Investigation of Pb–B Bonding in PbB₂(BO)_n⁻ (n = 0–2): Transformation from Aromatic PbB₂⁻ to Pb[B₂(BO)₂]^−/0 Complexes with B≡B Triple Bonds

Abstract

Boron has been found to be able to form multiple bonds with lead. To probe Pb–B bonding, here we report an investigation of three Pb-doped boron clusters, PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻, which are produced by a laser ablation cluster source and characterized by photoelectron spectroscopy and ab initio calculations. The most stable structures of PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻ are found to follow the formula, [PbB₂(BO)_n]⁻ (n = 0–2), with zero, one, and two boronyl ligands coordinated to a triangular and aromatic PbB₂ core, respectively. The PbB₂⁻ cluster contains a B=B double bond and two Pb–B single bonds. The coordination of BO is observed to weaken Pb–B bonding but strengthen the B=B bond in [PbB₂(BO)_n]⁻ (n = 1, 2). The anionic [PbB₂(BO)₂]⁻ and its corresponding neutral closed-shell [PbB₂(BO)₂] contain a B≡B triple bond. A low-lying Y-shaped isomer is also observed for PbB₄O₂⁻, consisting of a central sp² hybridized B atom bonded to two boronyl ligands and a PbB unit.

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1 Introduction

Three-dimensional (3D) cages, especially the well-known B₁₂-icosahedral cage, are key structural features prevalent in boranes and various boron allotropes.^1–3 However, in the past two decades, size-selected boron clusters have been found through systematic experimental and theoretical studies to be planar or quasi-planar (2D) up to very large sizes.^4–10 The first 3D borospherene cage (B₄₀) was discovered in 2014,¹¹ followed by the axially chiral borospherene B₃₉⁻ in 2015.¹² Subsequently, seashell-like borospherenes were found as minor isomers for the B₂₈⁻ and B₂₉⁻ clusters.^13,14 The largest boron cluster (B₄₈⁻), characterized experimentally to date, was found to have a bilayer-type structure.¹⁵ Significant experimental efforts have also been devoted to investigate metal-doped boron clusters, which have been shown to display a wide variety of novel structural patterns,^10,16–18 such as fan-shaped structures,^19–22 double-chain ribbons,^23,24 metal-centered boron wheels,^16,25–29 half-sandwich structures,^30–35 metallo-borophenes,^8,36,37 metal-centered boron drums,^37–42 metallo-borospherenes,⁴³ and metal-borozene complexes.^24,44,45 The most important chemical bonding features of boron and metal-doped boron clusters are found to be dominated by both delocalized σ and π bonds as a result of boron's electron deficiency.^{6–8,18,46–49}

In addition to forming delocalized bonds, boron is also capable of engaging in localized bonds. For instance, the boronyl group (BO), which is isoelectronic with the cyano group (CN), has been shown to have a strong B≡O triple bond⁵⁰ and has been synthesized.⁵¹ In fact, even B≡B triple bonds have been observed in isolated molecules^52–54 and synthetic compounds.⁵⁵ Earlier studies on boron oxide clusters showed that they all contained boronyl ligands^53,56–58 and the analogy between boronyl and H/Au was established, i.e. they are all single electron σ donors. Using this analogy, we have designed and observed experimentally many boron-boronyl clusters.^59–64 Recently, several interesting findings have also been made in metal-doped boron oxide clusters that feature unusual metal-boron (M–B) multiple bonds and boronyl ligands. The M≡B triple bonds were observed in linear [M≡B–B≡O]⁻ (M = Bi, Re) and bent (⁻OB)Ir≡B,^65,66 while the bent (⁻OB)RhB was confirmed to contain a Rh≡B quadruple bond.⁶⁷ The umbrella-like [(η⁷-B₇)-B-BO]⁻ cluster was even found to embody metallomimetic properties of boron.⁶⁸

Lead is one of the earliest metals acquainted and used by human beings. Despite their known toxicity, lead and its compounds are still important today and have wide applications in industries, including pigments, lead-acid batteries, and lead glasses, etc.⁶⁹ In fact, lead is the most common gamma-ray shielding material due to its high atomic number, high density, and wide availability.^70–72 Boron, on the other hand, has good shielding properties against neutron radiation because of its high thermal neutron absorption cross-section.^73,74 Recently, a series of lead borate crystals, Pb₃B₁₀O₁₆[OH]₄, have been synthesized and shown to have better co-shielding properties for gamma and neutron radiations than the simple PbO/B₂O₃ mixture with the same molar ratio of Pb and B.⁷⁵ Despite the progress achieved for synthesizing lead borate compounds with various morphologies, few lead-boron molecules are known and our knowledge about the lead-boron bonding is still limited. We have studied recently two lead-doped boron oxide clusters, PbB₂O^−/2− and PbB₃O₂⁻ and found a Pb≡B triple bond in the linear PbB₂O²⁻ species, a BPb multiple bond with a bond order of 2.5 in the linear PbB₂O⁻, and a B=Pb double bond in the Y-shaped PbB₃O₂⁻.⁷⁶

In this article, we report the observation of three lead-doped boron and boron oxide clusters, PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻, which are studied via photoelectron spectroscopy (PES) and ab initio calculations. The global minimum (GM) of PbB₂⁻ is found to be an isosceles triangle, while the GM structures of PbB₃O⁻ and PbB₄O₂⁻ can be viewed as successively coordinating a boronyl ligand colinearly to the B atoms of the triangular PbB₂⁻. The triangular PbB₂⁻ is aromatic and contains a B=B double bond and two Pb–B single bonds. The coordination of BO is observed to strengthen the B=B double bond in PbB₂⁻ but weaken Pb–B bonding. Thus, the GM structures of the three lead-doped boron clusters can be formulated as [PbB₂(BO)_n]⁻ (n = 0–2), with zero, one, and two boronyl units bonded to an aromatic PbB₂ triangle. It is found that Pb bonding with the B₂ part of the B₂(BO)₂ motif in [PbB₂(BO)₂]^−/0 is very weak and these entities can be characterized as the Pb^+/2+[B₂(BO)₂²⁻] charge-transfer complexes containing a B≡B triple bond. A low-lying Y-shaped isomer is also observed for PbB₄O₂⁻, which consists of a central B atom in sp² hybridization and coordinated by two boronyl ligands and a B=B double bond with the PbB unit [PbB = B(B≡O)₂⁻]. These findings not only broaden our understanding of Pb–B bonding but also help design novel lead-boron molecules and lead boride materials with excellent co-shielding properties for high-energy gamma and neutron radiations.

