Sc@B₂₈⁻, Ti@B₂₈, V@B₂₈⁺, and V@B₂₉²⁻: Spherically Aromatic Endohedral Seashell-like Metallo-Borospherenes

Abstract

Transition-metal-doped boron nanoclusters exhibit unique structures and bonding in chemistry. Using the experimentally observed seashell-like borospherenes C₂ B₂₈^−/0 and C_s B₂₉⁻ as ligands and based on extensive first-principles theory calculations, we predict herein a series of novel transition-metal-centered endohedral seashell-like metallo-borospherenes C₂ Sc@B₂₈⁻ (1), C₂ Ti@B₂₈ (2), C₂ V@B₂₈⁺ (3), and C_s V@B₂₉²⁻ (4) which, as the global minima of the complex systems, turn out to be the boron analogues of dibenzenechromium D_6h Cr(C₆H₆)₂ with two B₁₂ ligands on the top and bottom interconnected by four or five corner boron atoms on the waist and one transition-metal “pearl” sandwiched at the center in between. Detailed molecular orbital, adaptive natural density partitioning (AdNDP), and iso−chemical shielding surface (ICSS) analyses indicate that, similar to Cr(C₆H₆)₂, these endohedral seashell-like complexes follow the 18-electron rule in bonding patterns (1S²1P⁶1D¹⁰), rendering spherical aromaticity and extra stability to the systems.

1. Introduction

Extensive joint photoelectron (PE) spectroscopy and first-principles theory investigations in the past two decades have unveiled a great structural diversity in boron nanoclusters featuring multi-center-two-electron (mc-2e, m ≥ 3) bonding, including the planar or quasi-planar (2D) B_n^−/0 (n = 3–38, 41, 42) [1,2,3], cage-like D_2d B₄₀^−/0 and C₃/C₂ B₃₉⁻ [4,5], and bilayer D_2h B₄₈^−/0[6], with the smallest seashell-like C₂ B₂₈^−/0 [7] and C_s B₂₉⁻ [8] observed in gas phases competing with their 2D counterparts in experiments. Based on the experimentally observed cage-like B₄₀^−/0 and B₃₉⁻, the borospherene family have been extended to the B_n^q series (n = 36−42, q = n − 40) in theory [9,10,11]. Theoretical investigations have shown that metal-decorated seashell-like B₂₈ may serve as effective potential hydrogen storage materials [12]. The first theoretically predicted perfect cage-like B₈₀ in 2007 [13,14] spurred renewed interest in all-boron fullerenes although it was later proved to favor core–shell structures. The bilayer structural motif observed in B₄₈^−/0 has been extended to B₄₈-B₇₂ and B₈₄–B₉₈ at the density functional theory (DFT) level, with a bilayer bottom-up approach based on the experimentally observed C_6v B₃₆ proposed for the observed bilayer BL-α⁺ borophenes on Ag (111) [15,16,17,18,19]. Mononuclear