the dissociative interchange (Id) mechanisms were not observed for americyl(VI). Reaction 1 was investigated using both models. Computed Gibbs Activation Energies for Dissociative and Associative Mechanisms. The geometries and vibrational frequencies of the reactant, TSs, and intermediates were computed with the long-range-corrected functionals ωB97X21,22 and LC-BOP-LRD,19,20 with the latter exhibiting nonempirical dispersion corrections. Because of the presence of static correlation and near-degeneracy, these calculations were also performed with single-state and four-state MCSCF (Computational Details). For all of the geometries, the electronic energies were computed with WFT, 4st-XGMCQDPT2/SO-CI, taking into account static and dynamic electron correlation, near-degeneracy, and SO coupling (Computational Details). The latter contributed ≤15.5 kJ mol−1 to the electronic energies and 4.4 kJ mol−1 at most to the Gibbs activation energies and the energies for the formation of the intermediate (ΔG‡ and ΔG, respectively). In DFT, static correlation is treated approximately via local (DFT) exchange, near-degeneracy and SO effects are neglected, and the hydrogen bonds are difficult to treat accurately.40 The latter could be at the origin of the sizable differences of ΔG‡ and ΔG based on the WA and the WB models (see below), whereby the WB model is expected to be superior.4 With single-state MCSCF, static correlation is treated accurately, but near-degeneracy, SO coupling, and dynamic correlation are neglected, whereas, with four-state MCSCF, near-degeneracy effects are taken into account. The neglect of dynamic correlation in the geometry optimizations leads to too long Am−O(H2) bonds (Table 1), which, however, do not affect the ΔG‡ and ΔG values significantly.2 The geometries of the TS for the D mechanism were obtained with DFT and WFT, whereas, for the associative mechanisms, a TS for A was obtained with DFT, and one for Ia with WFT (Tables 1 and 2). In spite of the small contribution of SO effects to ΔG‡ and ΔG, at the DFT level, ΔG‡ and ΔG for the A mechanism differ strongly for the WA and the WB models. The corresponding WFT energy differences, based on DFT geometries, are smaller. Obviously, ΔG‡ calculated with DFT is less accurate, and will not be considered further. For geometries optimized with MCSCF or 4st-MCSCF (D and Ia mechanisms), however, ΔG‡ and ΔG are much less sensitive (by less than about 7 kJ mol−1) to the WA and WB models, which shows that the MCSCF geometries are superior. ΔG‡ for the D mechanism is in the range 34.4−37.5 kJ mol−1, based on DFT geometries, and 35.6−35.8 kJ mol−1, based on MCSCF and 4st-MCSCF geometries. Hence, for AmO2(OH2)52+ the D mechanism has a lower ΔG‡ (by more than 10 kJ mol−1) than for UO2(OH2)52+ and PuO2(OH2)52+.4 ΔG is considerably lower (by >8 kJ mol−1) than ΔG‡, indicating that, if a dissociative mechanism operates for AmO2(OH2)52+, it would be the stepwise D rather than the concerted Id pathway. Vallet et al.6 obtained an electronic energy (ΔEI) of 67.7 kJ mol−1 for the AmO2(OH2)42+ intermediate for the D mechanism; for the TS, it might be even higher, such that their activation energy for D is overestimated by more than 30 kJ mol−1.

LC-BOP-LRD ωB97X

ΔG

‡

28.6 28.6 32.0 32.0

MCSCF 4st-MCSCF

LC-BOP-LRD ωB97X

MCSCF 4st-MCSCF a

48.5 25.3 41.2 22.9

WFT ΔG

b

ΔG

‡

(i) D mechanism 19.7 37.5 23.9 37.5 25.0 34.4 31.6 34.4 35.6 35.6 35.8 35.8 (ii) A mechanism 49.5 38.2 26.3 27.8 39.3 45.6 21.0 29.0 (iii) Ia mechanism 40.1 35.3 40.1 35.5

ΔGb

model

27.7 26.8 25.9 25.6 27.4 20.7 27.5 20.9

WA WB WA WB WA WB WA WB

42.9 32.5 47.4 30.8

WA WB WA WB WA WB WA WB

Units: kJ mol−1. bValues, for which ΔG > ΔG‡ are italicized.