2 Method

2.1 Photoelectron spectroscopy

The lead-boron clusters were produced using a laser vaporization cluster source and were investigated using a magnetic-bottle PES apparatus, as described previously.^7,77 Briefly, the PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻ clusters were formed by laser vaporization of a cold-pressed Pb/¹⁰B mixed target with a helium carrier seeded with 5% Ar, and the 532 nm vaporization laser beam was directed collinearly with the cluster beam. The trace amount of oxide impurities on the target surface was sufficient to produce the O-containing species, PbB₃O⁻ and PbB₄O₂⁻. Seeding the helium carrier gas with O₂ would produce highly oxidized clusters (PbB_xO_y⁻). The clusters formed in the source were entrained in the carrier gas pulse delivered by two symmetrically mounted molecular beam valves and underwent a supersonic expansion. We used a large waiting room nozzle and a strong supersonic expansion to remove the substantial internal energies to maximize cluster cooling. After passing a skimmer, negatively charged clusters were extracted from the collimated cluster beam and analyzed using a time-of-flight mass spectrometer. The clusters of current interest were mass-selected and decelerated before photodetached by a pulsed laser beam at 266 nm (4.661 eV) produced from the fourth harmonics of a Nd:YAG laser. Photoelectron kinetic energies were calibrated using the known spectrum of the Bi⁻ atomic anion. The resolution of the magnetic-bottle PES apparatus was around 2.5%, that is, ∼25 meV for 1 eV electrons.

2.2 Computational methods

The GM structures were searched for PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻ using the Coalescence-Kick method⁷⁸ at the PBE0/lanl2dz^79–82 level of theory. Low-lying candidates were fully optimized at the PBE0 level with the augmented Dunning's all-electron basis set (aug-cc-pVTZ) for B and O atoms and the aug-cc-pVTZ-pp basis set with the relativistic pseudopotentials (ECP60MDF) for the Pb atom (abbreviated as AVTZ).^83,84 Vibrational frequencies were calculated at the same level to make sure that the obtained structures exhibited true minima of the systems. The relative energies of the top isomers within 1.0 eV were further refined at the CCSD(T)^85–87 /AVTZ//PBE0/AVTZ level [abbreviated as CCSD(T)/AVTZ]. To obtain more reliable structural parameters, we re-optimized the lowest-lying isomer for each species and the second lowest-lying isomer of PbB₄O₂⁻ at the CCSD/AVTZ level.^88,89 The first vertical detachment energies (VDE₁) and the adiabatic detachment energies (ADE) for the GM structures of PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻ were calculated at the CCSD(T)/AVTZ level. The VDE₁ was computed as the energy difference between the anionic ground state and the corresponding neutral ground state at the optimized anion geometry, whereas the ADE was calculated as the difference in energy between the optimized anion and the corresponding neutral at its optimized structure.

The higher VDEs were obtained by adding the neutral excitation energies to the VDE₁. To obtain the energies of the neutral excited states, the state-averaged (SA) complete active space self-consistent field (CASSCF) calculations^90,91 were performed using the AVTZ basis set, followed by multi-reference configuration interaction (MRCI) calculations,⁹² in which the spin–orbit (SO) coupling effect was considered.⁹³ The active space employed consisted of 8 electrons in 10 orbitals for PbB₂, 5 electrons in 6 orbitals for PbB₃O, and 4 electrons in 6 orbitals for PbB₄O₂. For the second isomer of PbB₄O₂⁻, the first two VDEs were calculated at the CCSD(T)/AVTZ level as the transition from the ground state of the anionic species to the lowest singlet and triplet states of the corresponding neutral species at the optimized anion geometry. The higher VDEs were calculated using the time-dependent (TD)-PBE0/AVTZ method. Vibrational frequencies for the ground state of neutral PbB₃O were computed at the PBE0/AVTZ level. Chemical bonding analyses were conducted using the adaptive natural density partitioning (AdNDP) method⁹⁴ and were then visualized using the VMD software.⁹⁵ The out-of-plane tensor components of the nucleus-independent chemical shift at ζ distance above the molecular plane [NICS_zz(ζ)]⁹⁶ were computed at the PBE0/TZP⁹⁷ level to examine the aromaticity of the experimentally confirmed species. Considering the influence of heavy metal doping on the aromaticity indices,⁹⁸ the centres of the ring currents were used instead of the geometry centres to calculate the NICS_zz(ζ) values, and the spin–orbit coupling effects were included in the NICS calculations.^99,100 Natural bond orbital (NBO) and natural resonance theory (NRT) analyses¹⁰¹ were performed at the PBE0/AVTZ level using the NBO 7.0 program.¹⁰² All geometry optimizations and frequency calculations at the PBE0 and CCSD levels and TD-PBE0 calculations were performed using the Gaussian 09 program.¹⁰³ The CCSD(T), CASSCF, and MRCI calculations were carried out using the Molpro package.¹⁰⁴ The NICS calculations were implemented using the ADF code,¹⁰⁵ while the centres of the ring current were searched using the GIMIC program.¹⁰⁶

3 Experimental results

The photoelectron spectra of PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻ at 266 nm are shown in Fig. 1–3, respectively. The well-resolved PES bands are labeled with letters, X, A, B, …, where band X represents the transition from the anionic ground state to the electronic ground state of the corresponding neutral cluster and bands A, B, … indicate detachment transitions to the excited electronic states of the neutral cluster. The electron affinity (EA) of the corresponding neutral cluster or the ADE was determined by drawing a straight line at the leading edge of band X and then adding the instrumental resolution. The VDEs were measured using the band maxima, as given in Tables 1–3, where they are compared with the theoretical results. A larger difference between the VDE₁ and ADE usually indicates a more significant geometry change from the anion to neutral cluster upon electron detachment.

