Metalloborospherene Analogs to Metallofullerene

Abstract

Boron, the neighbor element to carbon in the periodic table, is characterized by unique electron deficiency that fosters multicenter delocalized bonding, contributing to its diverse chemistry. Unlike carbon cages (fullerenes), which preserve their structural integrity under endohedral or exohedral doping, larger boron cages (borospherenes) exhibit diverse structural configurations. These configurations can differ from those of pure boron cages and are stabilized by various metals through unique metal–boron bonding, resulting in a variety of metalloborospherenes. Due to boron’s electron deficiency, metalloborospherenes exhibit fascinating chemical bonding patterns that vary with cluster size and the type of metal dopants. This review paper highlights recent advancements in metalloborospherene research, drawing comparisons with metallofullerenes, and focuses on the use of transition metals, lanthanides, and actinides as dopants across various cage dimensions.

1. Introduction

The discovery and characterization of fullerenes, a class of carbon cage structures, have profoundly impacted various fields of chemistry and materials science. Fullerenes, composed predominantly of pentagonal and hexagonal carbon rings, exhibit remarkable stability due to their unique ${\mathrm{sp}}^2$ hybridization and delocalized $\pi$-electron system [1,2]. Among these, ${\mathrm{C}}_{60}$, known as buckminsterfullerene, is the most well-known and stable fullerene, characterized by a structure comprising 12 pentagons and 20 hexagons [3,4]. This stability is attributed to the Isolated Pentagon Rule (IPR), which states that no two pentagons should share an edge, minimizing strain in the carbon network [5].

Boron, a neighbor of carbon in the periodic table, forms analogous cage-like structures known as borospherenes, first discovered in the ${\mathrm{B}}_{40}^{-}$ cage [6]. Unlike carbon, boron is electron-deficient, which gives rise to the formation of multicenter bonds to stabilize its structures [7,8]. This electron deficiency leads to diverse bonding patterns, including delocalized $\sigma$ and $\pi$ bonds, which stabilize planar or quasi-planar clusters for boron clusters up to ${\mathrm{B}}_{38}^{-}$ [6,9]. This delocalized bonding scheme imparts extraordinary stability to planar boron clusters due to multiple aromaticities, where the number of delocalized electrons satisfies the (4n + 2) Hückel rule, analogous to hydrocarbons [10]. However, larger boron cages, such as the seashell-like chiral ${\mathrm{B}}_{28}^{-}$ cluster and the ${\mathrm{B}}_{40}^{-}$, adopt fullerene-like structures [6,11] that are stabilized through delocalized multicenter bonding to maintain the structural integrity despite their larger size.

The unique electronic properties of boron make it an excellent candidate for forming stable metalloborospherenes through metal doping [7]. These structures can be stabilized by incorporating various metals, leading to significant changes in their geometrical and electronic configurations. Metalloborospherenes exhibit a range of fascinating bonding patterns and structural motifs that evolve with cluster size and metal composition. This review compares recent advancements in metalloborospherene research with metallofullerene studies, focusing on transition metals, lanthanides, and actinides as dopants in various cage dimensions.

Metallofullerenes are formed by encapsulating metal atoms within fullerene cages, such as ${\mathrm{C}}_{60}$ or its analogs, using methods like arc discharge, laser ablation, and chemical vapor deposition [12,13]. The encapsulated metal atoms significantly influence the properties of fullerenes, leading to various applications in materials science, medicine, and catalysis. For example, in materials science, metallofullerenes are used to enhance the mechanical and electronic properties of composite materials. In medicine, they are explored for drug delivery systems and diagnostic imaging due to their ability to encapsulate therapeutic agents or contrast materials [14,15,16]. By comparison, metalloborospherenes, though less understood, involve substantial interactions between the metal atoms and the boron framework. These interactions result in unique structural and electronic properties that differ significantly from those of metallofullerenes. Metalloborospherenes exhibit complex bonding patterns and structural motifs that evolve with cluster size and the type of metal dopant. The incorporation of different metals can lead to a variety of electronic properties, making metalloborospherenes potentially valuable for applications in catalysis, electronics, and nanotechnology [7,17]. Understanding these properties requires further research, but the potential for discovering new materials with tailored functionalities is significant.

