Predissociation measurements of the bond dissociation energies of EuO, TmO, and YbO

The use of resonant two-photon ionization (R2PI) spectroscopy to measure bond dissociation energies (BDEs) by the observation of a sharp predissociation threshold has served as a robust and widely applicable experimental method for many transition, lanthanide, and actinide metal-containing species.¹ To date, our group has used this method to report over 100 highly precise BDEs of diatomics consisting of metal atoms bonded to p-block atoms.^2–17 However, there exist inherent limitations associated with this technique that restrict the types of molecules that may be successfully investigated. One constraint is that the predissociation threshold must lie in an energy range that is accessible to the tunable optical parametric oscillator (OPO) excitation laser employed. A second constraint is that there must also be a dense manifold of vibronic states about the ground separated atom limit so that the molecule can find a pathway to dissociation among the myriad of potential energy curves in this region. To address the first restriction, we have recently developed a resonant three-photon ionization (R3PI) spectroscopic scheme to measure the BDEs of transition metal-containing molecules that are too strongly bound to be measured with our OPO laser.⁷ This newly developed method extends the range of our studies to molecules with BDEs greater than ∼5.8 eV, the useful limit of our OPO laser system. However, if the molecule is bound too strongly, to the point where the BDE is greater than the ionization energy (IE), a predissociation threshold can no longer be observed, as the molecule will ionize at a lower energy than it dissociates.

The unfortunate case in which the BDE is greater than the IE is true for most of the early transition metal oxides and many of the lanthanide oxides (LnO), foiling the measurement of their BDEs by the observation of a sharp predissociation threshold in R2PI or R3PI experiments.^18–20 A few of the LnO species, however, have BDEs that are smaller than their ionization energies and are therefore candidates for this technique. Table I lists the BDEs and ionization energies of the LnO molecules as known prior to this work, as well as the differences between the BDEs and IEs. Ionization energies have historically been measured by electron-impact measurements employing Knudsen effusion mass spectrometry, a technique that is frequently in significant error due to the population of excited electronic states at the high temperatures employed.¹⁸ Ionization energies measured by this method are generally underestimated, and in cases where more accurate values have been subsequently measured (LaO,²¹ CeO,²¹ PrO,²² NdO,¹⁹ SmO,²⁰ and GdO²³), the electron-impact values are too low by as much as 0.5 eV.^19,22 Thus, the IE and D₀-IE values listed in Table I for EuO, TbO, DyO, HoO, ErO, TmO, YbO, and LuO should be taken as approximate.

More recently, pulsed field ionization-zero electron kinetic energy (PFI-ZEKE) spectroscopy has been used to provide highly precise ionization energies of LaO,²¹ CeO,²¹ NdO,¹⁹ and SmO.²⁰ A third method that may be used to determine the IE employs the thermochemical cycle,

where D₀(AB) and D₀(A⁺-B) are the bond dissociation energies of the neutral and cationic diatomic molecules, respectively, and IE(A) is the ionization energy for atomic constituent A. As shown in Eq. (1.1), these energies can be used to derive IE(AB), the ionization energy of the neutral diatomic. This technique has been employed in the cases of PrO and GdO.^22,23 For the cases of LaO, CeO, PrO, NdO, GdO, and TbO, Table I shows that the IE of the molecule is clearly smaller than the BDE. For these species, the predissociation threshold method is useless in determining the BDE. On the opposite face of the coin, however, the most promising LnO candidates for observing a predissociation threshold using R2PI spectroscopy are EuO, TmO, and YbO. The remaining species, SmO, DyO, HoO, ErO, and LuO, are poor candidates for this approach but might be successful if the existing values of D₀(LnO) and IE(LnO) are sufficiently in error. Most of these BDEs lie beyond the range of our OPO laser, however, and will require the use of the R3PI method. In this paper, we report an investigation of the BDEs of EuO, TmO, and YbO by the observation of a predissociation threshold using the R2PI method. We also report the ionization energy of TmO, obtained by the observation of a two-photon ionization threshold amid a high density of states.

