Introduction

Oxidation state (OS) is a fundamental chemical concept1. The discovery of new and unusual OS for chemical elements has drawn persistent attention in chemistry and materials science. The OS of lanthanide elements has been of particular interest because it is directly related to the unique chemical, magnetic, and optical properties of lanthanide compounds2,3. Lanthanides were considered usually to exist mainly in the stable +III OS due to the chemical inertness of the 4 f electrons. Recent studies have provided evidence that all lanthanides can form divalent complexes4,5,6,7,8,9,10,11, whereas stable tetravalent compounds are known only for a few lanthanides12,13,14,15,16. The highest oxidation state known for lanthanides is +V, observed recently in gaseous species, PrO4, PrO2+, and NPrO17,18. However, monovalent Ln(I) species are quite rare. The lanthanide iodide (LaI) synthesized by heating LaI3 with metallic lanthanum has the nominal La(I) OS, but was shown to contain La–La metallic bonding19. Besides gas-phase diatomic lanthanide hydride and halide molecules20,21,22, the only other previous example of Ln(I) is the PrB4− [i.e., (PrI)(B42−)] cluster characterized by photoelectron spectroscopy (PES) and quantum chemistry calculations23. The rare earth Sc element, which is in the same group as La, was known to have Sc(I) OS in multi-decker molecular compounds24,25. Compounds with low OS lanthanides will not only expand the chemistry of the lanthanide elements, but can also potentially serve as strong reducing agents in organometallic syntheses26,27,28. It would be interesting to discover suitable ligands that can stabilize monovalent lanthanides.

Joint PES and quantum chemistry studies over the past decade have shown that size-selected anionic boron clusters (Bn−) are planar over a wide size range, stabilized by σ and π double aromaticity29,30,31,32,33. The π bonding patterns of many planar boron clusters are analogous to polycyclic aromatic compounds34,35. One of the first boron clusters found to exhibit σ and π double aromaticity was the wheel-like D8h B9−, which satisfies the (4 N + 2) Hückel rule with N = 1 for both the delocalized σ and π electrons36. The D8h B9− cluster inspired the design and characterization of a new class of borometallic molecular wheels (M©Bn−, n = 8–10) with double aromaticity37,38,39,40. Several small mono-lanthanide boron clusters have been studied23,41,42,43. Specifically, the PrB7− cluster was shown to form a half-sandwich structure, in which a Pr(II) center was coordinated by an aromatic η7-B73− ligand41. Recently, a series of di-lanthanide boron clusters Ln2Bn− (n = 7–9) were found to form inverse sandwich complexes with boron monocyclic rings44,45. An interesting question is if mono-lanthanide boron clusters would form Ln©Bn− type of molecular wheels, similar to the mono-transition-metal boron clusters37,38,39,40.

Here we report a PES and quantum chemistry study on a series of lanthanide-doped octa-boron clusters, LnB8− (Ln = La, Pr, Tb, Tm, Yb). Instead of the Ln©B8− wheel-like structures, we find two types of structures for Ln = La and Pr: a Cs three-dimensional (3D) global minimum and a low-lying co-existing C7v half-sandwich structure, whereas the latter becomes the global minimum for the late lanthanides (Tb, Tm, and Yb). The Cs 3D LnB8− clusters contain a Ln(III) center, but the C7v structures all contain a Ln(I) center coordinated by a η8-B82− doubly aromatic ligand. We found that the frontier orbitals of the B82− ligand match favorably with the Ln 5d orbitals to afford strong metal-ligand chemical bonding. The B82− ligand is shown to be one member of a series of doubly aromatic planar boron clusters, B73−, B82−, and B9−, which are analogous to the aromatic C5H5−, C6H6, and C7H7+ hydrocarbons, respectively. This series of aromatic boron ligands provides the possibility to design lanthanide boride complexes with tunable OS and magnetic properties.

