Cage-Like La4B24 and Core-Shell La4B290/+/-: Perfect Spherically Aromatic Tetrahedral Metallo-Borospherenes

Cage-Like La4B24 and Core-Shell La4B290/+/-: Perfect Spherically Aromatic Tetrahedral Metallo-Borospherenes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Cage-Like La 4 B 24 and Core-Shell La 4 B 29 0/+/- : Perfect Spherically Aromatic Tetrahedral Metallo-Borospherenes Xiao-Qin Lu, Cai-Yue Gao, Zhi-Hong Wei, Si-Dian Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-161832/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Apr, 2021 Read the published version in Journal of Molecular Modeling → Version 1 posted 5 You are reading this latest preprint version Abstract Cage-like and core-shell metallo-borospherenes exhibit interesting structures and bonding. Based on extensive global searches and first-principles theory calculations, we predict herein the perfect tetrahedral cage-like T d La 4 B 24 ( 1 ) and core-shell T d La 4 B 29 ( 2 ), T d La 4 B 29 + ( 3 ), and T d La 4 B 29 - ( 4 ) which all possess the same geometrical symmetry as their carbon fullerene counterpart T d C 28 , with four equivalent interconnected B 6 triangles on the cage surface and four nona-coordinate La centers in four conjoined η 9 -B 9 rings. In these tetra-La-doped boron complexes, La 4 [B@B 4 @B 24 ] 0/+/- ( 2/3/4 ) in the structural motif of 1+4+28 contain a B-centered tetrahedral T d B@B 4 core in a La-decorated tetrahedral La 4 B 24 shell, with the negatively charged tetra-coordinate B - at the center being the boron analog of tetrahedral C in T d CH 4 (B - ~C). Detailed orbital and bonding analyses indicate that these T d lanthanide boride complexes are spherically aromatic in nature with a universal La--B 9 (d-p) σ and (d-p) δ coordination bonding pattern. The IR, Raman, and UV-Vis or photoelectron spectra of these novel metallo-borospherenes are computationally simulated to facilitate their spectral characterizations. Cellular & Molecular Neuroscience First-Principles Theory Metallo-Borospherenes Tetrahedral Structures Bonding Patterns Spherical Aromaticity Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Boron as a prototypical electron-deficient element possesses a rich chemistry next only to carbon in the periodical table. It exhibits a strong propensity to form multi-center-two-electron (mc-2e) bonds in both bulk allotropes and polyhedral molecules [1, 2]. Persistent joint photoelectron spectroscopy (PES) and first-principles theory investigations in the past two decades have unveiled a rich landscape for size-selected boron clusters (B n −/0 ) from planar or quasi-planar structures (n = 3–38, 41, 42) to cage-like borospherenes ( C 3 /C 2 B 39 − and D 2 d B 40 −/0 ) which are all characterized with delocalized multi-center bonding [2–6]. Seashell-like borospherenes C 2 B 28 − and C s B 29 − were late observed in PES measurements as minor isomers competing with their quasi-planar global minimum (GM) counterparts [7, 8]. Endohedral M@B 40 (M = Ca, Sr) and exohedral M&B 40 (M = Be, Mg) metallo-borospherenes were predicted in theory shortly after the discovery of D 2d B 40 −/0 [9]. Endohedral metallo-borospherenes D 2 Ta@B 22 − and D 2 d U@B 40 were proposed to be superatoms matching the 18-electron rule and 32-electron principles, respectively [10, 11]. Joint ion-mobility measurements and density functional theory (DFT) investigations indicated that boron cluster monocations (B n + ) possess double-ring tubular geometries in the size range between n = 16–25 [12]. Extensive GM searches showed that complicated structural competitions exist in medium-sized B n clusters, with B 46 being the smallest core-shell boron cluster (B 4 @B 42 ) and B 48 , B 54 , B 60 , and B 62 being the first bilayer boron clusters predicted to date [13, 14]. Transition-metal-doping induces earlier planar→tubular→ cage-like→core-shell structural transitions in boron clusters, resulting in unique structures and bonding in chemistry. Typical examples include the experimentally observed transition-metal-centered boron wheels M@B n (Co@B 8 − , Ru@B 9 − , and Ta@B 10 − ) and transition-metal-centered boron drums M@B n − (Mn@B 16 − , Co@B 16 − , Rh@B 18 − , and Ta@B 20 − ) [15–20]. A family of di-La-doped inverse-sandwich-type mono-deck boron clusters La 2 B n − (n = 7–9) [21, 22] and inverse triple-decker La 3 B 14 − were observed in PES experiments [23]. The first tri-La-doped spherical trihedral metallo − borospherene D 3 h La 3 B 18 − with three La atoms as integral parts of the cage surface was discovered very recently in a joint experimental and theoretical investigation [24]. Our group predicted the possibility of the smallest inverse sandwich bi-decker tubular molecular rotor C 2 h La 2 B 20 (La 2 [B 2 @B 18 ]) [25] and the first core-shell spherical trihedral metallo-borospherenes D 3 h La 3 B 20 − (La 3 [B 2 @B 18 ] − ) which contains two equivalent eclipsed B 6 triangles on the top and bottom interconnected by three B 2 units on the waist and three deca-coordinate La atoms as integral parts of cage surface [26]. We also reported the smallest metallo-borospherene D 3 h Ta 3 B 12 − composed of two eclipsed B 3 triangles on the top and bottom interconnected by three B 2 units on the waist [27]. However, to the best of our knowledge, there have been no experimental or theoretical evidence reported on tetra-La-doped boron clusters to date. Tetra-metal-doped core-shell metallosilicon fullerenes T d M 4 @Si 28 ( M = Al and Ga) in the structural motif of 4 + 28 have been predicted [28] to have the same tetrahedral symmetry as their carbon fullerene counterpart T d C 28 [29]. It is natural to ask at current stage what geometrical structures and bonding patterns of the tetra-La-doped boron clusters may have and if perfect tetrahedral metallo-borospherenes are favored over other geometries in both thermodynamics and dynamics. Based on extensive GM searches and first-principles theory calculations, as an extension of the experimentally observed cage-like D 3 h La 3 B 18 − [24] and theoretically predicted core-shell D 3 h La 3 B 20 [25], we predict herein the perfect tetrahedral cage-like T d La 4 B 24 ( 1 ) and core-shell T d La 4 B 29 ( 2 ), T d La 4 B 29 + ( 3 ), and T d La 4 B 29 − ( 4 ) which possess four equivalent inter-connected B 6 triangles on the cage surface and four nona-coordinate La centers in four equivalent conjoined η 9 -B 9 nonagonal ligands, presenting the first metallo-borobspherene counterparts of the experimentally observed tetrahedral carbon fullerene T d C 28 [29]. More intriguingly, La 4 [B@B 4 @B 24 ] 0/+/− ( 2/3/4 ) in the structural pattern of 1 + 4 + 28 possess a tetra-coordinate B center encapsulated in an inner tetrahedron (B i ) 4 and an outer tetrahedron La 4 (B o ) 24 . These high-symmetry lanthanide boride complexes turn out to be spherically aromatic in nature with a universal La–B 9 (p-d) σ and (p-d) δ coordination bonding pattern. Methods Extensive GM searches were performed on La 4 B 24 , La 4 B 29 + and La 4 B 29 − using the TGmin2 code [30] at DFT level, with the initial seeds being manually constructed based on the experimentally observed La 3 B 18 − [24] and theoretically predicted La 3 B 19 − and La 3 B 20 − [26]. Over 2000 trial structures were explored for each species in both singlet and triplet states at PBE/TZVP. The low-lying isomers were subsequently optimized at the PBE0 [31] and TPSSh [32] levels with the basis set of 6-311 + G(d) [33] for B and Stuttgart relativistic small-core pseudopotential for La [34, 35] using the Gaussian 09 program suite [36], with the vibrational frequencies checked to make sure all the obtained structures are true minima on the potential surfaces. Low-lying isomers of the open-shell neutral La 4 B 29 were acquired from the corresponding low-lying isomers of La 4 B 29 + and La 4 B 29 − . Relative energies of the three lowest-lying isomers were further refined for La 4 B 24 and La 4 B 29 + at the coupled cluster CCSD(T)/6-31G(d) level [37–39] implemented in MOLPRO [40] at PBE0 geometries. Chemical bonding analyses were performed for La 4 B 24 ( 1 ) and La 4 [B@B 4 @B 24 ] + ( 3 ) using the adaptive natural density partitioning (AdNDP) approach [41] at the PBE0 