core–shell B₆₈, B₇₄, B₈₀, B_84, B₉₆, B₁₀₀, B₁₀₁, B_102, and B₁₁₂ and binuclear core–shell C_s B₁₈₀ ((B₁₂)₂@B₁₅₆), C_s B₁₈₂ ((B₁₂)₂@B₁₅₈), and C_s B₁₈₄ ((B₁₂)₂@B₁₆₀) with two interconnected icosahedral B₁₂ cores at the center have also been predicted at DFT, with C_s B₁₁₂ and C_s B₁₈₄ as the most stable mononuclear and binuclear species reported to date in thermodynamics [20,21,22,23,24,25,26,27], respectively. Transition-metal doping proves to induce dramatic structural changes in boron nanoclusters. Perfect transition-metal-centered wheel-like D_8h Co©B₈⁻, D_9h M©B₉⁻(M = Rh, Ir, Re), and D_10h M©B₁₀⁻(M = Ta, Nb), [28,29,30] half-sandwich C_3v CoB₁₂⁻ and IrB₁₂⁻, and double–ring tubular drum-like D_8d CoB₁₆⁻, MnB₁₆⁻, and RhB₁₈⁻, C_s B₂–Ta@B₁₈⁻, and D_10d Ta@B₂₀⁻ have been observed in experiments [31,32,33,34], with Ta@B₂₀⁻ possessing the highest coordination number of CN = 20 in tubular species [35]. Perfect lanthanide-metal-doped inverse sandwich D_nh La₂B_n⁻ (n = 7–9) and spherical trihedral metallo-borospherenes La₃B₁₈⁻ and Tb₃B₁₈⁻ have also been reported in experiments [36,37]. With inspirations from these experimental observations, our group predicted the smallest core–shell spherical trihedral metallo-boronospherene D_3h La₃[B₂@B₁₈]⁻, perfect spherically aromatic tetrahedral metallo-borospherenes T_d La₄B₂₄ and core–shell T_d La₄B₂₉^0/+/− (La₄[B@B₄@B₂₄]^0/+/−), endohedral metallo-borospherenes O_h La₆&[La@B₂₄]^+/0, and the spherically aromatic trihedral metallo-borospherene D_3h La₆B₃₀ in a series of recent papers [38,39,40,41]. Spherical trihedral metallo-borospherenes and endohedral Complexes of B₂₀TM_n (TM = Sc, Y; n = 3, 4) were predicted recently [42]. The Ta-centered metallo-borospherenes Ta@B₂₂⁻ and Ta@B_n^q (n = 23–28, q = −1–3) which follow the 18-electron rule, the smallest trihedral metallo-borospherene D_3h Ta₃B₁₂⁻ with three equivalent octacoordinate Ta centers in three η⁸–B₈ rings, and spherical tetrahedral metallo–borospherene T_d Ta₄B₁₈ with four equivalent nonacoordinate Ta centers in four η⁹–B₉ rings conforming to the 18-electron principle were proposed recently [43,44,45,46]. Alkaline-earth-metal-centered M@B₄₀ (M = Ca, Sr) [47] and actinide-metal-centered U@B₄₀ [48] were also predicted in theory. However, to the best of our knowledge, spherically aromatic transition-metal-centered endohedral metallo-borospherenes based on the experimentally observed seashell-like C₂ B₂₈^−/0 and C_s B₂₉⁻ as the global minima (GM) of the systems have not been reported in the literature.

