Note: Photoelectron imaging of MnO₃⁻ to probe its nuclear and electronic structure

Using anion photoelectron spectroscopy, a previous study by Gutsev et al.¹ found the ground state of MnO₃ to have a trigonal pyramidal structure. In this note, we revisit the MnO₃⁻ photoelectron spectrum using photoelectron imaging and reassess the assignment, showing that in fact, MnO₃ is planar in its ground electronic state. Furthermore, the photoelectron angular distributions (PADs) associated with electron emission to the neutral ground state provide insight into the highest occupied molecular orbital (HOMO) of the anion, showing that it is of predominantly Mn d_z² character. All these results agree with a simple d-block model and are further supported by electronic structure calculations.

The geometric and electronic structure of transition metal complexes are often complicated by a high density of states, electronic state degeneracy, and the potential for isomers of similar energy, with additional factors such as relativistic effects and spin–orbit coupling also contributing complexity, particularly for the second and third row transition metals.^2,3 As a result, geometry optimisation and electronic structure calculations can be challenging and can lead to unreliable results. Therefore, it is appealing to use simple models, such as the d-block model, which considers the relative ordering of the anti- and non-bonding d-orbitals on the transition metal centre within a ligand field, to propose likely structures.^4,5 In an earlier study on a series of manganese oxides by Gutsev et al., MnO₃ was determined to have a trigonal pyramidal (C_3v) structure through the use of anion photoelectron spectroscopy and electronic structure calculations, although no Franck–Condon simulations were presented.¹ This result is unusual as transition metal complexes with three ligands are normally trigonal planar (D_3h), as is the case for its anion MnO₃⁻.⁴ Here, we have repeated these experiments using anion photoelectron imaging and electronic structure calculations on MnO₃⁻ and MnO₃.

Anion photoelectron spectroscopy is a powerful tool for determining structural information about anions and their neutral counterparts, and has been applied to many transition metal complexes.^1,5–12 Determination of nuclear geometries is enabled though agreement of the experimental photoelectron spectra and simulated Franck–Condon spectra based on electronic structure calculations. As a representative example, structural isomers of Ti₂O₄ and Zr₂O could be determined by high-resolution, cryogenic slow electron velocity map-imaging.⁹ Furthermore, the PAD, often quantified by the anisotropy parameter β₂ that runs from −1 to +2, can give electronic structure information of the anion.^13–15 This approach has been used across a broad range of anions, including organic and inorganic species.^16–18 In contrast, photoelectron imaging studies of transition metal anions have been relatively scarce,^{5,8,10,19–21} despite their aid in assigning electronic configurations.

The experimental apparatus has been described in detail elsewhere and will only be summarised here.^22,23 MnO₃⁻ was produced via electrospray ionization of a 5 mM solution of KMnO₄ in acetonitrile. Anions entered the apparatus via a capillary, before being guided and trapped using a series of RF guides and subsequently accelerated to 2.2 kV using a Wiley McLaren time of flight spectrometer.²⁴ Mass selected anions were intersected with the variable wavelength output of a nanosecond optical parametric oscillator pumped via the third harmonic of a Nd:YAG. Ejected photoelectrons were focused onto the position sensitive microchannel plate and phosphor screen detector using a velocity map imaging setup. From the resulting images, the electron kinetic energy (eKE) and PADs were extracted following processing via the polar onion peeling algorithm.²⁵ Photoelectron imaging was performed at hv = 3.76 and 3.94 eV (λ = 330 and 315 nm), to determine how the spectral features shift with wavelength.

Electronic structure calculations were also performed using density functional theory (DFT) at the B3LYP, TPSSh and PBE0 level of theory with the aug-cc-pVTZ basis set.^26–29 Previously reported electronic structure calculations¹ used the BPW91 level of theory and the 6-311+G(d) basis set.^30–33 These calculations were repeated and expanded upon here. Geometry optimisations were performed, molecular orbitals visualised, and Franck–Condon factor simulations undertaken. All calculations were performed using Gaussian 16.³⁴ 

Figure 1 shows the photoelectron spectrum of MnO₃⁻ recorded at hv = 3.76 and 3.94 eV, as well as the raw symmetrised photoelectron image of MnO₃⁻ at the higher photon energy. Two distinctive features are seen in the photoelectron spectra: a feature peaking near eKE = 0 eV with an exponentially decaying distribution; and a series of narrow peaks that shift with photon energy, the most intense peak of which is centred at a fixed, eBE = hν − eKE = 3.37 ± 0.05 eV. From the photoelectron image in Fig. 1(b), the feature peaking at eKE = 0 eV is isotropic, whereas the higher energy features have an anisotropic PAD characterised by β₂ = 1.5 ± 0.25.

The feature peaking at eKE = 0 eV has all the characteristics of thermionic emission, corresponding to electron loss from internally hot anions in their electronic ground state. The presence of thermionic emission indicates that there is rapid internal conversion back to the ground state following absorption of a photon to an excited state, with electrons then “boiling” off from the hot anions that have returned to the ground state. Such features have been seen in many other molecular anions,^35,36 but it was not clearly observed by Gustev et al., although a gradual increase in signal near eKE ∼ 0 eV was seen.¹ This difference is likely due to the fact that the previous photoelectron spectrum was acquired at hv = 4.66 eV (λ = 266 nm) and utilised a magnetic bottle spectrometer, which does not efficiently detect low eKE electrons. We note that our peaks are broader than those from Gustev et al. (red, Fig. 2), which is likely as a result of the lower energy resolution of our photoelectron spectrometer (5% vs 3%).¹ Additionally, we do not observe the hot band presumably because of the methodology used to produce the anions (pulsed laser vaporization in a molecular beam, which often leaves vibrational excitation, vs electrospray ionisation, which produces room temperature ions).

