Observation of highly stable and symmetric lanthanide octa-boron inverse sandwich complexes

PES

The experiment was performed using a magnetic-bottle PES apparatus equipped with a laser vaporization supersonic cluster source (10) (see SI Appendix, Methods for more details). Briefly, lanthanide boron clusters were generated by laser ablation of a La/¹¹B or Pr/¹¹B mixed target, followed by supersonic expansion using a helium carrier gas seeded with 5% argon. Negatively charged clusters were extracted from the cluster beam and analyzed by a time-of-flight mass spectrometer. Clusters with different La_xB_y⁻ or Pr_xB_y⁻ compositions were produced. The La₂B₈⁻ and Pr₂B₈⁻ clusters of current interest were mass-selected and photodetached by the 193-nm radiation of an ArF excimer laser (6.424 eV). PES data at 193 nm were first obtained for the La₂B₈⁻ cluster, which was found to exhibit a particularly simple spectral pattern (Fig. 1A), suggesting a highly symmetric structure. Subsequently, the spectrum of Pr₂B₈⁻ was measured (Fig. 1B), revealing a similar spectral pattern as La₂B₈⁻ and indicating that the two di-Ln–octa-boron clusters should have similar structures and bonding.

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Fig. 1.

Photoelectron spectra of (A) La₂B₈⁻ and (B) Pr₂B₈⁻ at 193 nm and comparison with the simulated spectra for the (C) D_4h La₂B₈⁻ and (D) D_4h Pr₂B₈⁻. See SI Appendix, Tables S4 and S5 for the detachment energies of the observed bands and their assignments for La₂B₈⁻ and Pr₂B₈⁻, respectively.

The two spectra each displayed four well-resolved bands labeled as X, A, B, and C. PES involves electron detachment from the anions, resulting in neutral species. The lowest binding energy band (X) corresponds to detachment transition from the ground state of the Ln₂B₈⁻ anion to that of the corresponding neutral, whereas bands A, B, and C correspond to detachment transitions to excited states of neutral Ln₂B₈. The broad widths of some of the detachment bands suggest that they may contain multiple detachment transitions. The X band yielded the first vertical detachment energy (VDE) of 1.76 eV for La₂B₈⁻ and 1.75 eV for Pr₂B₈⁻. The adiabatic detachment energy (ADE) for band X was evaluated from its onset to be 1.64 ± 0.05 eV and 1.59 ± 0.05 eV, which represent the electron affinities (EAs) of neutral La₂B₈ and Pr₂B₈, respectively. The A band at 2.91 eV (La₂B₈⁻) and 2.94 eV (Pr₂B₈⁻) was broad and intense in both spectra. At around 4 eV, both spectra displayed a relatively sharp band B, closely followed by a weak band C. The signal/noise ratios above 5 eV were poor, and no specific detachment bands could be definitively identified. Some weak features appeared around bands A and B and also possibly above band C (labeled by *). These weak features were likely due to multielectron or shakeup processes, as a result of strong electron correlation effects expected for these systems (22). The well-resolved photoelectron spectral features served as electronic fingerprints to allow analyses of their structures and bonding by comparing with theoretical calculations.

Global Minimum Structure Searches

La₂B₈⁻.

The global minimum structure for La₂B₈⁻ was searched using the Tsinghua Global Minimum (TGMin) package (23, 24) with a constrained basin-hopping algorithm (25) (see SI Appendix, Methods for the computational details). A D_4h (²B_2u) inverse sandwich structure was found to be the global minimum (SI Appendix, Fig. S1). The D_4h structure of the La₂B₈⁻ anion was distorted from the perfect D_8h symmetry due to the Jahn–Teller effect. We optimized the neutral D_4h La₂B₈, which led to the perfect D_8h (³A_2g) structure, as shown in Fig. 2. The structural differences between the anion and neutral are relatively small. The coordinates of the anion and neutral global minima are given in SI Appendix, Table S1. For the first two isomers, CCSD(T) calculations with the PBE0/TZP geometries were further carried out to obtain more accurate relative energies. The CCSD(T) results were deemed reliable because the multiconfigurational characters were not significant from the T₁ diagnostic factors of CCSD calculations (0.018 for the global minimum of La₂B₈⁻).

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Fig. 2.