level. Natural bonding orbital (NBO) analyses were achieved using the NBO 6.0 program [42]. Born–Oppenheimer molecular dynamics (BOMD) simulations were carried out on La 4 B 24 ( 1 ), La 4 B 29 ( 2 ), La 4 B 29 + ( 3 ), and La 4 B 29 − ( 4 ) for 30 ps at 300 K and 1000K using the CP2K code [43]. Results And Discussion Strucutres and Stabilities With inspiration from the previously reported D 3 h La 3 B 18 − and D 3 h La 3 B 20 − [24, 26] which possess two equivalent eclipsed B 6 triangles interconnected by three B 2 units on the cage surface and three deca-coordinate La centers in three conjoined η 10 -B 10 rings, we manually constructed the perfect tetrahedral cage-like T d La 4 B 24 ( 1 ) with four equivalent interconnected B 6 triangles on the cage surface and four nona-coordinate La centers in four conjoined η 9 -B 9 rings (Fig. 1) Encouragingly, extensive GM searches show that, being overwhelmingly more stable than other low-lying isomers, La 4 B 24 ( 1 , 1 A 1 ) is the well-defined GM of the neutral (Fig. S1) with the lowest vibrational frequency of υ min = 119.87 cm − 1 at PBE0. It is 0.79 eV more stable than the second lowest-lying isomer C s La 4 B 24 with a B 2 core and 1.23 eV more stable than the third lowest-lying isomer C s La 4 B 24 with a B 3 core at CCSD(T) level, respectively (Fig. S1). The triplet cage-like C 1 La 4 B 24 ( 3 A) slightly distorted due to Jahn-Teller effect appears to be much less stable than the T d GM (by 1.28 eV) at PBE0 (Fig. S1). La 4 B 24 ( 1 ) possesses the B-B bond length of r B−B = 1.57 Å between the interconnected B 6 triangles, B-B bond length of r′ B−B = 1.66 Å within the central B 3 triangles in B 6 triangular motifs, and average La–B coordination bond length of r La−B = 2.75 Å between La atoms and their η 9 -B 9 ligands. The large calcualted HOMO–LUMO gap of Δ E gap = 2.35 eV at PBE0 well supports its high chemical stability. Cage-like La 4 B 24 ( 1 ) appears to be the first metallo-borospherene possessing the same tetrahedral symmetry as its carbon fullerene counterpart − the experimentally observed quintet T d C 28 ( 5 A 1 ) [29]. Extensive molecular dynamics simulations indicate that La 4 B 24 ( 1 ) is also highly dynamically stable, with the small calculated average root-mean-square-deviations of RMSD = 0.13 Å and maximum bond length deviations of MAXD = 0.43 Å at 1000 K, respectively (Fig. 2). Detailed NBO analyses show that the La centers in La 4 B 24 ( 1 ) possess the natural atomic charge of q La = + 1.49 |e| and electronic configuration of La[Xe]4f 0.16 5d 1.32 6s 0.09 , indicating that La donates its 6s 2 electron almost completely to the surrounding B 9 ligand in La 4 B 24 ( 1 ) while accepting partial valence electron (~ 0.32 |e|) from the boron ligand in its partially occupied 5d orbitals via p→d back donations. Bond order analyses show that the La centers in La 4 B 24 ( 1 ) possess the total Wiberg bond order of WBI La =2.79 and average La–B bond order of WBI La−−B =0.26, evidencing the formation of effective La–B coordination interactions in the complex. The high-symmetry tetrahedral T d La 4 [B@B 4 @B 24 ] ( 2) ( 2 A 2 ) was achieved by encapsulating a B-centered tetrahedral T d B@B 4 core inside cage-like La 4 B 24 ( 1 ), forming a perfect tetrahedral core-shell lanthanide boride complex with a tetra-coordinate B at the cage center (Fig. 1). Surprisingly and intriguingly, extensive DFT calculations indicate that, with a singly occupied non-degenerate highest occupied α-orbital (a 2 ), the doublet La 4 [B@B 4 @B 24 ] ( 2) well retains its identical tetrahedral T d symmetry during full structural optimizations. As the most stable isomer obtained, it lies 0.79 eV lower than the second lowest-lying isomer C 1 La 4 B 29 ( 2 A) (Fig. S2). The tetrahedral B@B 4 core and La 4 B 24 ( 1) shell turn out to match both geometrically and electronically in La 4 [B@B 4 @B 24 ] ( 2) which has the lowest vibrational frequency of υ min = 128.94 cm − 1 and α-HOMO-LUMO gap of △ E gap =2.23 eV. Detaching one election from or attaching one electron to La 4 [B@B 4 @B 24 ] ( 2) results in the perfect singlet T d La 4 [B@B 4 @B 24 ] + ( 3 , 1 A 1 ) and T d La 4 [B@B 4 @B 24 ] − ( 4 , 1 A 1 ) which also appear to be the well-defined GMs of the systems lying 0.79 eV and 0.69 eV lower than the second lowest-lying core-shell C s La 4 B 29 + and C 1 La 4 B 29 − at PBE0, respectively (Fig. S3 and Fig. S4). La 4 [B@B 4 @B 24 ] +/− ( 3/4) possess the large HOMO-LUMO gaps of △ E gap = 2.84/2.21 eV and lowest vibrational frequencies of υ min = 125.50/131.35 cm − 1 . The La 4 [B@B 4 @B 24 ] 0/+/− ( 2/3/4 ) core-shell complex series in a 1 + 4 + 28 structural motif possess the B-B bond lengths of r B−B =1.65/1.64/1.66 Å between the central B atom and inner tetrahedron (B i ) 4 , B-B distances of r B−B =1.73/1.73/1.73 Å between the inner tetrahedron (B i ) 4 and outer tetrahedron (B o ) 24 , and the La–B distances of r La−−B =2.88/2.93/2.85 Å between the B atom at the center and La atoms on the outer shell. They can thus be viewed as the first bi-shell metallo-borospherenes with the B center encapsulated in an inner tetrahedron (B i ) 4 and an outer tetrahedron La 4 (B o ) 24 . Similar to the previously reported endohedral metallosilicon fullerenes T d M 4 @Si 28 (M = Al and Ga) which follow the structural motif of 4 + 28 [28], core-shell La 4 [B@B 4 @B 24 ] 0/+/− ( 2/3/4 ) in the structural motif of 1 + 4 + 28 possess the same tetrahedral symmetry as their carbon fullerene counterpart T d C 28 [29]. These core-shell complexes also appear to be highly dynamically stable, as exemplified in Fig. 2 for La 4 [B@B 4 @B 24 ] − ( 4 ) which has the small calculated average RMSD = 0.13 Å and MAXD = 0.41 Å at 1000 K, respectively. The behavior of the central B atom in these core-shell complexes appears to be especially interesting. Detailed NBO analyses indcate that the central B in La 4 [B@B 4 @B 24 ] 0/+/− ( 2/3/4 ) possesses the natural atomic charge of q B =-1.00/-1.05/-1.00 |e|, electronic configurations of B[He]2s 0.51 2p 3.48 /B[He]2s 0.52 2p 3.52 / B[He]2s 0.52 2p 3.52 , and total Wiberger bond orders of WBI B = 3.71/3.71/3.71, respectively. The central B atom thus carries approximately a unitary negative charge of q B ≈-1.0 |e| in these complexes regardless of the charge states of the systems, resulting in a B − monoanion at the cage center which is isovalent with a neutral C atom. The negatively charged tetra-coordinate B − center in 2 , 3 , 4 is thus a boron analog of the tetrahedral C in T d CH 4 , indicating the B − ~C analogy [44] in these B-centered core-shell complexes. Bonding analyses To better interpret the high stabilities of these T d lanthanide boride complexes, we performed detailed AdNDP bonding analyses on the closed-shell La 4 B 24 ( 1 ) and La 4 [B@B 4 @B 24 ] + ( 3 ) to recover both the localized and delocalized bonds of the systems. As shown in Fig. 3(a), La 4 B 24 ( 1 ) possesses 6 2c-2e B-B σ bonds with the occupation number of ON = 1.88 |e| between the four inter-connected B 6 triangles on the cage surface and 16 3c-2e σ bonds with ON = 1.91 |e| on four equivalent B 6 triangular motifs, forming the σ skeleton of the cage-like system. As expected from chemical intuition, there exist 4 equivalent 6c–2e π bonds with ON = 1.91 over the four interconnected B 6 triangles. The remaining 16 delocalized bonds are mainly responsible for the La–B 9 coordination interactions in the complex, including 12 equivalent 5c-2e La–B 4 (d-p) σ bonds with ON = 1.72 and 4 equivalent 10c-2e La–B 9 (d-p) δ bond with ON = 1.62 evenly distributed over four La@B 9 nonagons on the cage surface. Such a bonding pattern renders spherical aromaticity to cage-like La 4 B 24 ( 1 ), as evidenced by the calculated negative nucleus-independent chemical shift (NICS) [45] values of NICS = − 31.69 ppm at the cage center and NICS = − 33.41 ppm 1.0 Å above the cage center along the C 2 molecular axes. Figure 3(b) indicates that the core-shell La 4 [B@B 4 @B 24 ] + ( 3) well inherits the main bonding elements of La 4 B 24 ( 1 ), with the 6 2c-2e B-B σ bonds, 16 3c-2e σ bonds, 12 5c-2e La–B 4 (d-p) σ bonds, and 4 10c-2e La-B 9 (d-p) δ bonds remaining basically unchanged. The main difference occurs at the 4 2c-2e