Richard M
Cox
*,
Kali M.
Melby
,
Amanda D.
French
and
Michael J.
Rodriguez
Pacific Northwest National Laboratory, Richland, WA 99352 USA, USA. E-mail: richard.cox@pnnl.gov
First published on 5th December 2023
f-Block chemistry offers an opportunity to test current knowledge of chemical reactivity. The energy dependence of lanthanide cation (Ln+ = Ce+, Pr+, Nd+–Eu+) and actinide cation (An+ = Th+, U+–Am+) oxidation reactions by CO2, was observed by inductively coupled plasma tandem mass spectrometry. This reaction is commonly spin-unallowed because the neutral reactant (CO2, 1Σ+g) and product (CO, 1Σ+) require the metal and metal oxide cations to have the same spin state. Correlation of the promotion energy (Ep) to the first state with two free d-electrons with the reaction efficiency indicates that spin conservation is not a primary factor in the reaction rate. The Ep likely influences the reaction rate by partially setting the crossing between the ground and reactive states. Comparison of Ln+ and An+ congener reactivity indicates that the 5f-orbitals play a small role in the An+ reactions.
While many current studies focus on condensed phases, gas phase studies offer an attractive alternative. Gas phase studies eliminate many perturbations in condensed phases like solvent effects so that the fundamental interaction of the analyte species can be probed. Indeed, mass spectrometry has proven adept at observing the reactions of actinides (An) and lanthanides (Ln). Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) has been utilized to study An+ (An+ = Th+–Cm+) with many small molecules.1–6 Similar reactions of the Ln+ with small molecules have been studied using selected ion flow tube mass spectrometry (SIFT-MS).7–9 Unfortunately, FTICR-MS and SIFT-MS are thermal methods where only barrierless, exothermic or thermoneutral reactions can be observed, somewhat limiting the impact of the studies and the reactions that can be probed. Furthermore, observation of a reaction at a single energy point can mislead conclusions. For example, the low efficiency reaction observed between Th+ + CH4 in FTICR-MS experiments was originally attributed to spin-restrictions;4 however, it was shown later in energy dependence studies by guided ion beam tandem mass spectrometry (GIBMS) to be caused by a small barrier10 where the low efficiency reaction was observed from a small population of reactants within the energy distribution with sufficient energy to overcome the reaction barrier.
GIBMS10–27 oxidation studies shed light on the reaction by observing it over a wide range of kinetic energies. The energy dependence of the reaction often simplifies the interpretation of results, as noted in the GIBMS study of Th+ + CH4,10 and allows the observation of endothermic reactions or reactions with a barrier. However, many of the An elements are significantly radioactive so that they are difficult to obtain and work with safely. Consequently, studies of the energy dependence of transuranic species have not been reported in the gas phase. Yet there remain examples of low efficiency reactions, for example Pu+ + CO2 from FTICR-MS studies,1 that may require knowing the energy dependence of the reaction to correctly interpret.
Additionally, the reactions of Ln+ and An+ with CO2 is an interesting system to study, in part because SIFT-MS7 and FTICR-MS1,2 studies provide examples of exothermic reactions where no or limited product is observed. Furthermore, atmospheric CO2 also remains a large reservoir of carbon that can potentially be tapped with the correct catalyst. However, CO2 is difficult to crack because activating the CO bond according to reaction (1) is formally spin-forbidden:
CO2(1Σ+g) → CO(1Σ+) + O(3P) | (1) |
For CO2, reaction (2) is often spin-forbidden because unpaired electrons in the metal cation (M+) and oxygen usually pair when forming MO+ to lower the spin in the metal oxide cation product:
M+(sL) + CO2(1Σ+) → MO+(s−2Λ) + CO(1Σ+) | (2) |
Here we present the energy dependence of An+ (An+ = Th+, U+–Am+) reactions with CO2 studied using an Agilent 8900 inductively coupled plasma tandem mass spectrometry (ICP-MS/MS) over an extended energy range. The goal of this study is to understand the role of the An+ valence electrons, and specifically the 5f-orbitals, in the reaction through observing the reactivity trend across the An series. For comparison as a baseline when f-electrons are not expected to contribute,29,30 the energy dependence of Ln+ (Ln+ = Ce+, Pr+, Nd+, Sm+, Eu+) reactions are also presented.
