Mechanism and Energetics of the Hydrolysis of Th+ To Form Th(OD)3

Article Cite This: J. Phys. Chem. A 2019, 123, 5893−5905

pubs.acs.org/JPCA

Mechanism and Energetics of the Hydrolysis of Th+ To Form Th(OD)3+: Guided Ion Beam and Theoretical Studies of ThO+, ThO2+, and OThOD+ Reacting with D2O Arjun Kafle and P. B. Armentrout*

Downloaded via NOTTINGHAM TRENT UNIV on August 13, 2019 at 12:13:43 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Department of Chemistry, University of Utah, 315 S 1400 E Rm 2020, Salt Lake City, Utah 84112, United States ABSTRACT: The kinetic energy dependences of the reactions of ThO+, ThO2+, and OThOD+ with D2O, ThO2+ with D2, and OThOD+ with Xe were studied using guided ion beam tandem mass spectrometry. Exothermic formation of OThOD+ is the dominant process observed in reactions of both ThO+ and ThO2+ with D2O. Minor products formed in endothermic reactions include ThO2+, DThO+, and ThO2D2+. OThOD+ is also formed in the reaction of ThO2+ with D2 but in an endothermic process. Collision-induced dissociation (CID) of OThOD+ with Xe leads to endothermic loss of the hydroxide ligand. OThOD+ reacts further with D2O to form the associative complex ThO3D3+, which is long-lived before dissociating back to the reactants. The OThOD+−D2O bond energy of the associative complex is measured to be 2.96 ± 0.05 eV by modeling the kinetic energy-dependent cross section for association using a phase space theory model that rigorously conserves angular momentum. By comparison with theory, this bond energy identifies the ThO3D3+ species as the trihydroxide cation, Th(OD)3+. From the endothermic reactions and CID of OThOD+ with Xe, the OTh+−D, OTh+−O, and OTh+−OD bond dissociation energies (BDEs) are measured to be 2.33 ± 0.24, 4.66 ± 0.15, and 6.00 ± 0.17 eV, respectively. All four of these BDEs are experimentally determined for the first time and agree reasonably well with values calculated at the B3LYP, B3PW91, and PBE0 levels of theory with cc-pVQZ basis sets. Complete potential energy surfaces for all reactions were calculated at the B3LYP/ccpVTZ level and elucidate the mechanisms for all processes observed.

■

INTRODUCTION

phase studies where solvent effects are absent can provide benchmarks most directly addressed by theory. Previously, both Cornehl et al.5 and Santos et al.6 have examined the reaction between Th+ and H2O by using Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) at thermal energies. They both observed exothermic processes with a branching ratio of 65% ThO+ + H2 to 35% [Th,O,H]+ + H at thermal energies. Cox and Armentrout7 have examined this process using guided ion beam tandem mass spectrometry (GIBMS), reproducing the thermal energy branching ratio and extending the study to much higher collision energies. This work shows that modeling of the competition between these two channels requires both accurate thermochemistry (in particular, consideration of spin−orbit interactions is needed) and conservation of angular momentum. Rutkowski et al. (RMG)8 have shown that OThOH+ (stable IV oxidation state), formed by electrospray ionization, exothermically hydrolyzes directly to ThO3H3+ by addition of a water molecule, which they concluded had the structure of Th(OH)3+ (stable IV oxidation state) on the basis of the failure to observe ligand exchange. Th(OH)3+ then hydrates by sequential addition of three water molecules. RMG carried out density functional theory (DFT) studies for this system, elucidating the structure and binding energies for the

The thermochemistry and reactivity of actinide compounds are of interest because of their role in nuclear power generation, reprocessing of nuclear fuels, and nuclear waste disposal.1,2 Water is ubiquitous in nature and often used as a coolant and neutron moderator in nuclear reactors. Therefore, a thorough understanding of chemical interactions of actinides with water is important. Despite this importance, actinide chemistry is still in development, in part because most actinides are dangerously radioactive making them difficult and potentially dangerous to investigate. Exceptions are Th and U, which are sufficiently stable to be readily handled outside high-level radiochemical facilities because of their very long half-lives: 232Th, t1/2 = 1.40 × 1010 years and 238U, t1/2 = 4.47 × 109 years.3 For the radioactive elements, theoretical calculations may provide a safe and cost-effective alternative to experimental research; however, accurate quantum chemical calculations on actinide species are problematic because of the need to implement relativistic and correlation effects associated with the large number of electrons, further complicated by the close energetic proximity of many electronic states involving the 5f, 6d, 6p, and 7s orbitals.4 The challenges of these calculations are further exacerbated by a shortage of accurate information on actinide molecules, which makes validation of the approximations employed in the theoretical models difficult. Reliable fundamental experimental benchmarks are necessary in order to investigate potential basis sets and theoretical models. Gas© 2019 American Chemical Society

Received: April 26, 2019 Revised: June 18, 2019 Published: June 18, 2019 5893

DOI: 10.1021/acs.jpca.9b03938 J. Phys. Chem. A 2019, 123, 5893−5905

Article

The Journal of Physical Chemistry A

quadrupole mass filter for mass analysis followed by detection using a Daly detector.19 Measured intensities of the reactant and product ions were corrected for the reaction outside the collision cell as well as for background noise by measuring their intensities with and without the neutral reactant (D2O, D2, or Xe) in the collision cell. These intensities were then converted to absolute reaction cross sections for product formation using I = I0 exp(−ρσl), where I is the reactant ion intensity after the collision cell, I0 is the reactant ion intensity before the collision cell, ρ is the number density of the neutral reactant, σ is the total reaction cross section, and l is the effective length of the collision cell, 8.62 cm. The advantage of the guided ion beam method is that few ions are lost such that I0 − I = ΣIp, the sum of all product ion intensities, and consequently, σp = σ × (Ip/ΣIp). Uncertainties in the absolute cross sections are estimated to be ±20%. The kinetic energy of the reactants was converted from the lab frame energy, Elab, to the center-of-mass frame energy, ECM, using ECM = Elab × m/(m + M), where m is the mass of the reactant neutral and M is the mass of the reactant ion. ECM represents the amount of energy available for inducing chemical reactions. In the low energy region, the conversion from lab to CM frame explicitly accounted for truncation of the ion energy distributions.17 The absolute zero of energy and kinetic energy distribution of the reactant ions were determined by using the octopole ion guide as a retarding potential analyzer.17 Typical full widths at half maximum of the energy distribution for these experiments were 0.4−0.6 eV (lab). The absolute energy scale has an uncertainty of about 0.05 eV (lab). Data Analysis for Association Reactions. Energy dependence of the association product cross section was analyzed using a model formulated by Koizumi and Armentrout 20 that explicitly conserves orbital angular momentum. This model assumes that the association and reverse dissociation occur on an ion-induced dipole + locked dipole (LD) potential surface, which provides an upper limit to the collision cross section. For the association reaction, conservation of angular momentum requires that the rotational angular momentum of the association complex equals the orbital angular momentum of the reactants, as given by L = μνb, where μ is the reduced mass of the reactants, ν is the relative velocity, and b is the impact parameter. This relationship ignores the rotational angular momentum of the reactants (much smaller than L), which should be a reasonable approximation as discussed elsewhere.20,21 This model further assumes that the lifetime of the association complex is limited by passage over a loose, orbiting phase space limit transition state back to reactants, as verified computationally (see below). Energy dependence of the association cross section was modeled with explicit conservation of angular momentum (J) according to eq 1.

addition of 1−4 H2O molecules to Th(OH)3+. To our knowledge, neither experimental thermodynamics nor a detailed understanding of the mechanism for the formation of Th(OH)3+ from the reaction of Th+ with water has been developed. In the current study, the formation of the stable Th(OD)3+ complex is investigated by reacting D2O with ThO+, ThO2+, and OThOD+ as a function of kinetic energy using GIBMS. Additional information concerning the OThOD+ species is obtained by examining the reaction of ThO2+ with D2 and the collision-induced dissociation (CID) of OThOD+ with Xe. Analysis of the kinetic energy-dependent cross sections yields OTh+−D, OTh+−O, OTh+−OD, and OThOD+−D2O bond dissociation energies (BDEs). Combined with theoretical calculations, this thermochemistry definitively identifies the Th(OD)3+ molecule and enables an elucidation of the mechanism for its formation from the hydration of Th+.