Results and discussion

Photoelectron spectroscopy

We conducted the PES experiments using a home-built magnetic-bottle apparatus, which consisted of a laser vaporization cluster source and a time-of-flight mass spectrometer (Methods and Supplementary Fig. 1 for more details)31. The LnB8− (Ln = La, Pr, Tb, Tm, Yb) clusters were generated by laser ablation of a disk target consisting of Ln and isotopically enriched 11B. The clusters were entrained by a helium carrier gas (containing 5% argon) and underwent a supersonic expansion. Negative ions were extracted from the cluster beam perpendicularly and separated by the time-of-flight mass spectrometer. The octa-boron clusters (LnB8−) were selected and decelerated before photodetachment. Two photon energies were used in the current study, including the third harmonic of a Nd:YAG laser (355 nm, 3.496 eV) and the 193 nm (6.424 eV) radiation from an ArF excimer laser. Photoelectrons were analyzed by the magnetic-bottle electron analyzer and calibrated using the Bi− atomic spectrum. Photoelectron spectra of LnB8− (Ln = La, Pr, Tb, Tm, Yb) at 193 nm are presented in Fig. 1, and the 355 nm spectra of LaB8−, PrB8−, and YbB8− are given in Supplementary Fig. 2. The PES bands are designated with letters (X, A, B, …), and the vertical detachment energies (VDEs) measured from the maxima of the observed bands are given in Supplementary Tables 1–5 for LaB8−, PrB8−, TbB8−, TmB8−, and YbB8−, respectively. Based on the observed spectral patterns, the five species can be divided into three groups, (1) LaB8− and PrB8−, (2) TbB8−, and (3) TmB8− and YbB8−.

Fig. 1: Photoelectron spectra at 193 nm (6.424 eV) of LnB8− (Ln = La, Pr, Tb, Tm, Yb).
figure 1

a LaB8−. b PrB8−. c TbB8−. d TmB8−. e YbB8−. The blue and red bars in a and b represent computed VDEs of isomer I (C7v) and isomer II (Cs), respectively. The gray bars indicate the calculated 4f-detachment channels.

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The photoelectron spectra of the two early-lanthanide octa-boron clusters (LaB8− and PrB8−) are similar, suggesting they should have similar structures and bonding. Both spectra display complicated spectral patterns with congested PES bands, most likely due to the existence of multiple isomers. In the low binding energy region of LaB8−, we observed four intense bands (X, A, B/C), where bands B and C overlapped and were only resolved in the 355 nm spectrum (Supplementary Fig. 2a). Band X should be the ground state transition of the major isomer, yielding a VDE1 of 2.40 eV and an estimated adiabatic detachment energy (ADE) of ~2.2 eV, which also represents the electron affinity (EA) of neutral LaB8. The VDE of the intense band A was measured to be 2.77 eV, whereas those of B and C were found to be 2.99 and 3.18 eV, respectively, from the 355 nm spectrum (Supplementary Fig. 2a). Following an energy gap, a well-resolved band D at 4.14 eV was observed. Beyond band D, almost continuous spectral features were observed. Bands E, F, G, and H were tentatively labeled for the sake of discussion. The broad weak features (X’, A’, B’) on the low binding energy side suggested the co-existence of low-lying isomers for LaB8− in the cluster beam. This part of the spectrum was resolved slightly better in the 355 nm spectrum (Supplementary Fig. 2a). Bands X’ and A’ were broad with VDEs of ~1.5 eV and 1.9 eV, respectively, while band B’ at 2.16 eV was better defined. Higher binding energy transitions of this isomer were likely buried in the signals of the main isomer. The observed features and binding energies for LaB8− are given in Supplementary Table 1, where they are compared with the calculated values. The photoelectron spectra of PrB8− are almost identical to those of LaB8− (Fig. 1 and Supplementary Fig. 2); the observed spectral features and their binding energies are given in Supplementary Table 2, along with the calculated values.

The 193 nm spectrum of TbB8− has a much simpler pattern in comparison to those of LaB8− and PrB8−, with four clearly resolved bands. The lowest-binding energy peak X gives rise to the first VDE at 1.98 eV and an ADE of 1.87 eV, followed by a close-lying band A at 2.18 eV. After a large energy gap of ~2 eV, two sharp and intense bands are displayed: band B at 4.02 eV and C at 5.06 eV. Beyond 5.5 eV, the spectrum becomes nearly continuous and a band D at around 6.1 eV is tentatively assigned. The binding energies of all the observed bands are given in Supplementary Table 3.