Experiments were conducted using an Agilent 8900 “triple quadrupole” mass spectrometer (ICP-MS/MS; Agilent Technologies, Santa Clara, CA, USA) located within a radiological facility at Pacific Northwest National Laboratory.31 This instrument utilized an ICP ion source equipped with a quartz double-pass spray chamber and 100 μL min−1 perflouroalkoxy alkane (PFA) nebulizer. The instrument utilizes a quadrupole mass filter (1 amu resolution) to mass select the reactant ion beam that is passed into a collision cell contained within an octopole ion guide where the reactant ion is reacted with the neutral gas, CO2. Products and unreacted ions drift to the end of the octopole where they are focused through a second quadrupole mass filter, mass selected, and subsequently detected at a standard electron multiplier detector.
Stock multi-element standard solutions containing 1 ng g−1 of Ce–Nd, Sm, Eu, Th, and U in 2% HNO3 were prepared. To minimize high activity radioisotopes within the instrument, a multi-element standard solution of 1 pg g−1 of Np–Am in 2% HNO3 was also prepared. Table 1 lists the isotopes used for each M+. Carbon dioxide (CO2; 99.99%; Oxarc) was used as the reaction gas. The flow rates ranged from 0.06–0.13 mL min−1, which corresponds to estimated pressures of 1.4 and 2.8 mTorr. Tuning parameters were optimized to provide maximum sensitivity for the high mass range using a 1 ng g−1 Th and U solution. The octopole bias was adjusted in intervals from +7 V to −45 V while keeping other cell parameters constant: octopole rf peak-to-peak voltage of 180 V, axial acceleration of 2.0 V, and a kinetic energy discrimination (KED, the voltage difference between the octopole bias in the CRC and the second quadrupole) of −10.0 V. Data were acquired in triplicate using 1 s acquisition times for the 1 ng g−1 solutions and 4 s for the 1 pg g−1 solutions.
M+ (isotope) | Mass (amu) | 300 K | 700 K | 5000 K | 8000 K | 9000 K | 10000 K |
---|---|---|---|---|---|---|---|
a Masses and electronic states taken from ref. 28 (https://physics.nist.gov/PhysRefData/Handbook/periodictable.htm). | |||||||
Ce+ (140) | 139.90 | 0.00 | 0.04 | 0.58 | 0.69 | 0.71 | 0.74 |
Pr+ (141) | 140.91 | 0.01 | 0.03 | 0.42 | 0.54 | 0.57 | 0.61 |
Nd+ (146) | 145.91 | 0.01 | 0.03 | 0.57 | 0.79 | 0.85 | 0.90 |
Sm+ (149) | 148.92 | 0.02 | 0.06 | 0.43 | 0.59 | 0.64 | 0.69 |
Eu+ (153) | 152.92 | 0.00 | 0.01 | 0.28 | 0.68 | 0.81 | 0.93 |
Th+ (232) | 232.04 | 0.00 | 0.02 | 0.66 | 0.85 | 0.90 | 0.93 |
U+ (238) | 238.05 | 0.01 | 0.03 | 0.51 | 0.67 | 0.71 | 0.74 |
Np+ (237) | 237.05 | 0.00 | 0.01 | 0.23 | 0.28 | 0.30 | 0.31 |
Pu+ (242) | 242.06 | 0.00 | 0.01 | 0.70 | 0.87 | 0.91 | 0.95 |
Am+ (243) | 243.06 | 0.00 | 0.00 | 0.19 | 0.52 | 0.63 | 0.75 |
I = I0e−ρσl | (3) |
The energy in the laboratory frame is estimated from the octopole bias by the relationship:33
(4) |
ECM = ELAB × M/(M + m) | (5) |
MO+ + CO2 → MO2+ + CO | (6) |
The cross sections of CeO+, PrO+, and NdO+ formed in reaction (2) initially decrease with increasing energy consistent with a barrierless exothermic reaction until energies near 2.4, 1.9, and 1.2 eV, respectively. Beyond the initial decline, the cross sections increase peaking near the OCO bond dissociation energy, D0(OC–O) = 5.453 eV36 where sufficient energy is available for MO+ to dissociate. It should be noted that the initial low energy feature obscures where this increase begins making it likely that the more efficient the reaction, the more likely the threshold of the higher energy feature is obscured. Conversely, the cross sections of SmO+ and EuO+ increase with increasing energy. For SmO+, where D0(Sm+–O) = 5.596 ± 0.004 eV,37 the observed cross section indicates a barrier to this reaction, which is exothermic by 0.143 eV. This behavior has been observed previously in GIBMS experiments.15 In the present experiment, the apparent threshold is shifted to lower energies than that observed in the GIBMS experiment, indicating the presence of excited states. Given the typical operating temperature of the ICP plasma is 8000–10000 K, the observation of excited states from this source is expected. A second increase in cross section magnitude is also observed for all Ln+ peaking around 10 eV. This may be an effect from ion focusing caused by the interaction between differing radio frequencies between the two quadrupoles and octopole regions within the instrument No effort is made to interpret or characterize this feature.