Fig. 1 Photoelectron spectrum of PbB₂⁻ at 266 nm (4.661 eV).

Fig. 2 Photoelectron spectrum of PbB₃O⁻ at 266 nm.

Fig. 3 Photoelectron spectrum of PbB₄O₂⁻ at 266 nm.

Table 1 The experimental VDEs for PbB₂⁻, and their assignments and comparison with the theoretical results. All energies are given in eV. The first VDE was calculated using the CCSD(T) method. MRCI and SO coupling calculations were conducted to calculate the higher VDEs

VDE (Exp)^a		Configurations	Terms	VDE (MRCI)	Levels	VDE (SO)	Composition of SO coupled states
a The experimental uncertainty was estimated to be ±0.02 eV.
X	2.08	1a1^22a1^21b2^23a1^21b1^24a1^0	^1A1	1.94	^1A1(0)	1.94	96.4%^1A1 + 3.3%^3B2 + 0.3%^3B1
A	2.48	1a1^22a1^21b2^23a1^11b1^24a1^1	^3A1	2.54	^3A1(0)	2.52	65.2%^3A1 + 34.8%^3B1
					^3A1(−1)	2.52	63.8%^3A1 + 36.2%^3B1
B	2.65	1a1^22a1^21b2^23a1^21b1^14a1^1	^3B1	2.65	^3A1(+1)	2.61	94.8%^3A1 + 3.6%^1B1 + 1.6%^3B2
					^3B1(+1)	2.69	87.0%^3B1 + 12.5%^1A1 + 0.4%^3B2
C	2.91				^3B1(−1)	2.86	62.2%^3B1 + 31.7%^3A1 + 6.1%^1B2
					^3B1(0)	2.90	63.6%^3B1 + 36.0%^3A1 + 0.4%^1B2
D	3.03	1a1^22a1^21b2^23a1^11b1^24a1^1	^1A1	3.00	^1A1(0)	3.11	68.6%^1A1 + 23.0%^3B2 + 8.4%^3B1
E	3.15	1a1^22a1^21b2^23a1^21b1^14a1^1	^1B1	3.09	^1B1(0)	3.25	81.0%^1B1 + 17.0%^3B2 + 2.0%^3A1
F	∼3.6	1a1^22a1^21b2^13a1^21b1^24a1^1	^3B2	3.85	^3B2(0)	4.06	96.4%^3B2 + 1.9%^3A1 + 1.7%^1B1
					^3B2(+1)	4.06	97.0%^3B2 + 1.9%^3A1 + 1.1%^1B1
					^3B2(−1)	4.08	96.7%^3B2 + 2.4%^1A1 + 0.9%^3B1

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Table 2 The experimental VDEs for PbB₃O⁻, their assignments and comparison with the theoretical results. All energies are given in eV. The first VDE was calculated using the CCSD(T) method. MRCI and SO coupling calculations were conducted to calculate higher VDEs

VDE (exp.)^a		Configurations	Terms	VDE (MRCI)	Levels	VDE (SO)	Composition of SO coupled states
a The experimental uncertainty was estimated to be ±0.02 eV.
X	3.10	…5a′^26a′^21a′′^27a′^28a′^22a′′^1	^2A′′	3.21		3.21	70.1%^2A′′ + 26.1%^2A′ + 2.1%^4A′ + 1.7%^4A′′
A	3.32	…5a′^26a′^21a′′^27a′^18a′^22a′′^2	^2A′	3.23		3.48	80.4%^2A′ + 15.9%^2A′′ + 1.6%^4A′ + 2.1%^4A′′
B	3.85	…5a′^26a′^21a′′^27a′^28a′^12a′′^2	^2A′	3.66		3.96	84.2%^2A′ + 9.6%^2A′′ + 3.3%^4A′ + 2.9%^4A′′

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Table 3 The experimental VDEs for PbB₄O₂⁻, their assignments and comparison with the theoretical results. All energies are given in eV. The first VDE was calculated using the CCSD(T) method. MRCI and SO coupling calculations were conducted to calculate higher VDEs

VDE (exp)^a		Configurations	Terms	VDE (MRCI)	Levels	VDE (SO)	Composition of SO coupled states
a The experimental uncertainty was estimated to be ±0.02 eV.
X	2.88	…1b1^21a2^24b2^26a1^22b1^27a1^25b2^0	^1A1	2.88	^1A1(0)	2.88	85.0%^1A1 + 9.6%^3B2 + 2.8%^3A2 + 2.5%^3B1
A	3.82	…1b1^21a2^24b2^26a1^22b1^27a1^15b2^1	^3B2	3.85	^3B2(0)	3.86	59.0%^3B2 + 36.3%^3A2 + 2.3%^3A1 + 2.4%^1B1
					^3B2(−1)	3.86	51.8%^3B2 + 41.3%^3A2 + 4.6%^1A1 + 2.2%^3B1
					^3B2(+1)	3.91	82.8%^3B2 +12.9%^1A2 + 3.2%^3B1 + 1.1%^3A1
B	4.01	…1b1^21a2^24b2^26a1^22b1^17a1^15b2^1	^3A2	3.96	^3A2(+1)	4.03	89.6%^3A2 + 6.9%^3A1 + 3.4%^1B2 + 0.1%^3B1
C	4.15				^3A2(−1)	4.15	56.1%^3A2 + 38.0%^3B2 + 4.7%^3A1 + 1.3%^1B1
D	4.33	…1b1^21a2^24b2^26a1^22b1^17a1^15b2^1	^1A2	4.19	^3A2(0)	4.38	54.4%^3A2 + 34.0%^3B2 + 11.6%^1A1
					^1A2(0)	4.34	76.2%^1A2 + 12.9%^3B2 + 9.7%^3A1 + 1.3%^3B1
E	4.53	…1b1^21a2^24b2^26a1^22b1^27a1^15b2^1	^1B2	4.56	^1B2(0)	4.70	81.9%^1B2 + 14.6%^3B1 + 3.4%^3A2

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3.1 PbB₂⁻

The 266 nm spectrum of PbB₂⁻ shown in Fig. 1 displays six sharp and intense peaks on the low binding energy side and weak and broader PES features above 3.5 eV. The first VDE of PbB₂⁻ is obtained from band X as 2.08 eV and the ADE is estimated to be 2.03 eV, which also represents the EA of PbB₂. An intense band A is observed at 2.48 eV, followed by a similarly intense band B at 2.65 eV. Three closely spaced bands C, D, E are observed at 2.91, 3.03, and 3.15 eV, respectively. Features beyond 3.5 eV are weak and congested, and they are labeled as F for the sake of discussion. All the VDEs for PbB₂⁻ are given in Table 1 and compared with the theoretical data.