The spectrum of TmB8− displays the simplest spectral pattern with four clearly resolved bands: X, A, B, and C. Band X with a VDE of 2.02 eV is well resolved and an ADE of 1.90 eV is evaluated from its onset. Following a large energy gap of about 1.5 eV, band A at 3.54 eV is broader and more intense, which may contain multiple detachment channels. Following another large energy gap of 1.2 eV, a sharp and intense band B is observed at 4.79 eV. The fourth band C is observed at the high binding energy side with a VDE of 6.1 eV. The spectrum of YbB8− is nearly identical to that of TmB8− except that a weak feature (A’) were resolved around the second main PES band. The binding energies of the observed PES bands for TmB8− and YbB8− are given in Supplementary Tables 4 and 5, respectively. The simple spectral patterns of TmB8− and YbB8− suggest their structures must be highly symmetric. The spectrum of TbB8− is more like those of the late lanthanides (TmB8− and YbB8−) than the early lanthanides (LaB8− and PrB8−), indicating TbB8− may have a similar structure as those of TmB8− and YbB8−.

Global minimum structural searches

The global minima for LnB8− (Ln = La, Pr, Tb, Tm, Yb) and their low-lying isomers in the cases of LaB8− and PrB8− are shown in Fig. 2a and b. More isomers within 50 kcal mol−1 for LaB8− and 65 kcal mol−1 for YbB8− are shown in Supplementary Figs. S3 and S4, respectively. At the PBE/TZP level, the most stable structure for LaB8− is found to be the 3D isomer II (Cs, 1A’), with the half-sandwich isomer I (C7v, 3E2) being 5.31 kcal mol−1 higher in energy. At the PBE0/TZP and CCSD(T)/Def2-TZVP levels, the 3D isomer II is still the global minimum. At the more accurate CCSD(T) level, the half-sandwich isomer I is only 2.71 kcal mol−1 higher in energy than the 3D isomer II, suggesting that it may be present in the experiment as a minor component. Two similar low-lying isomers are found for PrB8−; and they are within 4 kcal mol−1 in energy at the PBE/TZP, PBE0/TZP, and CCSD(T)/Def2-TZVP levels. Thus, for LaB8− and PrB8− both the 3D isomer I and the half-sandwich isomer II are close in energy and could co-exist under our experimental conditions. For the late lanthanide LnB8− (Ln = Tb, Tm, Yb), the half-sandwich C7v structure is found to be the global minimum at all levels of theory, with high stabilities over other isomers (Fig. 2c and Supplementary Fig. 4). As will be shown below, the OS of the Ln atoms in the half-sandwich C7v structure is +I, whereas that in the Cs 3D structures of LaB8− and PrB8− is +III. The second isomer of the three late lanthanide octa-boron clusters is similar to the Cs 3D isomer II of LaB8− and PrB8−, but they are much higher in energy (Fig. 2c and Supplementary Fig. 4). The relative stabilities of the +I OS structures and the +III OS isomers are exhibited in Fig. 2c for the five lanthanide octa-boron clusters. The coordinates of the global minima of LnB8− and the C7v low-lying isomers for LaB8− and PrB8−, as well as their corresponding neutrals are given in Supplementary Table 6.

Fig. 2: The structures of LnB8− (Ln = La, Pr, Tb, Tm, Yb).
figure 2

a The global minima and low-lying isomers of LaB8− and PrB8− at the PBE, PBE0 (in parenthesis), CCSD(T) (in bracket) levels, with each corresponding electronic configuration. b The global minima of TbB8−, TmB8−, and YbB8−. c The energy difference between the LnB8− structures with the +III OS (3D Cs structure) and +I OS (C7v structure) at the PBE0/TZP level, with the +I OS isomer as the reference.

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Comparison between experiment and theory

The VDEs of the global minima and low-lying isomers for the LnB8− clusters were calculated (see Methods) and compared with the experimental results in Fig. 1 and Supplementary Tables 1–5, respectively. Different levels of theory were used to calculate the VDE1 and ADE values for the C7v structures of all LnB8− and the Cs structures for LaB8− and PrB8− (see Supplementary Table 7). We found that the different levels of theory yielded similar VDE1 and ADE values, which all agree well with the measured values.

The global minima for both LaB8− and PrB8− are found to be the 3D isomer II with Cs symmetry at the CCSD(T)/Def2-TZVP level, while the half-sandwich C7v structure is a low-lying isomer (Fig. 2a and c). The structures and photoelectron spectra of PrB8− and LaB8− are nearly identical, because of the nonbonding nature of the highly contracted 4 f orbitals and the low detachment cross-sections of f-electrons41,44,46,47,48,49. Thus, we will only discuss LaB8− in detail as a representative of the early-lanthanide octa-boron clusters. The computed VDE1/ADE for the Cs isomer II of LaB8− is 2.47/2.25 eV at the CCSD(T)/Def2-TZVP level (Supplementary Table 7), in excellent agreement with the experimental value of 2.40/2.19 eV. Higher detachment channels of the Cs isomer are complicated as shown in Supplementary Table 1, in good accord with the congested experimental features (Fig. 1a and Supplementary Table 1).

