The SmO+ bond energy has been measured by monitoring the threshold for photodissociation of the cryogenically cooled ion. The action spectrum features a very sharp onset, indicating a bond energy of 5.596 ± 0.004 eV. This value, when combined with the literature value of the samarium ionization energy, indicates that the chemi-ionization reaction of atomic Sm with atomic oxygen is endothermic by 0.048 ± 0.004 eV, which has important implications on the reactivity of Sm atoms released into the upper atmosphere. The SmO+ ion was prepared by electrospray ionization followed by collisional breakup of two different precursors and characterized by the vibrational spectrum of the He-tagged ion. The UV photodissociation threshold is similar for the 10 K bare ion and the He tagged ion, which rules out the possible role of metastable electronically excited states. Reanalysis and remeasurement of previous reaction kinetics experiments that are dependent on D0(SmO+) are included, bringing all experimental results in accord.

The oxidation reactions of samarium in the atmosphere have recently come under increased scrutiny in the context of chemi-ionization experiments in the upper atmosphere.1 Samarium was selected for those experiments from only a small number of materials because of its relatively low vaporization temperature along with what was believed to be an exothermic chemi-ionization (CI) reaction.2,3 The relevant reaction is

Sm+OSmO++e.
(1)

The energetics that govern the kinetics and equilibrium concentrations of these species entail a delicate balance between the bond dissociation energies (BDEs) of SmO and SmO+ as is evident in the level diagram shown in Fig. 1. A thermodynamic cycle yields the enthalpy of reaction (1) through

ΔCIHO=D0SmOIE(SmO),
(2a)
ΔCIHO=D0SmO+IE(Sm).
(2b)

The ionization energies (IEs) of Sm and SmO have been measured accurately and precisely as 5.6437 ± 0.0002 eV4 employing a method of autoionizing Rydberg series and 5.7427 ± 0.0006 eV5 using REMPI/PFI-ZEKE. The bond dissociation energy (BDE) of neutral SmO has been reported with much less precision as 5.76 ± 0.08 eV as determined from recalculating the results from Hildenbrand’s data6 for oxygen exchange with aluminum.7 Pedley and Marshall have recommended a higher value of D0(SmO) = 5.88 ± 0.17 eV.8 Direct measurements of the SmO+ BDE resulted in a value of 5.725 ± 0.07 eV.5 The lack of precise BDE measurements of both the neutral SmO and cationic SmO+ molecules thus limits the accuracy of the determination of the chemi-ionization reaction enthalpy.

FIG. 1.

Energy cycle connecting the BDEs and IEs involved in reaction (1). The bond energy of SmO+, D0(SmO+), red dashed arrow, determines the energy of this reaction (ΔrH0) because IE(Sm) is already known. The neutral BDE, D0(SmO), can be calculated using Eqs. (2a) and (2b).

FIG. 1.

Energy cycle connecting the BDEs and IEs involved in reaction (1). The bond energy of SmO+, D0(SmO+), red dashed arrow, determines the energy of this reaction (ΔrH0) because IE(Sm) is already known. The neutral BDE, D0(SmO), can be calculated using Eqs. (2a) and (2b).

Close modal

BDEs are often measured with methods that have a higher associated uncertainty than spectroscopic experiments such as those employed to measure the IEs. Currently, the enthalpy of the chemi-ionization reaction is derived from both IEs and BDEs, and therefore, its precision is limited by the BDE values. In favorable cases, BDEs can also be determined spectroscopically, provided that there is significant oscillator strength for excitation at the dissociation threshold. This can occur when an electron is excited to a bound electronically excited state with a displaced equilibrium bond length. In that case, vertical excitation of the v = 0 level in the ground electronic state carries significant Franck–Condon factors for excitation of both the high-lying bound vibrational states and the dissociation continuum. That scenario was observed, for example, in the O2 system.9 