The reaction efficiencies (k/kcol) of the Ln+ reactions relative to the Langevin–Gioumousis–Stevenson (LGS) collision limit34 (kcol) are listed in Table 2. Two approaches were taken to calculate the reaction efficiency. The first approach was to average the k/kcol for all energies below 1 eV. The second approach was to calculate the k/kcol for the lowest observed energy, 0.15–0.2 eV, which corresponds to measuring the reaction efficiency at ≈1600–2300 K. For the Ln+, the difference between each approach is minimal. For comparison, the reaction efficiencies of GIBMS,15,17,19 selected ion flow tube mass spectrometry (SIFT-MS),7 and FTICR-MS38 efficiencies are also listed in Table 2. In general, the ICP-MS/MS values here are within the combined uncertainties of the previous measurements. The largest observed difference was for Pr+ where the GIBMS and SIFT-MS value are half of the ICP-MS/MS mean (but still within the combined measurement uncertainty). This difference can likely be attributed to the difference in the metal cation electronic distribution. Smaller differences for the other Ln+ can also be attributed to electronic distributions.
M+ | E p(nd2)b | This workc | This workd | GIBMS | SIFT-MSe | FTICR-MS |
---|---|---|---|---|---|---|
a k col is derived from the Langevin–Gioumosis-Stevenson model cross section for CO2. b See ref. 22 and references therein. c Average k/kcol for all energies <1 eV. d k/kcol for the lowest energy measured (0.15–0.20 eV). e Ref. 7. f Work in progress, see ref. 26. g Ref. 38. h Ref. 19. i Ref. 17. j No reaction observed. k A barrier in excess of the thermodynamic threshold was observed. See ref. 15. l Ref. 1. m Ref. 11. n Work in progress, see ref. 25. o Ref. 2. | ||||||
Ce+ | 0.00 | 0.86 ± 0.43 | 0.77 ± 0.38 | 0.48 ± 0.10f | 0.66 ± 0.20 | 0.70 ± 0.25g |
Pr+ | 0.73 | 0.50 ± 0.25 | 0.47 ± 0.23 | 0.25 ± 0.05h | 0.23 ± 0.07 | |
Nd+ | 1.14 | 0.12 ± 0.06 | 0.12 ± 0.06 | 0.09 ± 0.02i | 0.05 ± 0.02 | 0.08 ± 0.03g |
Sm+ | 2.35 | 0.01 ± 0.01 | NRj | NRjk | NRj | |
Eu+ | 3.74 | NRj | NRj | NRj | ||
Th+ | 0.00 | 1.19± 0.60 | 0.79 ± 0.40 | 0.88 ± 0.18b | 0.95 ± 0.33g | |
0.35 ± 0.18l | ||||||
U+ | 0.57 | 0.93 ± 0.47 | 0.66 ± 0.33 | >1m, 1.18 ± 0.24n | 1.02 ± 0.36g | |
0.29 ± 0.15l | ||||||
Np+ | 0.9 ± 0.4 | 0.77 ± 0.39 | 0.58 ± 0.29 | 0.30 ± 0.15l | ||
Pu+ | 2.14 | 0.05 ± 0.03 | NRj | 0.003 ± 0.002l | ||
Am+ | 3.6 ± 0.2 | NRj | NRj | 0.001 ± 0.001o |
A comparison of k/kcol between the two methods indicates that the average efficiency below 1 eV differs from the efficiency determined from the lowest energy point. This difference largely disappears when comparing the second energy point to the average. Previous measurements of reaction efficiency (Table 2), are primarily limited to FTICR-MS measurements by Gibson and coworkers.1,2 Additional measurements for Th+ and U+ are available from FTICR-MS,38 GIBMS (Th+),22 and an early ion beam experiment (U+).11 The Th+ and U+ efficiencies reported here compare well with the ion beam11,22 and FTICR-MS results from Cornehl et al.38 The FTICR-MS measurements of Gibson and coworkers1,2 are lower than those observed here with the exception of Pu+ and Am+ where very inefficient reactions under nominally thermal conditions were observed in the FTICR-MS work. Note that the FTICR-MS measurements of Gibson and coworkers1,5 are systematically lower than those observed in GIBMS experiments as observed for several reactions with Th+,13,18,22,40 U+,23 and Gd+.14,16 The differences in k/kcol between measurements has been previously attributed to a different starting ion electronic energy distribution.10,13