Two views of the global minima of the neutral D_8h Ln₂B₈. Bon lengths: Ln…Ln = 3.720 Å (La), 3.558 Å (Pr); Ln−B = 2.759 Å (La), 2.701 Å (Pr); B−B = 1.560 Å (La), 1.555 Å (Pr) at the PBE0/TZP level.

The closest isomer above the global minimum had C_s symmetry (SI Appendix, Fig. S1), which was 32.41 kcal/mol higher in energy at the CCSD(T) level, indicating the overwhelmingly high stability of the D_4h symmetrical inverse sandwich structure. The isomer of La₂B₈⁻ with a seven-atom ring and one B atom squeezed out was found to be the third isomer, which lies 36.37 kcal/mol above the global minimum at the PBE0/TZP level. The isomer with a pseudoC_7v B©B₇ moiety (the most stable structure for bare B₈) (26), sandwiched by the two La atoms, is even higher in energy (67.07 kcal/mol at the PBE0/TZP level).

Comparison Between the Experimental and Computational Results

To validate the global minima of La₂B₈⁻ and Pr₂B₈⁻, we calculated their ADEs and VDEs using the ΔSCF–TDDFT formalism. Fig. 1 C and D present the simulated spectra for the D_4h global minimum structures, showing excellent agreement with the experimental spectral patterns. The computed ADE/VDEs at the CCSD(T) level are 1.47/1.52 eV and 1.53/1.64 eV for La₂B₈⁻ and Pr₂B₈⁻, respectively, in good agreement with the experimental data of 1.64/1.76 eV and 1.59/1.75 eV (SI Appendix, Table S3). All of the computed detachment channels for La₂B₈⁻ and Pr₂B₈⁻ (including the electron configurations and final state symmetries) and their comparison with the experimental data are given in SI Appendix, Tables S4 and S5, respectively. As expected, each observed PES band corresponds to multiple detachment channels.

According to the valence molecular orbital (MO) correlation diagram of La₂B₈ and La₂B₈⁻ (SI Appendix, Fig. S3) and the MO contours of the La₂B₈⁻ anion (SI Appendix, Fig. S4), the bonding patterns of the neutral and anion species are similar. The lower symmetry of the anion is due to the Jahn–Teller effect, as a result of the extra electron in the 1e_2u MO (1e_2u³) in a D_8h anion, leading to the slight distortion to the D_4h symmetry. Electron detachments from the primarily 5d-type 1b_2u and 1b_1u MOs of La₂B₈⁻ give rise to three detachment channels with very close computed VDEs from 1.597 to 1.661 eV, corresponding to the X band in the PE spectrum (Fig. 1C and SI Appendix, Table S4). The remaining MOs are all B₈ ring-based fully occupied σ and π orbitals. Detachments from the 4e_u and 2e_g MOs give rise to four detachment channels with close computed VDEs from 2.798 to 2.856 eV, corresponding well to the A band around 3 eV. Detachments from the 4a_1g and 3a_2u MOs give rise to band B, whereas detachment from the 1a_2g MO gives rise to the weaker band C.

The MOs of Pr₂B₈⁻ are similar to those of La₂B₈⁻, except the two half-filled 4f-based 5e_u and 3e_g MOs (SI Appendix, Fig. S5), which contributed to the broad A band (SI Appendix, Table S5). Other detachment channels and assignments of Pr₂B₈⁻ are similar to those of La₂B₈⁻. Overall, the theoretical VDEs from the D_4h La₂B₈⁻ and Pr₂B₈⁻ and the simulated PE spectra agree well with the experimental data, providing considerable credence for the identified D_4h global minima for the anions and the D_8h global minima for the two Ln₂B₈ neutral complexes.