A schematic depiction of the qualitative potential curves at play in the SmO+ system is presented in Fig. 2 to illustrate how the electronic structure is expected to evolve with internuclear distance. At the equilibrium geometry, one expects formation of an ionic bond with the simplest description corresponding to Sm3+ and O2−, an electron configuration that should diabatically correlate to ionic products with very large potential energies arising from the long-range electrostatic attraction between multiply charged atoms. The lowest energy products, on the other hand, are Sm+8F + O 3P, which correspond to the BDE in question. The overall scenario in this case is a more complex version of the well-known curves for NaI where the diabatic curve evolving from the ionic ground state configuration passes through a curve crossing with the potential arising from the approach of neutral Na and I atoms. In the SmO+ case, there should be at least two such crossings as the system explores sequential one-electron transfers to pass from Sm3+/O2− to Sm2+/O to Sm+/O configurations. These diabatic curves are sketched in Fig. 2 in blue, green, and orange. Measurement of D0 by photodissociation thus requires accessing the repulsive wall of an excited state curve that correlates with ground state Sm+ + O products.

FIG. 2.

Schematic of diabatic potential energy curves leading to dissociation into Sm+ and O products. The three curves represent the qualitative behaviors of the electronic configurations differing by the ionicity of the electron configurations.

FIG. 2.

Schematic of diabatic potential energy curves leading to dissociation into Sm+ and O products. The three curves represent the qualitative behaviors of the electronic configurations differing by the ionicity of the electron configurations.

Close modal

The actual spectroscopic situation in the lanthanide MO diatomic oxides is more favorable than cases such as NaI because of the very large number of electronically excited states arising from the open f shells.10 For example, Morse and co-workers have recently exploited that scenario to determine the BDEs of dozens of neutral metal chalcogens, such as oxides, sulfides, and selenides by observing the sharp reduction in the ion signal that occurs when vibrational levels just above the dissociation energy are efficiently removed by predissociation.11–14 Here, we report the determination of the vibrational frequency of the SmO+ ground state using He-tagging, carried out with mass-selective, cryogenic IR photodissociation spectroscopy and high-level electronic structure calculations of the SmO+ ground and electronically excited states near the equilibrium bond lengths. We then explore the electronic spectrum of He-tagged SmO+ as well as that of the temperature-controlled bare ion. The resulting abrupt onset for one-photon photodissociation leading to Sm+ + O products provides a spectroscopic determination of the BDE, D0(SmO+). Finally, we address the impact of this refined value on the chemi-ionization reaction (1) as well as previous measurements of the SmO+ BDE.5 

For the generation of SmO+, samples of either 99.9% samarium(III) nitrate hexahydrate or samarium(III) bromide, acquired from Alfa Aesar, were dissolved and diluted to a 1 mM concentration in a 1:1 methanol:water solution. The diatomic cation was produced by electrospraying the solution into a Thermo Fischer Scientific LTQ Orbitrap Velos Pro mass spectrometer (“Orbitrap”). Primary ionic precursors (with mass spectrum displayed in Fig. S1) were then subjected to collision-induced dissociation in the high-pressure region of the ion source with kinetic energies on the order of 100 eV. The SmO+ ions were transferred via a series of radio frequency (RF) ion guides to a custom-built, cryogenic time-of-flight photofragmentation instrument displayed in Fig. S2, where they were cooled to 22–24 K before injection into the double-focusing photofragmentation mass spectrometer. He atoms or H2 molecules were condensed or “tagged” onto the samarium oxide cation, and the resulting complexes were passed to a time-of-flight photofragmentation mass spectrometer where they were intercepted by either an infrared (Laservision) or ultraviolet (Continuum Horizon) laser beam. Photofragments arising from these interactions were isolated from parent ions using a reflectron and detected with microchannel plates. The UV action spectra were taken at trap temperatures of 15, 100, and 200 K. The Horizon UV laser wavelengths were calibrated using a HighFinesse UV/vis wavemeter to measure the signal wave output before frequency doubling to the 4–6 eV range.

All details of the guided ion beam tandem mass spectrometry experiments are provided in our previous work.5 There, it is pointed out that the average internal temperature of the Sm+ ions is estimated as 700 ± 400 K or the average internal energy is 0.06 ± 0.05 eV. The internal energies of SmO+ ions are presumed to be at 300 K because the ions undergo >105 collisions with ambient flow gases.