The feature with the dominant peak at eBE = 3.37 eV is attributable to direct detachment resulting in different vibrational energy levels of MnO₃, with a second peak in the vibrational progression observed 0.1 eV lower in eKE. Gutsev et al. assigned the vibrational structure to the symmetric Mn–O stretch in MnO₃, which they predicted to have a pyramidal (C_3v) geometry with a 117° bond angle, at the BPW91/6-311+G(d) level of theory,¹ while MnO₃⁻ was found to be planar (D_3h). All our calculations confirm that the anion is trigonal planar, however our geometry optimisations for MnO₃ result in both pyramidal and trigonal planar structures depending on the functional used. PBE0 predicts a pyramidal (C_2v) structure with a 118° bond angle, TPSSh predicts an effectively planar geometry (>119.5° bond angle) and B3LYP predicts a trigonal planar (D_3h) structure. The relatively narrow spectral peaks, and small amount of vibrational excitation left in the neutral, would appear to be inconsistent with a geometry change upon photodetachment from D_3h to C_3v, where one might anticipate significant Franck–Condon activity in the umbrella mode of MnO₃ that would broaden the observed photoelectron peaks.

To enable direct comparison with experiment, Franck–Condon simulations were performed based on the optimised geometries calculated using different functionals. The results using BPW91/6-311+G(d) and B3LYP/aug-cc-p-VTZ are shown in Figs. 2(a) and 2(b), respectively, where we have included a Gaussian convolution to account for the spectral resolution of our experiment (full-width-at-half-maximum is 25 meV). The D_3h → D_3h photodetachment [Fig. 2(b)] shows a vibrational progression, associated with the symmetric Mn–O stretch, with a spacing of 927 cm⁻¹ (0.11 eV). In contrast, the spectrum calculated for a geometry change from D_3h → C_3v photodetachment has a series of low frequency modes [spacing of 160 cm⁻¹ (0.02 eV)], associated with the out-of-plane umbrella motion of MnO₃, resulting in a broadened spectrum as shown in Fig. 2(a). The geometry of MnO₃ was crucial in determining the simulated Franck–Condon envelopes, as using PBE0 (C_2v MnO₃) also predicted a broad unresolved spectrum like BPW91 [Fig. 2(a)], whereas using TPSSh predicted a resolved vibrational progression of four narrow bands, similar to B3LYP [Fig. 2(b)]. Comparison of the two differing simulations in Fig. 2 suggests that the Franck–Condon envelope for photodetachment to the ground state of MnO₃ with a D_3h geometry matches the direct detachment features of both our spectrum (black, Fig. 2) and the previously reported spectrum (red, Fig. 2) more closely than for a pyramidal MnO₃, concluding that the neutral is in fact trigonal planar.¹ 

Our experiments provide additional information about the electronic structure of MnO₃⁻ through the PADs. The simple d-block model of transition metal complexes can be used to estimate the nature of high lying molecular orbitals (MOs).⁴ These will have a large contribution from the partially filled d-orbitals of the metal and are expected to have anti- or non-bonding character overall.⁴ For MnO₃⁻, the metal-centred d_xy and d_x²+y² orbitals on Mn will be raised in energy due to overlap with the oxygen s-orbitals and p-orbitals orientated along the internuclear axes forming MOs of σ* character. The d_xz and d_yz orbitals will be raised somewhat in energy due to a π* interaction with the remaining p-orbitals on the O atoms. The d_z² orbital will be the lowest in energy and essentially non-bonding with the oxygen-centred orbitals. The resultant d-block picture is summarised in Fig. 3(a).

For comparison, the relevant MOs of MnO₃⁻ were also computed. The calculated highest occupied, lowest unoccupied and lowest unoccupied plus one molecular orbital (HOMO, LUMO, and LUMO+1, respectively) calculated at the B3LYP/aug-cc-pVTZ level of theory are shown in Fig. 3(b). The HOMO has predominantly d_z² character, with a small contribution from MOs localised on the O atoms. The LUMO and LUMO+1 are essentially degenerate and consist mainly of contributions from the d_xy and d_yz localised on the Mn and p-orbitals localised on the O atoms. Therefore, the orbitals predicted from electronic structure methods, from the d-block model, and from a symmetry-adapted linear-combination of atomic orbitals are all fully consistent.

Photoelectron imaging provides information about the nature of the high-lying occupied MOs via the PAD. According to Koopmans’ theory, photodetachment would remove an electron from the HOMO [see Fig. 3(a)], which has predominantly d_z² character. Ejection of an electron from this MO is expected to have predominantly p-wave character (partial waves of f-character will also contribute but are likely to have lower cross-sections based on centrifugal barriers), which would lead to a PAD characterised by a positive β₂ value.³⁷ This is consistent with the observed photoelectron image for MnO₃⁻ in Fig. 1(b). The excellent agreement between the experimental data, electronic structure calculations and simple d-block model, indicates the validity of the theoretical approaches, the value of the d-block model and the power of photoelectron imaging for understanding the electronic structure of transition metal complexes.

To conclude, comparison of the photoelectron spectrum of MnO₃⁻ to calculated Franck–Condon factors has allowed us to reassign the ground electronic state of MnO₃ to have a trigonal planar geometry as expected. The observed anisotropy for the photoelectron emission from MnO₃⁻ can be justified via a simple d-block model and verified by electronic structure calculations, both of which indicate that the HOMO has predominantly d_z² character.