Metal-metal bonding is well known in the chemistry of transition metals, but rare for the lanthanide (Ln).
Ln-Ln covalent bonding was first observed in endohedral Ln2 dimers encapsulated in fullerene cages. [1][2][3][4][5][6] In these metallofullerene molecules, both single-electron and two-electron Ln-Ln σ bonds have been observed, depending on the degree of charge transfer from the Ln atoms to the fullerene cage. Outside the confined environment of the fullerenes, the first single-electron Ln-Ln σ bond was recently observed in the (Cp iPr5 )2Ln2I3 complexes (Ln = Y, Gd, Tb, Dy; Cp iPr5 = pentaisopropylcyclopentadienyl), where the two lanthanide atoms are bridged by three I atoms and each coordinated axially by a Cp iPr5 ligand. 7 The mixed-valence Ln-Ln bond comes from the σ molecular orbital (MO) of 5dz 2 parentage, occupied by a single electron. Thus, the oxidation state of each Ln atom is formally +2.5. Ln-Ln bonding was not observed in the (Cp iPr5 )2Ln2I4 precursor because each Ln atom is in their favorite +3 oxidation state.
Ln-Ln bonding should exist in Ln clusters and has been studied in the La3 -cluster 8 and other lanthanide suboxide clusters, 9,10 which were investigated using photoelectron spectroscopy (PES) and theoretical calculations. We have recently investigated a series of di-lanthanum boron clusters, La2Bn -(n = 7-11), using PES and quantum chemistry and found that they all possess inverse-sandwich structures consisting of Bn monocyclic rings. [11][12][13][14] In addition to aromatic stabilization in the Bn ring, these complexes are stabilized by multi-center δ bonding between the p orbitals of the Bn rings and the 5d orbitals of the La atoms. Even though the La-La distance was found to be relatively short in the inverse-sandwich complexes, no La-La covalent bond was found because all the valence electrons of the La atoms are used to form bonds with the Bn ring. An interesting question is if La-La covalent bonding may exist in smaller La2Bn -clusters with n ≤ 6. There have been relatively few studies on lanthanide-doped boron clusters, 15- 22 mostly focusing on mono-Ln doped boron clusters. We have also studied several larger B-rich Ln3Bn - clusters, 23,24 including the inverse triple decker La3B14 -cluster and the Ln3B18 -(Ln = La, Tb) spherical trihedral metallo-borospherenes, which do not contain Ln-Ln bonding. Understanding the Ln-Ln and Ln-B bonding in small clusters is not only important in their own right, it may also provide insight into the electronic structure and chemical bonding of bulk lanthanide borides, 25 which are a class of technologically important materials. [26][27][28] Here we report a joint PES and theoretical investigation of di-lanthanum boron clusters, La2Bn -(n = 4-6) and the observation of La-La σ bonding of 6s/5d characters. The global minima of La2B4 -and La2B5 - are found to consist of open B4 and B5 rings, respectively, around a La2 dimer equatorially. A singleelectron s bond is observed in La2B4 -, whereas no direct La-La bond is found in La2B5 -. The global minimum structure of La2B6 -contains two different types of La atoms. One of the La atoms can be viewed as substituting a B atom of the C6v B7 cluster due to the electronic stability of the B7 3-borozene. 19,29 The resulting lanthaborozene [LaB6] 3-then forms a half-sandwich with the second La atom and a singleelectron La-La s bond at the same time. The single-electron La-La s bonds in La2B4 -and La2B6 -are of 6s/5d characters and are analogous to the single-electron Ln-Ln bond in the metallofullerenes and the (Cp iPr5 )2Ln2I3 complexes.