SmO+ is produced using the ESI source and accelerated to an energy of ∼100 eV at the entrance of a rectilinear quadrupole ion guide. The pressure in this region is sufficiently high (∼10−3 Torr) such that collisionally induced dissociation of the SmO+ yields a substantial fraction of Sm+. The Sm+ is subsequently mass-selected using a quadrupole mass filter prior to injection into the helium-buffered flow tube held at 0.35 Torr. This produced a population that showed two distinct branching ratios. The addition of CO2 to the beginning of the flow tube quenched the excited Sm+ reactants to the ground state before the reaction, resolving the mixed population down to a single more slowly reacting state, which is assumed to be the ground state.

To better understand the photophysical properties of SmO+, Fig. 3 presents the calculated (at the variational X2C-TDHF level of theory15–18) ground state potential energy curves from R = 1.6 to 2.9 Å (CCSD[T] calculated equilibrium bond length = 1.764 Å).19 The basis set for the Sm atom was Sapporo-DKH3-TZP-2012-diffuse,20 whereas a 6-311+G*21–23 basis set was used for the oxygen atom. At each distance, the electronic wave function was tested for stability.24 The ground state was found to occur with sextet spin multiplicity along the entire curve, consistent with an earlier analysis of the electronic level ordering by Armentrout and Cox.19 

FIG. 3.

Potential energy curves for the dissociation of SmO+ at the X2C-TDHF level of theory. The open black circles indicate the ground state potential energy surface, and the lowest 75 electronic excited states are plotted above by the markers. The hues and sizes of the markers represent the computed oscillator strengths (OS) for transitions arising from excitations as a function of bond lengths close to the equilibrium value of the ground electronic state. Darker and larger markers indicate larger OS values. Light blue markers located between the dashed vertical lines indicate final states with significant vibrational overlap (Franck–Condon factor) with the v = 0 wavefunction of the ground electronic state. Trace (A) (blue) shows a Morse extrapolation of calculated points that is characteristic of Sm3+O2−, while trace (B) (green) shows the Morse form corresponding to Sm2+O. The curve crossing between these two Morse potentials occurs at ∼2 Å. Groupings of excited state points indicated by α and β suggest excitation to the repulsive walls of nested electronic states.

FIG. 3.

Potential energy curves for the dissociation of SmO+ at the X2C-TDHF level of theory. The open black circles indicate the ground state potential energy surface, and the lowest 75 electronic excited states are plotted above by the markers. The hues and sizes of the markers represent the computed oscillator strengths (OS) for transitions arising from excitations as a function of bond lengths close to the equilibrium value of the ground electronic state. Darker and larger markers indicate larger OS values. Light blue markers located between the dashed vertical lines indicate final states with significant vibrational overlap (Franck–Condon factor) with the v = 0 wavefunction of the ground electronic state. Trace (A) (blue) shows a Morse extrapolation of calculated points that is characteristic of Sm3+O2−, while trace (B) (green) shows the Morse form corresponding to Sm2+O. The curve crossing between these two Morse potentials occurs at ∼2 Å. Groupings of excited state points indicated by α and β suggest excitation to the repulsive walls of nested electronic states.

Close modal

Interestingly, the calculated potential energy curve for the lowest electronic state exhibits a sharp discontinuity at around 2 Å. This also corresponds to an abrupt change in the qualitative character of the wave functions as illustrated in the insets of Fig. S3. This change is anticipated by the considerations regarding the R-dependence of the ionicity depicted in Fig. 2. As such, the points describing the ground electronic state in Fig. 3 were fit to two Morse functions as indicated by the solid lines. Note that the overall curve-crossing scenario is retained in the more accurate multireference CASPT2-SOC calculations of this system.

To interpret the electronic character along the surfaces, natural transition orbitals were computed for select transitions.25 Having established a stable ground state reference wave function, the lowest 75 electronic states were computed with X2C-TDHF. Because of the high number of states required, X2C-TDHF provides an affordable route to incorporate a variational treatment of spin–orbit and other relativistic effects. Generally, X2C-TDHF is known to perform well in describing the high energy states observed here (e.g., >5 eV).26,27 Specifically, it is less susceptible to the numerical instabilities often found in practical density functional approximations that are a particular challenge in describing reference states with multiple nearby spin solutions.