3.2 PbB₃O⁻

The 266 nm spectrum of PbB₃O⁻ (Fig. 2) is relatively simple with three sharp and well-resolved bands. Band X gives rise to the first VDE at 3.10 eV, with its ADE estimated as 3.08 eV, followed by band A at 3.32 eV. PbB₃O⁻ has the highest VDE among all three clusters due to its closed-shell electronic structure. Band B at 3.85 eV was vibrationally resolved with a vibrational spacing of ∼480 cm⁻¹. A very weak feature marked by an asterisk was observed at the low binding energy side, which might come from a contaminant due to the congested mass spectrum caused by the isotopic distribution of lead. The measured VDEs for PbB₃O⁻ are summarized in Table 2, where they are compared with the theoretical results.

3.3 PbB₄O₂⁻

The photoelectron spectrum of PbB₄O₂⁻ (Fig. 3) seems much more complicated than those for PbB₂⁻ and PbB₃O⁻ with more congested features. The PES bands labeled with X, A–E are intense and relatively sharp, which are likely from one species. On the other hand, the two bands labeled with X′ (3.13 eV) and A′ (3.40 eV) are weak and broad and they appear to come from a minor isomer of PbB₄O₂⁻. Band X yields a VDE of 2.88 eV with an estimated ADE of 2.84 eV. Following a relatively large energy gap of 1 eV, a sharp and intense band A is observed at 3.82 eV. The spectral features beyond band A become more complex, and a weaker peak B is observed at 4.01 eV, while a relatively broad band C is resolved at 4.15 eV. Two sharp bands, D and E, are observed at 4.33 and 4.53 eV, respectively. The bands C, D, and E appear to contain partially resolved vibrational features. The VDEs for band X, A–E are given in Table 3 and compared with the theoretical results to be presented below.

4 Theoretical results

Fig. 4 displays the optimized GM structures and their bond lengths of PbB₂⁻ and PbB₃O⁻ and the top two lowest-lying isomers of PbB₄O₂⁻ at the CCSD/AVTZ level. All low-lying structures within about 2.0 eV of the GM structure at the PBE0/AVTZ level are presented in Fig. S1–S3 (ESI†) for PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻, respectively, along with their symmetries, electronic states, and relative energies. The top isomers within 1.0 eV were further calculated at the single-point CCSD(T)/AVTZ level.

Fig. 4 The optimized structures of the GM of PbB₂⁻ (1), PbB₃O⁻ (2), PbB₄O₂⁻ (3) and its closed-shell PbB₄O₂ (3′), and a low-lying isomer of PbB₄O₂⁻ (4) and its closed-shell PbB₄O₂²⁻ (4′). The bond lengths are given in Å at the CCSD/AVTZ level.

4.1 PbB₂⁻

Only six structures with different spin multiplicities (doublet, quartet, and sextet) are located within ∼2.0 eV of the GM for the PbB₂⁻ cluster (Fig. S1, ESI†). These structures can be divided into two categories, i.e., C_2v isosceles triangle and linear Pb–B–B. It is found that the doublet isosceles triangle (C_2v, ²A₁) is the GM for PbB₂⁻, consisting of a B₂ dimer bridged by a Pb atom (Fig. 4, 1). The second lowest-lying isomer, a doublet linear Pb–B–B (C_∞v, ²Σ) structure, is more than 0.45 eV above the GM at both the PBE0 and CCSD(T) levels. The remaining isomers are at least 1.11 eV higher in energy at the PBE0 level.

4.2 PbB₃O⁻

Candidate structures for PbB₃O⁻ are composed of five isomers containing a terminal BO group bonded to a PbB₂ moiety and another five isomers based on a B₃ triangle (Fig. S2, ESI†). The GM of PbB₃O⁻ is 2 (C_s, ¹A′), as shown in Fig. 4 with all bond lengths labeled. The GM can be viewed as attaching a BO group to a B atom of the PbB₂ triangle along the B–B bond, weakening the Pb–B bond while strengthening the terminal Pb–B bond. The closest low-lying isomer consists of a B₃ triangle with a bridging Pb atom and a bridging O atom, which is 0.84 eV higher in energy than the GM at the PBE0 level and 1.00 eV higher at the CCSD(T) level. The large energy gap between the first two isomers indicates the high stability of GM 2.

4.3 PbB₄O₂⁻

For the PbB₄O₂⁻ cluster, we found fourteen isomers within 2 eV of the GM, most of which possess at least one terminal BO group (Fig. S3, ESI†). The GM of PbB₄O₂⁻ (3C_2v, ²B₂) is a planar structure, consisting of two terminal BO groups and a PbB₂ isosceles triangle (Fig. 4). It can be viewed as attaching a BO unit to each of the two B atoms of the GM of PbB₂⁻ (1) colinearly, significantly weakening the B–Pb bonds while strengthening the B–B bonds of the PbB₂ unit. The second lowest-lying isomer (4C_2v, ²B₂) is less stable than the GM by ∼0.95 eV at both the PBE0 and CCSD(T) levels (Fig. S3, ESI†). It has a Y-shaped structure (Fig. 4), similar to the recently reported C_2v PbB₃O₂⁻,⁷⁶ and can be viewed as two boronyl groups and one Pb–B unit coordinated to a central B atom. Overall, the GM structures of PbB₂⁻ (1), PbB₃O⁻ (2), and PbB₄O₂⁻ (3) can be expressed as [PbB₂(BO)_n]⁻ (n = 0–2), i.e., zero, one, and two boronyl ligands coordinated to a triangular PbB₂ core.

