THE JOURNAL OF CHEMICAL PHYSICS 142, 064305 (2015)
Photoelectron spectra of CeO− and Ce(OH)2− Manisha Ray, Jeremy A. Felton, Jared O. Kafader, Josey E. Topolski, and Caroline Chick Jarrolda) Department of Chemistry, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, USA
(Received 23 December 2014; accepted 27 January 2015; published online 11 February 2015) The photoelectron spectrum of CeO− exhibits what appears to be a single predominant electronic transition over an energy range in which numerous close-lying electronic states of CeO neutral are well known. The photoelectron spectrum of Ce(OH)2−, a molecule in which the Ce atom shares the same formal oxidation state as the Ce atom in CeO−, also exhibits what appears to be a single transition. From the spectra, the adiabatic electron affinities of CeO and Ce(OH)2 are determined to be 0.936 ± 0.007 eV and 0.69 ± 0.03 eV, respectively. From the electron affinity of CeO, the CeO− bond dissociation energy was determined to be 7.7 eV, 0.5 eV lower than the neutral bond dissociation energy. The ground state orbital occupancies of both CeO− and Ce(OH)2− are calculated to have 4 f 6s2 Ce+ superconfigurations, with open-shell states having 4 f 5d6s superconfiguration predicted to be over 1 eV higher in energy. Low-intensity transitions observed at higher electron binding energies in the spectrum of CeO− are tentatively assigned to the 1Σ+ (Ω = 0) state of CeO with the Ce+2 6s2 superconfiguration. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4907714]
I. INTRODUCTION
The electronic structure of the CeO diatomic molecule has been the subject of numerous detailed spectroscopic1–5 and ab initio6–9 investigations and, famously, the successful ligand field theory (LFT) treatment applied by Field.10 The crux of Field’s LFT treatment of the CeO molecule, described as Ce+2O−2, is that the [Xe] 4 f 6s occupancy of Ce+2 is stabilized relative to the [Xe] 4 f 2 Ce+2 ground state occupancy11 in the ligand field of O−2. The splittings between the possible atomic cation Ja states [Ja = 2, 3 from ( j f = 5/2, j s = 1/2); Ja = 4, 3 from ( j f = 7/2, j s = 1/2)] are largely preserved in the field set up by the O2− ligand, leading to numerous close-lying states in which the projection of the total angular momentum onto the CeO internuclear axis, Ω, equals Ja , Ja − 1, etc. As described by Field and subsequently by Heaven,1 the 16 states arising from this occupancy are, using the leading Λ-Σ description, 3 Φ and 1Φ (X12, X23, X34, and X43 states), 3∆ and 1∆ (W11, W22, W33, and W42 states), 3Π and 1Π (V10−, V21, V32, and V41 states), and 3Σ and 1Σ (U10+, U21, U30+, and T10− states) states. The terms in parentheses are labels established by Linton et al.4 The 16 states lie within an energy interval of approximately 4000 cm−1, ca. five vibrational spacings of the ground state. Because of the presence of numerous close-lying electronic neutral states in the transition metal- or lanthanide metal monoxides,12 their anion photodetachment spectra tend to be congested with transitions to numerous electronic neutral states accessed from one or more electronic states of the anion. Previously obtained PE spectra of LnO− species (Ln = La,13 Gd14) did indeed exhibit numerous transitions within an energy interval of several electron volts (eV). The dense a)Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2015/142(6)/064305/8/$30.00
spacing of 16 states of neutral CeO augurs an electronically complex anion and concomitant PE spectrum, yet the anion PE spectrum presented below exhibits what appears to be a single electronic transition. Additionally, the PE spectrum of Ce(OH)2−, a molecule in which the Ce center is in the same formal oxidation state as in CeO−, assuming a dihydroxide structure, is similarly simple. Results of density functional theory (DFT) calculations on the CeO neutral correctly predict the orbital occupancy and energy ordering of the non-spinorbit split low-lying neutral states resulting from the 4 f 6s superconfiguration. Our calculations on the anion agree with previously published results, predicting a ground state arising from the 4 f 6s2 Ce+ superconfiguration.15 The experimental results are consistent with the picture of negligible orbital angular momentum mixing of the contracted, single 4 f electron of the anionic and neutral CeO and Ce(OH)2. II. METHODS A. Experimental methods
PE spectra of CeO− and Ce(OH)2− were measured using an apparatus described in detail previously.16–18 The anionic species were generated using a pulsed laser ablation/molecular beam cluster source19 in which a solid Ce target was ablated with approximately 3 mJ/pulse of the second harmonic output of a Nd:YAG laser (532 nm, 2.33 eV) operated at 30 Hz repetition rate and entrained in a pulse of ultrahigh purity He carrier gas. The resulting mixture of atomic and molecular species in all charge states were swept through a 2.5-cm long, 0.3-cm diameter channel and expanded into a vacuum chamber. Anionic species that passed through a 3-mm skimmer were accelerated into a 1.2-m time-of-flight mass spectrometer and detected using a dual microchannel plate (MCP) detector assembly. The mass resolution (m/∆m) in the region of the Ce atom is 300; the two primary isotopes of
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Ce (140 and 142 amu) in both molecular CeO− and Ce(OH)2− were readily resolved. Prior to colliding with the ion detector, 140CeO− and 140Ce(OH)2− were selectively photodetached at the intersection of the ion drift tube and a 1-m field-free drift tube situated perpendicular to the ion drift path with the second and third harmonic outputs of a second Nd:YAG laser (532 nm/2.33 eV and 355 nm/3.49 eV wavelengths/photon energies, respectively) timed to intersect with the ions of interest. The drift times of the small fraction of photoelectrons that collided with a second MCP detector assembly at the end of the field-free drift tube were recorded with a digitizing oscilloscope. The drift times were converted to electron binding energy (e−BE) by identifying common transitions observed in the spectra collected using both photon energies and setting the difference in the electron kinetic energies (e−KE) to the fundamental energy (the difference between the energies of the second and third harmonics), which is specified as 1.1650(1) eV for the laser system used in this study, using the relationship, 2 2 ℓ ℓ 2(1.1650 eV) = − , (t 3ν − t o ) (t 2ν − t o ) me
(1)
where me is the electron mass, t 3ν is the drift time of electrons associated with a selected transition observed in the spectrum obtained using 3.49 eV photon energy that can readily be correlated with a transition in the spectrum obtained with 2.33 eV, appearing at t 2ν . The equation is solved for l and plotted as a function of t o. The intersection between this line and other lines generated from several sets of transitions observed in 3.49 eV and 2.33 eV give a unique l and to, the calibration parameters necessary to compute the e−KE values from electron drift times. The e−KE values are related to the anion and neutral states via e−KE = hν − EA − Teneutral + Teanion,
(2)
where EA is the neutral electron affinity. The data presented below show electron counts plotted as a function of e−BE: e−BE = hν − e−KE.
(3)
The e−BE values reflect the energy difference between the final neutral state and the initial anion state and are independent of the photon energy used. Laboratory to center-of-mass frame corrections were made to the e−KE (and e−BE) values. The CeO− and Ce(OH)2− spectra presented below were signal averaged between ca. 300 000 to 600 000 laser shots. Spectra were collected with the laser polarization both perpendicular to (θ = 90◦ ± 10◦) and parallel to (θ = 0◦ ± 10◦) the electron drift direction. The angular distribution of photoelectrons follows the expression:20 ( ) ∂σ σtotal 3 2 1 = 1 + β (E) cos θ − , ∂Ω 4π 2 2
The energy bandwidth, ∆E of the electron kinetic energy analyzer decays with e−KE3/2 following: e−KE ∆E = 0.004 eV + 0.0078 eV · eV (
) 32
.
(5)
Peaks observed in the spectrum obtained with 2.33 eV photon energy were therefore narrower than the same transitions observed in spectrum obtained with 3.49 eV. B. Computational methods
While the electronic structure of CeO is well-known and the anion would be best treated with a high-level method, the molecular and electronic structures of CeO and Ce(OH)2 anion and neutral were calculated using density functional theory with the primary goal of determining a general map of the energies of different electronic superconfigurations, in particular for the anions. All electronic structure calculations on CeO−, CeO, Ce(OH)2−, and Ce(OH)2 were performed with a development version of the GAUSSIAN suite of electronic structure programs22 using the B3LYP hybrid density functional method. To account for relativistic effects, a 28 electron pseudopotential with atomic natural orbital basis for the valence electrons (ECP28MWB_ANO) was used for Ce as developed by Dolg and Cao23 The atomic natural orbital contracted Gaussian valence basis set consists of (14s13p10d8 f 6g)/[6s6p5d4 f 3g] functions centered on Ce atom,23 and the aug-cc-pVTZ Dunning correlation consistent basis set24 was used for H and O atoms. DFT calculations were done on several spin states of anions and neutrals in various plausible structures for Ce(OH)2, including a CeO−·H2O complex. To underscore this need for caution with DFT calculations on these molecular species, calculations on neutral CeO defaulted to a 3∆g ground neutral state, with 4 f δ 6s occupancy, rather than the correct 4 f φ 6s 3Φ occupancy, though by editing the 3∆g orbital occupancy to 4 f φ 6s, the 3Φ state did converge with slightly lower energy. Further, the correct 4 f φ 6s 1Φ state correlating to the X43 state was found to be the lowest energy singlet neutral, which is consistent with the Λ-Σ description of this state, though again, appropriate caution should be taken with these results due to strong spin-orbit coupling and heavy mixing between the Λ-Σ states.7 Adiabatic and vertical detachment energies (ADE and VDE) of 1-e− transitions between anion and neutral states were calculated for both sets of species. The ADE is the energy difference between the zero point corrected energies of the optimized anion and neutral species, and the VDE is the difference between the ground state energy of anion and single point energy of neutral confined to the optimized structure of the anion.