To assess the distribution of oscillator strength from the ground electronic state, the transition dipole matrix element was calculated as a function of bond length. These are presented in Fig. 3, with the size of the circle representing the relative electronic contribution to the oscillator strength (i.e., the R-dependence of the square of the electric dipole matrix element). Note that the onset of significant absorption begins in the ultraviolet at around 4 eV and extends to about 6 eV. The range of excited states accessible with significant Franck–Condon factors from the ground vibrational state is indicated by the blue dashed lines. Most importantly, the points fall into two classes (denoted α and β) such that each exhibits a large increase in energy with decreasing bond length. This behavior suggests that the excitation occurs to repulsive electronically excited states, which is the situation most favorable for determination of the BDE by photodissociation near the threshold. The excited states appear to involve excitations from σ to π* molecular orbital, consistent with a decrease in bonding character of the potential energy curve. A more complete survey of the R-dependence of the ground and electronically excited wave functions, as well as the distribution of oscillator strength, is presented in Fig. S3.

FIG. 4.

Cryogenic photodissociation IR spectra of (a) SmO+(He)3 and (b) SmO+(He) at 20 K, showing the Sm+–O stretching fundamental. The line at 875.8 cm−1 shows the CCSD(T) calculated stretch.5 If we assume a linear progression of redshift from the addition of each He atom, then the untagged stretching frequency is estimated to occur 878 cm−1.

FIG. 4.

Cryogenic photodissociation IR spectra of (a) SmO+(He)3 and (b) SmO+(He) at 20 K, showing the Sm+–O stretching fundamental. The line at 875.8 cm−1 shows the CCSD(T) calculated stretch.5 If we assume a linear progression of redshift from the addition of each He atom, then the untagged stretching frequency is estimated to occur 878 cm−1.

Close modal

The method used to generate SmO+ relies on fragmentation of precursor ions in the high-pressure region of the ESI mass spectrometer ion source. This necessarily creates nascent ions with considerable internal (vibrational and rotational) excitation as well as raises the possibility of metastable electronically excited states. The latter is especially likely, given the large number of spin-multiplicities available in this system. Once formed, the ions were cryogenically cooled in a RF ion trap with pure He buffer gas as well as with a mixture of 10% H2 in a balance of He. Upon cooling to 20 and 25 K, this resulted in efficient condensation of He and H2 to the SmO+ ions, as indicated by the mass spectra displayed in Fig. S1.

The IR photodissociation spectra of the SmO+(He)n=1,3 complexes are displayed in Fig. 4. Each consists of a single band in the fingerprint region with a width of about 15 cm−1. The peak of this feature is observed to redshift by 4 cm−1 from n = 1 to 3, suggesting that the fundamental in the bare SmO+ ion is 878 cm−1. This value is remarkably close to the 875.8 cm−1 frequency calculated by Armentrout and Cox19 for the 6Δ state of the ion, lending support to the conclusion that the v = 0 level of the ground electronic state is indeed prepared in the ion source. As a further check, we also prepared the ion starting from a different salt (SmBr3) and obtained similar behavior (vide infra) in the UV photodissociation presented in Sec. III C. Finally, we also monitored the vibrational spectra of the SmO+(H2)n=6–8 series with the results displayed in Figs. S4 and S5.

FIG. 5.

Photodissociation (PD) action spectrum of 15 K SmO+, detected in the Sm+ photoproduct yield. The solid black line indicates the continuous scan, while the blue dots in the insert indicate averaged yields at fixed points. The full spectrum calibration is set by matching the single points. The rise in the PD yield occurs over a range of about 1.5 meV, where the photon energy accuracy of each point is ±3 meV.

FIG. 5.

Photodissociation (PD) action spectrum of 15 K SmO+, detected in the Sm+ photoproduct yield. The solid black line indicates the continuous scan, while the blue dots in the insert indicate averaged yields at fixed points. The full spectrum calibration is set by matching the single points. The rise in the PD yield occurs over a range of about 1.5 meV, where the photon energy accuracy of each point is ±3 meV.