■

EXPERIMENTAL AND THEORETICAL DETAILS General Experimental Section. The GIBMS instrument used in this study has been described in detail elsewhere.9 Briefly, Th+ ions were created in a direct current discharge flow tube (DC/FT) ion source,10 consisting of a cathode held at a negative voltage of ∼1.7 kV over which a flow of approximately 90% He and 10% Ar passed at a pressure of 0.5−0.7 Torr and ambient temperature. The dc-discharge ionized Ar and accelerated these ions into the cathode, which was a thorium rod attached to a tantalum holder, thereby sputtering Th+ ions. Ions traveled through a meter-long flow tube where they underwent ∼105 thermalizing collisions with He and Ar. Both ThO+ and ThO2+ were created by leaking O2 into the flow tube approximately 25 cm downstream of the source. OThOD+ was created by leaking D2O into the flow tube approximately 25 cm downstream of the source. Here, He was bubbled through a D2O-filled U-shaped container, and the mixture was leaked into vacuum through a leak valve. D2O was thoroughly deoxygenated by bubbling with N2 and degassed prior to use both in the source and in the reaction cell. For all reactant ions, ThO+, ThO2+, and OThOD+, we estimate the internal temperature to be 300 K because of the extensive number of collisions with the flow gases. Previous work on a number of systems is consistent with the production of thermalized molecular ions under similar conditions.10−15 In the present system, this conclusion is also validated by reasonable agreement between the experimental and theoretical BDEs measured here. Reactant ions were extracted from the source, accelerated, and focused into a magnetic momentum analyzer, where the reactant ions were mass selected. The mass-selected ions were then decelerated to a desired kinetic energy and focused into an octopole ion beam guide, where ions were radially trapped by a radio frequency electric field.16,17 The octopole passed through a static gas cell that contained the reactant gas at low pressures of D2O (0.04−0.2 mTorr), D2 (0.10−0.30 mTorr), and Xe (0.10−0.40 mTorr), so that multiple ion−neutral collisions were improbable. Independent measurements at several neutral reactant pressures were performed to determine pressure dependence of the product cross sections. In cases where reactions were pressure-dependent, the product cross sections were extrapolated to zero pressure, rigorously single collision conditions before analysis.18 After the collision cell, product ions and residual reactant ions drifted to the end of the octopole, where they were extracted and focused into a

σasso(E) =

π ℏ2 ∑g 2Eμ i i

∫0

Jmax

(2J + 1) exp[−k tot(E*, J )τ ]dJ (1)

Here, the summation is over the rovibrational states i of the reactant ion (before collision) having energies Ei and populations gi, where Σgi = 1. Rovibrational states taken from quantum chemical calculations of the ground state structures were directly counted using the Beyer−Swinehart− 5894


Article

The Journal of Physical Chemistry A Stein−Rabinovitch algorithm22−24 and used to assign gi on the basis of a Maxwell−Boltzmann distribution at 300 K. E* is the total available energy, that is, E* = E + Ei + D0, where E is the kinetic energy of reactants in the center-of-mass frame, and D0 is the association energy (here, D0[OThOD+−D2O]). τ is the experimental time-of-flight (∼1 × 10−4 s in our instrument).9 Jmax is the maximum angular momentum as given by eq 2

D0(OTh+−L) = D0(L−R) − E0

Here, the relevant neutral thermochemistry is D0(DO−D) = 5.212 ± 0.003 eV, D0(O−D2) = 5.111 ± 0.001 eV, and D0(D2) = 4.556 ± 0.001 eV.30 Equation 5 assumes that there are no barriers in excess of the endothermicity of the reaction, which is typical for ion−neutral reactions because of the attractive long-range ion-induced dipole interactions31 and for heterolytic bond cleavages.32 Potential energy surfaces (PESs) shown below confirm that no barriers are present in the systems being studied here, with one exception discussed below. Theoretical Calculations. Quantum calculations reported here were performed using the Gaussian 09 suite of programs.33 Geometries of all species were optimized using the B3LYP,34,35 B3PW91,36 and PBE037 functionals without any symmetry constraints. First order spin−orbit effects were considered when necessary but are absent or negligible for most of the systems being considered here. A pseudopotential (PP)-based correlation-consistent polarized valence quadrupleζ basis set, (20s17p12d11f7g4h1i)/[7s7p6d5f3g3h1i], ccpVQZ-PP developed by Peterson38 that utilizes the Stuttgart−Cologne multiconfigurational Dirac−Hartree−Fock fully relativistic small core (60 electron) effective core potential (ECP)39 was used for Th along with cc-pVQZ basis sets for D and O obtained from the EMSL basis set exchange.40−42 PESs for the reactions of both ThO+ and ThO2+ with D2O were calculated at the B3LYP level with cc-pVTZ-PP/cc-pVTZ basis sets for Th + /D,O where the cc-pVTZ-PP basis set (17s16p11d10f4g1h)/[8s8p7d6f4g1h] for Th was developed by Peterson.38 For brevity in the following, the basis sets will simply be referred to as cc-pVXZ, where X = T or Q.

Jmax (Jmax + 1) = [(2μ2 αq2E /πε0)1/2 + μD μ2 q/2πε0] /ℏ2 (2)

which is derived from the expression for the LD collision cross section of eq 3. σLD(E) = π (2αq2 /4πε0E)1/2 + (qμD /4ε0E)

(3)

Here, α and μD are the polarizability volume and the electric dipole moment of the neutral reactant molecule (1.450 Å3 and 1.840 D for H2O, respectively25), q is the charge on the electron, and ε0 is the permittivity of vacuum. When the exponential term in eq 1 is unity, that is, when the lifetime of the association complex exceeds the flight time of the instrument, the integration of eq 1 converges to σLD. The application of eq 1 in this work involves the careful treatment of lifetime effects, kinetic energy distributions of the ion and neutral reactants, reactant internal energy distributions, and angular momentum distributions.20 As will be seen below, the resulting modeled cross sections can reproduce the kinetic energy dependence and absolute magnitudes of our experimental cross sections in detail using only the single adjustable parameter, D0. Data Analysis for Endothermic Reactions. The kinetic energy-dependent cross sections of endothermic reactions were modeled using the empirical model shown in eq 4 σ(E) = σ0∑ gi(E + Ei−E0)N /E i

(5)

■

RESULTS Experimental Results. Reaction of ThO+ with D2O. Kinetic energy-dependent cross sections for the reaction of ThO+ with D2O are shown in Figure 1. Products are formed according to reactions 6−8b and do not exhibit any dependence on D2O pressure. Energies listed are those extracted from analysis of the data (see below) as listed in Table 1.

(4)

where E, Ei, and gi are defined above, σ0 is an energyindependent scaling parameter, E0 is the reaction threshold at 0 K, and N is an adjustable parameter that characterizes the energy deposition.26 Several effects are known to cause broadening of the cross sections, including the kinetic energy distribution of the reactant ion, the thermal motion of the neutral reactant gas (Doppler broadening), and the internal energies of the reactants.12,27,28 Thus, the model cross sections of eq 4 were convoluted over the kinetic energy distributions of the neutral and ion reactants before comparison with experimental data.17 The fitting parameters, σ0, N, and E0, were optimized using a nonlinear least-squares method to best reproduce the experimental cross section of each product. Uncertainties in the modeling parameters were obtained from analyses of several data sets, using a range of acceptable N values and including the uncertainty in the energy scale, ±0.05 eV (lab). At high energies, cross sections decline because of product dissociation, so eq 4 is modified to include a statistical model of the dissociation probability, as discussed in detail elsewhere.29 In brief, the dissociation probability is controlled by two adjustable parameters: P, a parameter similar to N that can hold only integer values, and Ed, the energy at which product cross section begins to decline. Inclusion of the high-energy model does not significantly alter the analysis of E0. In this work, E0 obtained from eq 4 was used to determine the BDE, D0(OTh+−L), using eq 5, where L = D or O.

ThO+ + D2 O → OThOD+ + D

ΔH0 = 09.79 eV (6)

+

→[Th, O, D] + OD

ΔH0 = 2.88 eV (7)

+

→ThO2 + D2

ΔH0 = 0.98 eV (8a)

→ThO2+ + 2D

ΔH0 = 5.01 eV (8b)

In addition to reactions 6−8b, at higher pressures of D2O, we also observe sequential addition of D2O ligands to the OThOD+ product to form ThO3D3+(D2O)n (where n = 0−3) in barrierless reactions at low energies with cross sections that are all dependent on D2O pressure. OThOD+ is the dominant product at all energies and is clearly formed in a barrierless exothermic reaction at low kinetic energies. The barrierless reaction shows that D0(OTh+−OD) > D0(D−OD) = 5.212 eV.30 The cross section declines with an energy dependence of E−0.8±0.1 until approximately 0.1 eV. This is similar to the kinetic energy dependence (E−0.7) expected from trajectory calculations.43 5895


Article


OThOD+ product can have enough energy to dissociate to ThO+ + OD. As discussed further below, this product can also dissociate to ThO2+ + D (leading to the second feature in this product cross section), but the magnitude of this cross section cannot account for the decline observed in the OThOD+ cross section. The origin of the endothermic feature in the OThOD+ cross section is not immediately obvious but potentially could be associated with the formation of a distinct isomer or of a different electronic state of the products. Both conjectures are explored computationally below. An approximate analysis of this endothermic feature is performed by subtracting a logarithmic polynomial fit to the exothermic portion of the OThOD+ cross section (below 0.5 eV, Figure 1) from the experimental cross section. Analysis of the remaining endothermic cross section with eq 4 gives a threshold of E0 = 0.54 ± 0.08 eV. Other optimized parameters of eq 4 are given in Table 1. In addition to the OThOD+ product, products formed in endothermic reactions 7, 8a and 8b, [Th,O,D+] and ThO2+, were also observed with low cross sections. Two distinct endothermic features are observed in the ThO2+ product cross section and presumably refer to reactions 8a and 8b, which should be separated by D0(D2) = 4.556 eV,30 which is roughly consistent with the observation. The lower threshold feature of ThO2+ starts near 1 eV, reaches a maximum near 3 eV, before declining. In general, product cross sections often decline at the BDE of the neutral reactant, that is, D0(O−D2) = 5.111 ± 0.001 eV here;30 however, the early decline in the ThO2+ cross section correlates with the onset of the [Th,O,D]+ product, indicating competition between these channels. The second ThO2+ feature starts near 4.5 eV and peaks near 7 eV. Here, the onset of this feature corresponds to the decline in the OThOD+ cross section, suggesting that reaction 8b occurs by decomposition of OThOD+ into ThO2+ + D, a pathway that is consistent with the thermochemistry determined below. The [Th,O,D]+ product cross section of reaction 7 has an apparent onset near 2.5 eV and levels out near D0(DO−D) = 5.212 eV,30 where sufficient energy is available for [Th,O,D]+ to dissociate to ThO+ + D. The [Th,O,D]+ cross section was modeled using eq 4 as shown in Figure 1. Optimized parameters of eq 4 obtained from analysis of these cross sections for multiple data sets are given in Table 1. Using E0 = 2.88 ± 0.24 eV in eq 5 with D0(DO−D) = 5.212 eV indicates that D0(OTh+−D) = 2.33 ± 0.24 eV. This is a plausible value as it is similar to D0(Th+−D) = 2.48 ± 0.07 eV, measured in our lab from the reactions of Th+ with H2, D2, and HD.45 This correspondence suggests that the [Th,O,D]+ product may have the DThO+ structure, a conclusion explored computationally below.