III. RESULTS AND ANALYSIS
(4)
where σ is the photodetachment cross section. The asymmetry parameter, β (E) varies from −1 to 2, depending on the symmetry of the orbital associated with the detachment.21
Figure 1 shows the mass spectrum of anionic species generated using the ablation source. The mass distribution is dominated by the CeO3− anion, though Ce−, CeO−, and Ce(OH)2− are generated in sufficient quantities to obtain PE spectra.25 The CeO2− ion is low-intensity relative to Ce(OH)2−.
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or a molecular π bonding orbital, which would result in β (E) < 0. However, we cannot distinguish unambiguously between detachment from other potential molecular orbitals. We also point out here that the asymmetry in the CeO− spectrum is not uniform over what appears to be a single vibrational progression, and β (E) of peak X1 is 0.75. Low-intensity signal observed between 1.7 eV and 2.5 eV in the CeO− PE spectrum is reproducible and observed in spectra obtained with both 3.49 eV and 2.33 eV photon energies. A portion of the 2.33 eV spectrum, shown in green over this energy range, is included to demonstrate that this lower intensity signal, labeled A and B, is real. The asymmetry parameter is approximately zero for this region of the spectrum. FIG. 1. Mass spectrum of anions generated using the laser ablation source.
−
Figure 2 shows the PE spectra of (a) CeO and (b) Ce(OH)2− obtained using 3.49 eV photon energy with the laser polarization set at θ = 0◦ (black traces) and θ = 90◦ (red traces). At first glance, both spectra appear to show a single electronic transition, with the CeO− spectrum exhibiting a cleanly resolved vibrational progression (X0, X1, and X2) and a vibrational hot band (x′). The two spectra show similar polarization dependence. Using the equation, β(E) =
I0 − I90 , 1 2 I0 + I90
(6)
the asymmetry parameters were determined to be 1.0 ± 0.1 at the origin for both molecules. Chi et al. measured the 1.165 eV photoelectron imaging spectrum of CeO− and reported β (E) = 0.975.26 This positive value is NOT consistent with detachment from an atomic p-like orbital
FIG. 2. PE spectra of (a) CeO− and (b) Ce(OH)2− obtained using 3.49 eV photon energy with laser polarization both parallel (black traces) and perpendicular (red traces) to the direction of electron detection. A portion of the PE spectrum of CeO− obtained with 2.33 eV (parallel polarization) in the 1.5–2.15 eV binding energy range, showing additional structure, is included.
A. PE spectrum of CeO−
Figure 3 shows the PE spectrum of CeO− obtained with 2.33 eV photon energy. Table I summarizes the peak positions and relative energies. The primary features of the spectrum obtained with 2.33 eV photon energy can readily be fit with Franck-Condon factors calculated from harmonic oscillator wavefunctions assuming an origin of 0.936(3) eV from the position of peak X0, the known ∆G(1/2) value for the neutral 824.3 cm−1 reported in Ref. 4 (we did not include anharmonicity because peak X2 is both low in intensity and broad compared to optical spectra), an anion frequency ranging from ω ′′ = 680 to 800 cm−1 based on the x′ − X0 interval, and a bondlength change of 0.040(3) Å. A vibrational temperature of 1500 K was necessary to reproduce the intensity of the presumed vibrational hot band, peak x′. A simulation generated using these parameters is shown in the supplementary material.27
FIG. 3. PE spectrum of CeO− obtained using 2.33 eV photon energy with laser polarization both parallel (black traces) and perpendicular (red traces) to the direction of electron detection. The energies of the 16 4 f 6s CeO neutral states relative to the EA of CeO are indicated along the top axis, based on Ref. 2.
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TABLE I. CeO− PE spectrum (Fig. 3) peak positions and assignments. Peak
Position (eV)
Relative energy (cm−1)
Tentative assignment
a x′ X0 X1 X2 A B
0.758 ± 0.015 0.828 − 0.848 0.936 ± 0.008 1.042 ± 0.010 1.149 ± 0.015 1.83 ± 0.01 1.99 ± 0.01
−1435 −871 to −709 0 855 ± 100 1720 ± 140 7210 ± 100 8500 ± 100
X12 (υ ′ = 0) + e− ← X12.5 (υ ′′ = 1) X12 (υ ′ = 0) + e− ← X12.5 (υ ′′ = 0) X12 (υ ′ = 1) + e− ← X12.5 (υ ′′ = 0) X12 (υ ′ = 2) + e− ← X12.5 (υ ′′ = 0) 6s 2 1Σ+ + e− ← X12.5 (υ ′′ = 0)a
a Tentative.
The electron affinity of O− is 1.4611 eV.28 Using the equivalence, D0 (CeO) + EA (CeO) = D0 (CeO−) + EA (O),
(7)
the bond dissociation energy of CeO to the Ce + O− asymptote is 0.53 eV lower than the bond dissociation energy of the neutral. The latter has been measured to be approximately 8.2 eV,29,30 giving a 7.7 eV bond dissociation energy for the anion. The lower anion vibrational frequency and bond dissociation energy relative to the neutral values point to a longer bondlength for the anion. The previously determined bondlength of the neutral ground state is 1.820 Å,1 giving a 1.860(3) Å anion bondlength. Given the experimental resolution (Eq. (5)) and assuming a 300 K rotational temperature, which is lower than the vibrational temperature assumed to simulate the spectrum, peak X0 should be 20 meV (160 cm−1) full width at half maximum (FWHM), which indeed is the actual measured width of peak X0. It is therefore not possible to ascertain whether there are two overlapping transitions separated by −
82 cm−1, the splitting between the ground X12 neutral state and the lowest-lying excited X23 states (vide supra).2 Results of DFT calculations on CeO predict the ordering of states with Λ-Σ designations that are consistent with the known neutral states associated with the 4 f 6s superconfiguration, as summarized in Table II. In order of increasing energy, the 3Φ, 3∆, 3Π, 3Σ, and associated openshell singlet states were predicted to fall within a 0.43 eV energy window, comparable to the known range of X, W, V, and U(T) states (0.55 eV).1 We acknowledge that DFT is valued for results on ground states, with excited state energies typically obtained using time-dependent density functional theory methods. However, this is an interesting case in which the relative energies of the four states with triplet spin multiplicity from the 4 f 6s occupancy are predicted correctly, and the nearly identical frequencies are expected for all states arising from the 4 f 6s superconfiguration. Results of calculations on the anion predict analogous 2 Φ, 2∆, 2Π, and 2Σ states from the 4 f 6s2 occupancy to be
TABLE II. DFT-calculated energies of CeO− states resulting from the 4 f 6s 2 Ce+ superconfiguration along with the two lowest energy quartet states that converged, and neutral CeO states resulting from the 4 f 6s Ce+2 superconfiguration along with bondlengths and vibrational frequencies.