Close modal

The action spectrum arising from the photofragmentation process

SmO++hνSm++O
(3)

is presented in Fig. 5. It displays a very sharp onset of ∼5.6 eV, about 0.1 eV below the previously reported value5 of the bond energy. The region near the threshold was probed at fixed points (blue in Fig. 5 insert) to eliminate errors arising from the laser wavelength readout during the scan. The analysis of the sudden onset in terms of strong absorption across the dissociation threshold implies that bound vibrational states are accessed below the threshold but not detected in photodissociation. To address the behavior of the region below the dissociation threshold, we carried out a study of He tagged SmO+ with the results summarized in Fig. S6. Indeed, below the threshold (at 5.577 eV), we observe the tag loss channel

SmO+(He)+hνSmO++He,
(4)

whereas above the threshold at 5.745 eV, both He and O are dissociated upon photo-absorption,

SmO+He+hνSm++O+He.
(5)

We carried out a survey of the photodissociation yield of the SmO+(He) ion over the range of 1.75–5.85 eV but only observed action in the neighborhood of 5.6 eV. This observation is significant because the release of Sm in the upper atmosphere is known to be associated with the emission of light in the visible region of the spectrum.1 As such, we conclude that this emission is not associated with transitions involving low vibrational levels of the ground electronic state of SmO+.

As mentioned earlier, to ensure that the spectrum displayed in Fig. 5 was not dependent on the source conditions, we also measured the photodissociation spectrum of SmO+ created under different reaction conditions. For example, the Sm(NO3)3 solution was changed to SmBr3, and the collision energy required to generate SmO+ was changed systematically over the range 65–100 eV in the high pressure region of the ion source. These variations in conditions did not result in any changes in either the vibrational or electronic spectra. These results, in addition to the fact that only a single vibrational feature is observed under all conditions, support the conclusion that our spectroscopic results reflect the properties of a single electronic state prepared at 15 K.

The lowest trap temperature at which useful yields of the bare ion occurred was ∼15 K, below which condensation of He overwhelms the yield of bare SmO+. As such, the resulting thermal excitation (1.3 meV) is expected to contribute to the width (∼1.5 meV) of the observed onset. To test this interpretation, spectra of SmO+ were taken at different temperatures, with the results displayed in Fig. 6. The onsets are indeed incrementally broadened with increasing temperature, consistent with rotational excitation of the ion in the ground vibrational and electronic states.

FIG. 6.

The three spectra monitor the dissociation of SmO+ at temperatures of (a) 15 K, (b) 100 K, and (c) 200 K. Dashed lines in red indicate models with statistical populations of rotational states at the shown temperatures using the BDE shown by the arrow in (a).

FIG. 6.

The three spectra monitor the dissociation of SmO+ at temperatures of (a) 15 K, (b) 100 K, and (c) 200 K. Dashed lines in red indicate models with statistical populations of rotational states at the shown temperatures using the BDE shown by the arrow in (a).

Close modal

The temperature dependence of the rotational level populations was calculated assuming that they follow statistical (Boltzmann) distributions

nJn0=(2J+1)eB*J(J+1)/(kBT),
(6)

with a rotational constant (B = 0.372 cm−1) derived from the CCSD(T) calculated bond length of 1.764 Å.19 The shape of the photodissociation onset depends on the nature of the electronic transitions responsible for the oscillator strength. Even in the simple case where there is only one state in play such as that found in the D0 measurement of O2, the onset was found to follow the population of lower rotational levels.9 That could be rationalized by the fact that the upper-level vibrational states near dissociation have a much smaller rotational constant such that the ΔJ = ±1 selection rule displaces the electronic spectrum below the threshold mostly by the energy of the ground rotational state. In the case of SmO+, the situation is likely to be even more favorable because of the very high density of electronic states near the threshold. These provide a plethora of possibilities for accessing the dissociation threshold from excited J levels in the ground state. The dashed lines in Fig. 6 present the curves obtained by assuming a Boltzmann shape and fitting the experimental points by using the onset [arrow in Fig. 6(a)] as the value of D0 and the trap temperature. This treatment recovers the observed behaviors at 100 and 200 K. We report an error in the value of D0 to be the residual rotational energy of ±0.001 plus ±0.003 eV from uncertainty associated with the wavelength calibration of the Horizon OPO. This procedure yields a D0 value of 5.596 ± 0.004 eV.