The differences here compared to the GIBMS experiments can likely be attributed (at least in part) to the starting electronic distribution. This is most evident in the shifted threshold or reaction (2) for Sm+ that must indicate the presence of excited states. The Agilent instrument does not include a high pressure region (∼500 mTorr) to collisionally cool reactants ions that the GIBMS41 instrument does. Indeed, the SIFT-MS incorporates a similar high pressure drift tube.7 Also, the present work was extrapolated to the single collision conditions where GIBMS naturally operates. Because the cross sections between the methods are within the combined uncertainties of those methods, this is probably an acceptable approach, but the cross section may retain some multi-collision character. In an ICP-MS/MS cross section of Co+ + O2 at higher pressures (3.5 mTorr), these pressure effects have appeared as increased cross section magnitude by a factor of 2 compared to GIBMS experiments.31 Another potential difference is that the octopole only spans the physical length of the collision cell in the Agilent instrument. Consequently, the effective cell length (from pumping gradients outside of the cell) will extend into regions pre and post octopole so that reactions or scattering outside of the collision cell may not be fully represented in the reaction cross section. Nevertheless, we anticipate that the relative trends from the work presented here are accurate.
Fig. 3 presents a similar analysis from the current work for both the Ln+ and An+, indicating a strong linear correlation between the k/kcol and Ep(nd2). Noticeably, the cross sections of SmO+ and EuO+ in Fig. 1 show clear barriers. The result for EuO+ is not surprising because this reaction is endothermic by 1.42 eV.42 In the case of SmO+, reaction (2) is exothermic by 0.143 eV, as noted above. This barrier was observed previously in GIBMS experiments with carefully thermalized Sm+ reactant ions.15Ab initio calculations indicate that this barrier could be attributed to the crossing seam between the potential energy surface (PES) of reaction (2) evolving from the ground state reactant asymptote and the PES evolving from an excited state reactant asymptote lying Ep(5d2) higher in energy, where the latter PES correlated with the formation of the SmO+ ground state product. Here, similar barriers are also observed for PuO+ and AmO+ in Fig. 2, where reaction (2) is expected to be exothermic by 1.3 ± 0.2 eV and 0.35 ± 0.29 eV for Pu+ (D0(Pu+–O) = 6.75 ± 0.20 eV) and Am+ (D0(Am+–O) = 5.80 ± 0.29 eV),39 respectively. As for Sm+, the barriers observed for Pu+ and Am+ can may also be attributed to the energy at the crossing seam between the PESs evolving from the ground and reactive states. Interestingly, FTICR-MS reactions have indicated that for the much less thermodynamically favored reaction of Pu+ with NO (D0(N–O) = 6.51 eV),36k/kcol = 0.17 was observed, even though ΔHr = −0.24 ± 0.20 eV is only mildly exothermic. Because the reaction of M+ + NO (2Π) has less spin-restrictions than reaction (2), this observation may argue that spin conservation could still be important for heavy metals.