B-B σ-bonds in the B@B 4 core beween the central B atom and (B i ) 4 inner tetrahedron and 4 7c-2e B 6 (π)-B(p) σ interactions between the four B i atoms in the inner shell and four capping B 6 triangles in the outer shell in the first row and 3 29c-2e π-p σ bonds totally delocalized on the core-shell B 29 framework ([B@B 4 @B 24 ]) in the fourth row. Interestingly, similar to La 4 B 24 ( 1 ), La 4 [B@B 4 @B 24 ] 0/+/− ( 2/3/4 ) possess the negative calculated NICS values of NICS=-33.92/-43.18/-28.19 ppm 1.0 Å above the B center along the C 2 molecular axes, respectively, indicating that these core-shell borospherenes are also spherically aromatic in nature. The 12 5c-2e La–B 4 (d-p) σ and 4 10c-2e La–B 9 (d-p) δ coordination bonds in La 4 B 24 ( 1 ) and La 4 [B@B 4 @B 24 ] + (3) play a vital role in stabilizing these perfect tetrahedral lanthanide boride complexes. IR, Raman, and UV-Vis/PES Spectral Simulations The IR, Raman, and UV-Vis spectra of La 4 B 24 ( 1 ) and IR, Raman, and PES spectra of La 4 [B@B 4 @B 24 ] − ( 4 ) are computationally simulated in Fig. 4 to facilitate their future characterizations. T d La 4 B 24 ( 1 ) possesses highly simplified IR and Raman spectra due to its high symmetry, including four sharp IR peaks at 215(t 2 ), 239(t 2 ), 810(t 2 ) and 1036 (t 2 ) cm − 1 and eight active Raman vibrations at 137 (a 1 ), 239(t 2 ), 391(a 1 ), 473(a 1 ), 1036(t 2 ), 1065(a 1 ), 1257(t 2 ) and 1267(a 1 ) cm −1 , respectively. Detailed vibrational analyses indicate that the symmetrical vibrations at 137 cm −1 (a 1 ) and 391 cm −1 (a 1 ) represent typical radial breathing modes (RBMs) of the cage-like complex which can be used to characterize single-walled hollow boron nanostructures [46]. The strong UV bands around 323, 341, 376, 436 and 459 nm originate from electronic transitions from deep inner shells of the neutral to its high-lying unoccupied molecular orbitals, while the weak broad bands around 490, 526, 625 and 772 nm mainly involve electronic excitations from the occupied frontier orbitals around the HOMO (t 2 ) of the neutral. As shown in Fig. 4(b), La 4 [B@B 4 @B 24 ] − ( 4 ) exhibits similar IR and Raman spectral features to La 4 B 24 ( 1 ), with the strongest IR vibration at 258 cm −1 (t 2 ) and typical RBM vibrations at 153 cm −1 (a 1 ) and 448 (a 1 ) cm −1 . The calculated PES spectrum of La 4 [B@B 4 @B 24 ] − ( 4 ) exhibits major spectral features at 2.08, 3.51, 3.75, 4.31, and 5.18 eV which correspond to vertical electronic transitions from the ground state of the anion ( 1 A 1 ) to the ground state ( 2 A 2 ) and excited states ( 2 T 1 , 2 T 2 , 2 T 2 , 2 T 2 ) of the neutral at the ground-state geometry of the anion, respectively. Conclusions Perfect tetrahedral cage-like La 4 B 24 ( 1) and core-shell La 4 B 29 0/+/− ( 2 / 3 / 4) with spherical aromaticity have been predicted in this work at first-principles theory level to be the first metallo-borospherenes reported to date possessing the same tetrahedral symmetry as their carbon fullerene counterpart T d C 28 . The tetrahedral B@B 4 core and tetrahedral La 4 B 24 ( 1) shell match both geometrically and electronically in the La 4 B 29 0/+/− ( 2 / 3 / 4 ) series. Such species could be synthesized and characterized in gas phases using a La-B binary target in PES experiments.[ 21 – 24 ] These high-symmetry lanthanide boride complexes and their chemically modified derivatives may serve as building blocks to form various nanoclusters and nanomaterials with novel electronic, magnetic, and optical properties. Declarations Funding : The work was supported by the National Natural Science Foundation of China (21720102006 and 21973057 to S.-D. Li). 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J Am Chem Soc 118, 6317-6318. https://doi.org/10.1021/JA960582D Ciuparu D, Klie R, Zhu YM, Pfefferle L (2004) Synthesis of Pure Boron Single-Wall Nanotubes. J Phys Chem B 108: 3967-3969. https://doi.org/10.1021/jp049301b Supplementary Files TOC.png PaperonLa4B24JMMSI2021122.docx Cite Share Download PDF Status: Published Journal Publication published 21 Apr, 2021 Read the published version in Journal of Molecular Modeling → Version 1 posted Editorial decision: Minor revisions needed 28 Feb, 2021 Reviewers invited by journal 06 Feb, 2021 Reviews received at journal 06 Feb, 2021 Editor assigned by journal 31 Jan, 2021 First submitted to journal 21 Jan, 2021 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-161832","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":10795475,"identity":"17576f8f-cd7d-41e9-8a6f-e68dc081d21d","order_by":0,"name":"Xiao-Qin Lu","email":"","orcid":"","institution":"Shanxi University","correspondingAuthor":false,"prefix":"","firstName":"Xiao-Qin","middleName":"","lastName":"Lu","suffix":""},{"id":10795476,"identity":"beefd692-ae23-4382-9ad7-6c6391c4a192","order_by":1,"name":"Cai-Yue Gao","email":"","orcid":"","institution":"Shanxi University","correspondingAuthor":false,"prefix":"","firstName":"Cai-Yue","middleName":"","lastName":"Gao","suffix":""},{"id":10795477,"identity":"9d4826f4-51cb-4f6f-ae00-9798b7b4a000","order_by":2,"name":"Zhi-Hong Wei","email":"","orcid":"","institution":"Shanxi University","correspondingAuthor":false,"prefix":"","firstName":"Zhi-Hong","middleName":"","lastName":"Wei","suffix":""},{"id":10795478,"identity":"129fb020-d15b-4bb9-8ccf-e4a7ff0eea50","order_by":3,"name":"Si-Dian Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYBACPmYGhgM8BgwM/BA+M2EtbDAtkg1EawERPEBscIBoLezsDw+8KbDLMz5/xkyCocI6sYH97AECDuMxODjHILnY7EZamgTDmfTEBp68BEJaGA7zGDAnbrvBfEyCse1wYoMEyGt4tbA/AGqpT9zcf7BNgvEfUVoYDIBaDiduYEgG2tJAlBawX44nzriRlmyRcCzduI0nB78Wfv7jjz+8+VOd2N9/xvDGhxpr2X72M/i1oIIEBmhMjYJRMApGwSigDAAAyeM+Zma25aIAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-5666-0591","institution":"Shanxi University","correspondingAuthor":true,"prefix":"","firstName":"Si-Dian","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2021-01-27 18:29:53","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-161832/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-161832/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00894-021-04739-8","type":"published","date":"2021-04-21T19:03:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":5797977,"identity":"f5b5f040-9f6d-4886-a13d-f681f3fcd39e","added_by":"auto","created_at":"2021-02-09 20:17:12","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":43617,"visible":true,"origin":"","legend":"Optimized structures of cage-like Td La4B24 (1) and core-shell Td La4[B@B4@B24] (2), Td La4[B@B4@B24]+ (3), and Td La4[B@B4@B24]- (4), with the central B atom highlighted in blue and four apex B atoms of the tetrahedral Td B@B4 core highlighted in red in 2, 3, and 4. ","description":"","filename":"Fig1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-161832/v1/bab0c6401ab77d531a486cda.jpg"},{"id":5797978,"identity":"b1aeda0a-e3cb-44bd-94c5-f5b2148a392f","added_by":"auto","created_at":"2021-02-09 20:17:12","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":81490,"visible":true,"origin":"","legend":"Born-Oppenheimer molecular dynamics simulations of La4B24 (1) (a) and La4[B@B4@B24]- (4) (b) at 1000 K. The root-mean-square-deviation (RMSD) and maximum bond length deviation (MAXD) values (on average) are indicated in Å.","description":"","filename":"Fig2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-161832/v1/892c4d7773bb751089045a13.jpg"},{"id":5798071,"identity":"a038ff4f-888a-4bb8-ac5a-9f928afc3532","added_by":"auto","created_at":"2021-02-09 20:20:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":4105262,"visible":true,"origin":"","legend":"AdNDP bonding patterns of the closed-shell La4B24 (1) (a) and La4[B@B4@B24]+ (3) (b), with the occupation numbers (ONs) indicated.","description":"","filename":"Fig.3.png","url":"https://assets-eu.researchsquare.com/files/rs-161832/v1/b6e03fc4b4ae4f7e593395e9.png"},{"id":5798139,"identity":"0269a1c7-e1ac-47c0-bdc9-5e722dd75d0e","added_by":"auto","created_at":"2021-02-09 20:23:12","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":54352,"visible":true,"origin":"","legend":"Simulated IR, Raman and UV-Vis spectra of La4B24 (1) (a) and IR, Raman and PES spectra of La4[B@B4@B24]- (4) (b) at PBE0 