5 Discussion

5.1 Comparison between experiment and theory

The predicted VDEs are summarized in Tables 1–3 for the GM structures of PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻, respectively, in comparison with the experimentally measured values, as well as in Fig. 5–7. The computed ADE/VDE₁ values for the GM structures of PbB₂(BO)_n⁻ (n = 0–2) and the VDE₁ for the low-lying isomer of PbB₄O₂⁻ are compared with the experimental results in Table 4. The theoretical VDEs were calculated using the CCSD(T) method for VDE₁ and using the SA-CASSCF method for higher VDEs. The valence molecular orbitals (MOs) of the GM structures of PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻ are depicted in Fig. S4 (ESI†).

Fig. 5 Comparison of the photoelectron spectrum of PbB₂⁻ with the computed VDEs. The vertical bars correspond to the computed VDEs using the CCSD(T) + SA-CASSCF method. The shortest bars correspond to singlet final states and the slightly longer bars correspond to triplet final states, and the longest bars indicate degenerate states at the same energy.

Fig. 6 Comparison of the photoelectron spectrum with the computed VDEs for the GM of PbB₃O⁻. The vertical bars correspond to the computed VDEs using the CCSD(T) + SA-CASSCF method.

Fig. 7 Comparison of the photoelectron spectrum with the computed VDEs for the C_2v GM of PbB₄O₂⁻. The vertical bars correspond to the computed VDEs using the CCSD(T) + SA-CASSCF method. The shortest bars correspond to singlet final states and the slightly longer bars correspond to triplet final states, and the longest bars indicate degenerate states at the same energy. Note that the detachment channel corresponding to band E has a computed VDE of 4.70 eV (Table 3), slightly out of the scale of the figure. The PES bands X′ and A′ are due to isomer 4 (see Fig. S5, ESI†).

Table 4 Comparison of the experimental ADE and VDE₁ with calculated values for the GM of PbB₂(BO)_n⁻ (n = 0–2) and a low-lying isomer for n = 2 at the PBE0/AVTZ and CCSD(T)/AVTZ levels. All energies are given in eV

Species	final state	ADE (theo.)		VDE1 (theo.)		ADE (exp)^a	VDE1 (exp)^a
		PBE0	CCSD(T)	PBE0	CCSD(T)
a The experimental uncertainty was estimated to be ±0.02 eV. b Measured from the observed weak band X′ in Fig. 3.
PbB2^−C2v (1)	^1A1	2.26	1.91	2.29	1.94	2.03	2.08
PbB3O^−, Cs (2)	^2A′′	3.10	3.16	3.18	3.21	3.08	3.10
PbB4O2^−, C2v (3)	^1A1	2.86	2.75	3.01	2.88	2.84	2.88
C 2v (4)	^1A1	3.27	3.16	3.29	3.16		3.13^b

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5.1.1. PbB₂⁻. For the C_2v GM of PbB₂⁻ (1), detachment of the electron from the 4a₁ SOMO (Fig. S4a, ESI†) leads to the singlet ¹A₁ ground state of neutral PbB₂O (Table 1). The calculated ADE of 1.91 eV and VDE₁ of 1.94 eV at the CCST(T) level agree well with the experimental values at 2.03 eV and 2.08 eV, respectively (Table 4). The next two detachment channels are derived from the removal of the β electron from the 3a₁ HOMO-2 and the 1b₁ HOMO-1, resulting in the triplet ³A₁ and ³B₁ final states, respectively (Table 1). The ³A₁ state splits into three closely-spaced SO states ³A₁₍₀₎, ³A₁₍₋₁₎, and ³A₁₍₊₁₎ with predicted VDEs of 2.52, 2.52, and 2.61 eV, while the ³B₁ state also gives rise to three SO states ³B₁₍₊₁₎, ³B₁₍₋₁₎, and ³B₁₍₀₎ with computed VDEs of 2.69, 2.86, and 2.90 eV, respectively (Table 1). These SO states should account for the observed PES bands A (2.48 eV), B (2.65 eV), and C (2.91 eV). The next two singlet final states ¹A₁ and ¹B₁ with the calculated VDEs of 3.11 and 3.25 eV are derived by removing the α electron from the HOMO-2 (3a₁) and the HOMO-1 (1b₁), in good agreement with the observed bands D and E at 3.03 and 3.15 eV, respectively. Detachment of the β electron from the deeper HOMO-3 (1b₂) results in the triplet ³B₂ final state, which gives rise to three SO-split final states, ³B₂₍₀₎, ³B₂₍₊₁₎, and ³B₂₍₋₁₎. These final states along with detachment from even deeper MOs should account for the congested PES signals beyond 3.5 eV. Overall, the theoretical VDEs for PbB₂⁻ with the SO effects are in good agreement with the experimental data (Fig. 5), confirming triangular structure 1 as the GM of PbB₂⁻.

5.1.2. PbB₃O⁻. The C_s GM of PbB₃O⁻ (2) possesses a closed-shell electronic configuration with a ¹A′ ground state and thus only doublet final states are expected upon one-electron detachment. The first detachment channel corresponds to the removal of an electron from the HOMO (2a′′) (Fig. S4b, ESI†), giving rise to a ²A′′ neutral ground state (Table 2). The calculated ADE/VDE₁ values are 3.16/3.21 eV at the CCSD(T) level (Table 4), in reasonable agreement with experimental values of 3.08/3.10 eV. Following a small energy gap of 0.27 eV, the second and third VDEs are predicted to be 3.48 eV and 3.96 eV (Table 2), resulting from electron detachment from the HOMO-2 (7a′) and the HOMO-1 (8a′), respectively. These two VDEs, separated by 0.48 eV, are consistent with observed bands A (3.32 eV) and B (3.85 eV). The energy intervals of these three detachment channels can well reproduce the observed energy gaps between bands X and A (0.22 eV) and between bands A and B (0.53 eV), as shown in Table 2 and Fig. 6. The observed vibrational structures with a spacing of ∼480 cm⁻¹ in band B are consistent with the calculated frequency for the terminal Pb–B stretching mode at 533 cm⁻¹. The good agreement between the theoretical and experimental results lends considerable credence to the predicted GM of PbB₃O⁻ (2).