State
Relative energy (eV)
⟨S 2⟩
CeO 1Σ 3Σ
1.30 1.24
2.0033
3Σ ← 2Σ 0.862/0.878
1.811
833
1.22 1.16
2.0029
3Π ← 2Π 0.863/0.878
1.809
835
3∆
0.91 0.90 0.873
1.0021 2.0027
1.813 1.808
842 840
3Φ
0.872
2.0014
1.813
842
CeO− 4H(4 f 5d 6s 2) φ δ 4Γ (4 f 5d 6s 2) δ δ 2Σ 2Π 2∆ 2Φ
1.56 1.51 0.37 0.29 0.002 0
3.732 3.754 0.7525 0.7522 0.7524 0.7513
1.890 1.886 1.844 1.841 1.842 1.845
712 712 782 783 789 790
1Π 3Π 1∆ 1Φ
Transition energies ADE/VDE (eV)
3∆
← 2∆ 0.871/0.890 3Φ ← 2Φ 0.872/0.890
Bondlength Vibrational frequency (Å) (cm−1)
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the lowest energy states, within a similarly narrow energy range of 0.37 eV. Depictions of the highest occupied and singly occupied orbitals in both the doublet anion and triplet and open-shell singlet neutral states are included in the supplementary material.27 Referring to the calculated transition energies summarized in Table II, the predicted ADE for the 2Φ ground state, 0.87 eV, is in fair agreement with the experimental value, 0.936 ± 0.008 eV. The anion and neutral vibrational frequencies are consistent with the observed peak spacings, and the predicted change in bondlength is in reasonable agreement with the bondlength change inferred from spectral simulation (vide supra). If the calculations correctly predict the basic Λ-Σ description of the anion ground state, it will have electronic structure derived from the Ce+ atomic cation 4 f 6s2 electronic configuration, which is stabilized relative to the lower-energy configurations in the O2− ligand field. In the free cation, the 2F5/2 and 2F7/2 states are 9779 cm−1 and 12261 cm−1, respectively, higher than the 4 H7/2 (4 f 5d 2) ground state.31 The energy between the Ja = 5/2 (from j f = 5/2) and 7/2 ( j f = 7/2) levels is 2482 cm−1, which is very similar to the energy interval between the ( j f = 5/2, j s = 1/2) and ( j f = 7/2, j s = 1/2) states in Ce2+. Describing CeO− as Ce+O2−, following Hund’s rules, gives a ground state with Ω = 5/2, correlating to the 2Φ5/2 state in the Λ-Σ description. The 2Φ7/2 state will be ca. 2000 cm−1 higher in energy. As with the neutral, states resulting from the lower-energy Ja = 5/2 and higher-energy Ja = 7/2 state with incrementally lower projections of Ja onto the internuclear axis, Ω, would have similar relative energies to the X, W, V, and U states in CeO, consistent with our computational results. The anion and neutral electronic orbital occupancy differs by a 6 s electron (σ orbital), giving a ∆Ω = ±1/2 selection rule. However, the allowed transitions are further confined to neutral states in which j f is preserved, since the angular momentum of the electron in the contracted 4 f orbital is not coupled to the molecular orbital angular momentum.32 Therefore, transitions from the CeO−Ω = 5/2 (Ja = 5/2) state to only the CeO X12 (Ω = 2, j f = 5/2; j s = 1/2) and X23 (Ω = 3, j f = 5/2; j s = 1/2) states should be observed, though the resolution of the apparatus is insufficient to resolve transitions spaced by 80 cm−1 (vide supra). Nonetheless, we conclude that, despite numerous close-lying electronic states of the neutral, the simple spectrum is consistent with Field’s description of CeO.10 Yamamoto and coworkers6 recently reported a fourcomponent relativistic configuration interaction study on the well-known 16 CeO 4 f 6s neutral states, along with extending the method to higher-lying states potentially accessed by various excitations. Of note was a state with nominally a 6s2 occupancy, predicted to lie 7875 cm−1 above the ground state. We tentatively assign peak A to the 1Σ+ ← X12 transition involving detachment of the 4 f electron, giving a term energy of 7210 cm−1 for the 1Σ+ state. The photodetachment cross section for transitions involving a 4 f electron is smaller than the cross section for the 6s electron,33 so the relative intensities of peaks in the X vibrational progression and peak A is consistent with the assignment. Peak B is 1390 cm−1 higher in energy than peak A, so it is unlikely to be the
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first vibrational level of the 1Σ+ state, and we leave peak B unassigned. B. PE spectrum of Ce(OH)2−
The PE spectrum of Ce(OH)2− obtained with 3.49 eV photon energy [Fig. 2(b)] exhibits a single intense transition (0.16 eV, 1300 cm−1, FWHM) with an ADE value of 0.69(3) eV and a VDE of 0.74(1) eV. Figure 4 shows higher resolution PE spectra of Ce(OH)2− obtained using 2.33 eV and 1.165 eV photon energies (green and red traces, respectively), along with an empirical simulation (black trace) and a simulation based on calculated spectroscopic parameters (top panel, vide infra). The empirical simulation (black trace) was generated with two active vibrational modes, 580(10) cm−1 (∆Q = 0.30 Å amu1/2) and 160(5) cm−1 (∆Q = 0.75 Å amu1/2) neutral frequencies. The anion frequencies were assumed to be similar, since no well-resolved hot-band features were observed in the spectra. The Ce(OH)2− molecular formula evokes a dihydroxide structure, and results of DFT calculations done on several different possible structures and spin states of the anions and neutrals predicted that a C2v dihydroxide structure is the most stable; the structure is shown in the top panel of Fig. 4. Linear- and trans- H-O-Ce-O-H structures converged to the C2v structure. CeO−·H2O charge-dipole or dipole-dipole complexes were calculated to be ca. 1 eV higher in energy than
FIG. 4. (a) Simulation of the Ce(OH)2− PE spectrum based on calculated spectroscopic parameters for the 3B1 + e− ← 2B1 transition. (a) Comparison of Ce(OH)2− PE spectra obtained with 2.33 eV (green trace) and 1.165 eV (red trace) photon energies, along a simulation including 160 cm−1 (∆Q = 0.750 Å amu1/2) and 584 cm−1 (∆Q = 0.300 Å amu1/2) active modes.
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the dihydroxide structure. Molecular structures and energies for the complexes are included in the supplementary material.27 As with CeO−, the lowest energy electronic configuration of Ce(OH)2− derives from the Ce+ 4 f 6s2 superconfiguration. Different orientations of the 4 f orbital within the C2v molecular framework result in different overall electronic terms, with energies that fall in a very narrow energy range: 2 B1, 2A1, 2A2, and 2B2 states resulting from the 4 f 6s2 superconfiguration are predicted to be within a 0.05 eV energy interval, all with nearly identical structures. Likewise, the lowest energy neutral states with triplet and singlet multiplicities resulting from the 4 f 6s superconfiguration are predicted to be within a 0.12 eV energy interval. These anion and neutral states are predicted to have very similar structures and vibrational frequencies, since they are identical except for the orientation of the contracted 4 f orbital, which is not involved in molecular bonding. Structures and a1 vibrational frequencies for several anion and neutral states are summarized in Table III, and a simulation based on the calculated frequencies and normal coordinate displacements for the 3B1 + e− ← 2B1 transition is included in Fig. 4(a). We do not presume that the 2B1 state is the ground electronic state of Ce(OH)2−, but this simulation is representative of all the one-electron transitions from the nearly degenerate 4 f 6s2 states that converged in the calculations. The transition energies for the other states are
included in the supplementary material.27 For the simulation, the origin was shifted to match the observed spectrum; the electron affinity of the 3B1 state was calculated to be 0.55 eV, which is in fair agreement with the observed value, 0.69 eV, given the systematic overestimation of exchange energy by the method used. The 583 cm−1 Ce–(OH)2 symmetric stretch frequency is also in good agreement with the higher of two frequencies used in the empirical simulation (the O–H stretch is not expected to be active, since the electron is detached from a Ce-local orbital that is not coupled to the O–H bond). However, the absence of a 160 cm−1 vibrational progression predicted in the calculations affirms some inadequacies in the calculations. Indeed, because no spin-orbit energies are included in the calculations, it is possible the anion and/or neutral are linear, driven by large spin-orbit stabilization. The barrier to linearity on the anion potential was calculated to be 900 cm−1, which is comparable to the spin-orbit coupling constant.10 If the anion were linear, the progression in the HO–Ce–OH bend mode would have a ∆υ = even selection rule, which is more readily reconciled with the calculated 95 cm−1 bend frequency. It is also possible that the observed 160 cm−1 progression is actually due to population of numerous 4 f 6s2 anion states, if their associated detachment energies varied by ca. 160 cm−1. Indeed, the neutral 4 f 6s states are calculated to be separated by approximately 160 cm−1 more than the 4 f 6s2
TABLE III. DFT-calculated energies of the numerous Ce(OH)2− states resulting from the 4 f 6s 2 Ce+ superconfiguration, with the lowest energy quartet state that converged, and neutral Ce(OH)2 states resulting from the 4 f 6s Ce+2 superconfiguration along with bondlengths and vibrational frequencies for the lowest energy states found for the superconfiguration. The other states have nearly identical structures and vibrational frequencies. Relative energies of CeO·H2O anion and neutral electrostatic complexes are included for comparison. Relative energy (eV)
Transition energies ADE/VDE (eV)
rCe–O, ∠O–Ce–O, ∠H–O–Ce
1A 1
2.04 1.80 1.70
1.70/1.75
2.084 Å 115◦ 163◦
3B 1
1.58
Electronic state Ce(OH)2 CeO·HOH Dipole-dipole Ce(OH)2 6s 2 Ce(OH)2 5d 6s Ce(OH)2 4 f 6s
3A 3A
1B , 3A , 3B , 1 1 2 1 1 1 2, A2, A1, B2
0.61 − 0.67
3A
Ce(OH)−2 −OCe-OH 2 Ce(OH)2−
3B 1
0.55
2A 4B 2
1.07 0.91
2A
0.85
4 f 5d 6s CeO−-HOH Ce(OH)2− 4f 6s2
1A
1,
1A , 2B 2 1 2B 1
a From
3A
1:
3A
2:
0.57/0.60 0.58/0.59 3B : 0.57/0.59 2 3B ← 2B 1 1 0.55/0.58
2.092 Å 116◦ 162◦
Totally symmetric vibrational frequenciesa
95, 336, 583, 3893
2.139 Å 117◦ 143◦
0.047-0.050 0.000
2.134 Å 120◦ 150◦
73, 240, 527, 3908
lowest to highest frequency, (HO)–Ce–(OH) symmetric bend, H–(OCeO)–H symmetric bend, (HO)–Ce–(OH) symmetric stretch, and H–(OCeO)–H symmetric stretch.