Predissociation-based measurements of the BDEs of the 4f⁷ and 4f¹⁴ molecules, EuO and YbO, pose potential problems with the second constraint noted above—the requirement that the molecule must possess a sufficient density of states at the ground separated atom limit to find a rapid pathway to dissociation. The ground separated atom limits for these species, Eu 4f⁷6s², ⁸S_u + O 2s²2p⁴, ³P_g and Yb 4f¹⁴6s², ¹S_g + O 2s²2p⁴, ³P_g, generate 72 and 9 electronic states, respectively. These low numbers of states arise for metal atoms with ground state S terms because of the lack of M_L degeneracy in the metal atom. Particularly, in the case of YbO, it is unclear that the molecule will dissociate as soon as it is excited above the ground separated atom limit. To avoid these potential difficulties, we have mostly avoided investigating the BDEs of molecules containing metal atoms with L = 0 ground terms (d⁵, d¹⁰, f⁷, or f¹⁴ ground configurations). Recently, however, we have put this issue to the test by investigating the bond dissociation energies of CrO,⁸ MoO,⁸ EuS,³ and EuSe,³ which all have half-filled nd⁵ or 4f⁷ subshells (L = 0) at the ground separated atom limit. Surprisingly, a sharp predissociation threshold was observed for all of these species, allowing precise BDEs to be assigned for the molecules that also agreed extremely well with previous precise thermochemical measurements of their bond dissociation energies. Although the ground separated atom limits of CrO, MoO, EuS, and EuSe may not generate as many electronic states as a molecule with an L > 0 metal atom, excited separated atom limits of these molecules must generate electronic states that drop down into the energetic vicinity of the ground separated atom limit. We believe that these states provide favorable Franck–Condon factors for the excitation process while also providing the density of interacting states that permits the molecule to find a pathway to dissociation as soon as the BDE is reached. Diatomic EuO is analogous to CrO, MoO, EuS, and EuSe in the sense that the metal constituents in all of these molecules have half-filled d or f subshells, thereby avoiding any orbital angular momentum degeneracy but retaining spin degeneracy. Diatomic YbO provides a more severe test of the idea that these small molecules find a way to dissociate as soon as the ground separated atom limit is exceeded because the closed shell nature of the ground Yb 4f¹⁴6s², ¹S_g term has neither orbital nor spin degeneracy. Consequently, only nine electronic states emanate from YbO’s ground separated atom limit, all due to different electronic states of the oxygen atom. As a result, YbO provides a profound test of the density of states limitation of this experimental method.

Along with the relevance of these lanthanide oxides in providing tests of the limits of our experimental method, these molecules are also highly relevant and are currently sought out for a variety of applications. Much like the transition metal oxides, lanthanides and their oxide compounds are ubiquitous in a variety of scientific disciplines.^24–28 The binary oxide EuO has recently been classified as multiferroic, a class of materials that exhibit both ferroelectricity and magnetic behavior. In contrast to most multiferroics, which are antiferromagnetic, bulk EuO exhibits ferromagnetism.²⁹ Europium oxide doped into borosilicate glass has found a wide variety of applications in optical devices, reflecting windows, and thermal sensors.³⁰ Additionally, europium itself is quite unique with its ability to form +2 and +3 oxidation states; in contrast, most lanthanides primarily only access a +3 oxidation state.³¹ As an antithesis of europium, thulium recently achieved the 2nd place in the search for “the most boring chemical element.”³² Nanoparticles of its oxide, however, are a promising new candidate for image-guided radiotherapies.³³ Two-dimensional ytterbium oxide nanodisks have recently been used to modify glassy carbon electrodes for urea biosensing.³⁴ On a more fundamental level, the ytterbium species YbF and YbOH are highly promising candidates for studies attempting to measure the electric dipole moment of the electron,^35–37 which is of great interest in extending particle physics beyond the Standard Model. Because of their demonstrably complex chemistries and important physiochemical properties, lanthanide and lanthanide oxide containing species have also been the subject of a multitude of computational studies, often focusing on methodological development.^38–53 

Whether the objective of these computational studies is to predict the properties of bulk-phase or small molecule lanthanide oxides, stringent and precisely derived experimental benchmarks are necessary for gauging the accuracy of any computational method.⁵⁴ In this article, we report new and highly precise values of the BDEs of EuO, TmO, and YbO that can be used as accurate benchmarks for future computational studies. Because these species have been well-studied both thermochemically and computationally, our newly reported BDEs can also provide clarity as to which previous computational methods are able to accurately predict the BDEs of these molecules.