level.","description":"","filename":"Fig4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-161832/v1/ea85ec489e374c135fb02035.jpg"},{"id":15670937,"identity":"d5429a82-12b3-4982-b245-5f651ce9853a","added_by":"auto","created_at":"2021-11-18 14:03:12","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1014781,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-161832/v1/0d5bb977-cca8-4e7e-b692-d3cf6b5ba2a7.pdf"},{"id":5798069,"identity":"d0596081-7730-498b-8c15-1f78192bfe50","added_by":"auto","created_at":"2021-02-09 20:20:12","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":827288,"visible":true,"origin":"","legend":"","description":"","filename":"TOC.png","url":"https://assets-eu.researchsquare.com/files/rs-161832/v1/83b68054f446e3cb4dfd081d.png"},{"id":5798072,"identity":"76fdcbe2-314d-4d4f-b8b0-5bf6c76a8b0b","added_by":"auto","created_at":"2021-02-09 20:20:12","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":2089670,"visible":true,"origin":"","legend":"","description":"","filename":"PaperonLa4B24JMMSI2021122.docx","url":"https://assets-eu.researchsquare.com/files/rs-161832/v1/f2047c4f1a6bd2b12b8eabda.docx"}],"financialInterests":"","formattedTitle":"\u003cp\u003eCage-Like La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e and Core-Shell La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e0/+/-\u003c/sup\u003e: Perfect Spherically Aromatic Tetrahedral Metallo-Borospherenes\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eBoron as a prototypical electron-deficient element possesses a rich chemistry next only to carbon in the periodical table. It exhibits a strong propensity to form multi-center-two-electron (mc-2e) bonds in both bulk allotropes and polyhedral molecules [1, 2]. Persistent joint photoelectron spectroscopy (PES) and first-principles theory investigations in the past two decades have unveiled a rich landscape for size-selected boron clusters (B\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u0026minus;/0\u003c/sup\u003e) from planar or quasi-planar structures (n\u0026thinsp;=\u0026thinsp;3\u0026ndash;38, 41, 42) to cage-like borospherenes (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003cem\u003e/C\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e B\u003csub\u003e39\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e and \u003cem\u003eD\u003c/em\u003e\u003csub\u003e2\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e B\u003csub\u003e40\u003c/sub\u003e\u003csup\u003e\u0026minus;/0\u003c/sup\u003e ) which are all characterized with delocalized multi-center bonding [2\u0026ndash;6]. Seashell-like borospherenes \u003cem\u003eC\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e B\u003csub\u003e28\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e B\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e were late observed in PES measurements as minor isomers competing with their quasi-planar global minimum (GM) counterparts [7, 8]. Endohedral M@B\u003csub\u003e40\u003c/sub\u003e (M\u0026thinsp;=\u0026thinsp;Ca, Sr) and exohedral M\u0026amp;B\u003csub\u003e40\u003c/sub\u003e (M\u0026thinsp;=\u0026thinsp;Be, Mg) metallo-borospherenes were predicted in theory shortly after the discovery of \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e2d\u003c/em\u003e\u003c/sub\u003e B\u003csub\u003e40\u003c/sub\u003e\u003csup\u003e\u0026minus;/0\u003c/sup\u003e [9]. Endohedral metallo-borospherenes \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e Ta@B\u003csub\u003e22\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e and \u003cem\u003eD\u003c/em\u003e\u003csub\u003e2\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e U@B\u003csub\u003e40\u003c/sub\u003e were proposed to be superatoms matching the 18-electron rule and 32-electron principles, respectively [10, 11]. Joint ion-mobility measurements and density functional theory (DFT) investigations indicated that boron cluster monocations (B\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e) possess double-ring tubular geometries in the size range between n\u0026thinsp;=\u0026thinsp;16\u0026ndash;25 [12]. Extensive GM searches showed that complicated structural competitions exist in medium-sized B\u003csub\u003en\u003c/sub\u003e clusters, with B\u003csub\u003e46\u003c/sub\u003e being the smallest core-shell boron cluster (B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e42\u003c/sub\u003e) and B\u003csub\u003e48\u003c/sub\u003e, B\u003csub\u003e54\u003c/sub\u003e, B\u003csub\u003e60\u003c/sub\u003e, and B\u003csub\u003e62\u003c/sub\u003e being the first bilayer boron clusters predicted to date [13, 14].\u003c/p\u003e\n\u003cp\u003eTransition-metal-doping induces earlier planar\u0026rarr;tubular\u0026rarr; cage-like\u0026rarr;core-shell structural transitions in boron clusters, resulting in unique structures and bonding in chemistry. Typical examples include the experimentally observed transition-metal-centered boron wheels M@B\u003csub\u003en\u003c/sub\u003e (Co@B\u003csub\u003e8\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e, Ru@B\u003csub\u003e9\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e, and Ta@B\u003csub\u003e10\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e) and transition-metal-centered boron drums M@B\u003csub\u003en\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e (Mn@B\u003csub\u003e16\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e, Co@B\u003csub\u003e16\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e, Rh@B\u003csub\u003e18\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e, and Ta@B\u003csub\u003e20\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e) [15\u0026ndash;20]. A family of di-La-doped inverse-sandwich-type mono-deck boron clusters La\u003csub\u003e2\u003c/sub\u003eB\u003csub\u003en\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e (n\u0026thinsp;=\u0026thinsp;7\u0026ndash;9) [21, 22] and inverse triple-decker La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e14\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e were observed in PES experiments [23]. The first tri-La-doped spherical trihedral metallo\u0026thinsp;\u0026minus;\u0026thinsp;borospherene \u003cem\u003eD\u003c/em\u003e\u003csub\u003e3\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e18\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e with three La atoms as integral parts of the cage surface was discovered very recently in a joint experimental and theoretical investigation [24]. Our group predicted the possibility of the smallest inverse sandwich bi-decker tubular molecular rotor \u003cem\u003eC\u003c/em\u003e\u003csub\u003e2\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e2\u003c/sub\u003eB\u003csub\u003e20\u003c/sub\u003e (La\u003csub\u003e2\u003c/sub\u003e[B\u003csub\u003e2\u003c/sub\u003e@B\u003csub\u003e18\u003c/sub\u003e]) [25] and the first core-shell spherical trihedral metallo-borospherenes \u003cem\u003eD\u003c/em\u003e\u003csub\u003e3\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e20\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e (La\u003csub\u003e3\u003c/sub\u003e[B\u003csub\u003e2\u003c/sub\u003e@B\u003csub\u003e18\u003c/sub\u003e]\u003csup\u003e\u0026minus;\u003c/sup\u003e) which contains two equivalent eclipsed B\u003csub\u003e6\u003c/sub\u003e triangles on the top and bottom interconnected by three B\u003csub\u003e2\u003c/sub\u003e units on the waist and three deca-coordinate La atoms as integral parts of cage surface [26]. We also reported the smallest metallo-borospherene \u003cem\u003eD\u003c/em\u003e\u003csub\u003e3\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e Ta\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e12\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e composed of two eclipsed B\u003csub\u003e3\u003c/sub\u003e triangles on the top and bottom interconnected by three B\u003csub\u003e2\u003c/sub\u003e units on the waist [27]. However, to the best of our knowledge, there have been no experimental or theoretical evidence reported on tetra-La-doped boron clusters to date. Tetra-metal-doped core-shell metallosilicon fullerenes \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e M\u003csub\u003e4\u003c/sub\u003e@Si\u003csub\u003e28\u003c/sub\u003e (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;Al and Ga) in the structural motif of 4\u0026thinsp;+\u0026thinsp;28 have been predicted [28] to have the same tetrahedral symmetry as their carbon fullerene counterpart \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e C\u003csub\u003e28\u003c/sub\u003e [29]. It is natural to ask at current stage what geometrical structures and bonding patterns of the tetra-La-doped boron clusters may have and if perfect tetrahedral metallo-borospherenes are favored over other geometries in both thermodynamics and dynamics.