The High Stability of the Ln₂B₈ Inverse Sandwich Complexes

Inverse sandwich structures represent a fascinating class of inorganic compounds, consisting of two metal atoms sandwiching an aromatic hydrocarbon molecule (27⇓⇓⇓⇓⇓⇓⇓–35). The central aromatic molecule forms interesting chemical bonds to the metals on both sides of the molecular plane. Specifically, a δ-bond has been identified to be critical for the arene-bridged diuranium inverse sandwich complexes (32⇓–34). The current La₂B₈⁻ and Pr₂B₈⁻ species are the first inverse sandwich structures observed for lanthanide borides. Because of the high symmetry of the corresponding neutral species, we will use the neutral Ln₂B₈ to discuss the stability and bonding of the lanthanide boron inverse sandwiches. The Ln−B bond lengths are around 2.70−2.76 Å (Fig. 2), indicating strong bonding between the Ln and the boron atoms. The Ln−B₈−Ln binding energies calculated for Ln₂B₈ → 2Ln + B₈ are quite large, 403.89 kcal/mol for La₂B₈ and 456.16 kcal/mol for Pr₂B₈ (SI Appendix, Table S6). It should be reiterated that the B₈ ring in the Ln₂B₈ inverse sandwiches is quite different from the bare B₈ cluster, which has a D_7h B©B₇ wheel structure (26). The isomer involving this B₈ wheel is much higher in energy, 67.07 kcal/mol above the global minimum (SI Appendix, Fig. S1).

Chemical Bonding in the Inverse Sandwich Ln₂B₈ Complexes

Localized MO Analysis in the B₈ Ring.

Due to the similarity in the electronic structure and bonding between the anion and neutral species (SI Appendix, Fig. S3), we chose the more symmetric neutrals (D_8h) to discuss the chemical bonding in the inverse sandwiches. We first analyzed the B₈ ring using the localized coordinate system (Fig. 3). The 32 2s–2p valence orbitals of B₈ can be divided into four categories using a Hückel-type approach—σ_s, σ(t)_p, σ(r)_p, and π_p—where “t” and “r” denote tangential and radial bonding, respectively. The occupied σ_s and σ(t)_p orbitals constitute the eight B−B bonds in the B₈ ring. Of particular importance are the two sets of delocalized σ(r)_p and π_p orbitals, which primarily participate in bonding with the two Ln atoms above and below the B₈ ring. These two sets of orbitals have smaller energy-level splitting because of less overlap between the B atoms as a result of the relatively large ring size (∼4.2 Å).

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Fig. 3.

The localized coordinate system (LCS) of the B₈ moiety from PBE/DZP calculations. The 32 valence orbitals are divided into four types: σ_s, σ(t)_p, σ(r)_p, and π_p. The “t” means tangential and “r” means radial. The σ and π orbitals are labeled with a subscript number from 0–4 according to the number of their orbital nodes. The orbital occupancy is also indicated. The occupied and unoccupied orbitals are color-coded.

Bonding in La₂B₈ and Ln₂B₈.

Fig. 4 presents the MO correlation diagram of La₂B₈ derived from the La…La and B₈ moieties. The exceptional stability of La₂B₈ is evident by the large energy gap between the HOMO (1e_2u) and LUMO (5a_1g). The 4f orbitals are well known to be radially too contracted in lanthanide elements to participate in chemical bonding. They form a nonbonding f-band in between the HOMO–LUMO region, giving rise to interesting magnetic properties for the Ln₂B₈ complexes (for Ln > La). The Ln 5d orbitals are much more extended than the 4f orbitals radially. Thus, the 5d_π and 5dδ orbitals of the two Ln atoms are significantly stabilized via bonding with the σ₁ and π₂ orbitals of the B₈ ring. Chemical bonding of the anionic Ln₂B₈⁻ and neutral Ln₂B₈ differs only in the electron occupation in the 1e_2u HOMO: It is half-filled (1e_2u²) in the neutral, whereas it has a 1e_2u³ occupation in the anion. Thus, the symmetry of Ln₂B₈⁻ is reduced from D_8h to D_4h due to the Jahn–Teller effect, and the 1e_2u orbital is split to 1b_2u and 1b_1u under D_4h symmetry (SI Appendix, Table S7). The occupied valence MOs for La₂B₈⁻ and Pr₂B₈⁻ are shown, respectively, in SI Appendix, Figs. S4 and S5. Our bonding analyses will focus on the more symmetric neutral Ln₂B₈.

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Fig. 4.

The MO bonding scheme of D_8h La₂B₈ at the level of PBE0/TZP, illustrating the bonding interactions between the La…La and B₈ fragments.