The spectroscopic measurement of D0(SmO+) = 5.596 ± 0.004 eV is outside the uncertainty limits of the previous direct measurement of this BDE, 5.725 ± 0.07 eV,5 although it does lie within the two standard deviations (95% confidence). The previous value was a weighted average of the results of three guided ion beam tandem mass spectrometry (GIBMS) measurements. The threshold for the reaction Sm+ + CO → SmO+ + C yielded a SmO+ BDE of 5.62 ± 0.15 eV, in good agreement with the present spectroscopic value. Likewise, the collision-induced dissociation (CID) reaction SmO+ + Xe → Sm+ + O + Xe yielded 5.67 ± 0.16 eV, also in agreement with the present value. The CID reaction SmO+ + O2 → Sm+ + O + O2 yielded a value of 5.78 ± 0.09 eV, which is the most precise (sharpest onset) of the three values and hence weighted the most in taking the previous average. Notably, the conclusion that the reaction Sm+ + SO2 → SmO+ + SO was exothermic also played a role in the final determination as this observation (made in both selected ion flow tube [SIFT] and GIBMS experiments) indicated that D0(SmO+) > D0(O–SO) = 5.661 ± 0.014 eV.28 Hence, the final value of 5.725 ± 0.07 eV agreed with this lower limit.

In examining the CID studies of other lanthanide oxides (GdO+, NdO+, and PrO+), we have observed that the threshold energies (which equal the BDEs) obtained using CO and O2 collision gases are systematically slightly higher than BDE values obtained from CID experiments with Xe and the endothermic exchange reactions, Ln+ + CO → LnO+ + C and LnO+ + CO → Ln+ + CO2.29–31 We believe that this may be a result of rotational or vibrational excitation of the diatomic collision partner near the threshold, a phenomenon that cannot occur with the atomic Xe collision partner. If we discount the SmO+ BDE obtained from CID with O2, a weighted average of the previous results would be 5.64 ± 0.11 eV, in good agreement with the present spectroscopic result.

Finally, we reexamined the Sm+ + SO2 → SmO+ + SO reaction because the present SmO+ BDE suggests this reaction should be endothermic by 0.065 ± 0.014 eV, in direct contrast to the conclusions in previous work that the reaction was exothermic.5 We therefore revisited the experimental results and data analyses leading up to these conclusions. In the case of the GIBMS work, we carefully examined the low energy part of the dataset, which normally is associated with larger errors. For the SIFT measurements, we repeated the measurements with an improved instrument that incorporates a better electrospray ionization (ESI) source and time-of-flight mass-selection. The latter yields improved mass resolution and acquisition of complete spectra at every data point. The previously published GIBMS cross section for this reaction5 paralleled the collision cross section calculated according to the Su–Chesnavich trajectory model32 at low energies, except for the lowest energy point at 0.014 eV. In the present evaluation, we reexamined six independent datasets and took the average of all of these. This is actually a nontrivial exercise as the data are not acquired at precisely the same kinetic energy (KE) in each experiment because of fluctuations in the average collision energy (CE) near zero as well as the distribution of CE values. In the present evaluation, data points for six datasets were averaged for comparable energies (those within the absolute energy uncertainty of 0.015 eV). This average cross section is shown in Fig. S7 of the supplementary material along with the previously published GIBMS data. This comparison shows that the average is slightly higher than the published data (but within the 20% absolute uncertainty) and has the same shape, even at the very lowest energies. Hence, the lowest energy point in the previously published data does not appear to be an artifact. Figure 7 shows the reevaluated data converted to rate constants, as described in detail previously and outlined in the supplementary material,33 and plotted vs mean kinetic temperature (converted using ⟨E⟩ = 3kBT/2). The lowest temperature behavior is consistent with a slightly endothermic process.

FIG. 7.

Rate constants for the reaction of Sm+ with SO2 to form SmO+ as a function of inverse temperature. Blue circles show the SIFT data. Red triangles show the GIBMS cross sections converted to rate constants vs 1/T = (3/2)kB/⟨E⟩, as described in the text.