Figure 1. Product cross sections for the reaction between ThO+ and D2O at a pressure of ∼0.1 mTorr as a function of kinetic energy in the center-of-mass (lower x-axis) and laboratory (upper x-axis) frames. The black line shows the collision cross section calculated using the trajectory model.43 The arrow shows the DO−D bond energy of 5.21 eV. The solid (dashed) blue, red, and green lines show the model of eq 4 with (without) convolution with the internal and kinetic energy distributions of the reactants. The dark blue line shows the logarithmic polynomial model of the low energy feature of the OThOD+ cross section. The dashed blue line corresponds to the model of eq 4 without the internal and kinetic energy distributions of the reactants for the apparent endothermic feature of the OThOD+ cross section determined as described in the text. The solid blue line represents the sum of the low and high energy features fit with convolution.

The observation of reaction 6 at low energies is consistent with the previous work of Cornehl et al.5 and Santos et al.,6 who studied the reaction between ThO+ and H2O using FT-ICRMSs. Because their experiments were conducted at thermal energies, neither of the endothermic reactions 7, 8a, and 8b were observed. Compared with the collision rate constant, kcol = 2.8 × 10−9 cm3/s, calculated according to the trajectory model,43 our observations indicate that reaction 6 proceeds with an efficiency (k/kcol) of 0.27 ± 0.05 at 0.01−0.05 eV. This efficiency is similar to those observed by Cornehl et al.5 (k/kcol = 0.24 ± 0.05) and Santos et al.6 (k/kcol = 0.07 ± 0.02) at thermal energies (where the efficiencies differ from those directly reported as both studies used average dipole orientation (ADO) theory44 to calculate kcol). As the energy increases, the OThOD+ cross section declines until it reaches a minimum near 0.5 eV and then rises until a maximum near D0(DO−D) = 5.212 eV. Above this energy, the

Table 1. Summary of Parameters of Eq 4 for the Endothermic Reactions, Respectivelya σ0

reaction ThO+ + D2O → OThOD+ + Db →DThO+ + OD →ThO2+ + D2 →ThO2+ + 2D ThO2+ + D2 → OThOD+ + D ThO2+ + D2O → OThOD+ + ODb OThOD+ + Xe → OTh+ + OD + Xe

7.09 1.45 0.08 1.30 3.23 2.38 0.25

N

(1.14) (0.20) (0.01) (0.21) (0.46) (0.20) (0.02)

1.4 1.1 1.1 1.0 1.6 1.1 2.2

(0.1) (0.1) (0.2) (0.2) (0.1) (0.1) (0.1)

E0 (eV) 0.54 2.88 0.98 5.01 0.85 0.65 6.00

(0.08) (0.24) (0.07) (0.15) (0.06) (0.07) (0.17)

P

Ed (eV)

2

4.9 (0.2)

1 2 2 2

2.2 6.9 4.5 4.0

(0.3) (0.2) (0.1) (0.2)

a

Uncertainties (in parentheses) are one standard deviation. bModeled after removing exothermic feature (see text and Figures 1 and 3). 5896


Article

The Journal of Physical Chemistry A Both features of the ThO2+ cross sections were modeled using eq 4 as shown in Figure 1. Optimized parameters of eq 4 obtained from analysis of reactions 8a and 8b for multiple data sets are given in Table 1. Threshold energies of 0.98 ± 0.07 and 5.01 ± 0.15 eV differ by 4.0 ± 0.2 eV, slightly lower than D0(D2) = 4.556 eV.30 As demonstrated in the next section, reaction 8a is limited by a barrier in excess of its endothermicity such that the thermodynamic onset should not be observed. Therefore, the threshold for reaction 8b was used to determine D0(OTh+−O) according to eq 5 and yields D0(OTh+−O) = 4.66 ± 0.15 eV. Reaction of ThO2+ with D2. To further explore the [Th,2O,2D]+ system examined above, we also examined the reaction of ThO2+ with D2 as shown in Figure 2. The only product observed is formed in reaction 9, and its cross section exhibited no dependence on D2 pressure. ThO2+ + D2 → OThOD+ + D

(as calculated using the thermochemistry determined here). The OThOD+ cross section was modeled using eq 4 as shown in Figure 2. Optimized parameters of eq 4 obtained from analysis of these cross sections for multiple data sets are given in Table 1. This analysis reveals a barrier height of 0.85 ± 0.06 eV. Reaction of ThO2+ with D2O. Kinetic energy-dependent cross sections for the reaction of ThO2+ with D2O are shown in Figure 3. Products are formed according to reactions 10 and 11 and do not exhibit a dependence on D2O pressure. ThO2+ + D2 O → OThOD+ + OD

ΔH0 = −0.59 eV (10)

→ ThO2 D2+ + O

(11)

ΔH0 = 0.85 eV (9)

Figure 3. Product cross sections for the reaction of ThO2+ with D2O at a pressure of ∼0.1 mTorr as a function of kinetic energy in the center-of-mass frame (lower x-axis) and the laboratory frame voltage (upper x-axis). The black line shows the collision cross section calculated using the trajectory model.43 The arrow shows the O−D2 bond energy of 5.11 eV. The dark blue line shows the logarithmic polynomial model of the low energy feature of the OThOD+ cross section. The dashed blue line corresponds to the model of eq 4 without the internal and kinetic energy distributions of the reactants for the apparent endothermic feature of the OThOD+ cross section determined as described in the text. The solid blue line represents the sum of the low and high energy features fit with convolution.

Figure 2. Cross section for reaction of ThO2+ with D2 at ∼0.1 mTorr as a function of kinetic energy in the center-of-mass frame (lower xaxis) and the laboratory frame (upper x-axis) energies. The solid (dashed) lines show the model of eq 4 with (without) convolution over the internal and kinetic energy distributions of the reactants. The arrow shows the D−D bond energy of 4.556 eV.

Products such as ThO+ and ThOD+ were looked for but not observed. The formation of OThOD+ in reaction 9 is exothermic by 1.24 ± 0.23 eV as determined by combining BDEs measured in this work and available in the literature, that is, D0(OTh+−OD) = 6.00 ± 0.17 eV (see below), D0(OTh+− O) = 4.66 ± 0.15 eV (see above), D0(O−D) = 4.455 ± 0.002 eV,30 and D0(D−D) = 4.556 eV. Clearly, the cross section for OThOD+ formation shown in Figure 2 exhibits a threshold, which unambiguously shows that there is a barrier in excess of the product asymptotes for reaction 9. This result is also consistent with the observation above that the threshold energy associated with reaction 8a corresponds to a barrier. The OThOD+ product cross section of reaction 9 has an apparent onset near 0.8 eV and reaches a maximum near D0(D−D) = 4.556 eV, where sufficient energy is available for OThOD+ to dissociate by D atom loss. Dissociation to ThO+ + OD instead has a similar threshold energy of 4.76 ± 0.15 eV

We also observe that D2O ligands sequentially add to the OThOD+ product to form ThO3D3+(D2O)n (where n = 0−3) in barrierless reactions at low energies with cross sections that are all dependent on D2O pressure. The formation of OThOD+ in reaction 10 is exothermic and barrierless, consistent with the previous work of Cornehl et al.5 on the thermal reaction between ThO2+ and H2O in a FT-ICRMS. Compared with the collision rate constant, kcol = 2.8 × 10−9 cm3/s, calculated according to the trajectory model,43 our results indicate that reaction 10 proceeds with an efficiency of 0.40 ± 0.08 below 0.05 eV. Cornehl et al.5 reported a lower efficiency of 0.06 ± 0.01 (corrected to be relative to the trajectory model for kcol, instead of the ADO theory44). The dominant OThOD+ product cross section exhibits two features, similar to that for OThOD+ formed in reaction 6, Figure 1. Here, the cross section declines with an energy 5897