As boron analogues of benzene (D_6h C₆H₆), the experimentally observed quasi-planar C_3v B₁₂ with three delocalized π bonds was first utilized as ligands to form the perfect sandwich-like complex D_3d Cr(B₁₂)₂ [49,50]. Unfortunately, such a manually designed complex appears to be a high-lying local minimum of the system unlikely to be produced in experiments. Using the experimentally observed smallest seashell-like borospherenes C₂ B₂₈^−/0 and C_s B₂₉⁻ as ligands which contain two B₁₂ ligands on the top and bottom interconnected by four or five corner boron atoms on the waist and based on extensive GM searches augmented with first-principles theory calculations, we predict in this work a series of transition-metal-centered seashell-like metallo-borospherenes C₂ Sc@B₂₈⁻ (1), C₂ Ti@B₂₈ (2), C₂ V@B₂₈⁺ (3), and C_s V@B₂₉²⁻(4) which, as the GMs of the systems with two interconnected B₁₂ ligands on the top and bottom and one transition metal center as the “pearl” sandwiched in between, follow the 18-electron rule in bonding patterns, making the transition-metal-doped boron complexes spherically aromatic in nature, highly stable in both thermodynamics and dynamics and possible to be targeted in future experiments.

2. Results and Discussions

2.1. Structures and Stabilities

The obtained transition-metal-centered seashell-like metallo-borospherenes C₂ Sc@B₂₈⁻ (1), C₂ Ti@B₂₈ (2), C₂ V@B₂₈⁺ (3), and C_s V@B₂₉²⁻ (4) as the GMs of the systems at PBE0/6-311+G(d) [51], TPSSh/6-311+G(d) [52,53], and CCSD(T)/6-31G(d) [54,55] levels are collectively depicted in Figure 1, with more alternative low-lying isomers summarized in Figures S1–S4 (ESI†). The isovalent Sc@B₂₈⁻ (1), Ti@B₂₈ (2), and V@B₂₈⁺ (3) with the calculated coordination energies of E_c = 9.56, 7.83, 7.57 eV and lowest calculated vibration frequencies of 181.13, 186.63, 184.70 cm⁻¹ at PBE0, respectively, turn out to have similar seashell-like structures in the same symmetry as their parent C₂ B₂₈ ligand [7], with two B₁₂ ligands on the top and bottom interconnected by four corner boron atoms on the waist and one transition metal pearl comfortably sandwiched in between. These axially chiral endohedral metallo-borospherene complexes contain a slightly distorted C₂ B₁₆ double-ring tube as the basis of the seashell-like structures, two heptagonal windows on the right and left, and thirty-six B₃ triangles on the cage surface, with a transition metal center sandwiched comfortably inside the B₂₈ cage along the C₂ molecular axis on the upper end of the B₁₆ double-ring tube (see detailed coordination bond lengths tabulated in Table S1). C₂ Sc@B₂₈⁻ (1), Ti@B₂₈ (2), V@B₂₈⁺ (3) possess the large calculated HOMO-LUMO energy gaps of ΔE_gap = 2.10, 2.97, and 3.20 eV at PBE0, respectively, well supporting their high chemical stabilities. It is noticed that the second isomer C₂ Sc&B₂₈⁻ (1b) in Figure S1, an exohedral metallo-borospherene with an octacoordinate Sc atom at the lower end of the B₁₆ double-ring tube, is actually iso-energetic with Sc@B₂₈⁻ (1) at CCSD(T), suggesting that the two degenerate C₂ isomers may coexist in experiments, while, as shown in Figures S2 and S3, the endohedral Ti@B₂₈ (2) and V@B₂₈⁺ (3) are 0.18 eV and 0.04 eV more stable than their second lowest-lying isomers at CCSD(T), respectively. Triplet and quintet isomers prove to be at least 0.85 eV less stable than their singlet GMs.

The optimized V-centered C_s V@B₂₉²⁻ (4) also possesses a seashell-like endohedral structure in the same symmetry as its parent ligand C_s B₂₉⁻ [8]. It contains two B₁₂ ligands on the top and bottom interconnected by five corner boron atoms on the waist, two equivalent octagonal windows on the right and left sides, and thirty-eight B₃ triangles on the cage surface, with a vanadium center coordinated inside. With a large calculated HOMO-LUOM energy gap of ΔE_gap = 2.39 eV, coordination energy of E_c = 4.79 eV and one small imagery vibrational frequency at −54.30 cm⁻¹, C_s V@B₂₉²⁻(4) appears to be the vibrationally averaged GM of the system between two slightly distorted C₁ V@B₂₉²⁻ isomers (4b in Figure S4) in an a″ vibrational mode in which the top B atom and V center swinging left and right reversibly. With zero-point corrections included, C_s V@B₂₉²⁻(4) turns out to be 0.02 eV and 0.06 eV more stable than the second seashell-like isomer C₁ V@B₂₉²⁻ (4b) and third tubular isomer C_s V@B₂₉²⁻ (4c) at CCSD(T), respectively (Figure S4). Triplet and quintet isomers are found to be 0.74 eV and 1.81 eV less stable than singlet C_s V@B₂₉²⁻(4) at PBE0 level, respectively, and all the other isomers lying at least 0.15 eV higher than the C_s GM (4).

Detailed natural bonding orbital (NBO) [56] analyses indicate that transition metal centers in Sc@B₂₈⁻ (1), Ti@B₂₈ (2), V@B₂₈⁺ (3), and V@B₂₉²⁻ (4) possess the net atomic charges 0.76, 0.36, -0.33, and -0.37 |e|, electronic configurations of Sc ([Ar]4s^0.193d^1.42), Ti ([Ar]4s^0.213d^2.02), V ([Ar]4s^0.223d^4.26), and V ([Ar]4s^0.203d^4.48), and total Wiberger bond orders of 4.03, 6.02, 6.70, and 6.44, respectively. Obviously, transition metal coordination centers in these complexes donate their 4s² electrons almost completely to the boron ligands, while in return, accept partial electrons in their partially filled 4d orbitals from the boron ligands via effective π→3d back-donations, enhancing the thermodynamical stabilities of systems.