FIG. 7.

Rate constants for the reaction of Sm+ with SO2 to form SmO+ as a function of inverse temperature. Blue circles show the SIFT data. Red triangles show the GIBMS cross sections converted to rate constants vs 1/T = (3/2)kB/⟨E⟩, as described in the text.

Close modal

In the remeasurement of the Sm+ + SO2 reaction in the SIFT, we found three sources of error that may have contributed to the conclusion that the reaction was exothermic: (1) the combination of the old (dim) ESI source, many isotopes, and a lower resolution quadrupole mass filter led us to miss that some of the reactant was SmH+; (2) excited state Sm+ could be formed; and (3) SO2 clustering occurred to a greater extent than previously thought. All three potential artifacts are straightforward to eliminate in the improved apparatus. The new experimental setup discussed above produces no observable SmH+; The Sm+ is primarily (∼75%) in an unidentified excited state(s), which may be quenched to the ground state through addition of CO2 to the flow tube. The total rate constant for the excited state is about 10% larger than for ground state Sm+, which results in only a subtle effect in the primary ion decay, which would have been missed in the previous experiments. In contrast, the different states have distinct product branching under these experimental conditions. At room temperature, ground state Sm+ reacts with SO2 either by oxygen transfer yielding SmO+ or by association yielding Sm(SO2)+ in approximately equal amounts, whereas the excited state makes primarily or entirely SmO+. For the present purposes, the most pertinent experiment involved adding enough CO2 upstream so that only the ground state was present at the SO2 inlet. Then, kinetics can be measured in the normal fashion with a small correction associated with a very slow clustering rate with CO2.34 To correct for the clustering, we monitored the product branching while extrapolating to zero SO2 flow, as is normal in SIFT experiments. The partial rate constant for SmO+ formation is shown in Fig. 7. Excellent agreement is found between the revised SIFT and GIBMS experimental data. Both show a barrier that is attributed to a small endothermicity.

A more quantitative assessment of the barrier obtained in these experiments can be obtained using a simple Arrhenius model: k(T) = A exp(−Ea/kBT). Such an Arrhenius analysis yields activation energies (Ea) of 0.06 ± 0.05 eV (GIBMS) and 0.035 ± 0.02 eV (SIFT) along with pre-exponential factors (A) of 19 × 10−10 and 7.5 × 10−10 cm3/s, respectively. An Arrhenius analysis is inappropriate at higher temperatures where the rates begin to decline with increasing temperature. Therefore, we also analyzed the data using a temperature dependent pre-exponential factor: k(T) = A′ Tm exp(−E0/kBT), which also has the advantage of yielding a 0 K barrier height, E0. Now, the data yield values for E0 of 0.07 ± 0.05 eV (GIBMS) and 0.05 ± 0.03 eV (SIFT) along with m = −0.26 and A′ = 1.2 × 10−8 (GIBMS) and m = −0.39 and A′ = 1.1 × 10−8 cm3 (SIFT). Converted to SmO+ bond strengths, these E0 values yield D0 = 5.59 ± 0.05 and 5.61 ± 0.03 eV, respectively, in excellent agreement with the spectroscopic value reported earlier in this paper. Importantly, the discrepancy between the spectroscopic value and the lower limit of the SmO+ BDE implied by the previously reported erroneous Sm+ + SO2 results is now resolved. Measurements of the rate constants for quenching the excited state with CO2 and N2 will be reported in a future paper on further reactions of Sm+ oxidation reactions.