The experiments were conducted using a magnetic-bottle PES apparatus, along with a laser vaporization cluster source and a time-of-flight mass spectrometer. Detailed information about the experimental apparatus and procedure has been published previously. 30 Briefly, the lanthanide boride clusters were generated by laser vaporization of a disc target made from a mixed powder of La (Alfa Aesar, 99.9% purity) and B (Alfa Aesar, 96% 11 B-enriched, 99.9% elemental purity) with a 5/2 La/B mass ratio. The resulting laser-induced plasma was quenched by a helium carrier gas mixed with 5% argon inside the nozzle, which initiated cluster formation. The nascent clusters were entrained by the carrier gas and underwent a supersonic expansion to create a cold cluster beam. After passing through a skimmer, negatively charged clusters were extracted from the collimated beam and analyzed using a timeof-flight mass spectrometer. A series of LaxBy -clusters were formed in the source and the cluster distribution can be optimized to some degree, i.e., the relative ratios of the La/B in the target and the resident time of the clusters in the nozzle. The clusters of current interest, La2Bn -(n = 4-6), were each mass-selected, and decelerated before being photodetached by the 193 nm radiation from an ArF excimer laser. As discussed previously, 30 the temperature of the clusters depended on their resident time inside the nozzle. To ensure colder clusters, we typically chose those with the longest resident time. Photoelectrons were collected at nearly 100% efficiency by the magnetic bottle and analyzed in a 3.5 m long electron flight tube. Photoelectron spectra were calibrated using the known spectrum of the Bi -atomic anion. The PES apparatus provided an electron kinetic energy (KE) resolution (ΔKE/KE) of around 2.5%, that is, ∼25 meV for 1 eV electrons.
We used a new global minimum search algorithm SDGMS developed in the Li group at UCSD to search for the global minima of the La2Bn -(n = 4-6) clusters. 31 The algorithm begins with a starting structure selected from the top of a stack, which is then explored in 6n directions corresponding to the ±x, ±y, and ±z coordinates for each atom. Each atom is displaced by a user-defined distance (0.2 Å in this study) in these directions. If the new structure does not violate covalent bonding requirements, an ab initio energy calculation is performed. This iterative process continues until the energy decreases, indicating the escape from the potential well, or until a predefined number of uphill steps is reached (20 steps in this study). Upon escaping the potential well, a geometry optimization is performed, and the new structure is added to the stack if it is unique from all previously optimized structures within a specified distance (0.2 Å). The algorithm employs a stack data structure to enable a depth-first search approach. Atomic distances are estimated heuristically, and the stack of structures is initialized via a seed generation algorithm that utilizes point group symmetries. Although each structure can theoretically be explored in infinite directions, all possible directions can be represented as combinations of vectors in the x, y, and z directions, assuming the vector size is infinitesimal.
Consequently, reducing the exploration to 6n directions per structure significantly narrows the search space without missing any local minima, provided the step size is sufficiently small. Furthermore, structure similarity searching and covalent criteria filtering at each step reduce the search space. The energies of different structures were calculated using ADF, 32,33 with the zero-order regular approximation (ZORA), 34 the TZP basis set with large frozen cores, 35 and the PBE exchange-correlation functional. 36 The adiabatic detachment energy (ADE) was computed for the global minimum using the energy difference between the anionic and neutral species, each at their optimized geometries (Table 1). Singlepoint calculations at the DLPNO-CCSD(T) level were performed using the Def2-TZVP basis sets for the first vertical detachment energy (VDE1) and the ADE of the global minima, implemented in the ORCA software. 37,38 Higher VDEs were obtained using the ΔSCF-TDDFT approach 39 using the SAOP exchangecorrelation functional 40 at the TZP level without frozen cores, to compare with the experimental PES data. Chemical bonding was analyzed using both the MOs and the AdNDP method, 41 carried out in Gaussian 16 42 using the PBE functional, the ECP28MWB pseudopotential for La, 43,44 along with the ECPMWB_SEG basis set and the cc-pVTZ basis set. [45][46][47] The energy decomposition analysis with natural orbitals for chemical valence method (EDA-NOCV) 48,49 was conducted using the PBE0 functional with the TZP basis set, a small frozen core, and ZORA to analyze the contributions of La and boron fragments towards the MOs. The spectrum of La2B4 -displays six detachment bands in the lower binding energy region, labeled as X-E (Figure 1a, top). The lowest binding energy band (X) gives rise to the VDE1 at 1.33 eV. The ADE is estimated from the onset of band X as 1.21 eV, which is also the electron affinity (EA) of the corresponding neutral La2B4. An overlapping band A is observed at a VDE of 1.59 eV, followed by two well-resolved bands B and C at 2.08 and 2.26 eV, respectively. A weaker band D is observed at 2.83 eV, followed by a prominent band E at 3.21 eV. Beyond 5 eV, the signal-to-noise ratio deteriorates, and a band F at ~5.7 eV is tentatively labeled for the sake of discussion. The spectrum of La2B4 -exhibits relatively complex features, due to its open-shell nature (vide infra).