Extensive Born–Oppenheimer molecular dynamics (BOMD) [57] simulations on Sc@B₂₈⁻ (1) at 600 K, Ti@B₂₈ (2) at 700 K, and V@B₂₉²⁻ (4) at 700 K in Figure S5 clearly indicate that these seashell-like transition metal boron complexes are highly dynamically stable at high temperatures, as evidenced by their small calculated root-mean-square-deviations of RMSD = 0.09, 0.10, 0.10 Å and maximum bond length deviations of MAXD = 0.30, 0.32, 0.33 Å, respectively. No high-lying isomers were observed during the simulations in 30 ps, with the basic structural motifs of the complex systems well maintained in reversible thermal vibrations.

2.2. Bonding Pattern Analyses

To better comprehend the high stabilities of these seashell-like endohedral complexes, detailed adaptive natural density partitioning (AdNDP) [58,59] bonding analyses are performed on Ti@B₂₈ (2) and V@B₂₉²⁻ (4) in Figure 2, in comparison with that of the prototypic sandwich complex D_6h (C₆H₆)₂Cr. As indicated in Figure 2a, D_6h (C₆H₆)₂Cr possesses 12 2c-2e C-C σ bonds and 12 2c–2e C–H σ bonds on the two C₆H₆ ligands with the occupation numbers ON = 1.95 |e|. Its remaining nine delocalized coordination bonds include 3 7c–2e C₆ (π)–Cr (d_π/σ) bonds between the Cr center and C₆H₆ ligand on the top, 3 7c-2e C₆ (π)–Cr (d_π/σ) bonds between the Cr center and C₆H₆ ligand at the bottom, and 3 13c C₆ (π)–Cr (d_π/σ)–C₆ (π) bonds between Cr center and the two C₆H₆ ligands with ON = 1.93~2.00 |e|, well demonstrating that D_6h (C₆H₆)₂Cr satisfies the 18-electron rule.

Detailed AdNDP analyses presented in Figure 2b indicate that neutral seashell-like C₂ Ti@B₂₈ (2) contains 34 3c–2e σ bonds on 34 B₃ triangles on the cage surface and 1 4c–2e σ bond shared by two edge-sharing B₃ triangles on the upper end, forming the σ-framework of the seashell-like complex. Its remaining nine delocalized coordination bonds include three 13c–2e B₁₂ (π)–Ti (d_π/σ) bonds between the Ti center and B₁₂ ligand on the top, three 13c–2e B₁₂ (π)–Ti (d_π/σ) between the Ti center and B₁₂ ligand at the bottom, and three 27c–2e B₁₃ (π)–Ti (d_π/σ)–B₁₃ (π) bonds mainly between Ti and its two B₁₂ ligands on the top and bottom with ON = 1.88~2.00 |e|. Such a delocalized coordination bonding pattern possesses a one-to-one correspondence relationship with that of D_6h (C₆H₆)₂Cr in Figure 2a, indicating that, similar to (C₆H₆)₂Cr, Ti@B₂₈ (2) follows the 18-electron principle in coordination bonding pattern. Both the isovalent C₂ Sc@B₂₈⁻ (1) and C₂ V@B₂₈⁺ (3) are found to follow similar bonding patterns (Figure S6).

C_s V@B₂₉²⁻ (4) appears to possess a similar bonding pattern. As shown in Figure 2c, it has 38 3c–2e σ bonds on 38 B₃ triangles on the cage surface, forming the σ-framework of the B₂₉⁻ ligand. The remaining nine delocalized coordination bonds include three 13c–2e B₁₂ (π)–V(d_π/σ) bonds between the V center and B₁₂ ligand on the top, three 13c–2e B₁₂ (π)–V (d_π/σ) between the V center and B₁₂ ligand at the bottom, and three 27c–2e B₁₄ (π)–V (d_π/σ)–B₁₂ (π) bonds mainly between V and its two B₁₂ ligands on the top and bottom with ON = 1.91~1.99 |e|, again well corresponding to bonding pattern of D_6h (C₆H₆)₂Cr in Figure 2a, showing that V@B₂₉²⁻ (4) also matches the 18-electron rule in coordination bonding pattern.