Article

The Journal of Physical Chemistry A dependence of E−0.6±0.1 until approximately 0.05 eV. This is similar to the kinetic energy dependence (E−0.7) expected from trajectory calculations.43 As the energy increases, the OThOD+ cross section declines until it reaches a minimum near 0.6 eV, then increases, which is consistent with opening of an endothermic pathway to this product. Similar to the results for reaction 6, the origin of the endothermic feature in the OThOD+ cross section is not immediately obvious, but similar possibilities as mentioned above are equally viable. An approximate analysis of this endothermic feature is performed after subtracting a logarithmic polynomial fit to the exothermic portion of the OThOD+ cross section (below 0.5 eV, Figure 3) from the experimental cross section. Analysis of the remaining endothermic cross section with eq 4 gives a threshold of E0 = 0.65 ± 0.07 eV, with other optimized parameters given in Table 1. At high energies, a ThO2D2+ product is formed in the endothermic reaction 11 with a relatively small cross section. The ThO2D2+ cross section rises from an apparent onset of ∼4 eV and peaks near D0(O−D2) = 5.111 eV. ThO2D2+ cross section is too small to glean any accurate thermodynamic information and hence is not analyzed further. Association Reaction of OThOD+ with D2O. Reaction of OThOD+ with D2O formed ThO3D3+ and its hydrated complexes, ThO3D3+(D2O)n where n = 0−3, as shown in Figure 4. These products can be formed according to reactions 12−14. OThOD+ + D2 O V ThO3D3+*

(12)

ThO3D3+* + D2 O V ThO3D3+ + D2 O

(13)

ThO3D3+ + n D2 O → ThO3D3+(D2 O)n

D2O molecule and be stabilized according to reaction 13. Additional collisions lead to the higher order adducts as in reaction 14. These observations are consistent with those of RMG,8 who observed that OThOH+ exothermically hydrolyzes directly to ThO3H3+. They indirectly identified this product as Th(OH)3+ rather than OThOH+(H2O) by failing to observe a reaction of ThO3H3+ with acetone, which should be able to displace a water ligand but presumably not a hydroxide ligand. Experimental cross sections for the reaction of OThOD+ with D 2 O were taken at several different pressures, approximately 0.04−0.20 mTorr. The experimental cross sections for all ThO3D3+(D2O)n products (n = 0−3) show a clear increase with increasing D2O pressure at all energies, which indicates collisional stabilization of ThO3D3+(D2O)n. The effect of such secondary collisions can be eliminated completely by extrapolation of the ThO3D3+ cross section to zero D2O pressure. At the lowest energies examined (below 0.02 eV), a quadratic D2O pressure dependence was needed for extrapolation, whereas a linear pressure dependence was sufficient at all higher energies. The zero-pressure extrapolated cross section of ThO3D3+ is shown in Figure 5. This cross section no longer has

(n = 1−3) (14)

In brief, reaction 12 proceeds because of the ion−dipole and ion-induced dipole attraction between OThOD+ + D2O and forms the energized ThO3D3+* complex. This energized complex has enough internal energy to dissociate back to the reactants or it can undergo a subsequent collision with another

Figure 5. Zero-pressure extrapolated experimental cross sections (blue circles) for the association reaction of OThOD+ with D2O as a function of kinetic energy in the center-of-mass (lower x-axis) and laboratory (upper x-axis) frames. The blue line is the PST model of eq 1 using the single adjustable model parameter, D0 = 2.96 ± 0.05 eV. The black line represents the LD cross section, σLD, of eq 3 divided by 50. The dashed line shows the collision cross section calculated using the trajectory model divided by 50.43

contributions from the collisional stabilization reaction 13 and is observed because the lifetime of ThO3D3+* is long enough to be detected. The ThO3D3+* association complex exhibits a cross section that declines with the increasing energy, consistent with an exothermic barrierless process, as should be the case for an association reaction with a long-range attractive potential. The magnitude of the experimental cross section is well below (∼2%) the collision cross section for a molecule having a permanent dipole, Figure 5. The cross section declines more rapidly than the collision limit at higher energies, indicating faster dissociation. This behavior is attributed to a decreasing lifetime of the association complex with increasing energy. As shown in Figure 5, when molecular

Figure 4. Product cross sections for the reaction of OThOD+ with D2O at ∼0.2 mTorr as a function of kinetic energy in the center-ofmass frame (lower x-axis) and the laboratory frame voltage (upper xaxis). 5898


Article


primarily the Th+ (7s) orbital, as shown in Figure 7. Here, we calculate a bond length of 1.807 Å at the B3LYP/cc-pVQZ

parameters for Th(OD)3+ are used (from the calculations detailed below), the association model cross section of eq 1 reproduces the experimental cross section throughout the entire energy range examined and 3 orders of magnitude in cross section. In the model shown, the only adjustable parameter, D0 is allowed to vary to best fit the data both in absolute magnitude and energy dependence, with an optimum value of 2.96 ± 0.05 eV. Alternatively, the model can utilize molecular parameters of the OThOD+(D2O) isomer, in which case, D0 = 2.78 ± 0.05 eV, with a comparable reproduction of the data. In either case, D0 is taken as equal to D0(OThOD+− D2O), which can be compared with the theory in order to make a structural identification (see below). CID of OThOD+ with Xe. Figure 6 illustrates a typical data set for the CID of OThOD+ with Xe. The dominant product

Figure 7. Ground state electronic configurations and molecular orbitals of ThO+, ThO2+, DThO+, and OThOD+, resulting from the valence electrons of Th+, O, and D calculated at the B3LYP/cc-pVQZ level. In the first two panels, the degenerate out-of-plane π orbitals are not shown.

level, which matches the experimental bond length of 1.807,46 as well as the bond lengths of 1.808, 1.809, and 1.808 Å calculated by Cox et al.,47 Zhou and Schlegel (ZS),48 and Mazzone et al. (MMRS),49 respectively. The 2Σu+ ground state of ThO2+ is a symmetric linear dioxide having a (1σg)2(1πg)4(1πu)4(1σu)1 valence electron configuration, where 1σg and 1πg are bonding orbitals formed by combining O (2p) and Th+ (6d) orbitals, 1πu are largely nonbonding and correspond to mainly O (2pπ) orbitals with some Th+ (5fπ) character, and 1σu is a bonding orbital formed by combining O (2pσ) orbitals with Th+ (5fσ), as shown in Figure 7. Here, we calculate Th+−O bond lengths of 1.875 Å at the B3LYP/cc-pVQZ level, which differs from the bond lengths of 1.832 Å calculated by Infante et al.50 This bond length is longer than that in triply bonded diatomic ThO+, reflecting the decreased bond order of about 1.5. Our calculations predict that the ground state of [Th,O,D]+ is DThO+ (1A′), which is lower in energy than the ThOD+ (3Δ) isomer by 0.91, 0.97, and 0.91 eV at the B3LYP, B3PW91, and PBE0 levels of theory, respectively. Our calculated results are consistent with calculations of MMRS,49 who have found the hydrido thorium oxide cation, HThO+ (1A′), to be lower in energy than ThOH+ by 0.99− 1.18 eV. Consistent with the calculations of MMRS49 and ZS,48 the 1A′ ground state of DThO+ is a bent molecule having a (1a′)2(1a″)2(2a′)2(3a′)2 valence electron configuration. As shown in Figure 7, the 1a′ and 1a″ bonding orbitals are primarily formed by combining the in-plane and out-of-plane O (2pπ) and Th+ (6dπ) orbitals. The 2a′ and 3a′ bonding orbitals combine 7s−6dσ hybrid orbitals on Th with O (2pσ) and D (1s) orbitals, respectively. Here, we calculate ThD+ and ThO+ bond lengths of 2.041 and 1.820 Å, respectively, and a DThO+ bond angle of 107° at the B3LYP/cc-pVQZ level. These are similar to values calculated for HThO+ by both ZS48 and MMRS49 using a B3LYP/SDD level of theory: 2.034 and 1.820 Å and 106°. Our calculations predict that the ground state of OThOD+ is 1 A′ with Cs symmetry. As shown in Figure 7, the 1a′ bonding orbital is formed by combining the OD (2pσ) and Th+ (7s− 6dσ) hybrid orbitals. The 1a″ and 2a′ bonding orbitals are the

Figure 6. Cross section for CID of OThOD+ with Xe at ∼0.1 mTorr as a function of kinetic energy in the center-of-mass frame (lower xaxis) and the laboratory frame voltage (upper x-axis). The solid (dashed) lines show the model of eq 4 with (without) convolution with the internal and kinetic energy distributions of the reactants.

observed in this CID reaction is ThO+, formed by a loss of the OD ligand in reaction 15. OThOD+ + Xe → ThO+ + OD + Xe ΔH0 = 6.00 eV

(15)

ThO2+

Evidence for the product was observed with a small cross section, but because this product lies very close in mass to the reactant beam, its cross section was not of sufficient quality for quantitative analysis. The ThO+ product cross section was analyzed using eq 4, as shown in Figure 6. Optimized parameters of eq 4 obtained from analysis of reaction 15 cross sections for multiple data sets are given in Table 1. Because all sources of energy in the reactants are explicitly included in the modeling, the threshold energy determined equals the desired BDE at 0 K, D0(OTh+−OD) = 6.00 ± 0.17 eV. Theoretical Results. The ground state of ThO+ is 2Σ+, as identified experimentally using pulsed field ionization-zero kinetic energy photoelectron spectroscopy.46 This state has a (1σ)2(1π)4(2σ)1 valence electron configuration, where the 1σ and 1π orbitals are bonding orbitals formed between O (2p) and Th+ (6d) orbitals and the 2σ nonbonding orbital is 5899


Article

The Journal of Physical Chemistry A Table 2. Comparison of Experimental 0 K Bond Energies (eV) to Theoretical Values bond Th −D Th+−C Th+−O OTh+−D OTh+−O OTh+−OD OThOD+−(D2O)

structure

+

Th(OD)3+ OThOD+(D2O)

expt 2.48 4.82 8.57 2.33 4.66 6.00 2.96 2.78

c

(0.07) (0.29)d (0.14)d (0.24) (0.15)e (0.17) (0.05) (0.05)