\u003c/p\u003e\n\u003cp\u003eBased on extensive GM searches and first-principles theory calculations, as an extension of the experimentally observed cage-like \u003cem\u003eD\u003c/em\u003e\u003csub\u003e3\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e18\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e [24] and theoretically predicted core-shell \u003cem\u003eD\u003c/em\u003e\u003csub\u003e3\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e20\u003c/sub\u003e [25], we predict herein the perfect tetrahedral cage-like \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) and core-shell \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e (\u003cstrong\u003e2\u003c/strong\u003e), \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e (\u003cstrong\u003e3\u003c/strong\u003e), and \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e) which possess four equivalent inter-connected B\u003csub\u003e6\u003c/sub\u003e triangles on the cage surface and four nona-coordinate La centers in four equivalent conjoined \u0026eta;\u003csup\u003e9\u003c/sup\u003e-B\u003csub\u003e9\u003c/sub\u003e nonagonal ligands, presenting the first metallo-borobspherene counterparts of the experimentally observed tetrahedral carbon fullerene \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e C\u003csub\u003e28\u003c/sub\u003e [29]. More intriguingly, La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e0/+/\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e2/3/4\u003c/strong\u003e) in the structural pattern of 1\u0026thinsp;+\u0026thinsp;4\u0026thinsp;+\u0026thinsp;28 possess a tetra-coordinate B center encapsulated in an inner tetrahedron (B\u003csup\u003ei\u003c/sup\u003e)\u003csub\u003e4\u003c/sub\u003e and an outer tetrahedron La\u003csub\u003e4\u003c/sub\u003e(B\u003csup\u003eo\u003c/sup\u003e)\u003csub\u003e24\u003c/sub\u003e. These high-symmetry lanthanide boride complexes turn out to be spherically aromatic in nature with a universal La\u0026ndash;B\u003csub\u003e9\u003c/sub\u003e (p-d) \u0026sigma; and (p-d) \u0026delta; coordination bonding pattern.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eExtensive GM searches were performed on La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e, La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e and La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e using the TGmin2 code [30] at DFT level, with the initial seeds being manually constructed based on the experimentally observed La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e18\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e [24] and theoretically predicted La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e19\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e and La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e20\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e [26]. Over 2000 trial structures were explored for each species in both singlet and triplet states at PBE/TZVP. The low-lying isomers were subsequently optimized at the PBE0 [31] and TPSSh [32] levels with the basis set of 6-311\u0026thinsp;+\u0026thinsp;G(d) [33] for B and Stuttgart relativistic small-core pseudopotential for La [34, 35] using the Gaussian 09 program suite [36], with the vibrational frequencies checked to make sure all the obtained structures are true minima on the potential surfaces. Low-lying isomers of the open-shell neutral La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e were acquired from the corresponding low-lying isomers of La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e and La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e. Relative energies of the three lowest-lying isomers were further refined for La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e and La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e at the coupled cluster CCSD(T)/6-31G(d) level [37\u0026ndash;39] implemented in MOLPRO [40] at PBE0 geometries. Chemical bonding analyses were performed for La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) and La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e+\u003c/sup\u003e (\u003cstrong\u003e3\u003c/strong\u003e) using the adaptive natural density partitioning (AdNDP) approach [41] at the PBE0 level. Natural bonding orbital (NBO) analyses were achieved using the NBO 6.0 program [42]. Born\u0026ndash;Oppenheimer molecular dynamics (BOMD) simulations were carried out on La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e), La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e (\u003cstrong\u003e2\u003c/strong\u003e), La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e (\u003cstrong\u003e3\u003c/strong\u003e), and La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e) for 30 ps at 300 K and 1000K using the CP2K code [43].\u003c/p\u003e"},{"header":"Results And Discussion","content":"\u003cdiv\u003e\n\u003ch2\u003eStrucutres and Stabilities\u003c/h2\u003e\n\u003cp\u003eWith inspiration from the previously reported \u003cem\u003eD\u003c/em\u003e\u003csub\u003e3\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e18\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e and \u003cem\u003eD\u003c/em\u003e\u003csub\u003e3\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e20\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e [24, 26] which possess two equivalent eclipsed B\u003csub\u003e6\u003c/sub\u003e triangles interconnected by three B\u003csub\u003e2\u003c/sub\u003e units on the cage surface and three deca-coordinate La centers in three conjoined \u0026eta;\u003csup\u003e10\u003c/sup\u003e-B\u003csub\u003e10\u003c/sub\u003e rings, we manually constructed the perfect tetrahedral cage-like \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) with four equivalent interconnected B\u003csub\u003e6\u003c/sub\u003e triangles on the cage surface and four nona-coordinate La centers in four conjoined \u0026eta;\u003csup\u003e9\u003c/sup\u003e-B\u003csub\u003e9\u003c/sub\u003e rings (Fig.\u0026nbsp;1) Encouragingly, extensive GM searches show that, being overwhelmingly more stable than other low-lying isomers, La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e, \u003csup\u003e1\u003c/sup\u003eA\u003csub\u003e1\u003c/sub\u003e) is the well-defined GM of the neutral (Fig. S1) with the lowest vibrational frequency of \u0026upsilon;\u003csub\u003emin\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;119.87 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e at PBE0. It is 0.79 eV more stable than the second lowest-lying isomer \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e with a B\u003csub\u003e2\u003c/sub\u003e core and 1.23 eV more stable than the third lowest-lying isomer \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e with a B\u003csub\u003e3\u003c/sub\u003e core at CCSD(T) level, respectively (Fig. S1). The triplet cage-like \u003cem\u003eC\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003csup\u003e3\u003c/sup\u003eA) slightly distorted due to Jahn-Teller effect appears to be much less stable than the \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e GM (by 1.28 eV) at PBE0 (Fig. S1). La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) possesses the B-B bond length of \u003cem\u003er\u003c/em\u003e\u003csub\u003eB\u0026minus;B\u003c/sub\u003e = 1.57 \u0026Aring; between the interconnected B\u003csub\u003e6\u003c/sub\u003e triangles, B-B bond length of \u003cem\u003er\u0026prime;\u003c/em\u003e\u003csub\u003eB\u0026minus;B\u003c/sub\u003e = 1.66 \u0026Aring; within the central B\u003csub\u003e3\u003c/sub\u003e triangles in B\u003csub\u003e6\u003c/sub\u003e triangular motifs, and average La\u0026ndash;B