The calculated VDE1/ADE for the C7v isomer I of LaB8−, 1.47/1.41 eV at the CCSD(T) level (Supplementary Table 7), are much lower than those of isomer II, agreeing well with the weak feature X’ at ~1.5 eV. The first electron detachment is from the singly occupied 3a1 orbital (primarily of La 6s character), as can be seen in Supplementary Table 1 and Supplementary Figs. 5 and 6. The second VDE for the C7v isomer, corresponding to detachment of the single 1e2 (La 5dδ) electron (Supplementary Figs. 5 and 6), was calculated to be 1.79 eV (Supplementary Table 1), consistent with the weak peak A’ observed experimentally. The weak band B’ in PrB8− is due to detachment from the 4a1 orbital (Pr 4 fσ) (Supplementary Table 2 and Supplementary Fig. 7). However, the 4a1 orbital of 4f character is not occupied in LaB8−. The very similar B’ band in LaB8− (Supplementary Fig. 2) could be contributed from other competitive electronic states (Supplementary Table 8) due to the strong electron correlation effects. Higher detachment transitions for the C7v isomer would be buried in the congested spectral features of the main Cs isomer. Overall, the complicated and congested experimental spectra of LaB8− and PrB8− can be well explained by the global minimum Cs structure as the major species and the C7v structure as a minor co-existing isomer.

The C7v structure of TbB8− gives rise to a calculated VDE1/ADE at 2.05/1.93 eV at the PBE0/TZP level (Supplementary Table 7), in good agreement with the experimental value from band X at 1.98/1.87 eV. Peaks X and A both correspond to electron detachment from the 4a1 (Tb 6s) doubly occupied orbital (Supplementary Table 3, Fig. 3a and Supplementary Fig. 8) with different spin states. Peak B primarily represents detachment from the 2e1 bonding MO between the Tb 5dπ and B8 π orbitals (Supplementary Fig. 8). Bands C and D correspond to the 1e1 and 1e3 orbitals, respectively, primarily of in-plane B–B bonding characters. As shown previously41,44,46, the detachment cross-sections of 4f-based MOs are very weak and they are usually buried in the strong detachment transitions from the boron-based MOs, which is why Ln-doped boron clusters with the same structures usually give rise to similar photoelectron spectra, despite their different 4 f electron configurations. Overall, the good agreement between the experimental and theoretical data confirms the C7v structure as the global minimum of TbB8−.

Fig. 3: Chemical bonding and orbital interactions.
figure 3

a Orbital correlation diagram of the C7v TbB8− with those of Tb+ (4 f86s2) and B82− at the PBE/TZP level. Similar diagrams for La/PrB8− and Tm/YbB8− are given in Supplementary Fig. 5. The dashed lines show the major contribution to the orbital interactions. The arrows on the 4 f orbitals represent f8 occupied electrons. The occupied 4f bands in TbB8− are indicated by the slash solid lines. b The local coordinate system (LCS) analysis for the C7v B82− ligand at the PBE/DZP level. The 32 valence orbitals of 2 s/2p characters are categorized into four groups. Herein, “t” and “r” represent “tangential” and “radial”, respectively. The subscript number corresponds to the nodal plane of the orbital contour. The superscript * indicates antibonding orbitals between the central B atom and the peripheral delocalized orbitals.

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The computed VDE1/ADE for the C7v global minimum of TmB8− are 1.93/1.83 eV at the CCSD(T)/Def2-TZVP level (Supplementary Table 7), which agree with the observed value at 2.02/1.90 eV. Since the detachment cross-sections for f-based MOs are known to be low41,44,46,47,48,49, Supplementary Table 4 shows that band A should predominantly correspond to electron detachment from the 2e1 bonding MO between Tm and B8 (Supplementary Fig. 9). Band B corresponds to detachments from the 1e1 and 1e3 orbitals (Supplementary Table 4). Feature C at the higher binding energy side should be due to detachment from the 2a1 and 1a1 orbitals, which are delocalized σ MOs over the B8 plane (Supplementary Fig. 9). The good agreement between the experimental and theoretical results (Fig. 1d) confirms unequivocally that the half-sandwich C7v structure is the global minimum for TmB8−. The photoelectron spectrum of YbB8− is almost identical to that of TmB8−. The calculated detachment transitions for the C7v global minimum for YbB8− are also in excellent agreement with the experimental data, as shown in Fig. 1e and Supplementary Table 5.