MADf

B3LYPa

B3PW91a

PBE0a

2.92 4.81 8.70 2.73 4.89 5.57 2.86 1.41 0.25

2.95 5.17 8.81 2.76 5.10 5.70 2.78 1.37 0.34

2.87 5.20 8.75 2.71 5.03 5.72 2.86 1.44 0.30

B3LYPb

2.70 1.32

All theoretical values include zero-point energy effects with unscaled frequencies as calculated using cc-pVQZ basis sets. For Th+−X bonds, theoretical energies include an estimated spin−orbit correction of −0.40 eV for Th+ (see ref 47) and a spin−orbit stabilization energy of 0.18 eV for the 3Δ1 level of ThD+ (see ref 45). bReference 8. cReference 45. dReference 47. eDerived from reaction 8b. fMean absolute deviation from experiment. a

as the value of 4.79 ± 0.37 eV recommended by Marçalo and Gibson.58 Combining our cationic BDE with the literature information suggests that IE(ThO2) = 8.81 ± 0.21 eV, which agrees with but is more precise than the 8.9 ± 0.4 eV value given by Marçalo and Gibson.58 Some support for this lower value comes from CCSD(T) calculations of Averkiev et al. who obtain 8.58 eV.60 Note that D0(OTh−O) is much higher than D0(OTh+−O) because ionization of ThO2 (1A1)50,61−63 removes an electron from a bonding orbital. Likewise, IE(ThO2) is much greater than IE(ThO) because ionization of ThO (1Σ+)50,62,64−70 removes an electron from the 2σ nonbonding orbital, primarily Th (7s).50 Comparison of Experimental and Theoretical Bond Energies. In the previous work, we have measured BDEs for ThD+, ThC+, and ThO+ and compared these to the same levels of theory utilized in the present work, as well as more advanced theoretical approaches. For ThD+, ThO+, and ThC+, the BDEs calculated here are almost identical to those calculated using the same levels of theory and similar cc-pwCVQZ-PP/aug-ccpwCVQZ basis sets by Cox et al.45,47 These results are summarized in Table 2 along with experimental and theoretical BDEs for DThO + , OThO + , OThOD + , and ThO 3 D 3 + determined here. The reasonable agreement between the well-established experimental BDE value for ThO+ and calculated values demonstrates that reasonable thermochemical data can be obtained from the levels of theory used here for the systems being studied. Theoretical BDEs for ThD+, ThO+, and ThC+ determined here include corrections for the spin−orbit interactions (as detailed in the associated previous work), which improve agreement with the experimental values. This demonstrates that the spin−orbit interaction is significant in these actinide systems; however, DThO+, OThO+ , OThOD+, and ThO3D3+ have no first order spin−orbit splittings. For all values in Table 2, theory predicts BDEs to be in reasonable agreement with the experimental values with mean absolute deviations (MADs) of 0.25−0.34 eV, Table 2. (Similar MADs are obtained for only the four BDEs measured in the present work.) The OTh+−D bond energy measured here, 2.33 ± 0.24 eV, is slightly overestimated by the theory, 2.71−2.76 eV, Table 2. The experimentally measured D0(OTh+−D) value compares well with D0(Th+−D) = 2.48 ± 0.07 eV, measured in our lab from the reactions of Th+ with H2, HD, and D2.45 In that study, theoretical values also slightly overestimated the experimental value, which is consistent with what we observe here. Indeed, the experimental difference in

Th+−OD π orbitals, and 2a″ and 3a′ are the Th+−O π orbitals. The 4a′ bonding orbital is formed by combining the O (2pσ) and Th+ (7s−6dσ) orbitals. Here, we calculate Th+−O, Th+−OD, and O−D bond lengths of 1.835, 2.069, and 0.963 Å, respectively, and a OThO bond angle of 114° at the B3LYP/cc-pVQZ level. This geometry is similar to that obtained for OThOH+ by RMG8 with bond lengths of 1.84, 2.08, and 0.97 Å, respectively, and a OThO bond angle of 113.6°. RMG used the B3LYP functional with the Stuttgart− Dresden ECP (60 electrons) and associated basis set for Th+51,52 with the 6-311++G(d,p) basis set for H and O.53−55 The ground state of OThOD+(D2O) is found to be 1A with no symmetry, which is consistent with the DFT calculations carried out by RMG.8 In OThOD+(D2O), we calculate Th+−O, Th+−OD, and Th+−OD2 bond lengths of 1.855, 2.089, and 2.531 Å, respectively, and O−Th+−OD and O−Th+−OD2 bond angles of 115° and 87°, respectively. This geometry is similar to that obtained for OThOH (H2O)+ by RMG,8 with bond lengths of 1.86, 2.10, and 2.55 Å, respectively, and bond angles of 114° and 87°, respectively. The ground state of Th(OD)3+ is calculated to be 1A1 with C3V symmetry, having uniform ThO and OD bond lengths of 2.071 and 0.961 Å, respectively, and OThO bond angles of 107° at the B3LYP/cc-pVQZ level. These are similar to values calculated for Th(OH)3+ by RMG8 with bond lengths of 2.08 and 0.96 Å, respectively, and bond angles of 106.8°. Comparison of Experimental Bond Energies with the Literature. To our knowledge, except for ThO2+, no experimental thermodynamic data on the species evaluated here are available for comparison with our results. For ThO2+, the D0(OTh+−O) bond energy has been reported previously as 4.49 ± 0.3156 and as 4.82 ± 0.22 eV in the gas-phase ion and neutral thermochemistry (GIANT) compilation57 (both at 298.15 K). Marçalo and Gibson58 took the weighted average of these and recommended a value of 4.79 ± 0.37 eV. The GIANT tables also report a 0 K value of 4.79 ± 0.22 eV, where the correction agrees with our own calculations of the 298−0 K conversion, −0.030 ± 0.003 eV. Konings et al. report thermochemistry for ThO and ThO2 that indicates a neutral BDE of D0(OTh−O) = 6.87 ± 0.15 eV.59 This value can be combined with IE(ThO2) = 8.9 ± 0.4 eV recommended by Marçalo and Gibson58 and IE(ThO) = 6.60263 ± 0.0002 eV from Goncharov and Heaven46 to yield D0(OTh+−O) = 4.57 ± 0.43 eV. We believe this latter value is probably the best available in the literature until now. Our measured BDE value of 4.66 ± 0.15 eV agrees well with this literature value as well 5900


Article

The Journal of Physical Chemistry A the Th+−D and OTh+−D BDEs, 0.15 ± 0.25 eV, is comparable to those predicted by theory, 0.16−0.19 eV. This comparison indicates that reaction 7 forms the lowest energy isomer, inserted DThO+, rather than ThOD+. Likewise, the OTh+−O bond energy measured here, 4.66 ± 0.15 eV, is slightly overestimated by the theory, 4.89−5.10 eV, whereas the OTh+−OD bond energy measured here, 6.00 ± 0.17 eV, is slightly underestimated by the theory, 5.57−5.72 eV, Table 2. The OThOD+−D2O bond energy measured here is 2.96 ± 0.05 eV, when the phase space theory (PST) model uses molecular parameters for Th(OD)3+ or 2.78 ± 0.05 eV, when OThOD+(D2O) molecular parameters are used. The former value agrees well with the values calculated here, that is 2.78− 2.86 eV, for Th(OD)3+, Table 2, and with the calculated BDE of 2.70 eV for Th(OH)3+ by RMG.8 In contrast, the latter value is much greater than the BDEs of 1.37−1.44 eV calculated here for loss of water from OThOD+(D2O) (where RMG calculated 1.32 eV). This comparison unambiguously determines that the ThO3D3+ species formed in reaction 12 is the trihydroxide, Th(OD)3+. Additional information can be obtained from our experimental results by using thermochemical cycles. Using D0(OTh+−OD) = 6.00 ± 0.17 eV and D0(D−OD) = 5.212 ± 0.003 eV,30 the experimental exothermicity of reaction 6 is derived to be 0.79 ± 0.17 eV. Similarly, the experimental BDE of OThO+−D can be derived as 5.80 ± 0.23 eV, which can be used to determine the experimental exothermicity of reaction 10, 0.59 ± 0.23 eV. PESs for the Reaction of ThO+ with D2O. The PESs for the reaction of ThO+ + D2O calculated at the B3LYP/ccpVTZ level are shown in Figure 8, with structures in Figure 9.

Figure 9. Structures of reactants, intermediates, transition states, and products along the PESs of ThO+ + D2O calculated at the B3LYP/ccpVTZ level. Selected bond lengths (Å) and bond angles (°) are indicated.

Table 3. Energies and Zero-Point Energies for Stationary States Calculated along the PESs for the Reaction of ThO+ and D2Oa species (state)

Figure 8. PESs for the reaction of ThO+ with D2O calculated at the B3LYP/cc-pVTZ level. See structures in Figure 9.