The spectrum of La2B5 -exhibits relatively simpler patterns with five well-resolved bands in the low binding energy region (Figure 1b top), indicating it is likely a closed-shell system (vide infra). The lowest binding energy band X gives rise to a VDE1 of 1.44 eV, and an estimated ADE of 1.35 eV, i.e. the EA for La2B5. Two sharp and well-resolved bands A and B are observed at VDEs of 1.82 eV and 2.13 eV, respectively. Two broader bands C and D are observed at 2.56 eV and 3.30 eV, respectively. Above 5 eV, the signal-to-noise ratio becomes poor and no major spectral transitions are observed; a band E at ~6 eV is tentatively labeled for the sake of discussion.
The spectrum of La2B6 -(Figure 1c top) again displays relatively congested spectral patterns, indicating an open-shell system (vide infra). The lowest binding energy band X yields the VDE1 at 1.73 eV, but its large spectral width suggests the possible presence of multiple detachment channels, i.e., the VDE1 may represent an average value. The ADE, i.e. the EA of neutral La2B6, is estimated from its onset at 1. 46 eV. An intense and broad band A is observed at a VDE of 2.23 eV, followed by two weak and overlapping bands B and C at VDEs of 2.91 and 3.12 eV, respectively. Three close-lying broad bands D, E, and F are observed at 3.48, 3.69, and 3.88 eV, respectively, followed by a broad band G at 4.57 eV. Beyond 5 eV, the signal-to-noise ratio deteriorates, and a band H at ~6 eV is tentatively labeled for the sake of discussion.
The optimized global minimum structures for La2Bn -(n = 4-6) at the PBE/TZP level are depicted in Figure 2 and their coordinates are given in Table S1. Lowlying isomers for each cluster within about 1 eV of the global minimum structure are presented in Figures S1-S3 for La2Bn -(n = 4-6), respectively. For La2B4 -, the SDGMS global minimum search resulted in 41 local minima. The global minimum is found to be open-shell ( 2 A') with Cs symmetry (Figure 2), all other structures being significantly higher in energy (Figure S1). This structure may be viewed as an incomplete inverse sandwich configuration with an open B4 ring built around the two La atoms. The SDGMS global minimum search for La2B5 -generated a total of 236 local minima. The closed-shell structure ( 1 A1) with C2v symmetry was identified as the global minimum (Figure 2), while all other structures were found to have higher energies (Figure S2). Similar to La2B4 -, the C2v structure of La2B5 -also features an incomplete inverse sandwich arrangement with an open B5 ring. The SDGMS global minimum search for La2B6 -resulted in more than 200 local minima. The openshell structure ( 2 A') with Cs symmetry was identified as the global minimum, overwhelmingly more stable than any other isomers (Figure S3). The expected inverse sandwich cluster consisting of a monocyclic B6 ring (C2h, 2 Au) is included in Figure 2 for comparison. However, this high symmetry structure was found to be energetically unfavorable, being 20.3 kcal/mol higher in energy than the global minimum at the PBE/TZ2P level and 25.1 kcal/mol higher at the PBE0/TZP level (Figure 2 and Figure S3). It is noteworthy that the global minimum structure of the La2B6 -cluster departs from the growth path toward the inverse-sandwich. Instead, the global minimum of La2B6 -contains two types of La atoms. One of the La atoms seems to substitute a B atom of a B7 cluster, 50 which then forms a half sandwich with the second La atom. Such substitutional B7-like structures were first observed in the AlB6 -cluster 51 and also in lanthanide-doped LnB6 -clusters, 16,18 as well as other main group 52 and transition metal doped MB6 - clusters, [53][54][55] as a result of the high electronic stability of the B7 3-borozene. 19,29 The structural evolution of La2Bn -(n = 4-6) is reminiscent of that found in Ta2Bn -(n = 4-6) previously, 56,57 except that the global minimum of Ta2B6 -is a perfect inverse sandwich (D6h) due to the strong d-p-d bonding between the B6 ring and the two Ta atoms. 57 The current results are also consistent with our previous conclusion that the smallest monocyclic Bn ring to form the inverse sandwich Ln2Bn - structures is B7. [11][12][13][14] Interestingly, the La-La distances calculated for the global minima of La2Bn -(n = 4-6) are 3.37 Å, 3.52 Å, and 3.45 Å, respectively (Figure 2), which are all shorter than the La-La single bond length of 3.60 Å, according to Pyykkö's atomic covalent radii. 58 These La-La bond distances are also shorter than the recently reported Ln-Ln distance in the (Cp iPr5 )2Ln2I3 compound. 7 MO analyses presented in Table S2 indicate that the La-La σ bonding arises from the hybridized 6s/5d orbitals of the La atoms (vide infra).