The instrumentation used in this work is the same as in our previous measurements of the BDEs of the lanthanide sulfides and selenides.³ An experimental cycle commences with the production of the molecule of interest. This is accomplished by first pulsing O₂ seeded in helium (5% O₂ in He, 40 psi) into a reaction block. During the gas pulse, a laser pulse from the 2nd harmonic of a pulsed Nd:YAG laser ablates the surface of a pure metal sample (1 in. square × 1 mm thick) perpendicularly to the gas pulse. This creates a hot, expanding plasma consisting of atoms, ions, and electrons emanating from the surface of the sample. The expanding plasma is entrained in the pulse of O₂/He gas, and LnO molecules are produced by reactions between the hot plasma and the O₂ molecules. Lanthanide oxides are known to have a propensity to form larger clusters,^55,56 but cluster production is suppressed by using a low vaporization laser fluence, which favors the production of the diatomic oxide of interest. Collisions between the molecule of interest and helium in the high-pressure reaction channel cool the LnO molecules electronically and vibrationally.

After the LnO molecules are produced, they undergo a supersonic expansion into a low-pressure chamber (10⁻⁵ Torr), further cooling the rotational degrees of freedom. The expanding gases then pass through a conical skimmer (∼1 cm diameter), roughly collimating the beam as it enters a differentially pumped chamber (10⁻⁶ Torr) that houses the Wiley–McLaren ion source of a reflectron time of flight mass spectrometer (TOFMS).^57,58 The Wiley–McLaren electrode assembly provides enhanced mass resolution, allowing us to straightforwardly identify the species that are ionized in each experimental cycle. The molecular beam is irradiated with a counterpropagating, wavelength-selected pulse from the OPO laser. This is used to excite the LnO molecule into a high-energy state by the absorption of one photon. Following excitation and an 80-ns delay, the excited molecules are ionized by a pulse from an exciplex laser operating on KrF (248 nm, 5.00 eV). The newborn ions are then accelerated in the Wiley–McLaren assembly and traverse the reflectron TOFMS, ultimately being detected by a dual microchannel plate (MCP) detector. The ions impact the MCP detector at different times depending on their mass, allowing a mass spectrum to be recorded. Mass-resolved optical spectra are then obtained by plotting the ion signal at a specific mass as the OPO laser is systematically stepped across a pre-specified wavelength range. The lasers used in the experiment are fired at 10 Hz, allowing ten experimental cycles to occur per second. Thirty repetitions at each wavelength point are summed before moving to the next wavelength. Multiple scans are averaged to improve the signal to noise ratio in all spectra recorded.

In studies of a number of other transition metal and lanthanide molecules that have high densities of electronic states at the ground separated atom limit,^3–17,59 we have shown that spin–orbit and nonadiabatic interactions among these states allow the molecule to dissociate promptly when the ground separated atom limit is exceeded. This phenomenon may be recognized by the abrupt drop of the molecular ion signal to baseline when the excitation photon energy exceeds the BDE. At this point, the molecules fall apart more rapidly than they can be ionized by absorption of a second photon. For the LnO molecules investigated in this study, ions can be produced either by the absorption of two photons from a single OPO pulse or by the absorption of one photon of OPO radiation followed by a second photon produced by an exciplex laser operating on KrF gas (248 nm, 5.00 eV). Because of the delay between the OPO and KrF lasers, each mass peak in the mass spectrum is doubled, with the OPO + OPO ions appearing earlier than the corresponding OPO + KrF ions. By monitoring the latter peak, we are able to detect molecules that have been excited and live long enough to be ionized by the subsequent KrF laser pulse. This capability allows us to identify with certainty the energy at which predissociation begins to occur.

Under the selection rules of spin–orbit and nonadiabatic coupling, interacting states must have the same value of Ω.⁶⁰ To ensure that the molecules studied here can undergo prompt dissociation to the ground separated atom limit as soon as that limit is reached, Table II provides the Ω″ values of the likely ground states, the Ω′ values that can be reached via electric dipole excitation, and the Ω values arising from the ground separated atom limit. Due to the high total angular momenta of the ground states of the separated atoms, all of the photoexcited molecules are able to dissociate to the ground separated atom limit while preserving the value of Ω. Thus, there are no Ω-based restrictions preventing prompt predissociation as soon as the ground separated atom limit is exceeded.