Energies and zero-point energies for stationary states calculated along the PESs are listed in Table 3. All transition states (TSs) obtained have only one imaginary frequency, and intrinsic reaction coordinate (IRC) scans were performed to verify that the TSs obtained connect the desired intermediates. In one case (INT2 going to TS2/3), the IRC scan failed because of the very loose nature of this TS (see below). In this case, a relaxed potential surface scan was shown to connect them. In the entrance channel, the ThO+(D2O) complex, INT1 is formed, lying 1.54 eV below the reactant asymptote. INT1 reacts further through the transition state, TS1/2, in which a deuterium atom is transferred from the D2O ligand to the

ZPE (Eh)b

energy (Eh)

ThO ( Σ ) + D2O ( A1) INT1 ThO+(D2O) (2A′) TS1/2 (2A′)

−558.382019 −558.441193 −558.409557

INT2 Th(OD)2+ (2A1) TS2/P (2A′)

−558.489791 −558.386886

P OThOD+ (1A′) + D (2S1/2) TS1/3 (2A) TS2/3 (2A) INT3 OThD(OD)+ (2A′) DThO+ (1A′) + OD (2Πu) ThOD+ (3Δ) + OD (2Πu) ThOD+ (1Σ+) + OD (2Πu) TS3/4 (2A′)

−558.398379

INT4 ThO2+(D2) (2B2) ThO2+ (2Σ+) + D2 (1Σg+) ThO2+ (2Σu+) + 2D (2S1/2)

−558.384810 −558.375055 −558.199369

+

2 +

1

−558.399806 −558.404314 −558.406101 −558.292577 −558.262711 −558.261424 −558.344834

0.017650 0.020070 0.016959 (1155) 0.019155 0.012348 (1199) 0.011792 0.014065 (658) 0.012405 (73) 0.013138 0.011411 0.014792 0.014864 0.011935 (1255) 0.012680 0.010430 0.003313

Erel (eV) 0.000 −1.544 −0.768 −2.892 −0.277 −0.605 −0.582 −0.749 −0.778 2.264 3.169 3.206 0.856 −0.211 −0.007 4.580

a

Calculated at the B3LYP/cc-pVTZ level. bFor transition states, imaginary frequencies in cm−1 are included in parentheses.

oxygen ligand. TS1/2 is 0.78 eV above INT1 but remains 0.77 eV below the reactants. TS1/2 leads to the global minimum INT2, thorium dihydroxide cation, Th(OD)2+, which lies 2.89 eV below the reactants. INT2 can react further by losing one D atom through TS2/P, which lies 2.61 eV above 2 and only 0.28 eV below the reactants. Ordinarily, such a simple bond 5901


Article

The Journal of Physical Chemistry A cleavage would occur through a loose TS; however, TS2/P lies 0.33 eV above the OThOD+ + D products (P). The reason for this barrier can be understood by examining the MOs for the OThOD+ product in Figure 7. As D (2S1/2) approaches the O ligand, its electron interacts with the doubly occupied 4a′ HOMO, leading to a repulsive interaction. A slightly lower energy path to these products is to pass through INT3, OThD(OD)+, 0.78 eV below the reactants. INT3 can be formed directly from INT1 via TS1/3 by transferring a D atom from water to thorium, or from INT2 via TS2/3 by transferring a D atom from OD to thorium. The former pathway is limited by TS1/3, 0.58 eV below the reactants, whereas the latter pathway is limited by TS2/3, 0.75 eV below the reactants. Note that INT3 has a long Th−D bond because the closed shell OThOD+ species cannot readily form another covalent bond. Thus, INT3 can lose the deuterium atom bonded directly to Th+ at a cost of only 0.17 eV to form the OThOD+ + D products (P). Note that TS2/P, TS1/2, TS2/3, and TS1/3 all lie below the reactant asymptote, consistent with the observed barrierless formation of OThOD+ + D in reaction 6, Figure 1. There are two isomers of [Th,O,D]+, that is, DThO+ and ThOD+. DThO+ (1A′) + OD (2Πu) is calculated to lie 2.26 eV above the ThO+ + D2O reactant asymptote, with ThOD+ (3Δ) + OD (2Πu) lying another 0.94 eV higher in energy. DThO+ can form by a loss of an OD ligand from INT3. ThOD+ can form directly from INT2 by a loss of OD ligand. As noted above, the theoretical BDE for OTh+−D is in reasonable agreement with the experimentally determined value, consistent with formation of the lower energy DThO+ species at the threshold for reaction 7. The formation of ThO2+ + D2 (reaction 8a) is calculated to be barely exothermic, 0.01 eV below the ThO+ + D2O reactant asymptote; however, the formation of ThO2+ + D2 is limited by the four-centered transition state, TS3/4, which lies 0.86 eV above the reactant asymptote. In TS3/4, the deuterium atoms in INT3 are transferred toward each other to form the ThO2+(D2) adduct, INT4, which lies only 0.20 eV below the final ThO2+ + D2 products. In contrast, ThO2+ + 2D formation (reaction 8b) can occur from the OThOD+ product by loss of the D atom, as suggested above. Note that the energy calculated for TS3/4 is consistent with the threshold measured for reaction 8a of 0.98 ± 0.07 eV. TS3/4 also limits reaction 9, where the measured threshold of 0.85 ± 0.06 eV agrees very well with the calculated energy difference of 0.863 eV between TS3/4 and ThO2+ + D2. PESs for the Reaction of ThO2+ with D2O. The PES and structures for the reaction of ThO2+ + D2O calculated at the B3LYP/cc-pVTZ level are shown in Figure 10. Energies and zero-point energies for stationary states calculated along the PESs are listed in Table 4. In the entrance channel, the ThO2+(D2O) complex (INT5) is formed, lying 1.61 eV below the reactant asymptote. INT5 reacts further through transition state TS5/6 in which a deuterium atom is transferred from the D2O ligand to one of the oxygen ligands. TS5/6 is 0.91 eV above INT5 but remains 0.69 eV below reactants. This process forms the global minimum intermediate, INT6, the bishydroxy thorium oxide cation, OTh(OD)2+, which lies 2.40 eV below the reactant asymptote. INT6 can lose one of the OD ligands over a loose TS to form the dominant product, OThOD+ + OD, which is 0.17 eV below the reactant asymptote, consistent with its barrierless, exothermic formation, Figure 3.

Figure 10. PES for the reaction of ThO2+ with D2O and structural information of intermediates and the transition state along the PES calculated at the B3LYP/cc-pVTZ level. Selected bond lengths (Å) and bond angles (°) are indicated.

Table 4. Energies and Zero-Point Energies for Stationary States Calculated along the PESs for the Reaction of ThO2+ and D2Oa species (state) +

Σu+)

2

1

+ D2O ( A1) ThO2 ( INT5 ThO2 (D2O)+ (2B2) TS5/6 (2A′) INT6 ThO(OD)2+ (2A1) OThOD+ (1A′) + OD (2Πu) Th(OD)2+ (2A1) + O (3P)

energy (Eh)

ZPE (Eh)b

Erel (eV)

−633.654896 −633.716708 −633.679930 −633.744613 −633.660350

0.018807 0.021612 0.018327 (1142) 0.020437 0.017925

0.000 −1.606 −0.694 −2.397 −0.172

−633.581655

0.019155

2.002

a

Calculated at the B3LYP/cc-pVTZ level. bFor the transition state, the imaginary frequency in cm−1 is included in parentheses.

The high energy product observed, ThO 2 D 2 + , can potentially be formed by an O atom loss from INT5, yielding INT1, or from INT6, yielding the more stable INT2, Th(OD)2+. Formation of this latter product in reaction 11 is calculated to require 2.00 eV, which is much lower in energy compared to the apparent experimental threshold near 4 eV, Figure 3. Clearly, the O atom loss is thermodynamically much less favorable than loss of OD from INT6 or D2O from INT5, which appear to inhibit reaction 11 at its threshold. PES for the Association Reaction of OThOD+ with D2O. The PES and structures for the association reaction of OThOD+ + D2O calculated at the B3LYP/cc-pVTZ level are shown in Figure 11. Energies and zero-point energies for stationary states calculated along the PESs are listed in Table 5. In the entrance channel, the OThOD+(D2O) complex (INT7) is formed, lying 1.50 eV below the reactant asymptote. INT7 can react further through the transition state, TS7/8 in which a deuterium atom is transferred from the D2O ligand to the oxide ligand. TS7/8 is 0.60 eV above INT7 but remains 0.90 eV below the reactants. TS7/8 forms the global minimum association complex, the trihydroxide complex, Th(OD)3+ (INT8), which is calculated to lie 2.96 eV below the reactant asymptote (2.78−2.86 eV using pVQZ basis sets, Table 2). Clearly, there is no overall barrier to the formation of the thorium trihydroxide cation. As noted above, the barrierless approach to INT8 is consistent with the observation of the association reaction 12, Figure 5, and the well depth 5902


Article


the experimental exothermicities of these reactions, 0.20 ± 0.15 eV, succinctly calculated as =D0(DO−D) − E0(8b). This correspondence suggests that the origins of the endothermic features in the OThOD+ cross sections in both reactions 6 and 10 are the same. All possible structures and different electronic states of ThO2D+ were explored computationally; however, none of these species lie at energies that correspond to the measured endothermic features. Rather, we suggest that these features may correspond to direct reactions analogous to stripping-like reactions. Reaction of OThOD+ with D2O formed the associative product, ThO3D3+, in an exothermic and barrierless reaction with significantly low efficiency under collision-less conditions (∼2%). This association product is long-lived before dissociating back to the reactants. Comparing the D0 obtained after analyzing the ThO3D3+ cross section using the PST model to the theoretical values in this work and available in the literature unambiguously determines that the ThO3D3+ species formed in this reaction is the trihydroxide, Th(OD)3+. Thus, the mechanism for the formation of the Th(OD)3+(IV) association complex is fully elucidated for the first time and happens according to the following reactions under single collision conditions

Figure 11. PES for the association reaction of OThOD+ + D2O and structural information of intermediates and the transition state along the PES calculated at the B3LYP/cc-pVTZ level. Selected bond lengths (Å) and bond angles (°) are indicated. The thick black horizontal line represents the well depth, D0 with its uncertainty experimentally measured for the association complex, ThO3D3+.