5.1.3. PbB₄O₂⁻. The calculated VDE₁ for the C_2v GM of PbB₄O₂⁻ (3) at the CCSD(T) level is 2.88 eV due to the electron detachment of the 5b₂ SOMO (Fig. S4c, ESI†), in excellent agreement with the observed band X at 2.88 eV. The ground state ADE is predicted as 2.75 eV at the CCSD(T) level, compared to the experimental value of 2.84 eV (Table 4). Detachment of the β electron from the HOMO-1 (7a₁) gives rise to the triplet ³B₂ final state, which results in three SO states ³B₂₍₀₎, ³B₂₍₋₁₎, and ³B₂₍₊₁₎ with calculated VDEs of 3.86, 3.86, and 3.91 eV, respectively, in agreement with the observed intense band A at 3.82 eV (Table 3). The removal of one electron from the 2b₁ HOMO-2 can produce a triplet ³A₂ state and a singlet ¹A₂ final state. The ³A₂ state splits into three SO states ³A₂₍₁₎, ³A₂₍₋₁₎, and ³A₂₍₀₎ with calculated VDEs of 4.03, 4.15, and 4.38 eV, respectively. The singlet ¹A₂ final state yields a calculated VDE of 4.34 eV. The SO states ³A₂₍₁₎ and ³A₂₍₋₁₎ agree well with the PES bands B and C at 4.01 and 4.15 eV, respectively, whereas the SO state ³A₂₍₀₎ and the singlet ¹A₂ state have similar VDEs, in agreement with band D at 4.33 eV. The next detachment channel with a calculated VDE of 4.70 eV corresponds to the ¹B₂ singlet final state due to the detachment of the α electron from the 7a₁ HOMO-1, in good agreement with the observed band E at 4.53 eV.

It should be noted that the calculated VDEs for the C_2v GM of PbB₄O₂⁻ (3) cannot interpret the observed minor bands X′ at 3.13 eV and A′ at 3.40 eV. However, the first two detachment channels of the second isomer, the Y-shaped C_2v PbB₄O₂⁻ (4), with the calculated VDEs of 3.16 and 3.45 eV (Table S1 and Fig. S5, ESI†), respectively, reproduce well the experimental VDEs of bands X′ and A′. Moreover, the next two detachment channels (3.71 and 4.52 eV) of 4 may contribute weakly to bands A and E at 3.82 and 4.53 eV, respectively (Table S1 and Fig. S5, ESI†). The Y-shaped isomer 4 is 0.95 eV higher in energy than the GM structure 3 at the CCSD(T) level (Fig. S3, ESI†). Thus, it was surprising that Y-shaped isomer 4 was present in the experiment at all. There is likely a large kinetic barrier between the two structures, providing dynamic stability for 4 relative to GM 3. Overall, the excellent agreement between the theoretical and experimental data provides considerable credence to the identified GM of PbB₄O₂⁻ (3) and the existence of the low-lying isomer 4.

5.2 Aromaticity in [PbB₂(BO)_n]⁻ (n = 0–2)

The GM structures of the three Pb/B clusters can be viewed as starting from a triangular PbB₂⁻ unit with successive addition of a boronyl unit in PbB₃O⁻ [PbB₂(BO)⁻] and PbB₄O₂⁻ [PbB₂(BO)₂⁻]. These structural features again confirm the previous finding that the boronyl unit, isoelectronic to CN,⁵⁰ is a strong ligand.^{51,53,56–68} To understand the intrinsic nature of the high stability of the experimentally observed [PbB₂(BO)_n]⁻ (n = 0–2) clusters, we analyzed the chemical bonding for the GM structures of PbB₂⁻ (1) and PbB₃O⁻ (2), as well as that of PbB₄O₂⁻ (3) and its corresponding neutral PbB₄O₂ (3′, Fig. 4) using the AdNDP method, as shown in Fig. 8. The AdNDP bonding analyses for the low-lying Y-shaped C_2v PbB₄O₂⁻ (4) is presented in Fig. 9.

Fig. 8 AdNDP bonding analyses for the GM of (a) C_2v PbB₂⁻ (1), (b) C_s PbB₃O⁻ (2), (c) C_2v PbB₄O₂⁻ (3), and (d) C_2v PbB₄O₂ (3′) at the PBE0/B,O/def2-TZVP/Pb/def2-TZVPP level. Isovalues for σ orbitals and π orbitals are 0.06 and 0.05, respectively. ON indicates the occupation numbers.

Fig. 9 The AdNDP bonding analysis for the Y-shaped C_2v PbB₄O₂⁻ (4) at the PBE0/B,O/def2-TZVP/Pb/def2-TZVPP level. Isovalues for σ orbitals and π orbitals are 0.06 and 0.05, respectively. ON indicates the occupation numbers.

The AdNDP bonding analysis revealed that the C_2v GM of PbB₂⁻ (1) possesses one Pb 6s lone pair, one 2c-1e B–B σ bond, two 2c-2e Pb–B σ bonds, one delocalized 3c-2e Pb–B–B σ bond, and one delocalized 3c-2e Pb–B–B π bond (Fig. 8a). Due to the strong relativistic effects,¹⁰⁷ the 6s orbital is significantly stabilized and acts like a lone pair with little 6s-6p hybridization, similar to that found in Bi–B clusters.^66,108 The Pb–B bonding is basically obtained through the 6p orbitals of Pb and the sp orbitals of B. The PbB₂⁻ cluster exhibits σ + π double aromaticity with two σ and two π delocalized electrons fulfilling the 4N + 2 Hückel rule for each system. When boronyl units are successively added to PbB₂⁻ to produce PbB₃O⁻ [PbB₂(BO)⁻] and PbB₄O₂⁻ [PbB₂(BO)₂⁻], the B–B σ bond in PbB₂⁻ is consumed to form new B–BO σ bonds, while the two localized Pb–B σ bonds are transformed to two delocalized Pb–B₂ σ bonds. As shown in Fig. 8b, the C_s GM structure of PbB₃O⁻ (2) displays one Pb 6s lone pair, one 2c-2e B–BO σ bond, and a terminal B≡O group (one 1c-2e O lone pair, the B≡O triple bond: one 2c-2e B–O σ bond, and two 2c-2e B–O π bonds). The bonding between Pb and B₂ in 2 consists of three delocalized σ bonds and one delocalized π bond. Thus, the closed-shell C_s PbB₃O⁻ (2) is doubly aromatic with six σ and two π delocalized electrons.