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anion states (see the supplementary material).27 However, the agreement between the observed 160 cm−1 progression and the calculated relative term energies of the anion and neutral using DFT methods seems fortuitous. Rather, the good alignment between the empirically simulated spectrum and experimental peak energies leads us to conclude that it is a vibrational progression.
IV. DISCUSSION
The PE spectra of both CeO− and Ce(OH)2− are surprisingly simple, in spite of numerous close-lying anion states from which numerous close-lying neutral states could be accessed via one-electron photodetachment transitions. The presence of what appear to be single electronic transitions in both spectra is in contrast to our recently obtained PE spectrum of Ce−, which exhibited numerous electronic transitions from close-lying anion states to numerous neutral states in a narrow energy interval.25 There are several points of comparison between CeO− and Ce(OH)2− that will now be made. DFT calculations on CeO− and Ce(OH)2− predict that the Ce+4 f 6s2 superconfiguration is the most stable in the O−2 and (OH−)2 ligand fields. Figure 5 shows depictions of the two highest occupied orbitals of CeO− and Ce(OH)2− (both orbitals shown are singly occupied in the lowest energy neutral states that converged in the calculations), one of which is clearly an atomic-like non-bonding 4 f orbital, the other of which is a p–polarized 6s orbital. Based on Hund’s rules, if Ce(OH)2− is linear, the singly occupied 4 f orbital would have φ-symmetry. The calculations on neutral CeO, for which the term energies of the sixteen 4 f 6s-derived states are well-known,1,4 correctly predicted the relative ordering of the different states resulting from 4 f orbital angular momentum projection onto the internuclear axis, if not the relatively equal energy intervals between all four states (in the absence of spin-orbit coupling). We cautiously conclude that DFT calculations are useful for qualitatively mapping the various electronic states in
FIG. 5. Highest singly occupied orbitals in neutral CeO and Ce(OH)2, illustrating the 4 f 6s Ce+2 superconfiguration. The 6s-like orbital is doubly occupied in both the anion ground states.
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these small lanthanide-based molecules. However, the need for caution is underscored by the poor agreement between the extended 160 cm−1 vibrational progression observed in the spectrum of Ce(OH)2−, for which the simulated spectrum based on calculated spectroscopic parameters is nearly vertical. This discrepancy may be due to spin-orbit stability driving a Ce(OH)2− linear structure. The bend mode in the anion is predicted to be very floppy (ωe = 73 cm−1; see Table III), and the orbital degeneracy breaking is ca. 50 meV, based on the four orbitals that resolved into the lowest energy a1, b1, b2, and a2 orbitals. The calculated low barrier to the linear structure (900 cm−1) does not include spin-orbit energy. If CeO− has numerous electronic states within an energy interval on the order of several vibrational quanta, why is there no evidence of transitions from these low-energy excited states to their one-electron accessible neutrals? The calculations predict the intuitive result that the relative energies of states resulting from different Ω = Ja , Ja − 1, . . . values are unaffected by the “extra” electron in the 6s orbital of the anion, so the 3 ∆ (Ω = Ja − 1 = 1) ← 2∆ (Ω = Ja − 1 = 1.5) transition may indeed be contributing to the spectrum if the 2∆ (Ω = 1.5) state is populated, but the transition energy is predicted to be nearly identical to the 3Φ ← 2Φ transition energy. We point out here that PrO10,34–36 and CeF37 are isoelectronic with CeO−, though with different effective charges on the constituent atoms, and have metal centers in the 4 f 2 6s (unpaired electrons in f φ and f δ orbitals) and 4 f 5d 6s superconfigurations, respectively. Both have 4 H3.5 ground states. For completeness, we attempted calculations on these two occupancies for CeO−. The 4 f 2 6s electronic occupancy would not converge in our calculations on CeO−, and the 4 f 5d 6s 4 H state was calculated to be 1.5 eV higher in energy than the 2Φ ground state (i.e., not bound with respect to the detachment continuum).
V. CONCLUSIONS
The photoelectron spectra of CeO− and Ce(OH)2− are dominated by single vibrationally resolved electronic transitions with vibrational profiles consistent with modest structure changes between the respective anions and neutrals. The adiabatic electron affinities of CeO and Ce(OH)2 were determined to be 0.936(8) eV and 0.69(3) eV, respectively. The measured asymmetry parameters and relatively high photodetachment cross sections are consistent with detachment from a 6s-like orbital, lending support for the similar electronic states derived from the Ce+ 4 f 6s2 orbital occupancies in both CeO− and Ce(OH)2−. We found reasonably good agreement between the experimental results and results from DFT calculations on CeO and CeO−, though calculations on Ce(OH)2 and Ce(OH)2−, while predicting an adiabatic electron affinity in reasonable agreement with the observed value, failed to adequately predict the observed 160 cm−1 vibrational progression in the spectrum. We suggest that the deficiency may be associated with exclusion of spinorbit coupling in the calculations. Low-intensity features observed at higher binding energy in the CeO− spectrum are tentatively assigned to transitions
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to the Ce+2 6s2–derived 1Σ+ state accessed via detachment of the lone 4 f electron in the anion, giving a term energy of 7210 cm−1. ACKNOWLEDGMENTS
C.C.J. thanks Professor R. W. Field for profound intellectual generosity and illuminating electronic communication, as well as Professor Kirk Peterson, for helpful conversations and for running preliminary CASSCF calculations on CeO−. This work was supported by the National Science Foundation Grant No. CHE-1265991. 1L.
A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 158, 40 (1993). 2L. A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 170, 166 (1995). 3C. Linton, J. Chen, and T. C. Steimle, J. Phys. Chem. A 113, 13379 (2009). 4C. Linton, M. Dulick, R. W. Field, P. Carette, P. C. Leyland, and R. F. Barrow, J. Mol. Spectrosc. 102, 441 (1983). 5R. F. Barrow, R. M. Clemments, S. M. Harris, and P. P. Jenson, Astrophys. J. 229, 439 (1979). 6H. Moriyanma, H. Tatewaki, and S. Yamamoto, J. Chem. Phys. 138, 224310 (2013). 7M. Dolg, H. Stoll, and H. Preuss, J. Mol. Struct.: THEOCHEM 231, 243 (1991). 8T. K. Todorova, I. Invfante, L. Gagliardi, and J. M. Dyke, Int. J. Quantum Chem. 109, 2068 (2009). 9M. Dolg, “Lanthanides and Actinides,” in Encyclopedia of Computational Chemistry (John Wiley & Sons Ltd., 2002). 10R. W. Field, Ber. Bunsenges. Phys. Chem. 86, 771 (1982). 11W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels- The Rare-Earth Elements, National Standard Reference Data Series, United States National Bureau of Standards, Vol. 60 (U.S. GPO Washington, D.C., 1978), found online at http://www.nist.gov/data/nsrds/NSRDS-NBS60.pdf; A. Kramida, Yu. Ralchenko, and J. Reader, NIST ASD Team NIST Atomic Spectra Database (ver. 5.1) (National Institute of Standards and Technology, Gaithersburg, MD, 2013), [Online]. Available: http://physics. nist.gov/asd [2013, October 22]. 12Y. Gong, M. F. Zhou, and L. Andrews, Chem. Rev. 109, 6765 (2009). 13R. Klingeler, G. Lüttgens, N. Pontius, R. Rochow, P. S. Bechtold, M. Neeb, and W. Eberhardt, Eur. Phys. J. D 9, 263 (1999). 14R. Klingeler, N. Pontius, G. Lüttgens, P. S. Bechthold, M. Neeb, and W. Eberhardt, Phys. Rev. A 65, 032502 (2002). 15Z. J. Wu, W. Guan, J. Meng, and Z. M. Su, J. Cluster Sci. 18, 444 (2007). 16V. D. Moravec and C. C. Jarrold, J. Chem. Phys. 108, 1804 (1998). 17S. E. Waller, J. E. Mann, D. W. Rothgeb, and C. C. Jarrold, J. Phys. Chem. A 116, 9639 (2012). 18J. A. Felton, M. Ray, S. E. Waller, J. O. Kafader, and C. C. Jarrold, J. Phys. Chem. A 118, 9960 (2014).