Table 5. Energies and Zero-Point Energies for Stationary States Calculated along the PES for the Reaction of OThOD+ and D2Oa species (state) +

1

OThOD ( A′) + D2O (1A1) INT7 OThOD+ (D2O) (1A) TS7/8 (1A) INT8 Th(OD)3+ (1A1)

energy (Eh)

ZPE (Eh)b

Th+ + D2 O → ThO+ + D2

ThO+ + D2 O → OThOD+ + D

Erel (eV)

−634.356063

0.027286

0.000

−634.413830

0.029883

−1.501

−634.388711 −634.466327

0.026898 (1095) 0.028959

−0.899 −2.955

OThOD+ + D2 O → Th(OD)3+

The products are formed in barrierless and exothermic reactions in all three cases. The exothermicities of these three reactions are experimentally derived to be 3.46 ± 0.14, 0.79 ± 0.17, and 2.96 ± 0.05 eV, respectively. BDEs for OTh+−D, OTh+−O, OTh+−OD, and OThOD+−D2O are measured for the first time to be 2.33 ± 0.24, 4.66 ± 0.15, 6.00 ± 0.17, and 2.96 ± 0.05 eV, respectively. Additionally, the barrier heights for reactions 8a and 9 are measured to be 0.98 ± 0.07 and 0.85 ± 0.06 eV, respectively. The BDEs and barrier heights calculated at the B3LYP, B3PW91, and PBE0 levels of theory agree reasonably well with the experimental values. RMG8 have pointed out that the solution chemistry of Th+ is complex in part because it readily hydrolyzes to Th(OH)n(4−n)+ (n = 1−4). The present study elucidates the detailed mechanism and energetics for this microscopic process in the case of n = 3. As such, it provides both experimental and theoretical benchmarks for understanding the mechanism of thorium hydrolysis in solution. Further, new insights into the solution chemistry of Th+ and actinides, in general, could be drawn on the basis of these results.

a

Calculated at the B3LYP/cc-pVTZ level. bFor the transition state, the imaginary frequency in cm−1 is included in parentheses.

determined by the PST analysis agrees well with the formation of INT8.

■

CONCLUSIONS OThOD+ is the dominant product formed in both the reactions of ThO+ and ThO2+ with D2O. In both reactions, the OThOD+ cross section exhibits two distinct features: a barrierless exothermic pathway at lower energies and an apparent endothermic feature at higher energies. At low energies, the efficiencies of the reactions of ThO+ and ThO2+ with D2O are quite low, 0.27 ± 0.05 and 0.40 ± 0.08, respectively, which is unusual for barrierless exothermic reactions. The low efficiencies of these reactions can be attributed to the tight TSs en route to the products, TS1/2 or TS1/3 and TS5/6, as shown in the PESs of reactions 6 and 10, Figures 8 and 10, respectively. Because passage over the tight TS is entropically unfavorable relative to dissociation back to the reactants, this also explains why the reaction efficiencies decrease with increasing energy in both reactions 6 and 10. Similar reasoning was given by Cornehl et al.5 for the lower reaction efficiencies of Th+ and additional metals5 with H2O to form metal oxide cations and H2. As mentioned above, approximate modeling of the thresholds for the apparent endothermic features in the OThOD+ cross sections for both reactions 6 and 10 yields 0.54 ± 0.08 and 0.65 ± 0.07 eV, respectively. The difference in these thresholds, 0.11 ± 0.11 eV, roughly matches the difference in

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

P. B. Armentrout: 0000-0003-2953-6039 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work is supported by the Heavy Element Chemistry Program, Office of Basic Energy Sciences, U.S. Department of Energy, grant no. DE-SC0012249. We thank the Center of 5903


Article


(21) Chesnavich, W. J.; Bowers, M. T. Statistical phase space theory of polyatomic systems. Application to the cross section and product kinetic energy distribution of the reaction C2H4+ + C2H4 → C3H5+ + CH3. J. Am. Chem. Soc. 1976, 98, 8301−8309. (22) Stein, S. E.; Rabinovitch, B. S. Accurate Evaluation of Internal Energy Level Sums and Densities Including Anharmonic Oscillators and Hindered Rotors. J. Chem. Phys. 1973, 58, 2438−2445. (23) Beyer, T.; Swinehart, D. F. Algorithm 448: number of multiplyrestricted partitions. Commun. ACM 1973, 16, 379. (24) Stein, S. E.; Rabinovitch, B. S. On the Use of Exact State Counting Methods in RRKM Rate Calculations. Chem. Phys. Lett. 1977, 49, 183−188. (25) Rothe, E. W.; Bernstein, R. B. Total collision cross sections for the interactions of atomic beams of alkali metals with gases. J. Chem. Phys. 1959, 31, 1619−1627. (26) Muntean, F.; Armentrout, P. B. Guided Ion Beam Study of Collision-Induced Dissociation Dynamics: Integral and Differental Cross Sections. J. Chem. Phys. 2001, 115, 1213−1228. (27) Chantry, P. J. Doppler Broadening in Beam Experiments. J. Chem. Phys. 1971, 55, 2746−2759. (28) Lifshitz, C.; Wu, R. L. C.; Tiernan, T. O.; Terwilliger, D. T. Negative Ion-molecule Reactions of Ozone and Their Implications on the Thermochemistry of O3‑. J. Chem. Phys. 1978, 68, 247−260. (29) Weber, M. E.; Elkind, J. L.; Armentrout, P. B. Kinetic Energy Dependence of Al+ + O2 → AlO+ + O. J. Chem. Phys. 1986, 84, 1521− 1529. (30) Johnson, R. D., III. NIST Computational Chemistry Comparison and Benchmark Database, NIST Standard Reference Database Number 101 Release 19; NIST, 2018; available online: http://cccbdb.nist.gov/. (31) Talrose, V. L.; Vinogradov, P. S.; Larin, I. K. On the Rapidity of Ion-molecule Reactions. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 1, pp 305−347. (32) Armentrout, P. B.; Simons, J. Understanding Heterolytic Bond Cleavage. J. Am. Chem. Soc. 1992, 114, 8627−8633. (33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision A.02; Gaussian Inc.: Pittsburgh, PA, 2009. (34) Becke, A. D. Density-functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (35) Lee, C.; Yang, W.; Parr, R. G. Development of the ColleSalvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785− 789. (36) Perdew, J. P.; Burke, K.; Wang, Y. Generalized gradient approximation for the exchange-correlation hole of a many-electron system. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 16533− 16539. (37) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158−6170. (38) Peterson, K. A. Correlation consistent basis sets for actinides. I. The Th and U atoms. J. Chem. Phys. 2015, 142, 074105. (39) Weigand, A.; Cao, X.; Hangele, T.; Dolg, M. Relativistic SmallCore Pseudopotentials for Actinium, Thorium, and Protactinium. J. Phys. Chem. A 2014, 118, 2519−2530. (40) Schuchardt, K. L.; Didier, B. T.; Elsethagen, T.; Sun, L.; Gurumoorthi, V.; Chase, J.; Li, J.; Windus, T. L. Basis Set Exchange: A Community Database for Computational Sciences. J. Chem. Inf. Model. 2007, 47, 1045−1052. (41) Feller, D.; Aprà, E.; Nichols, J. A.; Bernholdt, D. E. The structure and binding energy of K+−ether complexes: A comparison of MP2, RI-MP2, and density functional methods. J. Chem. Phys. 1996, 105, 1940−1950. (42) Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007−1023.

High Performance Computing (CHPC) at the University of Utah for the generous allocation of computing time.