As already mentioned, ΔG‡ for the A mechanism based on DFT geometries depends strongly on the WA and WB models. Furthermore, the difference ΔG‡ − ΔG is small or even negative (italicized values), which suggests that it is preferable to attribute the Ia instead of the A mechanism to this exchange reaction, if it follows an associative pathway. On the basis of the more accurate MCSCF and 4st-MCSCF geometries, ΔG‡ for the Ia mechanism is in the range 35.3−40.1 kJ mol−1. Interestingly, ΔG‡ for the associative water exchange reaction of UO2(OH2)52+ and PuO2(OH2)52+ is (approximately) equal within the error limits of the computations (∼10−15 kJ mol−1).4 ΔEI calculated by Vallet et al.6 for the A-intermediate AmO2(OH2)62+ is too low in contrast to the overestimated ΔEI for the D-intermediate. Tiwari et al.’s value based on classical MD simulations7 is closer to the present value, but lower by ∼5−10 kJ mol−1. For both mechanisms and models, ΔG‡ is equal for MCSCF and 4st-MCSCF geometries (Table 2) because they are virtually equal (Table 1). This shows that, for the geometry optimizations, it is not necessary to treat near-degeneracy. The americyl(VI) ions with a reduced (AmO2(OH2)42+) or an increased (AmO2(OH2)62+) coordination number exhibit greater G values (ΔG > 0) than AmO2(OH2)52+ (Table 2), which corroborates the finding41 that the americyl(VI) ion has five H2O ligands in the equatorial plane. Since, for the present computations on AmO2(OH2)52+, ΔG‡ for the associative and dissociative mechanisms is approximately equal, it is appropriate to emphasize the limitations of the CPCM model. The Gibbs energy of the TSs for the Ia and the D mechanisms is likely to be sensitive to the solute−solvent hydrogen bonds. With CPCM, their electrostatic contribution is treated, but not their directionality. Furthermore, the reaction pathway can depend critically on solvation, as shown for the water exchange reaction on Al(OH2)63+:42 Based on WFT and a minimal cluster model, the stereoretentive D mechanism was obtained. In contrast, classical MD simulations with 215 water D

DOI: 10.1021/acs.inorgchem.6b01793 Inorg. Chem. XXXX, XXX, XXX−XXX

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molecules provided the stereomobile Id pathway along with some minor stereoretentive Id exchange. Hence, for the present system, it would be desirable to perform MCSCF/molecularmechanical dynamics simulations with energies corrected for dynamical correlation, near-degeneracy, and SO coupling (with 4st-XGMC-QDPT2/SO-CI). However, such computations are prohibitive. Thus, a definitive statement on the preferred exchange mechanism of AmO2(OH2)52+ is not possible. To summarize, for the D mechanism, ΔG‡ for Am(VI) is lower than for U(VI) and Pu(VI), whereas, for the associative pathway, all three actinides exhibit equal calculated ΔG‡ values. Furthermore, for Am(VI) ΔG‡ is equal for D and Ia within the error limits. Thus, the present computations do not allow the determination of the preferred mechanism. The novel finding, being in contrast to the previous studies,6,7 is that the D mechanism cannot be ruled out. Cause of the low Gibbs Activation Energy for the Dissociative Water Exchange Mechanism of the Americyl(VI) Ion. As already mentioned, the AmO2(OH2)52+ ion exhibits a fδ2fϕ1 electron configuration. The singly occupied fϕ MO lies in the equatorial Am(OH2)5 plane and is antibonding because of the 5 Am−O(H2) bonds (Figure 1). In the TS AmO2(OH2)4···OH22+‡ for the D mechanism, one of these five equatorial Am−O(H2) bonds is elongated, which reduces the antibonding character of the fϕ MO (Figure 2). The leaving water ligand is located out of the equatorial plane, and the fϕ MO is rotated. For the LC-BOP-LRD and ωB97X functionals, the fϕ orbital energy reduction for the activation (eq 9) AmO2 (OH 2)52 + → AmO2 (OH 2)4 ···OH 2 2 +‡