coordination bond length of \u003cem\u003er\u003c/em\u003e\u003csub\u003eLa\u0026minus;B\u003c/sub\u003e = 2.75 \u0026Aring; between La atoms and their \u0026eta;\u003csup\u003e9\u003c/sup\u003e-B\u003csub\u003e9\u003c/sub\u003e ligands. The large calcualted HOMO\u0026ndash;LUMO gap of \u0026Delta;\u003cem\u003eE\u003c/em\u003e\u003csub\u003egap\u003c/sub\u003e = 2.35 eV at PBE0 well supports its high chemical stability. Cage-like La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) appears to be the first metallo-borospherene possessing the same tetrahedral symmetry as its carbon fullerene counterpart\u0026thinsp;\u0026minus;\u0026thinsp;the experimentally observed quintet \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e C\u003csub\u003e28\u003c/sub\u003e (\u003csup\u003e5\u003c/sup\u003eA\u003csub\u003e1\u003c/sub\u003e) [29]. Extensive molecular dynamics simulations\u003c/p\u003e\n\u003cp\u003eindicate that La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) is also highly dynamically stable, with the small calculated average root-mean-square-deviations of RMSD\u0026thinsp;=\u0026thinsp;0.13 \u0026Aring; and maximum bond length deviations of MAXD\u0026thinsp;=\u0026thinsp;0.43 \u0026Aring; at 1000 K, respectively (Fig.\u0026nbsp;2). Detailed NBO analyses show that the La centers in La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) possess the natural atomic charge of \u003cem\u003eq\u003c/em\u003e\u003csub\u003eLa\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;+\u0026thinsp;1.49 |e| and electronic configuration of La[Xe]4f\u003csup\u003e0.16\u003c/sup\u003e5d\u003csup\u003e1.32\u003c/sup\u003e6s\u003csup\u003e0.09\u003c/sup\u003e, indicating that La donates its 6s\u003csup\u003e2\u003c/sup\u003e electron almost completely to the surrounding B\u003csub\u003e9\u003c/sub\u003e ligand in La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) while accepting partial valence electron (~\u0026thinsp;0.32 |e|) from the boron ligand in its partially occupied 5d orbitals via p\u0026rarr;d back donations. Bond order analyses show that the La centers in La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) possess the total Wiberg bond order of WBI\u003csub\u003eLa\u003c/sub\u003e=2.79 and average La\u0026ndash;B bond order of WBI\u003csub\u003eLa\u0026minus;\u0026minus;B\u003c/sub\u003e=0.26, evidencing the formation of effective La\u0026ndash;B coordination interactions in the complex.\u003c/p\u003e\n\u003cp\u003eThe high-symmetry tetrahedral \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e] (\u003cstrong\u003e2)\u003c/strong\u003e (\u003csup\u003e2\u003c/sup\u003eA\u003csub\u003e2\u003c/sub\u003e) was achieved by encapsulating a B-centered tetrahedral \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e B@B\u003csub\u003e4\u003c/sub\u003e core inside cage-like La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e), forming a perfect tetrahedral core-shell lanthanide boride complex with a tetra-coordinate B at the cage center (Fig.\u0026nbsp;1). Surprisingly and intriguingly, extensive DFT calculations indicate that, with a singly occupied non-degenerate highest occupied \u0026alpha;-orbital (a\u003csub\u003e2\u003c/sub\u003e), the doublet La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e] (\u003cstrong\u003e2)\u003c/strong\u003e well retains its identical tetrahedral \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e symmetry during full structural optimizations. As the most stable isomer obtained, it lies 0.79 eV lower than the second lowest-lying isomer \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e (\u003csup\u003e2\u003c/sup\u003eA) (Fig. S2). The tetrahedral B@B\u003csub\u003e4\u003c/sub\u003e core and La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1)\u003c/strong\u003e shell turn out to match both geometrically and electronically in La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e] (\u003cstrong\u003e2)\u003c/strong\u003e which has the lowest vibrational frequency of \u0026upsilon;\u003csub\u003emin\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;128.94 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and \u0026alpha;-HOMO-LUMO gap of △\u003cem\u003eE\u003c/em\u003e\u003csub\u003egap\u003c/sub\u003e=2.23 eV. Detaching one election from or attaching one electron to La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e] (\u003cstrong\u003e2)\u003c/strong\u003e results in the perfect singlet \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e+\u003c/sup\u003e (\u003cstrong\u003e3\u003c/strong\u003e, \u003csup\u003e1\u003c/sup\u003eA\u003csub\u003e1\u003c/sub\u003e\u003cstrong\u003e)\u003c/strong\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e, \u003csup\u003e1\u003c/sup\u003eA\u003csub\u003e1\u003c/sub\u003e) which also appear to be the well-defined GMs of the systems lying 0.79 eV and 0.69 eV lower than the second lowest-lying core-shell \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e at PBE0, respectively (Fig. S3 and Fig. S4). La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e+/\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e3/4)\u003c/strong\u003e possess the large HOMO-LUMO gaps of △\u003cem\u003eE\u003c/em\u003e\u003csub\u003egap\u003c/sub\u003e = 2.84/2.21 eV and lowest vibrational frequencies of \u0026upsilon;\u003csub\u003emin\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;125.50/131.35 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e0/+/\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e2/3/4\u003c/strong\u003e) core-shell complex series in a 1\u0026thinsp;+\u0026thinsp;4\u0026thinsp;+\u0026thinsp;28 structural motif possess the B-B bond lengths of \u003cem\u003er\u003c/em\u003e\u003csub\u003eB\u0026minus;B\u003c/sub\u003e=1.65/1.64/1.66 \u0026Aring; between the central B atom and inner tetrahedron (B\u003csup\u003ei\u003c/sup\u003e)\u003csub\u003e4\u003c/sub\u003e, B-B distances of \u003cem\u003er\u003c/em\u003e\u003csub\u003eB\u0026minus;B\u003c/sub\u003e=1.73/1.73/1.73 \u0026Aring; between the inner tetrahedron (B\u003csup\u003ei\u003c/sup\u003e)\u003csub\u003e4\u003c/sub\u003e and outer tetrahedron (B\u003csup\u003eo\u003c/sup\u003e)\u003csub\u003e24\u003c/sub\u003e, and the La\u0026ndash;B distances of \u003cem\u003er\u003c/em\u003e\u003csub\u003eLa\u0026minus;\u0026minus;B\u003c/sub\u003e=2.88/2.93/2.85 \u0026Aring; between the B atom at the center and La atoms on the outer shell. They can thus be viewed as the first bi-shell metallo-borospherenes with the B center encapsulated in an inner tetrahedron (B\u003csup\u003ei\u003c/sup\u003e)\u003csub\u003e4\u003c/sub\u003e and an outer tetrahedron La\u003csub\u003e4\u003c/sub\u003e(B\u003csup\u003eo\u003c/sup\u003e)\u003csub\u003e24\u003c/sub\u003e. Similar to the previously reported endohedral metallosilicon fullerenes \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e M\u003csub\u003e4\u003c/sub\u003e@Si\u003csub\u003e28\u003c/sub\u003e (M\u0026thinsp;=\u0026thinsp;Al and Ga) which follow the structural motif of 4\u0026thinsp;+\u0026thinsp;28 [28], core-shell La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e0/+/\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e2/3/4\u003c/strong\u003e) in the structural motif of 1\u0026thinsp;+\u0026thinsp;4\u0026thinsp;+\u0026thinsp;28 possess the same tetrahedral symmetry as their carbon fullerene counterpart \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e C\u003csub\u003e28\u003c/sub\u003e [29]. These core-shell complexes also appear to be highly dynamically stable, as exemplified in Fig.\u0026nbsp;2 for La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e) which has the small calculated average RMSD\u0026thinsp;=\u0026thinsp;0.13 \u0026Aring; and MAXD\u0026thinsp;=\u0026thinsp;0.41 \u0026Aring; at 1000 K, respectively.