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E. Waller, J. E. Mann, and C. C. Jarrold, J. Phys. Chem. A 117, 1765 (2013). 20J. Cooper and R. N. Zare, J. Chem. Phys. 48, 942 (1968). 21A. Sanov, Annu. Rev. Phys. Chem. 65, 341 (2014). 22M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, G. Scalmani, B. Mennucci, V. Barone, G. A. Petersson, M. Caricato, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, X. Li, H. P. Hratchian, J. E. Peralta, A. F. Izmaylov, K. N. Kudin, J. J. Heyd, E. Brothers, V. Staroverov, G. Zheng, R. Kobayashi, J. Normand, J. L. Sonnenberg, F. Ogliaro, M. Bearpark, P. V. Parandekar, G. A. Ferguson, N. J. Mayhall, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. C. Burant, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, W. Chen, M. W. Wong, and J. A. Pople, Gaussian Development Version, Gaussian, Inc., Wallingford, CT, 2012. 23X. Cao and M. Dolg, J. Chem. Phys. 115, 7348 (2001). 24T. H. Dunning, J. Chem. Phys. 90, 1007 (1989). 25J. A. Felton, M. Ray, and C. C. Jarrold, Phys. Rev. A 89, 033407 (2014). 26C. Chi, H. Xie, R. Cong, Z.-c. Tang, and M. Zhou, Chin. J. Chem. Phys. 24, 604 (2011). 27See supplementary material at http://dx.doi.org/10.1063/1.4907714 for details on the CeO− PE spectral simulation, complete tables of calculated ADE/VDE values for states calculated for CeO− and Ce(OH)2−, depictions of highest occupied and singly occupied orbitals of the numerous anion and neutral states calculated for CeO and Ce(OH)2−, and a complete list of Cartesian coordinates and total energies for all structures that converged in the calculations. 28T. M. Miller, CRC Handbook of Chemistry and Phyiscs, Electron Affinities 94th ed. (CRC Press, Boca Raton, FL, 2013-2014), online edition, table 10–147. 29T. K. Todorova, I. Infante, L. Gagliardi, and J. M. Dyke, Int. J. Quantum Chem. 109, 2068 (2009). 30M. C. R. Cockett, J. M. Dyke, A. M. Ellis, M. Feher, and A. Morris, J. Am. Chem. Soc. 111, 5994 (1989). 31A. Kramida, Yu. Ralchenko, and J. Reader, NIST ASD Team NIST Atomic Spectra Database (ver. 5.2) (National Institute of Standards and Technology, Gaithersburg, MD, 2014), available online at http://physics.nist.gov/ asd [2014. December 11]. 32R. W. Field, personal communication (2014). 33S. M. O’malley and D. R. Beck, Phys. Rev. A 74, 042509 (2006). 34M. Dulick, R. W. Field, J. Cl. Beaufils, and J. Schamps, J. Mol. Spectrosc. 87, 278 (1981). 35M. Dulick, R. W. Field, and J. Cl. Beaufils, J. Mol. Spectrosc. 87, 268 (1981). 36M. Dulick and R. W. Field, J. Mol. Spectrosc. 113, 105 (1985). 37J. C. Bloch, M. C. McCarthy, R. W. Field, and L. A. Kaledin, J. Mol. Spectrosc. 177, 251 (1996).
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Photoelectron spectra of CeO− and Ce(OH)2− Manisha Ray, Jeremy A. Felton, Jared O. Kafader, Josey E. Topolski, and Caroline Chick Jarrolda) Department of Chemistry, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, USA
(Received 23 December 2014; accepted 27 January 2015; published online 11 February 2015) The photoelectron spectrum of CeO− exhibits what appears to be a single predominant electronic transition over an energy range in which numerous close-lying electronic states of CeO neutral are well known. The photoelectron spectrum of Ce(OH)2−, a molecule in which the Ce atom shares the same formal oxidation state as the Ce atom in CeO−, also exhibits what appears to be a single transition. From the spectra, the adiabatic electron affinities of CeO and Ce(OH)2 are determined to be 0.936 ± 0.007 eV and 0.69 ± 0.03 eV, respectively. From the electron affinity of CeO, the CeO− bond dissociation energy was determined to be 7.7 eV, 0.5 eV lower than the neutral bond dissociation energy. The ground state orbital occupancies of both CeO− and Ce(OH)2− are calculated to have 4 f 6s2 Ce+ superconfigurations, with open-shell states having 4 f 5d6s superconfiguration predicted to be over 1 eV higher in energy. Low-intensity transitions observed at higher electron binding energies in the spectrum of CeO− are tentatively assigned to the 1Σ+ (Ω = 0) state of CeO with the Ce+2 6s2 superconfiguration. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4907714]
I. INTRODUCTION
The electronic structure of the CeO diatomic molecule has been the subject of numerous detailed spectroscopic1–5 and ab initio6–9 investigations and, famously, the successful ligand field theory (LFT) treatment applied by Field.10 The crux of Field’s LFT treatment of the CeO molecule, described as Ce+2O−2, is that the [Xe] 4 f 6s occupancy of Ce+2 is stabilized relative to the [Xe] 4 f 2 Ce+2 ground state occupancy11 in the ligand field of O−2. The splittings between the possible atomic cation Ja states [Ja = 2, 3 from ( j f = 5/2, j s = 1/2); Ja = 4, 3 from ( j f = 7/2, j s = 1/2)] are largely preserved in the field set up by the O2− ligand, leading to numerous close-lying states in which the projection of the total angular momentum onto the CeO internuclear axis, Ω, equals Ja , Ja − 1, etc. As described by Field and subsequently by Heaven,1 the 16 states arising from this occupancy are, using the leading Λ-Σ description, 3 Φ and 1Φ (X12, X23, X34, and X43 states), 3∆ and 1∆ (W11, W22, W33, and W42 states), 3Π and 1Π (V10−, V21, V32, and V41 states), and 3Σ and 1Σ (U10+, U21, U30+, and T10− states) states. The terms in parentheses are labels established by Linton et al.4 The 16 states lie within an energy interval of approximately 4000 cm−1, ca. five vibrational spacings of the ground state. Because of the presence of numerous close-lying electronic neutral states in the transition metal- or lanthanide metal monoxides,12 their anion photodetachment spectra tend to be congested with transitions to numerous electronic neutral states accessed from one or more electronic states of the anion. Previously obtained PE spectra of LnO− species (Ln = La,13 Gd14) did indeed exhibit numerous transitions within an energy interval of several electron volts (eV). The dense a)Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2015/142(6)/064305/8/$30.00
spacing of 16 states of neutral CeO augurs an electronically complex anion and concomitant PE spectrum, yet the anion PE spectrum presented below exhibits what appears to be a single electronic transition. Additionally, the PE spectrum of Ce(OH)2−, a molecule in which the Ce center is in the same formal oxidation state as in CeO−, assuming a dihydroxide structure, is similarly simple. Results of density functional theory (DFT) calculations on the CeO neutral correctly predict the orbital occupancy and energy ordering of the non-spinorbit split low-lying neutral states resulting from the 4 f 6s superconfiguration. Our calculations on the anion agree with previously published results, predicting a ground state arising from the 4 f 6s2 Ce+ superconfiguration.15 The experimental results are consistent with the picture of negligible orbital angular momentum mixing of the contracted, single 4 f electron of the anionic and neutral CeO and Ce(OH)2. II. METHODS A. Experimental methods
PE spectra of CeO− and Ce(OH)2− were measured using an apparatus described in detail previously.16–18 The anionic species were generated using a pulsed laser ablation/molecular beam cluster source19 in which a solid Ce target was ablated with approximately 3 mJ/pulse of the second harmonic output of a Nd:YAG laser (532 nm, 2.33 eV) operated at 30 Hz repetition rate and entrained in a pulse of ultrahigh purity He carrier gas. The resulting mixture of atomic and molecular species in all charge states were swept through a 2.5-cm long, 0.3-cm diameter channel and expanded into a vacuum chamber. Anionic species that passed through a 3-mm skimmer were accelerated into a 1.2-m time-of-flight mass spectrometer and detected using a dual microchannel plate (MCP) detector assembly. The mass resolution (m/∆m) in the region of the Ce atom is 300; the two primary isotopes of
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Ce (140 and 142 amu) in both molecular CeO− and Ce(OH)2− were readily resolved. Prior to colliding with the ion detector, 140CeO− and 140Ce(OH)2− were selectively photodetached at the intersection of the ion drift tube and a 1-m field-free drift tube situated perpendicular to the ion drift path with the second and third harmonic outputs of a second Nd:YAG laser (532 nm/2.33 eV and 355 nm/3.49 eV wavelengths/photon energies, respectively) timed to intersect with the ions of interest. The drift times of the small fraction of photoelectrons that collided with a second MCP detector assembly at the end of the field-free drift tube were recorded with a digitizing oscilloscope. The drift times were converted to electron binding energy (e−BE) by identifying common transitions observed in the spectra collected using both photon energies and setting the difference in the electron kinetic energies (e−KE) to the fundamental energy (the difference between the energies of the second and third harmonics), which is specified as 1.1650(1) eV for the laser system used in this study, using the relationship, 2 2 ℓ ℓ 2(1.1650 eV) = − , (t 3ν − t o ) (t 2ν − t o ) me
(1)
where me is the electron mass, t 3ν is the drift time of electrons associated with a selected transition observed in the spectrum obtained using 3.49 eV photon energy that can readily be correlated with a transition in the spectrum obtained with 2.33 eV, appearing at t 2ν . The equation is solved for l and plotted as a function of t o. The intersection between this line and other lines generated from several sets of transitions observed in 3.49 eV and 2.33 eV give a unique l and to, the calibration parameters necessary to compute the e−KE values from electron drift times. The e−KE values are related to the anion and neutral states via e−KE = hν − EA − Teneutral + Teanion,
(2)
where EA is the neutral electron affinity. The data presented below show electron counts plotted as a function of e−BE: e−BE = hν − e−KE.