Unexpected structural and OS variations for the early and late lanthanide octa-boron clusters

The LnB8− series of lanthanide octa-boron clusters were expected to exhibit similar structures and photoelectron spectra, as was the case observed previously for the di-lanthanide Ln2B8− inverse sandwich complexes for Ln = La, Pr, Tb44. Surprisingly, we observed very different photoelectron spectra for the LnB8− clusters, from the complicated spectra for the earlier lanthanides to the simpler spectral features in the late lanthanides. These experimental observations were borne out by the structural variations from our theoretical studies. As discussed above, the global minima of LaB8− and PrB8− were found to be 3D structures with Cs symmetry. A high symmetry C7v structure was shown to be a low-lying isomer present experimentally along with the Cs global minima for both systems. We further found that the Ln atoms in the two structures adopt different OS:+III for the Cs isomer (4 fn−3) and +I for the C7v isomer (5d16 s1/4f36 s1 for La/Pr). The early lanthanides tend to lose more electrons to form higher oxidation states because their 4f/5d orbitals are less contracted and closer to each other in energy (Supplementary Fig. 5). Because of the preference of Ln(III) OS for these early lanthanides, their empty 5d orbitals tend to bond stronger with the Bn ligands, so that the C7v B©B7 wheel is distorted to the low-symmetry Cs B©B6+1 ligand to facilitate stronger Ln–B interactions.

The late lanthanides prefer to form lower OS due to the more contracted f orbitals (Fig. 3)47,48. Even though the C7v structure is the global minimum for the middle-lanthanide Tb, the spectrum of TbB8− is different from those of the late lanthanides TmB8− and YbB8−, because of the different electronic configurations of the 6s orbital. As can be seen in Supplementary Table 8, the 6s orbital prefers to be singly occupied for all the C7v LnB8− species except for TbB8−, for which the 6s orbital is doubly occupied. The TDDFT-PBE results showed that the state with the 4f96s1 configuration is 0.44 eV higher in energy than that for 4f86 s2 (Supplementary Table 8). In TbB8−, the 6s-based MO (4a1 in Supplementary Fig. 8) also shows a significant contribution (~8%) from the center B atom of the B8 ligand, while this contribution is negligible (~2%) in all other C7v LnB8− species. Hence, the 6s orbital is slightly more stabilized by the high-lying ligand orbitals in TbB8−, resulting in its full occupation (Fig. 3). In view of the likely configuration mixing in this species, ab initio multiconfigurational calculations were carried out with complete-active-space self-consistent field (CASSCF) and the results are shown in Supplementary Fig. 11. It was found that the 4 f86s2 configuration was slightly mixed with 4 f85d2 (12%), but the OS should not be affected by the small multiconfigurational character. The OS change from early to late lanthanides can be explained qualitatively by the reduction of the lanthanide atomic sizes due to the 4f orbital contractions. Overall, the structure transition of the LnB8− series from Cs to C7v can be understood by the preferred OS due to the orbital energies and radial contractions of the 4f/5d orbitals.

Supplementary Table 9 presents the energy decomposition analysis (EDA)50 for all the LnB8− species with their relative total energies decomposed into different terms to understand the relative stabilities of the C7v and the Cs isomers. The energetic competition between the steric effect (ΔEsteric, the sum of Pauli repulsion and electrostatic effect) and orbital interaction (ΔEorb) is the key to determining the overall stability of the clusters. In the early LaB8− and PrB8− species, the stabilization of ΔEorb in the C7v isomer is less than the stabilization of ΔEsteric in the Cs isomer, due to the elimination of Pauli repulsion between the Ln 6s1 and the ligand-based electrons in Ln(I). so that the C7v isomer is higher in total energy than the Cs isomer. However, the opposite is true for TbB8−, TmB8−, and YbB8−, for which the C7v structure shows stronger orbital interactions with the increased lanthanide contraction.