Fig. 3 Correlation of the reaction efficiency relative to the LGS collision rate (k/kcol) to the promotion energy Ep(nd2) for n = 5 (blue) and n = 6 (red). The solid blue and red line represent the least-squares linear regression fits of the Ln+ and An+ experimental data (R2 = 0.97 and R2 = 0.99). Sm+ has been excluded from the Ln+ linear regression fit. The dashed lines represent Ep(nd2) of the indicated cation with dark blue and dark red lines corresponding to Ln+ and An+ species, respectively. See also Table 1. |
Reaction (2) requires that M+ and MO+ have the same spin state for the reaction to conserve spin. Table 3 lists the ground states of M+ and the expected state of MO+ from theoretical calculations and indicates that for the majority of M+ in this study, the formation of ground state MO+ from reaction (2) is indeed spin-forbidden. The exception is U+ (4I, 5f37s2)28 that likely forms UO+ (4Γ, πδϕ)6 (where the orbital configuration listed is for the unpaired, non-bonding f-orbitals). Because the ground level of Th+ is actually a mixed 4F3/2–2D3/2 (6d27s/6d7s2)43 configuration, reaction (2) forming ThO+ (2Σ+, σ)44 may also conceivably be considered spin-allowed. Given that reaction (2) is not spin-restricted for some of the An+ but is for most, the strong correlation of reaction rate to Ep(6d2) in Fig. 3 suggests that Ep(6d2) has a stronger effect on the reaction rates than spin conservation.
Ln+ | Ce+ | Pr+ | Nd+ | Pm+ | Sm+ | Eu+ |
---|---|---|---|---|---|---|
a Ref. 28 (https://physics.nist.gov/PhysRefData/Handbook/periodictable.htm). b Ref. 26. c Ref. 19. d Ref. 17. e Presumed based on calculation trends. f Ref. 15. g Ref. 43 (https://www.lac.universite-paris-saclay.fr/Data/Database/). h See also ref. 13 and ESI. i Unless otherwise noted, ref. 6. j Ref. 44. | ||||||
M+a | 4H (4f5d2) | 5I (4f36s) | 6I (4f46s) | 7H (4f56s) | 8F (4f66s) | 9S (4f76s) |
MO+ | 2Φ (ϕ)b | 3H (δϕ)c | 4H (σδϕ)d | 5Λ (4f4)e | 6Δ (ϕ2δπ2)f | 7Λ (4f6)e |
An+ | Th+ | Pa+ | U+ | Np+ | Pu+ | Am+ |
M+bg | 4F–2Dh (6d27s/6d7s2) | 3H (5f27s2) | 4I (5f37s2) | 7L(5f46d7s) | 8F (5f67s) | 9S (5f77s) |
MO+i | 2Σ+ (σ)j | 3Φ (σϕ) | 4Γ (πδϕ) | 5Γ (σπδϕ) | 6Σ+ (σδ2ϕ2)n | 7Σ− (π2δ2ϕ2) |
Unlike the An+, reaction (2) is likely formally spin-unallowed for the Ln+ in this study, Table 3. There is a noticeable change in reaction efficiency between the Ln+ and An+, but many k/kcol are within the combined experimental uncertainties for each An+ and Ln+ congener of similar excitation energy, so it is also unlikely that spin-conservation plays a significant role at least at the lower energies. Like the An+, the strong correlation of Ep(5d2) to the rates of reaction (2) in Fig. 3 strongly suggests that Ep(5d2) more strongly influences the reaction rate than spin-conservation. Nevertheless, spin conservation may still play a role at higher energies.
A high energy feature is observed for CeO+, PrO+, and NdO+ in Fig. 1 with apparent thresholds of ≈1–2.5 eV. Similar high energy features appear in the An+ reactions, but these are less pronounced than those in the Ln+ reactions. This feature was also observed in GIBMS studies of reaction (2) for Pr+ and Nd+, and it was speculated that this higher energy pathway was the formation of an excited state LnO+ by a spin-allowed reaction. This was further substantiated by quantum chemical calculations that indicated at least one excited state with the correct spin and consistent excitation energy to the observed threshold.17,19 These features appear inversely correlated with Ep(nd2); however, this is likely an artifact from the magnitude of the reaction cross section of the lower feature that obscures the start of the threshold region of the higher energy feature cross section. Indeed, when subtracting the low energy feature of the LnO+ and AnO+ cross sections in Fig. 1 and 2 by scaling the LGS cross section, the apparent thresholds are indistinguishable within the limits of uncertainty.