This refined determination of the SmO+ BDE has important implications on the energetics of reaction (1). Specifically, using the previous D0 value of 5.725 ± 0.07 eV, the CI reaction would be exothermic by 0.08 ± 0.07 eV, while the 5.596 ± 0.004 eV value reported here changes the ergodicity so that reaction (1) is now slightly endothermic (by 0.048 ± 0.004 eV). Although this is a small change, it is consequential when evaluating the efficacy of the CI method to generate free electrons in the atmosphere. The CI rate constants may be estimated from prior experimental work;2,3 however, no measurements of the reverse dissociative recombination (DR) rate constants or cross sections have been reported. Thermodynamic19,35,36 and kinetic2,3 properties of these reactions as a function of temperature are shown in Table I. The largest source of uncertainty in the calculated entropies and enthalpies of reaction is the electronic energy levels of SmO+, which have been estimated as described by Armentrout and Cox.19 The DR rate constant evaluated with the revised D0 value is estimated to be rapid at room temperature and above. Previously, using D0 = 5.725 eV, the DR rate estimated with the same protocol is 100× smaller at 300 K and 4× smaller at 1000 K than the current values, which are included in Table I. These temperatures are chosen to be a reasonable description of the atmosphere at the relevant altitude for the CI processes.37 

TABLE I.

Calculated thermodynamic and kinetic properties of the chemi-ionization (CI) reaction Sm + O → SmO+ + e and the reverse dissociative recombination (DR) process. K is the equilibrium constant, whereas kCI and kDR are the reaction rate constants for the CI and DR reactions.

T (K)ΔSr (J mol−1 K−1)ΔHr (kJ mol−1)KkCIa (cm3 s−1)kDR (cm3 s−1)
300 −71.6 ± 3 3.9 ± 1 4.0 ± 2 ×10−5 7.0 × 10−12 1.7 ± 0.5 × 10−7 
500 −68.2 5.0 8.2 ± 3 ×10−5 2.3 × 10−11 2.8 ± 0.8 × 10−7 
700 −65.9 7.7 10 ± 4 × 10−5 3.9 × 10−11 4.1 ± 1.2 × 10−7 
1000 −64.5 11.6 11 ± 4 × 10−5 5.7 × 10−11 5.4 ± 15 × 10−7 
T (K)ΔSr (J mol−1 K−1)ΔHr (kJ mol−1)KkCIa (cm3 s−1)kDR (cm3 s−1)
300 −71.6 ± 3 3.9 ± 1 4.0 ± 2 ×10−5 7.0 × 10−12 1.7 ± 0.5 × 10−7 
500 −68.2 5.0 8.2 ± 3 ×10−5 2.3 × 10−11 2.8 ± 0.8 × 10−7 
700 −65.9 7.7 10 ± 4 × 10−5 3.9 × 10−11 4.1 ± 1.2 × 10−7 
1000 −64.5 11.6 11 ± 4 × 10−5 5.7 × 10−11 5.4 ± 15 × 10−7 
a

Estimated from Refs. 2 and 3.

We report the determination of the BDE of the SmO+ ion by analyzing the threshold photodissociation onset starting from the cryogenically cooled ion. The sharp onset for Sm+ photoproducts at 15 K yields a dissociation energy D0 = 5.596 ± 0.004 eV. This onset is observed to broaden with increasing temperature, consistent with rotational hot band absorption. The vibrational spectrum of the “tagged” SmO+(He) complex yields a single feature centered at 876 ± 3 cm−1, assigned to the fundamental transition of the bare ion. This new determination of the bond energy implies that the Sm + O → SmO+ + e chemi-ionization (CI) reaction, previously thought to be exothermic, is actually slightly endothermic (by 0.048 ± 0.004 eV). Previous results related to SmO+ BDE measurements are re-evaluated in light of the revised D0 value reported here and found to be consistent with it. The revised energetics of the CI reaction have important implications for the rates of Sm chemi-ionization in the upper atmosphere.

See the supplementary material for auxiliary experimental and computational data including mass spectrometric data (CID-MS), vibrational predissociation data, guided ion beam kinetic data, and calculated orbital occupation results.

This material is based upon work supported by the Air Force Office of Scientific Research under AFOSR Award Nos. FA9550-18-1-0213 (MJ), FA9550-21-1-0344 (XL), and FA9550-20-1-0329 (PBA). The AFRL authors acknowledge support from the Air Force Office of Scientific Research for this work under Project No. AFOSR-19RVCOR042. All involved would like to thank Mike Berman of AFOSR for support and his ability to form teams of researchers to solve problems such as that reported here. Early mass spectrometric studies on SmO+ were carried out on the Thermo Fischer Q Exactive Orbitrap provided by NSF MRI Grant No. CHE-1828190.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material