(3)
The e−BE values reflect the energy difference between the final neutral state and the initial anion state and are independent of the photon energy used. Laboratory to center-of-mass frame corrections were made to the e−KE (and e−BE) values. The CeO− and Ce(OH)2− spectra presented below were signal averaged between ca. 300 000 to 600 000 laser shots. Spectra were collected with the laser polarization both perpendicular to (θ = 90◦ ± 10◦) and parallel to (θ = 0◦ ± 10◦) the electron drift direction. The angular distribution of photoelectrons follows the expression:20 ( ) ∂σ σtotal 3 2 1 = 1 + β (E) cos θ − , ∂Ω 4π 2 2
The energy bandwidth, ∆E of the electron kinetic energy analyzer decays with e−KE3/2 following: e−KE ∆E = 0.004 eV + 0.0078 eV · eV (
) 32
.
(5)
Peaks observed in the spectrum obtained with 2.33 eV photon energy were therefore narrower than the same transitions observed in spectrum obtained with 3.49 eV. B. Computational methods
While the electronic structure of CeO is well-known and the anion would be best treated with a high-level method, the molecular and electronic structures of CeO and Ce(OH)2 anion and neutral were calculated using density functional theory with the primary goal of determining a general map of the energies of different electronic superconfigurations, in particular for the anions. All electronic structure calculations on CeO−, CeO, Ce(OH)2−, and Ce(OH)2 were performed with a development version of the GAUSSIAN suite of electronic structure programs22 using the B3LYP hybrid density functional method. To account for relativistic effects, a 28 electron pseudopotential with atomic natural orbital basis for the valence electrons (ECP28MWB_ANO) was used for Ce as developed by Dolg and Cao23 The atomic natural orbital contracted Gaussian valence basis set consists of (14s13p10d8 f 6g)/[6s6p5d4 f 3g] functions centered on Ce atom,23 and the aug-cc-pVTZ Dunning correlation consistent basis set24 was used for H and O atoms. DFT calculations were done on several spin states of anions and neutrals in various plausible structures for Ce(OH)2, including a CeO−·H2O complex. To underscore this need for caution with DFT calculations on these molecular species, calculations on neutral CeO defaulted to a 3∆g ground neutral state, with 4 f δ 6s occupancy, rather than the correct 4 f φ 6s 3Φ occupancy, though by editing the 3∆g orbital occupancy to 4 f φ 6s, the 3Φ state did converge with slightly lower energy. Further, the correct 4 f φ 6s 1Φ state correlating to the X43 state was found to be the lowest energy singlet neutral, which is consistent with the Λ-Σ description of this state, though again, appropriate caution should be taken with these results due to strong spin-orbit coupling and heavy mixing between the Λ-Σ states.7 Adiabatic and vertical detachment energies (ADE and VDE) of 1-e− transitions between anion and neutral states were calculated for both sets of species. The ADE is the energy difference between the zero point corrected energies of the optimized anion and neutral species, and the VDE is the difference between the ground state energy of anion and single point energy of neutral confined to the optimized structure of the anion.
III. RESULTS AND ANALYSIS
(4)
where σ is the photodetachment cross section. The asymmetry parameter, β (E) varies from −1 to 2, depending on the symmetry of the orbital associated with the detachment.21
Figure 1 shows the mass spectrum of anionic species generated using the ablation source. The mass distribution is dominated by the CeO3− anion, though Ce−, CeO−, and Ce(OH)2− are generated in sufficient quantities to obtain PE spectra.25 The CeO2− ion is low-intensity relative to Ce(OH)2−.
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or a molecular π bonding orbital, which would result in β (E) < 0. However, we cannot distinguish unambiguously between detachment from other potential molecular orbitals. We also point out here that the asymmetry in the CeO− spectrum is not uniform over what appears to be a single vibrational progression, and β (E) of peak X1 is 0.75. Low-intensity signal observed between 1.7 eV and 2.5 eV in the CeO− PE spectrum is reproducible and observed in spectra obtained with both 3.49 eV and 2.33 eV photon energies. A portion of the 2.33 eV spectrum, shown in green over this energy range, is included to demonstrate that this lower intensity signal, labeled A and B, is real. The asymmetry parameter is approximately zero for this region of the spectrum. FIG. 1. Mass spectrum of anions generated using the laser ablation source.
−
Figure 2 shows the PE spectra of (a) CeO and (b) Ce(OH)2− obtained using 3.49 eV photon energy with the laser polarization set at θ = 0◦ (black traces) and θ = 90◦ (red traces). At first glance, both spectra appear to show a single electronic transition, with the CeO− spectrum exhibiting a cleanly resolved vibrational progression (X0, X1, and X2) and a vibrational hot band (x′). The two spectra show similar polarization dependence. Using the equation, β(E) =
I0 − I90 , 1 2 I0 + I90
(6)
the asymmetry parameters were determined to be 1.0 ± 0.1 at the origin for both molecules. Chi et al. measured the 1.165 eV photoelectron imaging spectrum of CeO− and reported β (E) = 0.975.26 This positive value is NOT consistent with detachment from an atomic p-like orbital
FIG. 2. PE spectra of (a) CeO− and (b) Ce(OH)2− obtained using 3.49 eV photon energy with laser polarization both parallel (black traces) and perpendicular (red traces) to the direction of electron detection. A portion of the PE spectrum of CeO− obtained with 2.33 eV (parallel polarization) in the 1.5–2.15 eV binding energy range, showing additional structure, is included.
A. PE spectrum of CeO−
Figure 3 shows the PE spectrum of CeO− obtained with 2.33 eV photon energy. Table I summarizes the peak positions and relative energies. The primary features of the spectrum obtained with 2.33 eV photon energy can readily be fit with Franck-Condon factors calculated from harmonic oscillator wavefunctions assuming an origin of 0.936(3) eV from the position of peak X0, the known ∆G(1/2) value for the neutral 824.3 cm−1 reported in Ref. 4 (we did not include anharmonicity because peak X2 is both low in intensity and broad compared to optical spectra), an anion frequency ranging from ω ′′ = 680 to 800 cm−1 based on the x′ − X0 interval, and a bondlength change of 0.040(3) Å. A vibrational temperature of 1500 K was necessary to reproduce the intensity of the presumed vibrational hot band, peak x′. A simulation generated using these parameters is shown in the supplementary material.27
FIG. 3. PE spectrum of CeO− obtained using 2.33 eV photon energy with laser polarization both parallel (black traces) and perpendicular (red traces) to the direction of electron detection. The energies of the 16 4 f 6s CeO neutral states relative to the EA of CeO are indicated along the top axis, based on Ref. 2.
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TABLE I. CeO− PE spectrum (Fig. 3) peak positions and assignments. Peak
Position (eV)
Relative energy (cm−1)
Tentative assignment
a x′ X0 X1 X2 A B
0.758 ± 0.015 0.828 − 0.848 0.936 ± 0.008 1.042 ± 0.010 1.149 ± 0.015 1.83 ± 0.01 1.99 ± 0.01
−1435 −871 to −709 0 855 ± 100 1720 ± 140 7210 ± 100 8500 ± 100
X12 (υ ′ = 0) + e− ← X12.5 (υ ′′ = 1) X12 (υ ′ = 0) + e− ← X12.5 (υ ′′ = 0) X12 (υ ′ = 1) + e− ← X12.5 (υ ′′ = 0) X12 (υ ′ = 2) + e− ← X12.5 (υ ′′ = 0) 6s 2 1Σ+ + e− ← X12.5 (υ ′′ = 0)a
a Tentative.