As noted above, it has been previously proposed that the role of Ep(nd2) in modulating the reaction rate is by partially determining the energy relative to the reactants of the crossing seam between the PESs originating from the ground state M+ and the excited state with two d-electrons.22 Here, we consider a simple potential energy surface that consists of an initial intermediate formed, an association of CO2 with ground state M+, forming the M+–CO2 adduct. This has been demonstrated for both Sm+ and Gd+, where D0(Sm+–CO2) = 0.42 ± 0.03 eV15 and D0(Gd+–CO2) = 0.38 ± 0.05 eV16 have been measured in collision induced dissociation (CID) reactions. A second intermediate presumably exists where the metal inserts into activated carbon dioxide bond forming O–M+–CO. This is likely equivalent to an association complex between ground state MO+ and CO. Indeed, CID reactions of such species yield D0(OSm+–CO) = 0.97 ± 0.09 eV15 and D0(OGd+–CO) = 0.57 ± 0.05 e,V16 bond energies consistent with a weakly bound ion–dipole interaction. Thus, Table 3 indicates that M+–CO2 and O–M+–CO will usually have different spin states. Because formation of the MO+ ground state requires two nd-electrons from M+, the surface that includes the second intermediate must evolve from the excited state asymptote Ep(nd2) higher in energy than the ground state M+. The MO+ bond energy for An+ and Ln+ also depend upon Ep(nd2) because of the requirement of the two d-electrons to form the ground state bond so that the energy of the second intermediate is also partially set by this energy (the remaining influence is the strength of the OM+–CO bond). The ground and excited state surfaces interact to form a crossing seam that must be traversed to form ground state products from the ground state reactants. Therefore, when Ep(nd2) is sufficiently high, as is the case for Sm+, Eu+, Pu+, and Am+, the barrier exceeds the reactants energy. When Ep(nd2) is sufficiently low, as is the case for Ce+, Pr+, Nd+, Th+, U+, and Np+ the barrier is localized between the two intermediates. Notably, the observed reaction rate is the equilibrium between the M+–CO2 falling apart forming the reactants and the forward reaction forming the products. Thus, the height of the crossing seam relative to the M+–CO2 adduct defines how competitive the forward reaction is compared to the backward reaction, and, therefore, the rate limiting step. Fig. 4 illustrates this concept using reaction (2) surfaces for U+ and Pu+. Fig. 4 is semiquantitative estimating intermediate well depths from Sm+ CID reactions15 and product energies from UO+ and PuO+ BDEs.23,39
Fig. 4 Semiquantitative potential energy surface of M+ + CO2 →MO+ + CO indicating that Ep and the intermediate well depth determine the crossing seam between the surface originating from the ground state reactant asymptote (black) and the surface leading to the ground state products. For species like Pu+ (blue) that have a sufficiently high promotion energy, Ep = 2.14 eV,39 the crossing between surfaces exceeds the reactant energy and a barrier is observed. For species like U+ (blue) that have a lower promotion energy, Ep = 0.57eV,39 is lower than the reactant energy forming a localized barrier between the intermediates that affects the observed reaction efficiency. The intermediates are considered electrostatic interactions between ground state M+ and CO2 (M+–CO2) and ground state MO+ and CO (O–M+–CO). Values are estimated from Sm+ CID reactions.15 Product asymptotes are taken from the BDEs from Marcalo and Gibson39 or Zhang et al.23 |
The use of the Sm+ data is likely reasonable assuming that the intermediates are only electrostatic interactions between the ground state reactant and the ground state product and the corresponding ligand (CO2 and CO). However, there may be fundamental differences between Sm+ and the An+ that make this analysis, Fig. 4, semiquantitative. Most notably, f-orbital participation cannot be ruled out with the present data. Nevertheless, there are key similarities between Sm+ and Pu+ that suggests that this explanation is plausible. Both Sm+ and Pu+ have similar promotion energies, Ep(Sm+) = 2.35 eV and Ep(Pu+) = 2.14 eV,28 and both M+ have barriers to an otherwise exothermic reaction as shown in Fig. 1 and 2. Computational modelling of the potential energy surface may provide additional information, but that is beyond the scope of this text.