\u003c/p\u003e\n\u003cp\u003eThe behavior of the central B atom in these core-shell complexes appears to be especially interesting. Detailed NBO analyses indcate that the central B in La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e0/+/\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e2/3/4\u003c/strong\u003e) possesses the natural atomic charge of \u003cem\u003eq\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e=-1.00/-1.05/-1.00 |e|, electronic configurations of B[He]2s\u003csup\u003e0.51\u003c/sup\u003e2p\u003csup\u003e3.48\u003c/sup\u003e/B[He]2s\u003csup\u003e0.52\u003c/sup\u003e2p\u003csup\u003e3.52\u003c/sup\u003e\u003cem\u003e/\u003c/em\u003eB[He]2s\u003csup\u003e0.52\u003c/sup\u003e2p\u003csup\u003e3.52\u003c/sup\u003e, and total Wiberger bond orders of WBI\u003csub\u003eB\u003c/sub\u003e = 3.71/3.71/3.71, respectively. The central B atom thus carries approximately a unitary negative charge of q\u003csub\u003eB\u003c/sub\u003e\u0026asymp;-1.0 |e| in these complexes regardless of the charge states of the systems, resulting in a B\u003csup\u003e\u0026minus;\u003c/sup\u003e monoanion at the cage center which is isovalent with a neutral C atom. The negatively charged tetra-coordinate B\u003csup\u003e\u0026minus;\u003c/sup\u003e center in \u003cstrong\u003e2\u003c/strong\u003e, \u003cstrong\u003e3\u003c/strong\u003e, \u003cstrong\u003e4\u003c/strong\u003e is thus a boron analog of the tetrahedral C in \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e CH\u003csub\u003e4\u003c/sub\u003e, indicating the B\u003csup\u003e\u0026minus;\u003c/sup\u003e~C analogy [44] in these B-centered core-shell complexes.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv\u003e\n\u003ch2\u003eBonding analyses\u003c/h2\u003e\n\u003cp\u003eTo better interpret the high stabilities of these \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e lanthanide boride complexes, we performed detailed AdNDP bonding analyses on the closed-shell La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) and La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e+\u003c/sup\u003e (\u003cstrong\u003e3\u003c/strong\u003e) to recover both the localized and delocalized bonds of the systems. As shown in Fig.\u0026nbsp;3(a), La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) possesses 6 2c-2e B-B \u0026sigma; bonds with the occupation number of ON\u0026thinsp;=\u0026thinsp;1.88 |e| between the four inter-connected B\u003csub\u003e6\u003c/sub\u003e triangles on the cage surface and 16 3c-2e \u0026sigma; bonds with ON\u0026thinsp;=\u0026thinsp;1.91 |e| on four equivalent B\u003csub\u003e6\u003c/sub\u003e triangular motifs, forming the \u0026sigma; skeleton of the cage-like system. As expected from chemical intuition, there exist 4 equivalent 6c\u0026ndash;2e \u0026pi; bonds with ON\u0026thinsp;=\u0026thinsp;1.91 over the four interconnected B\u003csub\u003e6\u003c/sub\u003e triangles. The remaining 16 delocalized bonds are mainly responsible for the La\u0026ndash;B\u003csub\u003e9\u003c/sub\u003e coordination interactions in the complex, including 12 equivalent 5c-2e La\u0026ndash;B\u003csub\u003e4\u003c/sub\u003e (d-p) \u0026sigma; bonds with ON\u0026thinsp;=\u0026thinsp;1.72 and 4 equivalent 10c-2e La\u0026ndash;B\u003csub\u003e9\u003c/sub\u003e (d-p) \u0026delta; bond with ON\u0026thinsp;=\u0026thinsp;1.62 evenly distributed over four La@B\u003csub\u003e9\u003c/sub\u003e nonagons on the cage surface. Such a bonding pattern renders spherical aromaticity to cage-like La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e), as evidenced by the calculated negative nucleus-independent chemical shift (NICS) [45] values of NICS = \u0026minus;\u0026thinsp;31.69 ppm at the cage center and NICS = \u0026minus;\u0026thinsp;33.41 ppm 1.0 \u0026Aring; above the cage center along the C\u003csub\u003e2\u003c/sub\u003e molecular axes.\u003c/p\u003e\n\u003cp\u003eFigure\u0026nbsp;3(b) indicates that the core-shell La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e+\u003c/sup\u003e (\u003cstrong\u003e3)\u003c/strong\u003e well inherits the main bonding elements of La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e), with the 6 2c-2e B-B \u0026sigma; bonds, 16 3c-2e \u0026sigma; bonds, 12 5c-2e La\u0026ndash;B\u003csub\u003e4\u003c/sub\u003e (d-p) \u0026sigma; bonds, and 4 10c-2e La-B\u003csub\u003e9\u003c/sub\u003e (d-p) \u0026delta; bonds remaining basically unchanged. The main difference occurs at the 4 2c-2e B-B \u0026sigma;-bonds in the B@B\u003csub\u003e4\u003c/sub\u003e core beween the central B atom and (B\u003csup\u003ei\u003c/sup\u003e)\u003csub\u003e4\u003c/sub\u003e inner tetrahedron and 4 7c-2e B\u003csub\u003e6\u003c/sub\u003e(\u0026pi;)-B(p) \u0026sigma; interactions between the four B\u003csup\u003ei\u003c/sup\u003e atoms in the inner shell and four capping B\u003csub\u003e6\u003c/sub\u003e triangles in the outer shell in the first row and 3 29c-2e \u0026pi;-p \u0026sigma; bonds totally delocalized on the core-shell B\u003csub\u003e29\u003c/sub\u003e framework ([B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]) in the fourth row. Interestingly, similar to La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e), La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e0/+/\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e2/3/4\u003c/strong\u003e) possess the negative calculated NICS values of NICS=-33.92/-43.18/-28.19 ppm 1.0 \u0026Aring; above the B center along the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e molecular axes, respectively, indicating that these core-shell borospherenes are also spherically aromatic in nature. The 12 5c-2e La\u0026ndash;B\u003csub\u003e4\u003c/sub\u003e (d-p) \u0026sigma; and 4 10c-2e La\u0026ndash;B\u003csub\u003e9\u003c/sub\u003e (d-p) \u0026delta; coordination bonds in La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) and La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e+\u003c/sup\u003e\u003cstrong\u003e(3)\u003c/strong\u003e play a vital role in stabilizing these perfect tetrahedral lanthanide boride complexes.\u003c/p\u003e\n\u003cdiv\u003e\n\u003ch2\u003eIR, Raman, and UV-Vis/PES Spectral Simulations\u003c/h2\u003e\n\u003cp\u003eThe IR, Raman, and UV-Vis spectra of La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) and IR, Raman, and PES spectra of La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e) are computationally simulated in Fig.\u0026nbsp;4 to facilitate their future characterizations. \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) possesses highly simplified IR and Raman spectra due to its high symmetry, including four sharp IR peaks at 215(t\u003csub\u003e2\u003c/sub\u003e), 239(t\u003csub\u003e2\u003c/sub\u003e), 810(t\u003csub\u003e2\u003c/sub\u003e) and 1036 (t\u003csub\u003e2\u003c/sub\u003e) cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and eight active Raman vibrations at 137 (a\u003csub\u003e1\u003c/sub\u003e), 239(t\u003csub\u003e2\u003c/sub\u003e), 391(a\u003csub\u003e1\u003c/sub\u003e), 473(a\u003csub\u003e1\u003c/sub\u003e), 1036(t\u003csub\u003e2\u003c/sub\u003e), 1065(a\u003csub\u003e1\u003c/sub\u003e), 1257(t\u003csub\u003e2\u003c/sub\u003e) and 1267(a\u003csub\u003e1\u003c/sub\u003e) cm\u003csup\u003e\u0026minus;1\u003c/sup\u003e, respectively. Detailed vibrational analyses indicate that the symmetrical vibrations at 137 cm\u003csup\u003e\u0026minus;1\u003c/sup\u003e (a\u003csub\u003e1\u003c/sub\u003e) and 391 cm\u003csup\u003e\u0026minus;1\u003c/sup\u003e (a\u003csub\u003e1\u003c/sub\u003e) represent typical radial breathing modes (RBMs) of the cage-like complex which can be used to characterize single-walled hollow boron nanostructures [46]. The strong UV bands around 323, 341, 376, 436 and 459 nm originate from electronic transitions from deep inner shells of the neutral to its high-lying unoccupied molecular orbitals, while the weak broad bands around 490, 526, 625 and 772 nm mainly involve electronic excitations from the occupied frontier orbitals around the HOMO (t\u003csub\u003e2\u003c/sub\u003e) of the neutral. As shown in Fig.