In La₂B₈, the two La atoms provide four electrons to fill the σ_r1 orbital of B₈, which is transformed to the 3e_1u MO in La₂B₈ (Fig. 4). This (d–p)π type bonding orbital contributes the most (74.6%) to the total orbital interactions between La…La and B₈, as revealed through EDA–NOCV analyses [see ΔE_orb(1) and ΔE_orb(1)' in SI Appendix, Table S8]. The La…La d–σ_g orbital interacts with the σ_r0 of B₈ to form the 4a_1g (d–p)σ MO, which only accounts for 2.2% of the total bonding [see ΔE_orb(3) in SI Appendix, Table S8]. The d–π_g orbital of La…La only bonds marginally with the π₁ orbital of B₈ due to symmetry compatibility, accounting for 2.6% of the orbital interactions [see ΔE_orb(4) and ΔE_orb(4)′ in SI Appendix, Table S8]. Remarkably, the d–δ_u orbital of La…La and the π₂ orbital of B₈ are significantly stabilized because of favorable energy matching and effective orbital overlap to form the 1e_2u bonding MO occupied with two unpaired electrons. This bond is reminiscent of the δ bond that plays a key role in stabilizing diuranium inverse sandwiches (32⇓–34). This unique (d–p)δ bond is also important for the La₂B₈ inverse sandwich, contributing 17.6% to the total orbital interactions [see ΔE_orb(2) and ΔE_orb(2)′ in SI Appendix, Table S8].

The bonding patterns are similar in all Ln₂B₈ inverse sandwich complexes, albeit a different number of 4f electrons will give rise to different magnetic properties. The total charge and spin densities of both the anion and neutral Ln₂B₈ species were computed using several methods (SI Appendix, Table S9). The spin densities indicate that each Pr holds two unpaired 4f electrons, while no 4f electron is on La. The B atoms also have spin densities because of the two unpaired electrons in the (d–p)δ bonding orbitals. Upon one electron detachment from the 1b_1u orbital of (d–p)δ character, the reduction of electrons on Ln is more than that on the B atoms, suggesting that the (d–p)δ bond is contributed slightly more by the Ln–5d orbitals. The B₈ ring acts as a doubly aromatic motif to form the inverse sandwich Ln−B₈−Ln complexes. Interestingly, we found some nonnegligible Ln…Ln interactions via the σ and π delocalized orbitals of the B₈ ring (SI Appendix, Table S6). The distance between the two Ln atoms is about 3.6∼3.7 Å, which is remarkably close to the Ln−Ln single bond length (3.60 Å for La−La and 3.52 Å for Pr−Pr based on the self-consistent covalent radii of Pyykkö) (36).

AdNDP Bonding Analysis.

The chemical bonding in Ln₂B₈ can be further understood using AdNDP analyses (37), as shown in Fig. 5 for La₂B₈. The AdNDP results show clearly eight two-center two-electron (2c–2e) bonds in the B₈ ring. The remaining bonds are all delocalized 10c–2e bonds. The three delocalized bonds in the first row represent in-plane σ bonds within the B₈ ring involving interactions with the La 5dσ/π orbitals. These bonds give rise to σ aromaticity because they fulfill the Hückel 4N+2 rule. The five delocalized bonds in the second row represent π bonds in Ln₂B₈, giving rise to π aromaticity for triplet states (38), because of the two single-electron bonds corresponding to the two singly occupied (d–p)δ MOs. Adding two electrons to these MOs would result in a filled (d–p)δ bonding MO and a closed-shell La₂B₈²⁻ with 10 π electrons. The B2p orbitals and the Ln4f orbitals are close in energy. This energetic factor and the fact that boron has low electronegativity make it difficult for Pr or other Ln elements with 4f electrons to donate more electrons to the B₈ ring to fill the (d–p)δ bonding MOs. Hence, even though Pr is known to reach a maximum oxidation state of +V with highly electronegative elements (39), in the Pr₂B₈ inverse sandwich complex each Pr center still retains two 4f electrons (SI Appendix, Fig. S5).

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Fig. 5.

AdNDP bonding analyses for La₂B₈ at the PBE0/cc-pVTZ level. Occupation numbers (ON) are shown.

Magnetism in La₂B₈ and Pr₂B₈

The La₂B₈ inverse sandwich is magnetic due to the two unpaired electrons in the (d–p)δ (e_2u) orbitals. Ferromagnetism was observed in La-doped CaB₆ crystals at high temperatures (40) and has stimulated intense interests due to the many fundamental issues associated with this novel phenomenon (41⇓–43). The divalent CaB₆ is a semiconductor with a band gap of ∼1 eV (44). The observed ferromagnetism in La-doped CaB₆ is due to the partially filled impurity band formed by the La 5d orbitals (45), analogous to the half-filled (d–p)δ orbitals in La₂B₈.