Figures 1–3 display the recorded predissociation thresholds of EuO, TmO, and YbO, respectively. In each of these figures, the blue trace is the detected LnO⁺ signal calibrated to the atomic transitions that are shown in the bottom trace. An arrow is placed at the assigned predissociation threshold of each molecule, where a sharp drop in the molecular signal converges to a flat baseline. The horizontal bar atop each arrow represents the assigned error limit, which is ±25 cm⁻¹ for the BDEs of EuO and YbO and ±50 cm⁻¹ for that of TmO. These error limits account for the rotational temperature of the molecule (≤20 cm⁻¹),⁶¹ the linewidth of the OPO laser (≈10 cm⁻¹), the calibration error in each spectrum (≤5 cm⁻¹), and a subjective assessment of where the signal drops to zero. Each recorded spectrum is calibrated to atomic transitions tabulated in the NIST Atomic Spectra Database.⁶² For EuO, TmO, and YbO, the lanthanide atoms were inconvenient for calibration because appropriate transitions were difficult to identify unambiguously. To perform the necessary calibration, Ti, Ta, and Cu metals were installed and their atomic transitions were collected for calibration immediately after each LnO experiment. The (x,y) coordinates of the spectra plotted in Figs. 1–4 are provided in the supplementary material.

Figure 3 shows two traces of averaged scans over YbO’s predissociation threshold, with each trace representing a different ionization scheme. The top trace is the signal generated by a scheme in which the molecule was excited by the OPO laser, and after an 80 ns time delay, the excited states were ionized by absorption of a photon from a KrF exciplex laser (248 nm, 5.00 eV). The center trace is a one-color two-photon ionization scheme with both photons being absorbed from the same OPO laser pulse, which has a pulse duration of ∼5 ns. It is clear from the center trace that above the YbO predissociation threshold, there exist discrete, short-lived excited states that have lifetimes significantly shorter than 80 ns. This makes the determination of the predissociation threshold ambiguous when both the excitation and ionization photons come from the same pulse, as discrete spectroscopic features persist above the true predissociation threshold. However, when an appropriate time-delayed two-color two-photon ionization scheme is used (upper trace), these short-lived excited states have sufficient time to fall apart, allowing the predissociation threshold to be unambiguously identified. In the present work, all of the reported predissociation thresholds were based on the more accurate time-delayed resonant two-photon ionization method. Similar examples of spectroscopic features that correspond to short-lived excited states above the predissociation threshold have also been identified in other R2PI experiments from this group.^6,59

The two-photon ionization onset threshold of TmO is displayed in Fig. 4, along with a simultaneously collected atomic Tm R2PI spectrum. Both spectra were recorded using only the tunable OPO laser, with the first absorbed photon exciting the species and a second photon from the same laser ionizing the excited state. The TmO two-photon ionization threshold at ∼26 400(80) cm⁻¹ is then doubled and corrected for the field ionization shift to obtain the ionization energy of TmO as 6.56(2) eV, where the assigned uncertainty has been increased to account for the imprecisely known field ionization shift in our instrument.^3,63,64 This represents a significant improvement in precision over the previous value, 6.44(10) eV.¹⁸ Also evident in this spectrum is the phenomenon of a sharp depletion in the TmO⁺ ion signal whenever the excitation laser is resonant with an intense atomic Tm transition, most evident in the pair of Tm atomic transitions near 26 646 and 26 701 cm⁻¹. When the excitation laser is resonant with a strong atomic transition, so many atomic ions are produced that space charge effects cause the entire ion cloud to expand significantly as it traverses the time-of-flight path, preventing the majority of ions of all species from reaching the detector. At these wavelengths, all species are depleted from the mass spectrum except for the atomic ions. These are produced in such great numbers that an intense atomic signal is observed despite the expansion of the ion cloud. Artifacts of this type are present in all of the spectra displayed in Figs. 1–4 and are frequently observed in our work.^2,10 Attempts were also made to measure the ionization energies of EuO and YbO using this method, but the discrete nature of the spectrum for these molecules prevented the observation of a clear two-photon ionization threshold.