The AdNDP analysis for the C_2v GM structure of PbB₄O₂⁻ (3) readily identified the Pb 6s lone pair, two 2c-2e B–BO σ bonds, and two terminal B≡O triple bonds (Fig. 8c). The remaining valence electrons in the open-shell 3 consist of one 3c-1e σ bond, two 3c-2e σ bonds, and one 3c-2e delocalized π bond over the triangular PbB₂ core, giving rise to five delocalized σ electrons and two delocalized π electrons. When the unpaired electron of 3 is detached to form the closed-shell neutral C_2v PbB₄O₂ (3′), the singly occupied 3c-1e σ bond is removed, and one of the delocalized 3c-2e σ bonds is transformed to the localized 2c-2e B–B bond. The closed-shell 3′, thus, possesses one delocalized 3c-2e σ bond and one delocalized 3c-2e π bond on its PbB₂ unit (Fig. 8d), making it σ + π doubly aromatic with two σ and two π delocalized electrons.

To quantitatively assess the double aromatic character of C_2v PbB₂⁻ (1), C_s PbB₃O⁻ (2), and C_2v PbB₄O₂^−/0 (3 and 3′), NICS_zz(ζ) values of these clusters were calculated and compared with those of B₃⁻ clusters shown in Table 5. NICS values are usually calculated using the ring critical points,^109,110 but the PbB₂ triangle does not have one. The centres of the ring currents (Fig. S6 and Table S2, ESI†) are used instead of the ring critical points. For these Pb/B species, all examined points located within or above the molecular planes possess large negative NICS_zz values, and the NICS_zz values decrease significantly as the ζ values increase from 0 to 1 Å (Table 5). These phenomena appear to be similar to the computed NICS_zz values for the prototypical σ + π doubly aromatic B₃⁻. We conclude that C_2v PbB₂⁻ (1), C_s PbB₃O⁻ (2), and C_2v PbB₄O₂^−/0 (3 and 3′) are σ + π doubly aromatic in nature, in agreement with the AdNDP results discussed above.

Table 5 NICS_zz(ζ) values (ppm) of C_2v PbB₂⁻ (1), C_s PbB₃O⁻ (2), C_2v PbB₄O₂^−/0 (3 and 3′), and D_3h B₃⁻ computed at the centres of the ring current using the ADF code with the PBE0/TZP all-electron basis, including the noncollinear spin–orbit coupling effect

	PbB2^−	PbB3O^−	PbB4O2^−	PbB4O2	B3^−
ζ = 0.0	−183.9	−136.4	−193.5	−209.1	−76.5
ζ = 0.2	−173.4	−128.7	−185.3	−188.7	−74.2
ζ = 0.4	−149.8	−111.5	−165.3	−144.3	−67.7
ζ = 0.6	−126.0	−94.9	−142.0	−103.2	−58.6
ζ = 0.8	−106.8	−82.1	−119.8	−75.4	−49.0
ζ = 1.0	−90.4	−71.2	−99.4	−56.9	−40.0

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5.3 Multiple B–B bonding in [PbB₂(BO)_n]⁻ (n = 0–2)

According to the chemical bonding analyses shown in Fig. 8, [PbB₂(BO)_n]⁻ (n = 0–2) exhibit obvious multiple B–B bonding characteristics. With two 2c-2e Pb–B σ bonds, one 2c-1e B–B σ bond, and two delocalized 3c-2e σ/π bonds (Fig. 8a), C_2v PbB₂⁻ (1) possesses two Pb–B single bonds and one B–B double bond with the NRT bond orders of 1.04 and 1.68 (Table S3, ESI†), respectively. The Pb–B bond length and B–B bond length in 1 are 2.283 Å and 1.553 Å (Fig. 4), respectively, in good accord with the Pb–B single-bond length (2.29 Å) and B=B double-bond length (1.56 Å) predicted from Pyykkö's additive atomic covalent radii,¹¹¹ respectively. Compared with the C_2v PbB₂⁻ (1) which possesses three localized σ bonds (Fig. 8a), C_s [PbB₂(BO)]⁻ (2) and C_2v [PbB₂(BO)₂]⁻ (3) both have four delocalized σ/π bonds covered on their PbB₂ cores (Fig. 8b and c), causing the Pb–B bonding to be weakened, while the B–B bonds to be strengthened. The less symmetric 2 contains one weakened Pb–B bond with a NRT bond order of 0.63, one strengthened terminal Pb–B bond with a bond order of 1.55, and one strengthened B–B bond with a bond order of 1.78 (Table S3, ESI†). The terminal Pb–B bond length of 2.147 Å in 2 (Fig. 4) is consistent with the Pb=B double-bond length of 2.13 Å, based on Pyykkö's atomic covalent radii.¹¹¹ The central B–B bond length of 1.515 Å lies between the B=B double-bond length (1.56 Å) and the B≡B triple-bond length (1.46 Å) predicted by Pyykkö's atomic covalent radii.¹¹¹

The two delocalized 3c-2e σ bonds and one delocalized 3c-2e π bond in the open-shell C_2v PbB₄O₂⁻ (3) are mainly concentrated on the B–B moiety of the PbB₂ core (Fig. 8c). The central B–B bond with a NRT bond order of 1.76 is shortened to 1.498 Å (Fig. 4) which is close to the B≡B triple bond (1.46 Å) based on Pyykkö's atomic covalent radii. It is worth noting that the delocalized 3c-1e σ bond in 3 exhibits clearly partial anti-bonding nature, mainly derived from a Pb 6p orbital (Fig. 8c). With the unpaired electron detached, the length of the central B–B bond with the NRT bond order of 1.86 in neutral C_2v PbB₄O₂⁻ (3′) is further shortened to 1.478 Å which can be approximately treated as a B≡B triple bond. In fact, the B≡B triple bond length in 3′ is slightly shorter than the corresponding value of 1.481 Å previously reported in the perfect linear D_∞h B₂(BO)₂²⁻ and slightly longer than that (1.468 Å) observed in D_∞h B₂(CO)₂.^53,112 Natural bonding orbital (NBO) analyses indicated that there exist substantial charge transfers from the Pb atoms to the B₄O₂ units in C_2v PbB₄O₂^−/0 (3 and 3′) (0.45 |e| for 3, 1.09 |e| for 3′). Thus, these two charge-transfer complexes can be approximately viewed as Pb⁺/Pb²⁺ units weakly interacting with the linear B₂(BO)₂²⁻ motifs, i.e., Pb⁺[B₂(BO)₂²⁻]/Pb²⁺[B₂(BO)₂²⁻], with Pb–B bond lengths (2.383 Å for 3, 2.399 Å for 3′; Fig. 4) obviously longer than the Pb–B single bond (2.29 Å).¹¹¹