Chemical bonding analyses

The C7v structure can be viewed as a monovalent Ln(I) interacting with a doubly aromatic B82− ligand. Neutral B8 was known to be a triplet with two unpaired electrons with D7h symmetry36. The closed-shell B82− was realized in the LiB8− cluster due to charge transfer from Li to the B8 moiety51. To understand the chemical bonding in the C7v LnB8−, we carried out MO analyses as shown in Fig. 3 and Supplementary Fig. 5, illustrating the orbital correlations of LnB8− with those of the Ln+ and B82− moieties. The MO pictures for the LnB8− complexes are depicted in Supplementary Figs. 6 to 10. As shown in Fig. 3 and Supplementary Fig. 5, the 2e1 orbitals describe the main bonding interactions between Ln+ and B82−, which is further verified by EDA in conjunction with the natural orbitals for chemical valence (NOCV)50 method (Supplementary Table 11). Electron detachment from the 2e1 orbital can be approximately characterized by the second main peak of the C7v global minima in the photoelectron spectra (Fig. 1): peak B for TbB8−, and peak A for TmB8− and YbB8−. The compositions of the 2e1 bonding orbital given in Supplementary Table 10, as well as the percentage of the electrostatic effect given in Supplementary Table 12, show consistently that ionic characters tend to be stronger for the late lanthanide complexes, as compared with the ionic KB8− species. From the EDA-NOCV analysis presented in Supplementary Table 11, we also found a strong 6s deformation corresponding to ΔEorb(1), due to slight mixing of the 5d orbitals and symmetry-adapted B8 group orbitals. The 4f orbitals are well known to be radially too contracted in the lanthanide elements to participate in chemical bonding. Due to the low oxidation state of Ln(+I) in LnB8−, the partially filled 4f shells remain almost atom-like with ferromagnetic character (Fig. 3a and Supplementary Fig. 5), giving rise to interesting magnetic properties with potential applications in single-molecule magnet52,53,54 and magnetic nanowire55,56.

Chemical bonding patterns obtained from the adaptive natural density partitioning (AdNDP) analyses57 can achieve a seamless description of different types of chemical bonds, recovering both Lewis-type bonding [one-center two-electron (1c-2e) lone pairs and classical two-center two-electron (2c-2e) bonds] and delocalized multicenter bonding associated with the concepts of aromaticity and antiaromaticity. Bonding schemes obtained from the AdNDP method for all the C7v LnB8− complexes are similar; the only differences are in the localized electrons in the Ln-based atomic-like orbitals. Figure 4a displays the AdNDP results of YbB8−, which has a closed 4f14 shell, to represent the bonding in all the C7v LnB8− complexes. The first row displays the seven pairs of the 4f electrons and the single unpaired 6s electron of Yb. The seven 2c-2e localized B–B bonds in the periphery of the B82− ligand are shown in the second row. Of particular importance are the two sets of multicenter bonds: the three delocalized in-plane 8c-2e σ bonds and the three delocalized 9c-2e π bonds. The latter represents π bonding interactions between the Yb 5d orbitals and the B82− ligand. The delocalized σ and π bonds of B82− are similar to those in B73− and B9−, giving rise to double aromaticity36,41,51. The AdNDP results for the C7v and Cs isomers of LaB8− are compared in Supplementary Fig. 12, showing that the two nonbonding unpaired La 6s and 5dδ electrons in the C7v isomer evolve into a 9c-2e π bond in the Cs isomer. The transformation of the two nonbonding La-based electrons in the C7v isomer into a bonding pair in the Cs isomer explains why the latter is more stable, as well as why La exhibits +III OS in the Cs isomer.

Fig. 4: AdNDP bonding analyses of YbB8− and comparison with that of YbC8H8−.
figure 4

a YbB8− (C7v, 2A1). b YbC8H8− (C8v, 2A1). The occupation numbers (ONs) are indicated.

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The doubly aromatic B82− ligand is found to be analogous to the C8H82− aromatic cyclooctatetraenyl anion in terms of their planar structures and aromatic properties. The half-sandwich YbC8H8 complex was a well-known organometallic compound58,59,60,61, where Yb adopts +II OS. There are strong similarities in the chemical bonding between the monovalent YbC8H8− and YbB8−, as shown in Fig. 4. The first row for both species is identical with seven 4f lone pairs and one unpaired 6s electron, suggesting a monovalent Yb(I). Similar to the 2c-2e B–B σ bonds in YbB8−, there are eight localized 2c-2e C–C σ bonds and eight 2c-2e C–H σ bonds in the second row on the C8H82− ligand. The five delocalized 9c-2e π bonds involve C 2pπ and 5d interactions, corresponding to the five delocalized π bonds of C8H82−. Even though YbB8− only has three delocalized aromatic π bonds, its σ aromaticity gives rise to additional stability.