global minimum structures of the three La2Bn -clusters at three levels of theory are compared with the experimental values in Table 1. The simulated spectra are compared with the experimental data in Figure 1. In the case of La2B4 -and La2B6 -, the first detachment channel corresponds to the removal of the singly occupied HOMO, i.e., 46a' for La2B4 -(Table 2) and 50a' for La2B6 -(Table 4). These orbitals mainly involve La-La σ bonding primarily from the hybridized 6s/5d atomic orbitals, as illustrated in Table S2.
The three methods give similar and consistent ADE and VDE1 values, with the computed values slightly underestimated relative to the experimental data. The calculated VDE1 values are 1.31 eV for La2B4 -and 1.55 eV for La2B6 -at DLPNO-CCSD(T), which agree well with the experimental values of 1.33 eV and
a Experimental uncertainty: ±0.05 eV.
1.73 eV, respectively (Table 1). For La2B5 -, the first detachment channel comes from electron removal from the 5b1 orbital (Table 3), which involves La-B bonding through d-p δ interaction (Table S2). The calculated VDE1 value of 1.34 eV at DLPNO-CCSD(T) is in good accord with the experimental value of 1.44 eV (Table 1).
Higher VDEs were computed using the ∆SCF-TDDFT method, 39 as compared with the experimental results in Tables 2-4 for La2Bn -(n = 4-6), respectively. Because La2B4 -and La2B4 -are open shell with an unpaired electron in the HOMO, both singlet and triplet final states are possible. In the case of La2B4 -, band A corresponds to two final spin states ( 3 A" and 1 A") due to electron detachment from the fully occupied 22a" orbital. This orbital consists of interactions between La2 (dπu) and B4 (σ1), as depicted in Figure 3 and Table S2. Band B, with a calculated VDE of 2.09 eV, corresponds to the 3 A" final state due to electron detachment from the 21a" MO, which involves interactions between La2 (dπg) and B4 (π1).
EDA-NOCV analyses, as presented in Table S3, indicate that the 22a" and 21a" orbitals contribute significantly to the total orbital interaction energy (ΔEorb), with the 22a" orbital contributing 45% and the 21a" orbital contributing 31%. Higher detachment channels C and D arise from the B4-dominated orbitals 45a' and 20a", respectively. Band E contains contributions from multiple detachment channels, primarily from the B4-dominated 44a' and 43a' orbitals. These orbitals have relatively small contributions to the ΔEorb, as given in Table S3 (only 2.7% from 44a'). The high binding energy signals around F likely come from the 42a' MO, which is almost a pure σ orbital on the B4 motif (92%), as shown in Table S2.
Table 3. VDEs of La2B5 -measured from the photoelectron spectrum and compared with the computed VDEs at the SAOP/TZP level for the global minimum structure of La2B5 -(Figure 2). All energies are in eV.
State Final-state Electron Configuration VDE (theo)
a Experimental uncertainty: ±0.05 eV.
Unlike in La2B4 -, there is no occupied La-La σ bonding orbital in La2B5 -, because the corresponding orbital (8a1) is unoccupied, as shown in Table S2. Since La2B5 -is closed-shell, detachment from each occupied MO leads to one PES peak, which is responsible for its relatively simple photoelectron spectrum (Figure 1b). Peaks A and B in Figure 1b correspond to the La-B bonding orbitals 5b2 and 2a2, respectively.