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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.6b01793. Modified ECP for Am; atomic coordinates (MCSCF and 4st-MCSCF geometries) of the reactant, TSs, and intermediates (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: francois.rotzinger@epfl.ch. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Bühl, M.; Kabrede, H. Mechanism of Water Exchange in Aqueous Uranyl(VI) Ion. A Density Functional Molecular Dynamics Study. Inorg. Chem. 2006, 45, 3834−3836. (2) Rotzinger, F. P. The Water-Exchange Mechanism of the [UO2(OH2)5]2+ Ion Revisited: The Importance of a Proper Treatment of Electron Correlation. Chem. - Eur. J. 2007, 13, 800−811. (3) Kerisit, S.; Liu, C. Structure, Kinetics, and Thermodynamics of the Aqueous Uranyl(VI) Cation. J. Phys. Chem. A 2013, 117, 6421− 6432. (4) Prlj, A.; Rotzinger, F. P. Investigation of the water exchange mechanism of the Plutonyl(VI) and Uranyl(VI) ions with quantum chemical methods. J. Coord. Chem. 2015, 68, 3328−3339. (5) Rotzinger, F. P. Reply to the Comment on “The Water-Exchange Mechanism of the [UO2(OH2)5]2+ Ion Revisited: The Importance of a Proper Treatment of Electron Correlation. Chem. - Eur. J. 2007, 13, 10298−10302. (6) Vallet, V.; Privalov, T.; Wahlgren, U.; Grenthe, I. The Mechanism of Water Exchange in AmO2(H2O)52+ and in the Isoelectronic UO2(H2O)5+ and NpO2(H2O)52+ Complexes as Studied by Quantum Chemical Methods. J. Am. Chem. Soc. 2004, 126, 7766−7767. (7) Tiwari, S. P.; Rai, N.; Maginn, E. J. Dynamics of actinyl ions in water: a molecular dynamics simulation study. Phys. Chem. Chem. Phys. 2014, 16, 8060−8069. (8) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. General atomic and molecular electronic structure system. J. Comput. Chem. 1993, 14, 1347−1363. (9) Gordon, M. S.; Schmidt, M. W. In Theory and Applications of Computational Chemistry: The First Forty Years; Dykstra, C. E., Frenking, G., Kim, K. S., Scuseria, G. E., Eds.; Elsevier: Amsterdam, The Netherlands, 2005; pp 1167−1189. (10) Küchle, W.; Dolg, M.; Stoll, H.; Preuss, H. Energy-adjusted pseudopotentials for the actinides. Parameter sets and test calculations for thorium and thorium monoxide. J. Chem. Phys. 1994, 100, 7535− 7542. (11) Cao, X.; Dolg, M.; Stoll, H. Valence Basis Sets for Relativistic Energy-Consistent Small-Core Actinide Pseudopotentials. J. Chem. Phys. 2003, 118, 487−496. (12) Rotzinger, F. P. Structure and Properties of the Precursor/ Successor Complex and Transition State of the CrCl2+/Cr2+ Electron Self-Exchange Reaction via the Inner-Sphere Pathway. Inorg. Chem. 2014, 53, 9923−9931. (13) Schäfer, A.; Huber, C.; Ahlrichs, R. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829−5835. (14) Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297−3305. (15) Bode, B. M.; Gordon, M. S. Macmolplt: a graphical user interface for GAMESS. J. Mol. Graphics Modell. 1998, 16, 133−138. (16) Barone, V.; Cossi, M. Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model. J. Phys. Chem. A 1998, 102, 1995−2001. (17) Tomasi, J. Thirty years of continuum solvation chemistry: a review, and prospects for the near future. Theor. Chem. Acc. 2004, 112, 184−203. (18) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999−3094. (19) Sato, T.; Nakai, H. Density functional method including weak interactions: Dispersion coefficients based on the local response approximation. J. Chem. Phys. 2009, 131, 224104. (20) Sato, T.; Nakai, H. Local response dispersion method. II. Generalized multicenter interactions. J. Chem. Phys. 2010, 133, 194101.

amounts to 37.3 and 37.5 kJ mol−1, respectively, whereby, for the two singly occupied fδ MOs, this reduction is smaller than 10 kJ mol−1. Obviously, the low ΔG‡ for the D mechanism is due to ligand-field effects, being well-known in transition metal chemistry. In the analogous uranyl(VI) and plutonyl(VI) aqua ions, the antibonding fϕ MOs are unoccupied. Hence, there is no stabilization of the fϕ orbital energy during the dissociative activation. This is the reason why the activation energy for the dissociative water exchange reaction of these ions is higher.

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Article

ACKNOWLEDGMENTS

Some of the computations were performed by T. Fovanna. E

DOI: 10.1021/acs.inorgchem.6b01793 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.6b01793 Inorg. Chem. XXXX, XXX, XXX−XXX