Boron cluster analogues of benzene (“borozene”)

Most planar boron clusters are aromatic and their π electron systems are analogous to benzene or polycyclic aromatic hydrocarbons29,30,31,32,33,34,35,36. The planar B73−, B82−, and B9− series are interesting; their π orbitals are compared with those of benzene in Fig. 5. Even though all these three boron clusters are also σ aromatic with six delocalized σ electrons, their π orbitals are almost identical to those of benzene. In fact, the trends of size and charge states of B73−, B82−, and B9− are analogous to the C5H5−, C6H6, and C7H7+ series of aromatic hydrocarbons, respectively. Thus, this series of benzene-like aromatic boron clusters may be properly named as “borozene”. In fact, large planar aromatic boron clusters30,31,32,33,35 may be called “polycyclic aromatic borozenes” (PABs), analogous to polycyclic aromatic hydrocarbons (PAHs)62. We note that “borozene” was previously used for the planar B12H6 cluster, which was studied computationally63. However, the planar B12H6 structure was later found to be a very high energy isomer on the potential energy surface, where a partially hydrogenated 3D icosahedral-like B12H6 structure was found to be 35 kcal/mol lower in energy64. Thus, we think that “borozene” is more suitable for the B73−, B82−, and B9− series of benzene-like aromatic planar boron clusters since the planar B12H6 species does not exist. Because the B73−, B82−, and B9− borozenes are charged, they can be coordinated with lanthanide elements with tunable OSs. For example, the Pr atom is in +II OS in PrB7−, whereas in neutral PrB7 it is in +III OS41. It is conceivable that zero OS lanthanides may exist for late lanthanide LnB9− clusters, similar to Ln(C6H6) complexes65,66,67. Supplementary Table 13 summarizes LnBn− (n = 7–9) lanthanide borozene complexes with different OS of the lanthanides. Finally, the low-lying π2-MOs of borozenes (Fig. 5) are possible to accept four extra electrons to form sandwich-type compounds with actinides (An), similar to C7H73− in An(η7-C7H7)2 complexes68.

Fig. 5: Comparison of the π orbitals of C6H6 with those of borozenes, B73−, B82−, and B9− with different nodal planes.
figure 5

Black solid dots correspond to occupied electrons for the neutral species and blue circles represent the additional electrons in the closed-shell anions in the borozenes.

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In conclusion, we report a joint photoelectron spectroscopy and quantum chemical study of lanthanide octa-boron clusters (LnB8−, Ln = La, Pr, Tb, Tm, Yb). For the early-lanthanide species (La and Pr), complicated photoelectron spectra are observed, whereas much simpler spectra are obtained for the late lanthanide species (Tb, Tm, Yb). The global minima of the early-lanthanide octa-boron clusters are found to be low-symmetry (Cs) structures with a C7v half-sandwich low-lying isomer that is also present experimentally, in agreement with the congested photoelectron spectra. The C7v half-sandwich structure is found to be the global minimum for the late lanthanide (Tb, Tm, Yb) species, in accord to their relatively simple photoelectron spectral patterns. The C7v half-sandwich octa-boron lanthanide complexes possess a rare monovalent Ln(I) center coordinated by a B82− ligand [LnI(ƞ8-B82−)]. The B82− ligand is doubly aromatic with six delocalized π and six delocalized σ electrons, underlying the stability of the monovalent Ln(I) complexes. The B82− ligand is a member of a class of doubly aromatic planar boron ligands (B73−, B82−, and B9−), named borozene. The current study represents a systematic characterization of monovalent lanthanide complexes coordinated with the B82− ligand, suggesting that borozenes with different charge states can serve as potential ligands to modulate oxidation states in lanthanide complexes.

Methods

Photoelectron spectroscopy

The experiments were performed using a magnetic-bottle photoelectron spectroscopy apparatus equipped with a laser vaporization supersonic cluster source, as shown schematically in Supplementary Fig. 1. More details for the apparatus could be found elsewhere31,69. In the current study, the Ln/11B target (5/2 mass ratio, Ln = La, Pr, Tb, Tm, Yb) was prepared by mixing a Ln powder (Alfa Aesar, −200 mesh, 99.9%) and 11B-enriched powder (Alfa Aesar, 96% 11B-enriched, −100 mesh, 99.9% metal basis) in a glove box. The mixed Ln/11B powder was then cold-pressed into a 12 mm diameter disk target, which was then transferred into the vacuum chamber for the generations of binary Ln–B clusters using a laser vaporization supersonic cluster source.