The electron affinity of O− is 1.4611 eV.28 Using the equivalence, D0 (CeO) + EA (CeO) = D0 (CeO−) + EA (O),
(7)
the bond dissociation energy of CeO to the Ce + O− asymptote is 0.53 eV lower than the bond dissociation energy of the neutral. The latter has been measured to be approximately 8.2 eV,29,30 giving a 7.7 eV bond dissociation energy for the anion. The lower anion vibrational frequency and bond dissociation energy relative to the neutral values point to a longer bondlength for the anion. The previously determined bondlength of the neutral ground state is 1.820 Å,1 giving a 1.860(3) Å anion bondlength. Given the experimental resolution (Eq. (5)) and assuming a 300 K rotational temperature, which is lower than the vibrational temperature assumed to simulate the spectrum, peak X0 should be 20 meV (160 cm−1) full width at half maximum (FWHM), which indeed is the actual measured width of peak X0. It is therefore not possible to ascertain whether there are two overlapping transitions separated by −
82 cm−1, the splitting between the ground X12 neutral state and the lowest-lying excited X23 states (vide supra).2 Results of DFT calculations on CeO predict the ordering of states with Λ-Σ designations that are consistent with the known neutral states associated with the 4 f 6s superconfiguration, as summarized in Table II. In order of increasing energy, the 3Φ, 3∆, 3Π, 3Σ, and associated openshell singlet states were predicted to fall within a 0.43 eV energy window, comparable to the known range of X, W, V, and U(T) states (0.55 eV).1 We acknowledge that DFT is valued for results on ground states, with excited state energies typically obtained using time-dependent density functional theory methods. However, this is an interesting case in which the relative energies of the four states with triplet spin multiplicity from the 4 f 6s occupancy are predicted correctly, and the nearly identical frequencies are expected for all states arising from the 4 f 6s superconfiguration. Results of calculations on the anion predict analogous 2 Φ, 2∆, 2Π, and 2Σ states from the 4 f 6s2 occupancy to be
TABLE II. DFT-calculated energies of CeO− states resulting from the 4 f 6s 2 Ce+ superconfiguration along with the two lowest energy quartet states that converged, and neutral CeO states resulting from the 4 f 6s Ce+2 superconfiguration along with bondlengths and vibrational frequencies.
State
Relative energy (eV)
⟨S 2⟩
CeO 1Σ 3Σ
1.30 1.24
2.0033
3Σ ← 2Σ 0.862/0.878
1.811
833
1.22 1.16
2.0029
3Π ← 2Π 0.863/0.878
1.809
835
3∆
0.91 0.90 0.873
1.0021 2.0027
1.813 1.808
842 840
3Φ
0.872
2.0014
1.813
842
CeO− 4H(4 f 5d 6s 2) φ δ 4Γ (4 f 5d 6s 2) δ δ 2Σ 2Π 2∆ 2Φ
1.56 1.51 0.37 0.29 0.002 0
3.732 3.754 0.7525 0.7522 0.7524 0.7513
1.890 1.886 1.844 1.841 1.842 1.845
712 712 782 783 789 790
1Π 3Π 1∆ 1Φ
Transition energies ADE/VDE (eV)
3∆
← 2∆ 0.871/0.890 3Φ ← 2Φ 0.872/0.890
Bondlength Vibrational frequency (Å) (cm−1)
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the lowest energy states, within a similarly narrow energy range of 0.37 eV. Depictions of the highest occupied and singly occupied orbitals in both the doublet anion and triplet and open-shell singlet neutral states are included in the supplementary material.27 Referring to the calculated transition energies summarized in Table II, the predicted ADE for the 2Φ ground state, 0.87 eV, is in fair agreement with the experimental value, 0.936 ± 0.008 eV. The anion and neutral vibrational frequencies are consistent with the observed peak spacings, and the predicted change in bondlength is in reasonable agreement with the bondlength change inferred from spectral simulation (vide supra). If the calculations correctly predict the basic Λ-Σ description of the anion ground state, it will have electronic structure derived from the Ce+ atomic cation 4 f 6s2 electronic configuration, which is stabilized relative to the lower-energy configurations in the O2− ligand field. In the free cation, the 2F5/2 and 2F7/2 states are 9779 cm−1 and 12261 cm−1, respectively, higher than the 4 H7/2 (4 f 5d 2) ground state.31 The energy between the Ja = 5/2 (from j f = 5/2) and 7/2 ( j f = 7/2) levels is 2482 cm−1, which is very similar to the energy interval between the ( j f = 5/2, j s = 1/2) and ( j f = 7/2, j s = 1/2) states in Ce2+. Describing CeO− as Ce+O2−, following Hund’s rules, gives a ground state with Ω = 5/2, correlating to the 2Φ5/2 state in the Λ-Σ description. The 2Φ7/2 state will be ca. 2000 cm−1 higher in energy. As with the neutral, states resulting from the lower-energy Ja = 5/2 and higher-energy Ja = 7/2 state with incrementally lower projections of Ja onto the internuclear axis, Ω, would have similar relative energies to the X, W, V, and U states in CeO, consistent with our computational results. The anion and neutral electronic orbital occupancy differs by a 6 s electron (σ orbital), giving a ∆Ω = ±1/2 selection rule. However, the allowed transitions are further confined to neutral states in which j f is preserved, since the angular momentum of the electron in the contracted 4 f orbital is not coupled to the molecular orbital angular momentum.32 Therefore, transitions from the CeO−Ω = 5/2 (Ja = 5/2) state to only the CeO X12 (Ω = 2, j f = 5/2; j s = 1/2) and X23 (Ω = 3, j f = 5/2; j s = 1/2) states should be observed, though the resolution of the apparatus is insufficient to resolve transitions spaced by 80 cm−1 (vide supra). Nonetheless, we conclude that, despite numerous close-lying electronic states of the neutral, the simple spectrum is consistent with Field’s description of CeO.10 Yamamoto and coworkers6 recently reported a fourcomponent relativistic configuration interaction study on the well-known 16 CeO 4 f 6s neutral states, along with extending the method to higher-lying states potentially accessed by various excitations. Of note was a state with nominally a 6s2 occupancy, predicted to lie 7875 cm−1 above the ground state. We tentatively assign peak A to the 1Σ+ ← X12 transition involving detachment of the 4 f electron, giving a term energy of 7210 cm−1 for the 1Σ+ state. The photodetachment cross section for transitions involving a 4 f electron is smaller than the cross section for the 6s electron,33 so the relative intensities of peaks in the X vibrational progression and peak A is consistent with the assignment. Peak B is 1390 cm−1 higher in energy than peak A, so it is unlikely to be the
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first vibrational level of the 1Σ+ state, and we leave peak B unassigned. B. PE spectrum of Ce(OH)2−
The PE spectrum of Ce(OH)2− obtained with 3.49 eV photon energy [Fig. 2(b)] exhibits a single intense transition (0.16 eV, 1300 cm−1, FWHM) with an ADE value of 0.69(3) eV and a VDE of 0.74(1) eV. Figure 4 shows higher resolution PE spectra of Ce(OH)2− obtained using 2.33 eV and 1.165 eV photon energies (green and red traces, respectively), along with an empirical simulation (black trace) and a simulation based on calculated spectroscopic parameters (top panel, vide infra). The empirical simulation (black trace) was generated with two active vibrational modes, 580(10) cm−1 (∆Q = 0.30 Å amu1/2) and 160(5) cm−1 (∆Q = 0.75 Å amu1/2) neutral frequencies. The anion frequencies were assumed to be similar, since no well-resolved hot-band features were observed in the spectra. The Ce(OH)2− molecular formula evokes a dihydroxide structure, and results of DFT calculations done on several different possible structures and spin states of the anions and neutrals predicted that a C2v dihydroxide structure is the most stable; the structure is shown in the top panel of Fig. 4. Linear- and trans- H-O-Ce-O-H structures converged to the C2v structure. CeO−·H2O charge-dipole or dipole-dipole complexes were calculated to be ca. 1 eV higher in energy than
FIG. 4. (a) Simulation of the Ce(OH)2− PE spectrum based on calculated spectroscopic parameters for the 3B1 + e− ← 2B1 transition. (a) Comparison of Ce(OH)2− PE spectra obtained with 2.33 eV (green trace) and 1.165 eV (red trace) photon energies, along a simulation including 160 cm−1 (∆Q = 0.750 Å amu1/2) and 584 cm−1 (∆Q = 0.300 Å amu1/2) active modes.