The eigenvalue spectra of D_6h (C₆H₆)₂Cr, C₂ Ti@B₂₈ (2), and C_s V@B₂₉²⁻ (4) compared in Figure S7 indicate that these transition metal-centered complexes possess nine delocalized atomic-like canonical molecular orbitals (CMOs) in the pseudo-superatomic [60] electronic configuration of 1S²1P⁶1D¹⁰ via effective spd-π interaction/hybridizations, indicating that they follow the 18-electron principle and match the 2(n + 1)² electron counting rule (n = 2), making them spherically aromatic in nature and chemically stable both thermodynamically and dynamically.

The calculated iso-chemical shielding surfaces (ICSSs) [61] of Ti@B₂₈ (2) and V@B₂₉²⁻ (4) based on the ZZ components of the calculated nuclear-independent chemical shifts (NICS-ZZ) shown in Figure 3a,c appear to be similar with that of the experimentally known spherically aromatic C₂ B₂₈ (Figure 3b) [7] and C_s B₂₉⁻ (Figure 3d) [8], respectively, well supporting the spherical aromaticity of these endohedral seashell-like endohedral complexes. The spaces inside the boron cage or within 1 Å above the cage surface in vertical directions with negative NICS–ZZ values belong to chemical shielding regions (highlighted in yellow), while the belt-like region outside the cage in the horizontal direction around the waist belongs to the chemical de-shielding area (highlighted in green).

2.3. IR, Raman, and PE Spectral Simulations

Joint experimental spectroscopic and first-principles theory investigations have proven to be the most effective method to characterize gas phase clusters [62]. The infrared (IR) and Raman spectra of C₂ Sc@B₂₈⁻ (1), C₂ Ti@B₂₈ (2), and C_s V@B₂₉²⁻ (3) are simulated at PBE0/6-311+G(d) in Figure 4 to facilitate their future spectroscopic characterizations. As shown in Figure 4a, C₂ Sc@B₂₈⁻ (1) exhibits strong IR active peaks at 257 (a), 461 (b), 593 (a), 872 (a), 912 (a), 936 (b), 1030 (a), 1210 (a), and 1365 (a) cm⁻¹ which mainly belong to the vibrational modes of the B₂₈ skeleton, while its strong Raman active vibrations occur at 181 (a), 258 (b), 411 (a), 515 (a), 621 (a), 1210 cm⁻¹ (a), with the 411 cm⁻¹ (a) peak corresponding to typical “radial breathing mode” (RBM) [63] of the C₂ B₂₈ ligand which can be used to characterize hollow boron nanostructures. The IR and Raman spectra of Ti@B₂₈ (Figure 4b) is similar to that of Sc@B₂₈⁻, with the IR active vibrational modes at 268 (a), 351 (b), 403 (a), 935 (a), 1050 (a), and 1400 (a) and Raman active vibrations at 187 (a), 245 (b), 410 (a), 530 (a), and 631(a) cm⁻¹, respectively, with the 530 cm⁻¹ (a) peak belonging to typical RBM. The strong IR peaks of V@B₂₉²⁻ (4) occur at 306 (a′), 441 (a′), 572 (a′), 850 (a′), 1022 (a″), 1234 (a″), and 1386 (a″), while its Raman features are located at 253 (a′), 499 (a′), 557 (a′), 648 (a′), 854 (a″), 1100 (a′), and 1373 (a″) (Figure 4c). Simulated IR and Raman spectra of (a) C₂ V@B₂₈⁺ are shown in Figure S8.