The broader bands C and D each result from two close detachment channels: 4b2 and 7a1 for band C and 4b1 and 6a1 for band D (Table 3). The computed VDE for detachment from the B5-domianted 3b2 MO (Table S2) is 5.4 eV, which is consistent with the weak signals beyond 5 eV in the photoelectron spectrum (Figure 1b).
Table 4. VDEs of La2B6 -measured from the photoelectron spectrum and compared with the computed VDEs at the SAOP/TZP level for the global minimum structure of La2B6 -(Figure 2). All energies are in eV.
Feature VDE (exp.) a State Configuration VDE (theo.)
a Experimental uncertainty: ±0.05 eV.
-is open shell like La2B4 -, both singlet and triplet final states are possible, giving rise to a more congested spectrum (Figure 1c). Several PES bands in Figure 1c correspond to multiple detachment channels, as shown in Table 4. In fact, the first PES band X contains two detachment channels:
the detachment from the 50a' HOMO leading to the 1 A' ground state of La2B6 (computed VDE at 1.48 eV) and the detachment from the 49a' HOMO-1 leading to the 3 A' excited state (computed VDE at 1.86 eV).
The singly occupied HOMO involves La-La d/s s bonding, whereas the 49a' HOMO-1 is a La-B p bonding orbital (57% La dp), as shown in Table S2. The relatively small energy gap between the HOMO and HOMO-1 of La2B6 -, which also corresponds to the LUMO-HOMO gap of neutral La2B6, suggests that the La-La bonding is important in the La2B6 -cluster. The intense and broad band A contains four detachment channels: the 1 A' final state from the 49a' MO, the 3 A" and 1 A" final states from the 23a" MO, and the 3 A' final state from the 48a' MO. The computed VDEs for the higher detachment channels are all in good agreement with the congested spectral features (Table 4), including the weak signals beyond 5 eV (around H), which correspond to detachment from the B6-based 45a' MO (95% B 2s/2p, see Table S2).
The good agreement between the experimental data and the computed ADE and VDEs for all the La2Bn -(n = 4-6) clusters validates their global minimum structures shown in Figure 2. 4.2. The Electronic Structure and La-La Bonding in La2Bn -(n = 4-6). We conducted MO analyses for La2B4 -as an example to understand the electronic structure and bonding mechanisms in the La2Bn -
systems, as depicted in Figure 3. The analyses utilized the La2 and B4 -fragments, with the group orbitals of B4 -labeled based on their shape and number of nodal planes. The 46a' HOMO mainly involves La-La bonding, primarily from the La sσ and dσ orbitals (72%, Table S2) with minor contributions from the B atoms. The antibonding La-La MO is the LUMO 47a' at an energy of 1.51 eV, indicating a large HOMO-LUMO gap in the anion. On the other hand, the energy separation between 46a' and 22a'' is relatively small, suggesting that filling another electron in the 46a' orbital would yield an electronically stable La2B4 2-system with a full La-La s bond (vide infra).
According to the EDA-NOCV analyses shown in Table S3, the La2B4 -cluster exhibits slight ionic character, with electrostatic interactions accounting for 53% of the sum of ΔEorb and ΔEelest. The most significant interaction originates from electron flow from La2 dπ to B4 -π1, forming the 21a'' orbital. The second most significant interaction arises from the 22a'' orbital, with electron flow from La2 dπ to B4 -σ1.
Additionally, using the La2 (sσ²dπ⁴) fragment, we identified a NOCV orbital on the β spin channel with electron flow from La2 d/s σ to the B4 group orbital, where Δρ is 0.78. However, the corresponding α spin counterpart has negligible contributions, with only 0.8% to the total ΔEorb, indicating that the singly occupied electron in La2B4 -primarily arises from La-La σ bonding with minimal contribution from La-B interactions. In La2B5⁻, however, strong La-B5-La interactions involving the La 5d orbitals are observed, as demonstrated by the EDA-NOCV analyses (Table S4). Similar to the inverse-sandwich complexes La2Bn⁻ (n = 7-9), [11][12][13] the dominant contribution arises from d-p-d π/δ interactions. The orbital corresponding to ΔEorb(4) features La-B5-La d-p-d σ bonding, in contrast to the La-La σ bonding observed in La2B4⁻. In the inverse sandwich complexes, the strong La-Bₙ-La interactions lead to increased 6s-6s repulsion, disfavoring efficient d/s hybridization necessary for La-La σ bonding.