To clarify the meaning of the error limits assigned to the BDE values reported in this work, these have been chosen so that if another investigator repeated the work, a BDE value would be obtained that lies within the stated error limits more than 95% of the time. In this respect, the assigned error limits represent a conservative estimate of the precision of the measurement. However, the possibility remains that the molecule could possess a barrier to dissociation, possibly even on all of the potential curves that lead to ground state separated atoms. In such a case (which we believe to be highly unlikely), the observed predissociation threshold still provides a rigorous upper limit to the thermochemical BDE of the molecule. At this point in time, it is not feasible to compute all of the potential energy curves that exist in the vicinity of the ground separated atom limit to determine whether barriers to dissociation exist; nor is it feasible to calculate the mechanism or rate of predissociation as a function of the energy in excess of the thermochemical threshold. The electronic state density is simply too great for such efforts. However, if the molecules do predissociate as soon as the ground separated atom limit is exceeded in energy, as we believe they do, then the assigned error limits also provide the accuracy of the measurements.

As noted previously, the BDE of EuO has been investigated both experimentally and computationally. These previous investigations are summarized in Table III. The BDE of EuO was first measured over 50 years ago using Knudsen effusion mass spectrometry. In 1967, Ames et al. measured a BDE of 5.80(20) eV.⁶⁵ This was in good agreement with a subsequent experiment where a lower limit of >5.70(3) eV was assigned by Dickson and Zare in 1975 by studying the chemiluminescence of chemical reactions between Eu atoms and NO₂ gas.⁶⁶ Both of these values greatly overestimate the BDE of EuO and are almost 1 eV larger than our value of 4.922(3) eV. Deviating greatly from these two studies, but in close agreement with our result, was a reactive collision experiment by Dirscherl and Michel that studied the endothermic Eu + O₂ → EuO + O reaction, obtaining a BDE of 4.97(22) eV.⁶⁷ Two subsequent Knudsen effusion measurements of the EuO BDE by Murad and Hildenbrand and Balducci et al. obtained values of 4.85(10) and 4.84(7) eV, respectively.^68,69 The latter value’s error limit falls just out of our measured value by 0.01 eV and marks the last time the BDE of EuO was experimentally investigated, almost 45 years ago.

These five experimental studies shaped the recommended values of the EuO BDE that were reported in a plethora of LnO molecule reviews over the next two decades.^70–75 Many of these reviews of the bonding and electronic structure of the diatomic LnO molecules correlated the experimentally measured BDEs with atomic promotion energy schemes. Almost all of the recommended values for D₀(EuO) and their error limits from this time period, which were assigned to each recommended value on the basis of the experimental error limits and the authors’ personal judgments, encompass our measured value. Our result, however, reduces the assigned error limit by a factor of over 30.

A large number of computational studies on EuO have been performed with a variety of levels of theory, different sized basis sets, and various effective core potentials.^42–53 These computational studies have generated a very large set of predicted values for the BDE of EuO, ranging from 3.14 to 5.55 eV.

While the various density functional theory (DFT) methods, combined with different basis sets, lead to a bewildering array of results, none of these methodologies provide results that are uniformly good for all of the lanthanide molecules studied. Indeed, none of the DFT methods tested in a recent investigation gave a mean absolute deviation in the BDEs of the LnX test set below 17.3 kcal/mol (0.75 eV),⁴⁵ a rather disappointing result. For the DFT studies cited in Table III that employed a variety of methods, we list the result that comes closest to our measured value. A complete listing of the values obtained by all the different calculations is impractical and not very informative.

In an impressive computational study of lanthanide diatomics that employed a composite methodology, Solomonik and Smirnov calculated the BDE of EuO to be 4.90 eV, differing from our value by only 0.02 eV.⁴² The final values for the BDEs, bond lengths, and harmonic frequencies for the 17 lanthanide diatomics investigated in that study were derived from a sophisticated composite scheme based on the singles, doubles, and perturbative triples coupled-cluster method [CCSD(T)] that included calculations of core–valence correlation effects, second-order spin–orbit coupling effects, and higher order correlation effects.