\u0026nbsp;4(b), La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e) exhibits similar IR and Raman spectral features to La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e), with the strongest IR vibration at 258 cm\u003csup\u003e\u0026minus;1\u003c/sup\u003e (t\u003csub\u003e2\u003c/sub\u003e) and typical RBM vibrations at 153 cm\u003csup\u003e\u0026minus;1\u003c/sup\u003e (a\u003csub\u003e1\u003c/sub\u003e) and 448 (a\u003csub\u003e1\u003c/sub\u003e) cm\u003csup\u003e\u0026minus;1\u003c/sup\u003e. The calculated PES spectrum of La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e\u0026minus;\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e) exhibits major spectral features at 2.08, 3.51, 3.75, 4.31, and 5.18 eV which correspond to vertical electronic transitions from the ground state of the anion (\u003csup\u003e1\u003c/sup\u003eA\u003csub\u003e1\u003c/sub\u003e) to the ground state (\u003csup\u003e2\u003c/sup\u003eA\u003csub\u003e2\u003c/sub\u003e) and excited states (\u003csup\u003e2\u003c/sup\u003eT\u003csub\u003e1\u003c/sub\u003e, \u003csup\u003e2\u003c/sup\u003eT\u003csub\u003e2\u003c/sub\u003e, \u003csup\u003e2\u003c/sup\u003eT\u003csub\u003e2\u003c/sub\u003e, \u003csup\u003e2\u003c/sup\u003eT\u003csub\u003e2\u003c/sub\u003e) of the neutral at the ground-state geometry of the anion, respectively.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e"},{"header":"Conclusions","content":" \u003cp\u003ePerfect tetrahedral cage-like La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cb\u003e1)\u003c/b\u003e and core-shell La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e0/+/\u0026minus;\u003c/sup\u003e (\u003cb\u003e2\u003c/b\u003e/\u003cb\u003e3\u003c/b\u003e/\u003cb\u003e4)\u003c/b\u003e with spherical aromaticity have been predicted in this work at first-principles theory level to be the first metallo-borospherenes reported to date possessing the same tetrahedral symmetry as their carbon fullerene counterpart \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e C\u003csub\u003e28\u003c/sub\u003e. The tetrahedral B@B\u003csub\u003e4\u003c/sub\u003e core and tetrahedral La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cb\u003e1)\u003c/b\u003e shell match both geometrically and electronically in the La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e0/+/\u0026minus;\u003c/sup\u003e (\u003cb\u003e2\u003c/b\u003e/\u003cb\u003e3\u003c/b\u003e/\u003cb\u003e4\u003c/b\u003e) series. Such species could be synthesized and characterized in gas phases using a La-B binary target in PES experiments.[\u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] These high-symmetry lanthanide boride complexes and their chemically modified derivatives may serve as building blocks to form various nanoclusters and nanomaterials with novel electronic, magnetic, and optical properties.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe work was supported by the National Natural Science Foundation of China (21720102006 and 21973057 to S.-D. Li).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest//Competing interests\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing financial interests\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and material\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eAll the data in this work are transparent\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e: N/A\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors' contributions: \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eS.-D. Li and Z.-H. Wei designed the project and X.-Q. Lu and C.-Y. Gao carried out the calculations. 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J Phys Chem B 108: 3967-3969. https://doi.org/10.1021/jp049301b\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-molecular-modeling","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmmo","sideBox":"Learn more about [Journal of Molecular Modeling](https://www.springer.com/journal/894)","snPcode":"894","submissionUrl":"https://submission.nature.com/new-submission/894/3","title":"Journal of Molecular Modeling","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"First-Principles Theory, Metallo-Borospherenes, Tetrahedral Structures, Bonding Patterns, Spherical Aromaticity","lastPublishedDoi":"10.21203/rs.3.rs-161832/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-161832/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCage-like and core-shell metallo-borospherenes exhibit interesting structures and bonding. Based on extensive global searches and first-principles theory calculations, we predict herein the perfect tetrahedral cage-like \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e (\u003cstrong\u003e1\u003c/strong\u003e) and core-shell \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e (\u003cstrong\u003e2\u003c/strong\u003e), \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e (\u003cstrong\u003e3\u003c/strong\u003e), and \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e La\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e29\u003c/sub\u003e\u003csup\u003e-\u003c/sup\u003e (\u003cstrong\u003e4\u003c/strong\u003e) which all possess the same geometrical symmetry as their carbon fullerene counterpart \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e C\u003csub\u003e28\u003c/sub\u003e, with four equivalent interconnected B\u003csub\u003e6\u003c/sub\u003e triangles on the cage surface and four nona-coordinate La centers in four conjoined η\u003csup\u003e9\u003c/sup\u003e-B\u003csub\u003e9\u003c/sub\u003e rings. In these tetra-La-doped boron complexes, La\u003csub\u003e4\u003c/sub\u003e[B@B\u003csub\u003e4\u003c/sub\u003e@B\u003csub\u003e24\u003c/sub\u003e]\u003csup\u003e0/+/-\u003c/sup\u003e (\u003cstrong\u003e2/3/4\u003c/strong\u003e) in the structural motif of 1+4+28 contain a B-centered tetrahedral\u003cem\u003e T\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e B@B\u003csub\u003e4\u003c/sub\u003e core in a La-decorated tetrahedral\u003cem\u003e \u003c/em\u003eLa\u003csub\u003e4\u003c/sub\u003eB\u003csub\u003e24\u003c/sub\u003e shell, with the negatively charged tetra-coordinate B\u003csup\u003e-\u003c/sup\u003e at the center being the boron analog of tetrahedral C in \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e CH\u003csub\u003e4\u003c/sub\u003e (B\u003csup\u003e-\u003c/sup\u003e~C). Detailed orbital and bonding analyses indicate that these \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e lanthanide boride complexes are spherically aromatic in nature with a universal La--B\u003csub\u003e9\u003c/sub\u003e (d-p) σ and (d-p) δ coordination bonding pattern. The IR, Raman, and UV-Vis or photoelectron spectra of these novel metallo-borospherenes are computationally simulated to facilitate their spectral characterizations.\u003c/p\u003e","manuscriptTitle":"Cage-Like La4B24 and Core-Shell La4B290/+/-: Perfect Spherically Aromatic Tetrahedral Metallo-Borospherenes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-02-09 20:17:10","doi":"10.21203/rs.3.rs-161832/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Minor revisions needed","date":"2021-02-28T09:26:53+00:00","index":"","fulltext":""},{"type":"reviewersInvited","content":"","date":"2021-02-07T00:00:00+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2021-02-07T00:00:00+00:00","index":0,"fulltext":""},{"type":"editorAssigned","content":"","date":"2021-02-01T00:00:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Molecular Modeling","date":"2021-01-22T03:04:40+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-molecular-modeling","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmmo","sideBox":"Learn more about [Journal of Molecular Modeling](https://www.springer.com/journal/894)","snPcode":"894","submissionUrl":"https://submission.nature.com/new-submission/894/3","title":"Journal of Molecular Modeling","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"36c72da1-1475-44fb-8ecb-06297727e7a8","owner":[],"postedDate":"February 9th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":2318213,"name":"Cellular \u0026 Molecular Neuroscience"}],"tags":[],"updatedAt":"2021-08-18T19:15:58+00:00","versionOfRecord":{"articleIdentity":"rs-161832","link":"https://doi.org/10.1007/s00894-021-04739-8","journal":{"identity":"journal-of-molecular-modeling","isVorOnly":false,"title":"Journal of Molecular Modeling"},"publishedOn":"2021-04-21 19:03:04","publishedOnDateReadable":"April 21st, 2021"},"versionCreatedAt":"2021-02-09 20:17:10","video":"","vorDoi":"10.1007/s00894-021-04739-8","vorDoiUrl":"https://doi.org/10.1007/s00894-021-04739-8","workflowStages":[]},"version":"v1","identity":"rs-161832","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-161832","identity":"rs-161832","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}