In the global minimum structure of La2B6 -, we observed La-La σ bonding similar to that in La2B4 -, as illustrated in the 50a' orbital shown in Table S2. Unlike the inverse sandwich complexes without La-La bonding, the global minimum structure of La2B6 -features one La atom within the B6 plane forming a B7like structure, 50 which then forms a half-sandwich with the other La atom. This structure is a direct result of the high electronic stability of the B7 3-borozene. 19,29 Most interestingly, there is direct La-La σ bonding in this structure, with a large bond order of 1.01 from the Gopinathan-Jug method 59 and 1.06 from the Nalewajski-Mrozek (N-M) method, [60][61][62] as shown in Table S5. The AdNDP analyses for La2B5 -shown in Figure 5 revealed four 2c-2e B-B σ bonds within the open B5 ring and two 3c-2e La-B-La bonds involving both La atoms and the two terminal boron atoms. The remaining five bonds are all 7c-2e bonds involving interactions between the open B5 ring and the two La atoms. These bonds are remarkably similar to those observed in the La2Bn -(n = 7-9) inverse
sandwiches, [11][12][13] suggesting that the C2v La2B5 -cluster is an incomplete inverse-sandwich. This conclusion is supported by the fact that there is no La-La bond in La2B5 -. The relatively short La-La distance in La2B5 -is a consequence of the strong La-B5-La sandwich interactions, exactly the same as that in the La2Bn -(n = 7-9) inverse sandwiches. In the AdNDP analyses for La2B6 -(Figure 6), we observed one 2c-1e La-La σ bond, four 2c-2e peripheral B-B σ bonds, and two 2c-2e La-B σ bonds. Most interestingly, the three 8c-2e σ bonds and the three 8c-2e p bonds are reminiscent of the doubly aromatic bonding in the B7 3-borozene. 19,29 This observation suggests that one of the La atom substitutes one B atom in B7 3-to form a [LaB6] 3 ⁻ lanthaborozene. Thus, removing the electron from the HOMO of La2B6 -leads to the closed-shell neutral La2B6, which can be viewed as a lanthanide lanthaborozene complex, [La 3+ ][LaB6 3 ⁻] (Figure S4a), similar to the [Pr 3+ ][B7 3 ⁻] borozene complex reported previously. 15 However, the photoelectron spectrum of PrB7⁻ revealed a large HOMO-LUMO gap of ~1.5 eV, suggesting that the neutral PrB7 borozene complex is a much more stable electronic system. On the other hand, the LUMO of La2B6 is the La-La bonding orbital (50a', Table S2) and PES did not reveal a large HOMO-LUMO gap (the LUMO feature is so close to the HOMO feature that it is not resolved in band X in Figure 1c). Our calculation indicates a HOMO-LUMO gap of ~0.4 eV. Thus, filling the 50a' La-La bonding orbital will result in a stable [La2B6] 2 ⁻ borozene complex with a La-La s bond, as shown in the AdNDP analysis in Figure S4c. The La-La bonding in the La2Bn -(n = 4-6) clusters was further investigated using various bond order indices, as given in Table S5. The La-La bond order indices in La2B4 -and La2B6 -are found to be significantly larger than that in La2B5 -. These results agree with the above bonding analyses, which reveal true La-La bonding in La2B4 -and La2B6 -. On the other hand, there is no true La-La bonding in the incomplete inverse sandwich La2B5 -, where the relatively short La-La distance is a result of strong La-B5-La sandwich interactions. It should also be noted that the La-La bonding in the La2B4 -and La2B6 - clusters is reminiscent of the Ln-Ln bonding in the metallofullerenes 1 and the recently reported (Cp iPr5 )2Ln2I3 complexes, 7 suggesting that lanthanide boride clusters afford an interesting platform to study Ln-Ln bonding.