The BDE of TmO was first measured in 1967 using Knudsen effusion mass spectrometry by Ames et al., who report a BDE of 6.04(20) eV.⁶⁵ This exceeds our value, 5.242(6) eV, which is at worst an upper bound, by 0.80 eV. The magnitude of this difference is similar to what was found in the case of EuO and suggests a systematic error in the study of Ames et al. The only other experimental measurement of the BDE of TmO was another Knudsen effusion study by Murad et al., who investigated the high temperature gaseous equilibrium Al(g) + TmO(g) ⇌ Tm(g) + AlO(g).⁷² From these data, a BDE of 5.28(13) eV was derived, in excellent agreement with our value. In the literature, most of the cited BDEs for TmO are found in comprehensive reviews on the electronic structure and bonding of the LnO diatomic molecules.^{70,71,73–77} In most of these reviews, the authors selected a recommended value based on the Knudsen effusion results of Ames et al. and Murad et al., supplemented by considerations of the correlations of the other LnO BDEs with various atomic promotion energy schemes. For a majority of these values and their estimated error limits, our measured value of TmO is in good agreement with the authors’ predicted and recommended BDEs.

Predicting the BDE and electronic structure of TmO has also been the objective of theoretical studies. The first theoretical study that aimed to predict the BDE of TmO employed the relatively rudimentary polarized ion model and applied it to the alkaline-earth and lanthanide monoxide series of molecules.⁴⁷ While this study was able to achieve a good prediction for the BDEs of EuO and YbO, the predicted BDE for TmO exceeds our result by about 0.4 eV. In 2007, 33 years later, the BDE of TmO was computationally revisited by Wu et al. in a systematic study of every LnO molecule using density functional theory with the B3LYP method.⁴⁶ In this work, the BDE was severely underestimated, obtaining a value of 4.01 eV. This underestimation is likely a result of this study not adequately accounting for spin–orbit, relativistic, and higher-order correlation effects that have been demonstrated to be highly important in DFT calculations involving lanthanide constituents.⁴⁵ Finally, as with EuO, de Oliveira et al. also used TmO to benchmark their newly reported basis sets for the lanthanide series of atoms.⁴⁴ By using the B3LYP functional and their basis set scheme, they calculated a BDE of 5.30 eV for TmO, in excellent agreement with our value of 5.242(6) eV. Table IV provides a list of all previous experimental and computational values of the BDE of TmO, along with previously reported values for its cationic BDE and ionization energy.

As with EuO and TmO, the BDE of YbO has also been thoroughly and comprehensively studied by both experiment and computation. Previous studies are listed in Table V. In the same Knudsen effusion study by Ames et al. that reported the BDEs of EuO and TmO, an upper limit of 3.83(20) eV was assigned to the YbO BDE.⁶⁵ In contrast to this upper limit, Yokozeki and Menzinger assigned a lower limit of 4.08(6) eV after studying the chemiluminescence spectrum of the Yb + O₃ reaction in varying pressure environments.⁷⁸ This lower limit is in excellent agreement with our measured value of 4.083(3) eV. The most recent experimental measurement comes from a 2005 Knudsen effusion study by Brutti et al. in which a BDE of 3.98(10) eV was obtained. Our value falls at the upper end of this assigned error limit. In the same review articles that spanned the 1970s and the 1980s on the bonding and electronic structure of the LnO molecules, which recommended BDE values for EuO and TmO, recommended values for the BDE of YbO were also provided.^70–77 Our measured value for the BDE of YbO falls within the estimated error limits for nearly all of these recommended values.

Accurately predicting and benchmarking YbO’s BDE has also been the objective of a plethora of computational studies over the last six decades.^{44–52,79–81} Computational studies have almost entirely focused on DFT approaches, often examining a large number of functionals, pseudopotentials, basis sets, and methodologies. For many of these investigations, one method or another may have a fortuitous agreement with our result. For investigations that employed a variety of approaches, we report the method that gave the closest value to our measurement in Table V, which also reports previous literature values of the ionization energy of YbO and the BDE of YbO⁺.