The simulated PE spectra of C₂ Sc@B₂₈⁻ (1) and C₁ Ti@B₂₈⁻ and C_s V@B₂₉ ⁻ derived from C₂ Ti@B₂₈ (2) and C_s V@B₂₉²⁻ (4) are shown in Figure 4d–f using the time-dependent TD-PBE0/6-311+G(d) approach [64,65], with their first calculated vertical detachment energies (VDEs) located at 3.55, 2.73, and 3.36 eV and first adiabatic detachment energies (ADEs) located at 3.33, 2.41, and 3.21 eV, respectively. Detachment of one electron from singlet C₂ Sc@B₂₈⁻ (1) leads to doublet final states in its neutral, with the major spectroscopic features at 3.55, 3.73, 4.18, 4.57, 5.10, 5.30, 5.61, 5.75, 6.21, and 6.43 eV, respectively (Figure 4d). Detachment of one electron from the open-shell doublet C₁ Ti@B₂₈⁻ and C_s V@B₂₉⁻ generates both singlet or triplet final states in their neutrals, with the major spectral peaks located at 2.73, 3.55, 3.92, 4.19, 4.55, 5.31, 5.83, and 6.12 eV for Ti@B₂₈⁻ and 3.36 3.66, 4.00, 4.30, 4.74, 5.29, and 6.36 eV for V@B₂₉⁻, respectively (Figure 4e,f).

3. Computational Details

Extensive GM searches were performed on Sc@B₂₈⁻, Ti@B₂₈, and V@B₂₈⁺, V@B₂₉²⁻ at DFT level with electronic multiplicities considered, using both the TGmin2 [66,67] and Minima Hopping (MH) [68,69] codes, in conjunction with manual constructions based on the experimentally observed C₂ B₂₈^−/0 and C_s B₂₉⁻ at PBE/DZVP, with about 3500 stationary points probed for each species on its potential surface. The low-lying isomers were then fully optimized at both PBE0/6-311+G(d) [51] and TPSSh/6-311+G(d) [52,53] levels using the Gaussian 09 program, with vibrational frequencies checked to make sure all the obtained low-lying isomers are true minima of the systems. Single point CCSD(T)/6-31G(d) calculations were performed on the five lowest–lying isomers to further refine their relative energies employing the Molpro (2013) program [54,55], with the T₁ diagnostics checked to make sure that multi-reference interactions make non-significant contributions in these closed-shell complexes. Natural bonding orbital (NBO) analyses were carried out using the NBO 6.0 program [56]. Extensive Born–Oppenheimer molecular dynamics (BOMD) simulations were performed on C₂ Sc@B₂₈⁻(1) at 600 K, C₂ Ti@B₂₈ (2) at 700 K, and V@B₂₉²⁻(4) at 700 K for 30 ps using the CP2K program [57] utilizing the hybrid Gaussian and plane waves method, with the GTH–PBE pseudopotential and DZVP–MOLOPT–SR–GTH basis set for boron and transition metal, respectively. Detailed bonding analyses were carried out utilizing the adaptive natural density partitioning (AdNDP) approach [58,59]. Iso-chemical shielding surfaces (ICSS) [61] were calculated using the Multiwfn 3.8 software [70]. Bonding analyses and ICSS surfaces were visualized using the visual molecular dynamics (VMD) [71] software. The IR and Raman spectra of C₂ Sc@B₂₈⁻ (1), C₂ Ti@B₂₈ (2), C_s V@B₂₉²⁻ (4) were simulated at PBE0/6-311+G(d). The PE spectra of C₂ Sc@B₂₈⁻ (1), C₁ Ti@B₂₈⁻ and C_s V@B₂₉⁻ were simulated using the time-dependent DFT approach (TD-DFT) at PBE0/6-311+G(d) level [64,65]. An overall calculation scheme used in this work is presented in Figure S9.

4. Conclusions

Based on the experimentally observed seashell-like C₂ B₂₈^−/0 and C_s B₂₉⁻ and extensive first-principles theory calculations, we propose in this work the transition-metal-centered endohedral seashell-like metallo-borospherenes Sc@B₂₈⁻ (1), Ti@B₂₈ (2), V@B₂₈⁺ (3), and V@B₂₉²⁻ (4) which, as the boron analogues to the well-known sandwich complex Cr(C₂H₆)₂ highly stable both thermodynamically and dynamically, follow the 18-electron rule in coordination bonding patterns and are spherically aromatic in nature. The IR, Raman, and PE spectra of the concerned species are theoretically simulated to facilitate their future spectroscopic characterizations in gas-phase experiments via laser ablations of boron-transition-metal mixed binary targets. Further combined theoretical and experimental investigations on metal-doped boron complexes are expected to unveil novel structures and bonding in chemistry and materials science and shed new insights on boron-based nano-devices.