5.4 Multiple Pb–B and B–B bonding in Y-shaped PbB₄O₂^−/2−

The structure of the low-lying Y-shaped isomer C_2v PbB₄O₂⁻ (4) is interesting. Our AdNDP analysis for 4 (Fig. 9) showed the Pb 6s lone pair, two O lone pair lone pairs, two B≡O triple bonds, and two B–B≡O single bonds. The remaining valence electrons form one 2c-2e B–B σ bond, one 3c-2e B–B–Pb π bond, one 2c-2e Pb–B σ bond, and one 2c-1e Pb–B π bond, resulting in the B=B bond and the Pb–B bond along the two-fold main molecular axis which have the formal bond orders of 2.0 and 1.5, respectively. The B=B double bond length of 1.565 Å in 4 (Fig. 4) is comparable to the corresponding value of 1.56 Å obtained from Pyykkö's double-bond covalent atomic radii.¹¹¹ The Pb–B length of 2.195 Å lies between the Pb–B single bond length (2.29 Å) and the Pb=B double-bond length (2.13 Å) computed from Pyykkö's covalent atomic radii, consistent with its formal bond order of 1.5. Adding an electron to 4 yields the closed-shell C_2v PbB₄O₂²⁻ (4′, Fig. 4) with an even shortened Pb–B bond length of 2.188 Å, closer to a Pb=B double bond (2.13 Å).¹¹¹ Thus, the Y-shaped C_2v PbB₄O₂²⁻ (4′) can be formulated as [Pb=B=B(B≡O)₂]²⁻. NRT analyses predicted a B–B bond order of 1.59 for 4 and 1.69 for 4′, which are slightly lower than 2.0 due to the existence of the delocalized B–B–Pb 3c-2e π bond. The calculated NRT bond orders for Pb–B in 4 and 4′ are 1.72 and 2.08, respectively, consistent with the 1.5 bond order for the Pb–B multiple bond in 4 and the Pb=B double bond in 4′, respectively. The central B atom in 4′ undergoes sp² hybridization and forms two single B–B bonds with the two boronyl ligands and a double bond with the B atom bonded to Pb. The B atom that is bonded to Pb undergoes sp hybridization, forming a Pb=B double bond and a B=B double bond, similar to the central C atom in the allene molecule (H₂C=C=CH₂). In other words, the closed-shell C_2v PbB₄O₂²⁻ (4′) is an electron-precise molecule with distinct hybridizations for the two central B atom and it is isovalent with Pb=C=CH₂ and should be a highly stable species. However, the open-shell C_2v PbB₄O₂⁻ (4) misses one electron, which may explain why it is less stable than the C_2v GM of PbB₄O₂⁻ (3). Nevertheless, it is conceivable that a large energy barrier may exist from isomer 4 to GM 3, allowing 4 to be present in the experiment despite its relatively high energy.

6. Conclusion

In conclusion, we report an investigation on the structures and chemical bonding of three lead-boron clusters, PbB₂⁻, PbB₃O⁻, and PbB₄O₂⁻, using photoelectron spectroscopy and ab initio calculations. The global minima of these three species are found to be planar and can be formulated as [PbB₂(BO)_n]⁻ (n = 0–2), consisting of a triangular PbB₂ core coordinated by zero, one, and two boronyl ligands, respectively. In addition, a Y-shaped low-lying isomer with a Pb=B=B unit coordinated by two BO ligands to the terminal B atom was also observed to be present in the cluster beam of PbB₄O₂⁻. Chemical bonding analyses indicate that the global minima of PbB₂⁻ and PbB₃O⁻ have 2σ/2π and 6σ/2π delocalized electrons, respectively, rendering them doubly aromatic. The global minimum of the C_2v PbB₄O₂⁻ contains 5σ/2π delocalized electrons and is also shown to display double aromaticity. The Pb and B₂ bonding is weak in the global minimum of PbB₄O₂⁻ and its corresponding neutral species of PbB₄O₂, which can be alternatively viewed as Pb^+/2+ units coordinated to the linear B₄O₂²⁻ ligand with the B≡B triple bond. The open-shell Y-shaped C_2v PbB₄O₂⁻ isomer contains a Pb–B multiple bond with a bond order of 1.5, while the closed-shell Y-shaped PbB₄O₂²⁻ possesses a Pb=B double bond with the bond order of 2.0, which is an electron-precise molecule with distinct hybridization for the two B atoms, [Pb=B=B(BO)₂]²⁻. Investigation of the lead-boron cluster enriches the understanding of Pb–B bonding and provides new insights for the rational design of novel Pb–B molecules and potential lead boride materials.

Author contributions

W. J. C. and T. T. C. performed the experiments. Q. C., X. Y. W., R. N. Y., and H. G. L. performed the computational calculations. S. D. L. and L. S. W. guided the work. Q. C., W. J. C., D. F. Y., S. D. L., and L. S. W. wrote and revised the manuscript. All authors analyzed the experimental and theoretical results.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgements

We thank Dr H. S. Hu for help with the NICSzz calculations. This work was supported by the US National Science Foundation (CHE-2053541 to L.S.W.) and the National Natural Science Foundation of China (22003034 to Q. C., 21973057 and 21720102006 to S.D.L.). Q.C. gratefully acknowledges the start-up fund from Shanxi University for the support.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp02800c

‡ Q. Chen, W.-J. Chen and X-Y. Wu contributed equally to this work.

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