Thermochemical cycles allow for thermochemical quantities to be derived if every other thermochemical value in the cycle is known. Alternatively, when all of the quantities have been experimentally measured, the cycles allow for a stringent check of self-consistency among these values. The latter situation has been accomplished for V₂, where the four independently measured thermochemical quantities of Eq. (1.1) agree to an accuracy of 0.0019(21) eV.^82–85 

For the LnO molecules considered here, a relevant thermochemical cycle relates the gaseous enthalpies of formation at 0 K to the molecular BDE,

Here, $ΔfH0K0$ represents the standard enthalpy of formation at 0 K of a gaseous species (either LnO, Ln, or O). D₀(LnO) is the BDE of the LnO molecule, as measured in this study. For EuO, TmO, and YbO, the gaseous enthalpies of formation for the lanthanide atom are taken from the NBS tables of chemical thermodynamic properties, where the values given imply an uncertainty between 0.80 and 0.08 kJ/mol.⁸⁶ To be conservative, the larger uncertainty limit is chosen for error propagation. The gaseous enthalpy of formation of the O atom is taken from the active thermochemical tables, maintained by Argonne National Laboratory.⁸⁷ Employing Eq. (4.1), the derived gaseous enthalpies of formation of the LnO molecules at 0 K are tabulated in Table VI.

In addition to the enthalpies of formation, our measurement of both the IE(TmO) and D₀(TmO) may be combined with the IE(Tm), 6.184 31(6) eV,⁶² to obtain the bond dissociation energy of Tm⁺–O using Eq. (1.1). The derived value of D₀(Tm⁺–O) = 4.87(2) eV is also listed in Table IV.

The criteria for spectroscopically resolving a molecule’s predissociation threshold with R2PI spectroscopy and assigning it to the bond dissociation energy have long been a topic of discussion for our group.^1,84,88–90 The rationale of why a predissociation threshold could be observed for certain molecules and not for others was originally developed following our spectroscopic investigations of the group 10 metal dimers Ni₂, Pd₂, Pt₂, NiPt, NiPd, and PdPt.^88,91,92 In spectroscopic studies of Ni₂, NiPt, and Pt₂ using R2PI spectroscopy, sharply resolved predissociation thresholds or dramatic differences in lifetimes of excited states below and above a predissociation threshold were measured, allowing a precise assignment of the BDE of each species.^91–94 Conversely, abrupt predissociation thresholds for NiPd and PdPt were not observed.⁸⁶ Further compounding this predicament was the investigation of Pd₂, where no spectroscopic transitions were initially observed at all,⁸⁶ although subsequent studies have found one vibronic band system.⁹⁵ 

A notable difference between Pd and Ni or Pt is that the highly stable, 4d¹⁰5s⁰, ¹S_g ground term of Pd is nondegenerate, in contrast to the nearly degenerate 3d⁹4s¹, ³D_g and 3d⁸4s², ³F_g terms of Ni and the ground 5d⁹6s¹, ³D_3g level of Pt, which generate much larger numbers of states. This results in a far lower density of electronic states in NiPd and PdPt than in Ni₂, NiPt, or Pt₂. Dipalladium, Pd₂, exhibits an even lower density of states resulting in an exceptionally sparse electronic spectrum in the visible region. In addition, the empty 5s orbital in the ground level of atomic Pd ensures that Pd can act as a Lewis acid, accepting electrons from the 4s orbital of Ni or the 6s orbital of Pt to form attractive potential curves. The lack of repulsive curves originating from the ground separated atom limit, along with the low density of electronic states, was thought to be key to the lack of a sharp predissociation threshold in the examples of NiPd and PdPt.

Interestingly, however, YbO clearly shows a sharp predissociation threshold in Fig. 3 despite the fact that Yb, like Pd, has a closed-shell ground term. In YbO, the ground separated atom limit only generates nine electronic states, all emerging from different arrangements of the 2p electrons on oxygen. The next excited separated atom limit, located almost 15 900 cm⁻¹ higher in energy, is generated from Yb in its ground state and oxygen in its first excited state, ¹D_2g, where the two previously unpaired p-electrons in oxygen are now spin-paired. This excited separated atom limit generates an additional five electronic states for YbO. It is shocking that a sharp predissociation threshold at what appears to be the thermochemical threshold should be observed in YbO, given that only 14 molecular states arise from separated atom limits lying within 2 eV of the ground limit.