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the dihydroxide structure. Molecular structures and energies for the complexes are included in the supplementary material.27 As with CeO−, the lowest energy electronic configuration of Ce(OH)2− derives from the Ce+ 4 f 6s2 superconfiguration. Different orientations of the 4 f orbital within the C2v molecular framework result in different overall electronic terms, with energies that fall in a very narrow energy range: 2 B1, 2A1, 2A2, and 2B2 states resulting from the 4 f 6s2 superconfiguration are predicted to be within a 0.05 eV energy interval, all with nearly identical structures. Likewise, the lowest energy neutral states with triplet and singlet multiplicities resulting from the 4 f 6s superconfiguration are predicted to be within a 0.12 eV energy interval. These anion and neutral states are predicted to have very similar structures and vibrational frequencies, since they are identical except for the orientation of the contracted 4 f orbital, which is not involved in molecular bonding. Structures and a1 vibrational frequencies for several anion and neutral states are summarized in Table III, and a simulation based on the calculated frequencies and normal coordinate displacements for the 3B1 + e− ← 2B1 transition is included in Fig. 4(a). We do not presume that the 2B1 state is the ground electronic state of Ce(OH)2−, but this simulation is representative of all the one-electron transitions from the nearly degenerate 4 f 6s2 states that converged in the calculations. The transition energies for the other states are
included in the supplementary material.27 For the simulation, the origin was shifted to match the observed spectrum; the electron affinity of the 3B1 state was calculated to be 0.55 eV, which is in fair agreement with the observed value, 0.69 eV, given the systematic overestimation of exchange energy by the method used. The 583 cm−1 Ce–(OH)2 symmetric stretch frequency is also in good agreement with the higher of two frequencies used in the empirical simulation (the O–H stretch is not expected to be active, since the electron is detached from a Ce-local orbital that is not coupled to the O–H bond). However, the absence of a 160 cm−1 vibrational progression predicted in the calculations affirms some inadequacies in the calculations. Indeed, because no spin-orbit energies are included in the calculations, it is possible the anion and/or neutral are linear, driven by large spin-orbit stabilization. The barrier to linearity on the anion potential was calculated to be 900 cm−1, which is comparable to the spin-orbit coupling constant.10 If the anion were linear, the progression in the HO–Ce–OH bend mode would have a ∆υ = even selection rule, which is more readily reconciled with the calculated 95 cm−1 bend frequency. It is also possible that the observed 160 cm−1 progression is actually due to population of numerous 4 f 6s2 anion states, if their associated detachment energies varied by ca. 160 cm−1. Indeed, the neutral 4 f 6s states are calculated to be separated by approximately 160 cm−1 more than the 4 f 6s2
TABLE III. DFT-calculated energies of the numerous Ce(OH)2− states resulting from the 4 f 6s 2 Ce+ superconfiguration, with the lowest energy quartet state that converged, and neutral Ce(OH)2 states resulting from the 4 f 6s Ce+2 superconfiguration along with bondlengths and vibrational frequencies for the lowest energy states found for the superconfiguration. The other states have nearly identical structures and vibrational frequencies. Relative energies of CeO·H2O anion and neutral electrostatic complexes are included for comparison. Relative energy (eV)
Transition energies ADE/VDE (eV)
rCe–O, ∠O–Ce–O, ∠H–O–Ce
1A 1
2.04 1.80 1.70
1.70/1.75
2.084 Å 115◦ 163◦
3B 1
1.58
Electronic state Ce(OH)2 CeO·HOH Dipole-dipole Ce(OH)2 6s 2 Ce(OH)2 5d 6s Ce(OH)2 4 f 6s
3A 3A
1B , 3A , 3B , 1 1 2 1 1 1 2, A2, A1, B2
0.61 − 0.67
3A
Ce(OH)−2 −OCe-OH 2 Ce(OH)2−
3B 1
0.55
2A 4B 2
1.07 0.91
2A
0.85
4 f 5d 6s CeO−-HOH Ce(OH)2− 4f 6s2
1A
1,
1A , 2B 2 1 2B 1
a From
3A
1:
3A
2:
0.57/0.60 0.58/0.59 3B : 0.57/0.59 2 3B ← 2B 1 1 0.55/0.58
2.092 Å 116◦ 162◦
Totally symmetric vibrational frequenciesa
95, 336, 583, 3893
2.139 Å 117◦ 143◦
0.047-0.050 0.000
2.134 Å 120◦ 150◦
73, 240, 527, 3908
lowest to highest frequency, (HO)–Ce–(OH) symmetric bend, H–(OCeO)–H symmetric bend, (HO)–Ce–(OH) symmetric stretch, and H–(OCeO)–H symmetric stretch.
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anion states (see the supplementary material).27 However, the agreement between the observed 160 cm−1 progression and the calculated relative term energies of the anion and neutral using DFT methods seems fortuitous. Rather, the good alignment between the empirically simulated spectrum and experimental peak energies leads us to conclude that it is a vibrational progression.
IV. DISCUSSION
The PE spectra of both CeO− and Ce(OH)2− are surprisingly simple, in spite of numerous close-lying anion states from which numerous close-lying neutral states could be accessed via one-electron photodetachment transitions. The presence of what appear to be single electronic transitions in both spectra is in contrast to our recently obtained PE spectrum of Ce−, which exhibited numerous electronic transitions from close-lying anion states to numerous neutral states in a narrow energy interval.25 There are several points of comparison between CeO− and Ce(OH)2− that will now be made. DFT calculations on CeO− and Ce(OH)2− predict that the Ce+4 f 6s2 superconfiguration is the most stable in the O−2 and (OH−)2 ligand fields. Figure 5 shows depictions of the two highest occupied orbitals of CeO− and Ce(OH)2− (both orbitals shown are singly occupied in the lowest energy neutral states that converged in the calculations), one of which is clearly an atomic-like non-bonding 4 f orbital, the other of which is a p–polarized 6s orbital. Based on Hund’s rules, if Ce(OH)2− is linear, the singly occupied 4 f orbital would have φ-symmetry. The calculations on neutral CeO, for which the term energies of the sixteen 4 f 6s-derived states are well-known,1,4 correctly predicted the relative ordering of the different states resulting from 4 f orbital angular momentum projection onto the internuclear axis, if not the relatively equal energy intervals between all four states (in the absence of spin-orbit coupling). We cautiously conclude that DFT calculations are useful for qualitatively mapping the various electronic states in
FIG. 5. Highest singly occupied orbitals in neutral CeO and Ce(OH)2, illustrating the 4 f 6s Ce+2 superconfiguration. The 6s-like orbital is doubly occupied in both the anion ground states.
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these small lanthanide-based molecules. However, the need for caution is underscored by the poor agreement between the extended 160 cm−1 vibrational progression observed in the spectrum of Ce(OH)2−, for which the simulated spectrum based on calculated spectroscopic parameters is nearly vertical. This discrepancy may be due to spin-orbit stability driving a Ce(OH)2− linear structure. The bend mode in the anion is predicted to be very floppy (ωe = 73 cm−1; see Table III), and the orbital degeneracy breaking is ca. 50 meV, based on the four orbitals that resolved into the lowest energy a1, b1, b2, and a2 orbitals. The calculated low barrier to the linear structure (900 cm−1) does not include spin-orbit energy. If CeO− has numerous electronic states within an energy interval on the order of several vibrational quanta, why is there no evidence of transitions from these low-energy excited states to their one-electron accessible neutrals? The calculations predict the intuitive result that the relative energies of states resulting from different Ω = Ja , Ja − 1, . . . values are unaffected by the “extra” electron in the 6s orbital of the anion, so the 3 ∆ (Ω = Ja − 1 = 1) ← 2∆ (Ω = Ja − 1 = 1.5) transition may indeed be contributing to the spectrum if the 2∆ (Ω = 1.5) state is populated, but the transition energy is predicted to be nearly identical to the 3Φ ← 2Φ transition energy. We point out here that PrO10,34–36 and CeF37 are isoelectronic with CeO−, though with different effective charges on the constituent atoms, and have metal centers in the 4 f 2 6s (unpaired electrons in f φ and f δ orbitals) and 4 f 5d 6s superconfigurations, respectively. Both have 4 H3.5 ground states. For completeness, we attempted calculations on these two occupancies for CeO−. The 4 f 2 6s electronic occupancy would not converge in our calculations on CeO−, and the 4 f 5d 6s 4 H state was calculated to be 1.5 eV higher in energy than the 2Φ ground state (i.e., not bound with respect to the detachment continuum).
V. CONCLUSIONS
The photoelectron spectra of CeO− and Ce(OH)2− are dominated by single vibrationally resolved electronic transitions with vibrational profiles consistent with modest structure changes between the respective anions and neutrals. The adiabatic electron affinities of CeO and Ce(OH)2 were determined to be 0.936(8) eV and 0.69(3) eV, respectively. The measured asymmetry parameters and relatively high photodetachment cross sections are consistent with detachment from a 6s-like orbital, lending support for the similar electronic states derived from the Ce+ 4 f 6s2 orbital occupancies in both CeO− and Ce(OH)2−. We found reasonably good agreement between the experimental results and results from DFT calculations on CeO and CeO−, though calculations on Ce(OH)2 and Ce(OH)2−, while predicting an adiabatic electron affinity in reasonable agreement with the observed value, failed to adequately predict the observed 160 cm−1 vibrational progression in the spectrum. We suggest that the deficiency may be associated with exclusion of spinorbit coupling in the calculations. Low-intensity features observed at higher binding energy in the CeO− spectrum are tentatively assigned to transitions
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to the Ce+2 6s2–derived 1Σ+ state accessed via detachment of the lone 4 f electron in the anion, giving a term energy of 7210 cm−1. ACKNOWLEDGMENTS
C.C.J. thanks Professor R. W. Field for profound intellectual generosity and illuminating electronic communication, as well as Professor Kirk Peterson, for helpful conversations and for running preliminary CASSCF calculations on CeO−. This work was supported by the National Science Foundation Grant No. CHE-1265991. 1L.
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