The clusters were generated by focusing a 532 nm laser beam from the second harmonic of a Nd:YAG laser onto the Ln/11B targets. The laser-induced plasma was quenched by a helium carrier gas seeded with 5% argon, initiating nucleation and cluster formation. Nascent clusters inside the nozzle were entrained in the carrier gas and underwent a supersonic expansion. After passing a skimmer, anionic clusters were extracted from the collimated cluster beam for time-of-flight (TOF) mass spectrometric analyses. The LnB8− clusters of current interest were mass selected and decelerated before being photodetached by the 193 nm radiation (6.424 eV) from an ArF excimer laser or the 355 nm radiation (3.496 eV) from the third harmonic of a Nd:YAG laser. The photoelectron spectra were calibrated using the known spectrum of Bi−. The kinetic energy resolution of the apparatus was about 2.5%, i.e., 25 meV for 1 eV electrons.

Theoretical methods

Because of the similarities of the observed photoelectron spectra and the anticipated similar structures, we performed more thorough global minimum searches only for LaB8− and YbB8− with different spin multiplicities using the TGMin 2.0 package70,71,72. More than 300 trial structures for each species were examined using the ADF 2017.114 software73 with the PBE density functional74 and the triple-ζ Slater-type plus one polarization function (TZP) basis set75. Herein, the frozen-core approximation was applied to the inner shells [1s24d10] for lanthanides and [1s2] for B in the all-electron ADF calculations. The scalar relativistic effects were taken into consideration by the zero-order regular approximation76. Calculations using the hybrid PBE0 functional77 and TZP basis sets were further carried out to correct the relative energies of different isomers. Since two isomers were found to compete for the global minima of LaB8− and PrB8−, single-point calculations at the CCSD(T) level were performed with the Def2-TZVP basis sets for the two lowest isomers, implemented in the ORCA software78. As low-valent metal compounds tend to possess multireference features, we checked these possibilities in our calculations. The T1 diagnostic factors in the CCSD calculations are 0.036, 0.039, 0.027, and 0.025 for LaB8−, PrB8−, TmB8−, and YbB8−, respectively, indicating the multiconfigurational characters were not significant as they lie within the accepted threshold of T1 < 0.04 for open-shell systems. Therefore, the DFT methods with single Slater determinant can well describe the ground states of these lanthanide species41,44. For TbB8−, however, a strong multireference character was found with higher T1. Consequently, we further determined the oxidation states using ab initio complete active space SCF method (CASSCF), where the active space included 14 electrons in 12 orbitals, consisting of seven 4 f orbitals, one 6 s orbital, two d-pπ bonding orbitals (mainly derived from B 2p orbitals) and two corresponding d-pπ* antibonding orbitals (mainly derived from Tb 5d orbitals). The ECP28MWB SDD pseudopotential and the SEG basis set was used for Tb79,80,81 and the cc-pVTZ basis set for B82.

Photoelectron spectra of LaB8−, PrB8−, TmB8−, and YbB8− were simulated using the ΔSCF-TDDFT83 approach along with the SAOP model84. The first vertical detachment energy (VDE1) was computed as the difference in energy between the anionic ground state and the corresponding neutral at the same anionic geometry. The adiabatic detachment energy (ADE) was calculated as the energy difference between the anionic and neutral species at their respective optimized structures. We found the TDDFT method, used to compute higher VDEs, was not suitable to simulate the spectrum of TbB8−, probably due to the stronger spin contamination and the correlation effects. Thus, we used generalized Koopman’s theorem (GKT)85 based on Kohn-Sham orbitals to obtain the higher theoretical VDEs for the TbB8− cluster. Chemical bonding analyses were performed using molecular orbital (MO) theory at the PBE0/TZP level and the AdNDP method57, where the first-order reduced density matrix was diagonalized with optimal convergence of the electron density description. At every step in the search for nc-2e bonds, the density matrix is depleted of the density, corresponding to the appropriate bonding elements and finally generating 1c-2e, 2c-2e, …, and nc-2e bonds. The Ln+…B82− interactions in the C7v isomers were further analyzed with the EDA-NOCV method50 at the level of PBE/TZ2P.