The comparison of the Ln+ and An+reaction (2) cross sections are also instructive. In general, the absolute magnitude of the AnO+ cross sections are consistently higher than their Ln+ counterparts. Because the primary difference between the Ln+ and the An+ is the possibility of the f-orbitals participating in the reaction, this difference may indicate 5f-orbital participation for the An+. As noted above, the rate limiting step, the crossing seam energy, appears to be influenced by Ep and the insertion intermediate, O–M+–CO. The interaction of the carbonyl with M+ may indicate whether the 5f-orbitals participate in the O–An+–CO through π* back-bonding; however, CID reactions of ThCO+ [D0(Th+–CO) = 0.94 ± 0.06 eV] indicate that even when back-bonding does occur,21 it may not be sufficiently strong to distinguish between cases where it does not. Consequently, the carbonyl interaction is unlikely to greatly affect the energy of the crossing seam. The energy of the O–M+–CO intermediate's energy is also set by the ground state product asymptote. Previous work has suggested an intrinsic BDE model39,42 for both the LnO+ and AnO+. This model assumes that the orbitals used throughout both series to bind O are constant (i.e. the d-orbitals). Thus any LnO+ or AnO+ BDE could be calculated with knowledge of the intrinsic BDE [D0(M+–O)*] and the M+Ep(nd2) according to eqn (7):42
D0(M+–O) = D0(M+–O)* − Ep(nd2) | (7) |
Fig. 5 LnO+ (blue) and AnO+ (red) BDEs as a function of Ep(nd2) for n = 5 and 6. Vertical dashed lines are Ep(nd2) for the indicated M+. The solid lines represent the least-squares linear regression fit of each series. The LnO+ fit is 8.41–1.01Ep(5d2), R2 = 0.98. The AnO+ fit is 8.53–0.79Ep(6d2), R2 = 0.98. Ln+Ep and LnO+ BDEs are taken from Gibson42 or Armentrout and coworkers.14,17,19,27,37 An+Ep and AnO+ BDEs are taken from Marcalo and Gibson39 or Armentrout and coworkers.13,23 PaO+ is not shown but included in the fit. |
Finally, Fig. 1 and 2 establish the presence of excited states in the current work when comparing the previous GIBMS work.15,17,19 This is most notably evident in the threshold region of SmO+, where the apparent threshold of the ICP-MS/MS work is approximately 1.5 eV lower in energy than the GIBMS work.15 Excited states are expected in the current work because the ICP source temperature is 8000–10000 K, and there is limited ability in the ICP-MS/MS to quench excited states prior to injection into the reaction cell. By contrast, the GIBMS work utilizes a 1 m tube pressurized to ≈0.5 Torr of buffer gas where ions undergo ≈105 collisions.41 A conservative estimate of the ion electronic distribution in the GIBMS experiments is 700 ± 400 K.45–49 Likewise, the SIFT-MS experiments utilize a drift tube pressurized to 0.35 Torr with the reactive gas introduced downstream.7 The Gibson and coworkers FTICR-MS work thermalized ions produced by laser desorption/ionization by cooling periods in 10−5 Torr Ar.1–3,5 Notably, the FTICR-MS data is consistently low compared to GIBMS data. The difference is unclear. Nevertheless, GIBMS and SIFT-MS k/kcol for CO2 are in good agreement, Table 2. This is likely due to similar thermalization processes of the ions prior to reaction that presumably yield similar electronic energy distributions. Assuming a 700 K distribution, the average electronic energy (Eel) is 0.00–0.06 eV, Table 1. By contrast, at 5000 K, Eel is 0.19–0.66 eV.
Excited states can, in principle, be more or less reactive than the ground state depending on how the PES evolves from that state. When many surfaces exist with crossing seams, then presumably a pathway exists for the reaction to proceed to product despite the contour of the starting PES. In this limit, Eel would act as additional energy for reaction. Because more energy is available for reaction, a more efficient reaction is observed. The Ln and An have many low-lying states,28 so presumably the density of states in the reactant channel allows the extra Eel to act as additional energy available for reaction. Consequently, the higher electronic distribution in the ICP-MS/MS experiments likely leads to a higher observed reaction efficiency than the more thermalized GIBMS and SIFT-MS experiments, Table 2.
Notably, reaction (2), where CO2 and CO are both singlets, is often spin-forbidden for M+ all metals considered here except Th+ and U+. The correlation of the reaction rate to Ep(nd2) regardless of whether the reaction is spin-allowed indicate that for the Ln+ and An+, spin-restrictions do not appear to be a strong influence on the reaction rate.
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