■

REFERENCES

(1) Wang, D.; van Gunsteren, W. F.; Chai, Z. Recent advances in computational actinoid chemistry. Chem. Soc. Rev. 2012, 41, 5836− 5865. (2) Schneider, E.; Sachde, D. The Cost of Recovering Uranium from Seawater by a Braided Polymer Adsorbent System. Sci. Global Secur. 2013, 21, 134−163. (3) Aspinall, H. C. Chemistry of the f-Block Elements; Gordon and Breach: London, 2001. (4) Eliav, E.; Kaldor, U. Study of Actinides by Relativistic Coupled Cluster Methods. Computational Methods in Lanthanide and Actinide Chemistry; John Wiley & Sons Ltd, 2015; pp 23−54. (5) Cornehl, H. H.; Wesendrup, R.; Diefenbach, M.; Schwarz, H. A Comparative Study of Oxo-Ligand Effects in the Gas-Phase Chemistry of Atomic Lanthanide and Actinide Cations. Chem. Eur. J. 1997, 3, 1083−1090. (6) Santos, M.; Marçalo, J.; Leal, J. P.; Pires de Matos, A.; Gibson, J. K.; Haire, R. G. FTICR-MS study of the gas-phase thermochemistry of americium oxides. Int. J. Mass Spectrom. 2003, 228, 457−465. (7) Cox, R. M.; Armentrout, P. B. Activation of Water by Thorium Cation: A Guided Ion Beam and Quantum Chemical Study. J. Am. Soc. Mass Spectrom. 2019, in press. (8) Rutkowski, P. X.; Michelini, M. d. C.; Gibson, J. K. Proton Transfer in Th(IV) Hydrate Clusters: A Link to Hydrolysis of Th(OH)2 2+ to Th(OH)3 + in Aqueous Solution. J. Phys. Chem. A 2013, 117, 451−459. (9) Loh, S. K.; Hales, D. A.; Lian, L.; Armentrout, P. B. CollisionInduced Dissociation of Fen+ (n = 2 − 10) with Xe: Ionic and Neutral Iron Cluster Binding Energies. J. Chem. Phys. 1989, 90, 5466−5485. (10) Schultz, R. H.; Armentrout, P. B. Reactions of N4+ with Rare Gases from Thermal to 10 eV c.m.: Collision-Induced Dissociation, Charge Transfer, and Ligand Exchange. Int. J. Mass Spectrom. Ion Processes 1991, 107, 29−48. (11) Khan, F. A.; Clemmer, D. E.; Schultz, R. H.; Armentrout, P. B. Sequential Bond Energies of Cr(CO)x+, x = 1 − 6. J. Phys. Chem. 1993, 97, 7978−7987. (12) Schultz, R. H.; Crellin, K. C.; Armentrout, P. B. Sequential Bond Energies of Fe(CO)x+ (x = 1 − 5): Systematic Effects on Collision-Induced Dissociation Measurements. J. Am. Chem. Soc. 1991, 113, 8590−8601. (13) Clemmer, D. E.; Aristov, N.; Armentrout, P. B. Reactions of scandium oxide (ScO+), titanium oxide (TiO+) and vanadyl (VO+) with deuterium: M+-OH bond energies and effects of spin conservation. J. Phys. Chem. 1993, 97, 544−552. (14) Clemmer, D. E.; Chen, Y.-M.; Khan, F. A.; Armentrout, P. B. State-Specific Reactions of Fe+(a6D, a4F) with D2O and Reactions of FeO+ with D2. J. Phys. Chem. 1994, 98, 6522−6529. (15) Hinton, C. S.; Citir, M.; Manard, M.; Armentrout, P. B. Collision-induced Dissociation of MO+ and MO2+ (M = Ta and W): Metal Oxide and Dioxide Cation Bond Energies. Int. J. Mass Spectrom. 2011, 308, 265−274. (16) Teloy, E.; Gerlich, D. Integral Cross Sections for Ion-Molecule Reactions. 1. The Guided Beam Technique. Chem. Phys. 1974, 4, 417−427. (17) Ervin, K. M.; Armentrout, P. B. Translational Energy Dependence of Ar+ + XY → ArX+ + Y (XY = H2, D2, HD) from Thermal to 30 eV c.m. J. Chem. Phys. 1985, 83, 166−189. (18) Hales, D. A.; Lian, L.; Armentrout, P. B. Collision-Induced Dissociation of Nbn+ (n = 2 − 11): Bond Energies and Dissociation Pathways. Int. J. Mass Spectrom. Ion Processes 1990, 102, 269−301. (19) Daly, N. R. Scintillation Type Mass Spectrometer Ion Detector. Rev. Sci. Instrum. 1960, 31, 264−267. (20) Koizumi, H.; Armentrout, P. B. The Kinetic Energy Dependence of Association Reactions. A New Thermokinetic Method for Large Systems. J. Chem. Phys. 2003, 119, 12819−12829. 5904


Article


OThCO, and Other Products. J. Am. Chem. Soc. 2000, 122, 11440− 11449. (63) Zhou, M.; Andrews, L. Infrared spectra and pseudopotential calculations for NUO+, NUO, and NThO in solid neon. J. Chem. Phys. 1999, 111, 11044−11049. (64) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand Reinhold: New York, 1979; Vol. IV. (65) Paulovič, J.; Nakajima, T.; Hirao, K.; Seijo, L. Third-order Douglas−Kroll ab initio model potential for actinide elements. J. Chem. Phys. 2002, 117, 3597−3604. (66) Paulovič, J.; Nakajima, T.; Hirao, K.; Lindh, R.; Malmqvist, P. Å. Relativistic and correlated calculations on the ground and excited states of ThO. J. Chem. Phys. 2003, 119, 798−805. (67) Watanabe, Y.; Matsuoka, O. All-electron Dirac−Fock− Roothaan calculations for the ThO molecule. J. Chem. Phys. 1997, 107, 3738−3739. (68) 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. (69) Seijo, L.; Barandiarán, Z.; Harguindey, E. The ab initio model potential method: Lanthanide and actinide elements. J. Chem. Phys. 2001, 114, 118−129. (70) Marian, C. M.; Wahlgren, U.; Gropen, O.; Pyykkö, P. Bonding and electronic structure in diatomic ThO: Quasirelativistic effective core potential calculations. J. Mol. Struct.: THEOCHEM 1988, 169, 339−354.

(43) Su, T.; Chesnavich, W. J. Parameterization of the Ion-polar Molecule Collision Rate Constant by Trajectory Calculations. J. Chem. Phys. 1982, 76, 5183−5185. (44) Su, T.; Bowers, M. T. Classical ion-molecule collision theory. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 1, pp 83−118. (45) Cox, R. M.; Armentrout, P. B.; de Jong, W. A. Reactions of Th+ + H2, D2, and HD Studied by Guided Ion Beam Tandem Mass Spectrometry and Quantum Chemical Calculations. J. Phys. Chem. B 2016, 120, 1601−1614. (46) Goncharov, V.; Heaven, M. C. Spectroscopy of the ground and low-lying excited states of ThO+. J. Chem. Phys. 2006, 124, 064312. (47) Cox, R. M.; Citir, M.; Armentrout, P. B.; Battey, S. R.; Peterson, K. A. Bond Energies of ThO+ and ThC+ : A Guided Ion Beam and Quantum Chemical Investigation of the Reactions of Thorium Cation with O2 and CO. J. Chem. Phys. 2016, 144, 184309. (48) Zhou, J.; Schlegel, H. B. Ab Initio Molecular Dynamics Study of the Reaction between Th+ and H2O. J. Phys. Chem. A 2010, 114, 8613−8617. (49) Mazzone, G.; Michelini, M. d. C.; Russo, N.; Sicilia, E. Mechanistic Aspects of the Reaction of Th+ and Th2+ with Water in the Gas Phase. Inorg. Chem. 2008, 47, 2083−2088. (50) Infante, I.; Kovacs, A.; Macchia, G. L.; Shahi, A. R. M.; Gibson, J. K.; Gagliardi, L. Ionization Energies for the Actinide Mono- and Dioxides Series, from Th to Cm: Theory versus Experiment. J. Phys. Chem. A 2010, 114, 6007−6015. (51) 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. (52) Cao, X.; Dolg, M.; Stoll, H. Valence basis sets for relativistic energy-consistent small-core actinide pseudopotentials. J. Chem. Phys. 2003, 118, 487−496. (53) Clark, T.; Chandrasekhar, J.; Spitznagel, G. n. W.; Schleyer, P. V. R. Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements, Li−F. J. Comput. Chem. 1983, 4, 294−301. (54) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Selfconsistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys. 1980, 72, 650−654. (55) Blaudeau, J.-P.; McGrath, M. P.; Curtiss, L. A.; Radom, L. Extension of Gaussian-2 (G2) theory to molecules containing thirdrow atoms K and Ca. J. Chem. Phys. 1997, 107, 5016−5021. (56) Hildenbrand, D. L.; Gurvich, L. V.; Yungman, V. S. The Chemical Thermodynamics of Actinide Elements and Compounds. Part 13: The Gaseous Actinide Ions; IAEA: Vienna, 1985. (57) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. Gas-Phase Ion and Neutral Thermochemistry. J. Phys. Chem. Ref. Data 1988, 17, 1. ISBN 0883185628 (58) Marçalo, J.; Gibson, J. K. Gas-Phase Energetics of Actinide Oxides: An Assessment of Neutral and Cationic Monoxides and Dioxides from Thorium to Curium. J. Phys. Chem. A 2009, 113, 12599−12606. (59) Konings, R. J. M.; Benes, O.; Kovacs, A.; Manara, D.; Sedmidubsky, D.; Gorokhov, L.; Iorish, V. S.; Yungman, V.; Shenyavskaya, E.; Osina, E. The Thermodynamic Properties of the f-Elements and their Compounds. Part 2. The Lanthanide and Actinide Oxides. J. Phys. Chem. Ref. Data 2014, 43, 013101. (60) Averkiev, B. B.; Mantina, M.; Valero, R.; Infante, I.; Kovacs, A.; Truhlar, D. G.; Gagliardi, L. How accurate are electronic structure methods for actinoid chemistry? Theor. Chem. Accounts 2011, 129, 657−666. (61) Kovács, A.; Konings, R. J. M. Computed Vibrational Frequencies of Actinide Oxides AnO0/+/2+ and AnO20/+/2+ (An = Th, Pa, U, Np, Pu, Am, Cm). J. Phys. Chem. A 2011, 115, 6646−6656. (62) Andrews, L.; Zhou, M.; Liang, B.; Li, J.; Bursten, B. E. Reactions of Laser-Ablated U and Th with CO2: Neon Matrix Infrared Spectra and Density Functional Calculations of OUCO, 5905


Mechanism and Energetics of the Hydrolysis of Th+ To Form Th(OD)3

Recommend Documents