To put context to these numbers, we may compare YbO to NiPd, where there are 21 electronic states generated at NiPd’s ground separated atom limit (³F_g + ¹S_g). Compounding this number is NiPd’s next excited separated atom limit (³D_g + ¹S_g), only 200 cm⁻¹ above its ground limit, which generates an additional 15 electronic states. From these considerations, it is clear that NiPd at least has the potential for a denser manifold of electronic states in the vicinity of its ground separated atom limit than YbO. Nevertheless, no predissociation threshold was observed for NiPd, while one has been observed for YbO. The key distinction between these systems, however, is that YbO is highly ionic and NiPd is not. Thus, the separated ion limits of Yb⁺ + O⁻ and Yb²⁺ + O²⁻ are important contributors to the density of electronic states in YbO. In this context, we note that the ¹Σ⁺ ground state of YbO is highly ionic in nature and is generated from an ion-pair separated atom limit of Yb²⁺ (4f¹⁴) and O²⁻.^96,97 Moreover, electronic states correlating with the ion-pair limit of Yb⁺ (4f¹⁴6s¹) and O⁻ have also been spectroscopically observed,⁹⁶ and high angular momentum states (Ω = 2, 3, and 4) that correlate with a 4f¹³ configuration have been calculated to lie quite low in energy in ligand field models.^76,98 The large BDE of YbO (4.083 eV) along with ion-pair curves that sharply drop into the region of the ground separated atom limit provides a surprisingly large density of states in this molecule, allowing predissociation to proceed at the thermochemical threshold.

In short, it is not just the number of electronic states generated from the ground separated atom limit that allows a sharp predissociation threshold to occur. If electronic states emanating from higher-lying excited separated atom limits or separated ion limits can drop into the energetic vicinity of a molecule’s ground separated atom limit, then a sharp predissociation threshold may also be obtained. This will be the case for molecules with large BDEs so that there inherently exists a greater potential for a larger number of electronic states to exist in the molecule’s energetic region about its BDE and for molecules that are innately ionic in nature, allowing for ion-pair states to contribute to the density of states of the molecule.

Resonant two-photon ionization spectroscopy has been used to precisely determine the bond dissociation energies of three lanthanide oxide molecules, EuO [4.922(3) eV], TmO [5.242(6) eV], and YbO [4.083(3) eV], along with the ionization energy of TmO [6.56(2) eV]. Each of these molecules represents a different category in our study of predissociation thresholds. Thulium oxide, TmO, is an open-shell metal oxide with a very large density of electronic states, making it electronically analogous to almost all of the other species we have measured using R2PI spectroscopy. Europium oxide, EuO, on the other hand displays a greatly reduced density of electronic states arising from its ground separated atom limit due to its half-filled 4f⁷ subshell. It joins a short list of half-filled nd⁵ and 4f⁷ species whose BDEs we have measured: CrO, MoO, EuS, and EuSe. In all of these molecules, a sharp predissociation threshold was found, allowing a precise BDE to be assigned that compared very well to previous thermochemical studies. These results signal that the extension of our BDE measurements to other nd⁵ or nf⁷ molecules could be a productive future direction. Ytterbium oxide, YbO, derives from a metal atom with a completely closed valence shell and was not originally thought to be a good candidate for these studies. However, even in this case, a sharp predissociation threshold was found that can be convincingly assigned to the BDE. This makes it clear that a sharp predissociation threshold that can be assigned as the bond dissociation energy is not just dependent on the electronic states emanating from the molecule’s ground separated atom limit. Large numbers of electronic states arising from excited separated atom limits or ion-pair limits that drop below the ground separated atom limit can also provide a very effective pathway to dissociation.

With this knowledge, one objective of future BDE studies will be centered around investigating molecules containing half-filled valence shell transition metal and lanthanide atoms, such as Cr, Mn, Mo, Re, and Eu. Successful measurement of predissociation thresholds in these molecules is contingent on the presence of a manifold of electronic states deriving from excited separated atom and ion-pair limits. As demonstrated with EuO and YbO in this work, along with our previous studies on CrO and MoO,⁸ this is most likely to occur when the molecule is strongly bound so that potential energy curves that derive from excited separated atom limits will drop down below the ground separated atom limit. Studies of these molecules will contribute to building a comprehensive library of BDEs assigned from a predissociation threshold via R2PI spectroscopy as well as enhancing our understanding of the predissociation phenomenon.

The spectra displayed in Figs. 1–4 are provided in the supplementary material.

The authors acknowledge the National Science Foundation for support of this research under Grant No. CHE-1952924.

The authors have no conflicts to disclose.

The data that support the findings of this study are available within the article and its supplementary material.