The Pr₂B₈ inverse sandwich has more complicated and interesting magnetic properties due to the partially filled 4f shells. We carried out a series of calculations to determine the electron configurations and spin states of Pr₂B₈⁻ and Pr₂B₈ (SI Appendix, Table S10). The isomers with the promotion of a 4f electron to the 5d orbital, …(d–p)δ²Pr(4f²)Pr(4f²), is energetically preferable to the isomer with the …(d–p)δ⁴Pr(4f¹)Pr(4f¹) configuration by 42.77 kcal/mol at the CCSD(T)/VTZ level. Thus, the bonding in Pr₂B₈ remains the same as in La₂B₈, as discussed above. We also examined the relative energies of possible ferromagnetic and antiferromagnetic configurations and found that the state with septuplet multiplicity is most favorable energetically with the two unpaired electrons in the (d–p)δ bonding MO and the four 4f electrons ferromagnetically coupled. The corresponding antiferromagnetic state (triplet) lies 12.12 kcal/mol higher in energy, calculated using the PBE0/TZP broken-symmetry approach. As expected, the energy differences are small for different occupations of the 4f manifold of orbitals (SI Appendix, Table S10). For example, the energy difference between the septuplet …(d–p)δ²Pr(4fδ²)Pr(4fδ²) and septuplet …(d–p)δ²Pr(4fϕ²)Pr(4fϕ²) configurations is only 4.99 kcal/mol at the PBE0 level.

The above single-configurational theoretical results are further examined using the wavefunction theory in the ab initio multiconfigurational framework. State-averaged CASSCF calculations indicate that the ground state of Pr₂B₈ is dominated by the …(d–p)δ²Pr(4f²)Pr(4f²) configuration (CI weight: ∼98%), even though the four 4f electrons distribute on almost every type of the near-degenerate 4f orbitals. The corresponding antibonding (d–p)δ* natural orbitals are shown to have occupation numbers only on the order of 0.03 (SI Appendix, Fig. S6). The CASPT2 results (SI Appendix, Table S11) confirm the septuplet ground state with a CI weight of 94%, which has two unpaired 4fδ and 4fϕ electrons on each Pr atom and two electrons in the degenerate singly occupied (d–p)δ bonding orbitals coupled ferromagnetically. Other calculations based on different occupation situations in the 4f orbitals were further performed. Overall, the septuplet …(d–p)δ²Pr(4f²)Pr(4f²) configuration is favored, no matter which type of 4f orbitals is occupied within an energy range of 5 kcal/mol (SI Appendix, Table S11). The triplet state dominated by the …(d–p)δ⁴Pr(4f¹)Pr(4f¹) configuration has shorter Pr…Pr distance (3.30 Å at the PBE0/TZP level) due to the enhanced (d–p)δ bonding, but it lies 38.79 kcal/mol higher in energy than the …(d–p)δ²Pr(4f²)Pr(4f²) septuplet ground state.

The antiferromagnetic coupling exhibits strong multiconfigurational characters due to configuration mixing. The lowest antiferromagnetic triplet excited state with two spin-up and two spin-down 4f electrons was evaluated to be 8.73 kcal/mol higher in energy than the septuplet ground state from the CASPT2 calculation (SI Appendix, Table S11). The ferromagnetic coupling in the Pr₂B₈ inverse sandwich involves the two f² centers and the (d–p)δ bonding diradical (e_2u)² on the central B₈ ring, which is highly unusual and is quite different from most Ln compounds with only Ln-centered unpaired spins. We further calculated the relative energies of a ferromagnetic and an antiferromagnetic 1D chain using the periodic VASP code with constrained D_8h Pr…B₈…Pr repeating units. The ferromagnetic coupling is found to be more favorable by 11.90 kcal/mol, with nearly 2 μ_b magnetization on each Pr atom and the B₈ ring. If such a highly magnetic nanowire can be realized, it could have potential applications in magnetoresistance or quantum computing, in particular for the Gd…B₈…Gd system with seven f electrons per Gd.