Recent studies have explored the incorporation of lanthanide atoms within borospherenes; ${\mathrm{La}}_3$${\mathrm{B}}_{18}^{-}$ was the first observed metalloborospherene [18], and exhibits distinctive bonding interactions due to charge transfer and significant (d–p)$\pi$ and (d–p)$\delta$ bonding [19,20]. These interactions lead to novel structural motifs, including inverse-sandwich and trihedral configurations, which are not commonly observed in other types of boron clusters [18,21]. Similarly, transition-metal-based and actinide-based metalloborospherenes have been theoretically predicted, revealing complex electronic structures and unique bonding patterns that differ from those of their lanthanide counterparts [22,23]. These theoretical predictions indicate the possibility of forming stable complexes with actinides, which could have implications for both fundamental chemistry and potential applications. Although the study of metalloborospherenes is still in its early stages and lacks extensive experimental evidence, the initial findings suggest that both fullerene and borospherene cages have the potential to stabilize unconventional metal clusters, paving the way for new materials with advanced properties. These materials could find applications in various fields, including catalysis, electronic devices, and materials science, due to their unique structural and electronic characteristics. The exploration of these novel metalloborospherenes and metallofullerenes opens up exciting avenues for future research, highlighting the need for further experimental and theoretical investigations to fully understand their potential and to harness their properties for practical applications.

2. Structures of Fullerene and Borospherene

Fullerenes are enclosed cages of carbon molecules composed of many adjacent rings, with rings of size n = 5 or n = 6 being more prevalent than other ring sizes, suggesting that fullerenes consisting of pentagons and hexagons exhibit increased stability [1,2]. The smallest fullerene that satisfies these requirements is ${\mathrm{C}}_{60}$, as shown in Figure 1 [3]. This cage structure is a network of ${\mathrm{sp}}^2$-hybridized carbon atoms, where paired valence electrons from the 2 s orbitals collectively inhabit molecular orbitals arranged in triangular units centered around each carbon atom individually, forming a delocalized $\sigma$ network [4]. The triangular ${\mathrm{sp}}^2$ hybrid orbitals of every adjacent carbon atom then overlap from end to end to form pentagonal rings, which constitute the faces of the “soccer ball” structure of the fullerene [4]. This concept is referred to as the Isolated Pentagon Rule (IPR), which asserts that the most stable state of a purely carbon or metal-doped fullerene is a network with the minimum number of separate pentagons required for the carbon atom count, with every bonding electron being fully delocalized over the $\sigma$ molecular orbital [5]. The remaining two valence 2p electrons in carbon inhabit a fully occupied 2p state, overlapping in a $\pi$ formation, where the lobes (amplitudes) of the 2p wavefunctions conjoin to cover a continuous $\pi$ (2p) orbital over the full carbon cage surface [5]. In these carbon fullerenes, the presence of two electrons in the 2p state enhances stability by resulting in occupancy of one electron in both the degenerate $2p_x$ and $2p_y$ orbitals of carbon in accordance with Hund’s rule. This results in a sufficient number of electrons being distributed throughout both delocalized molecular orbitals [5].

Boron fullerenes, known as borospherenes [6], are analogous to carbon fullerenes. Figure 1 summarizes the reported borospherene structures validated by theoretical studies and photoelectron spectroscopy (PES) [24]. Unlike carbon, boron is electron-deficient, possessing only one 2p electron, which leads to the formation of delocalized $\sigma$ and $\pi$ bonds [6,7,8,9]. This electron deficiency necessitates a more complex bonding scheme to achieve stability. Boron clusters often adopt planar or quasi-planar structures (up to ${\mathrm{B}}_{38}^{-}$) [7] to maximize electron delocalization and minimize electronic repulsion, a stark contrast to the spherical structures of carbon fullerenes that adhere to a $2{(n+1)}^2$$\pi$-electron counting rule to determine spherical aromaticity [25]. In borospherenes, more electrons need to be delocalized over the structure to mitigate the electron deficiency effect, resulting in unique bonding characteristics and stability [26]. The presence of delocalized $\sigma$ and $\pi$ bonds in borospherenes allows for a double delocalization pattern, which is observed less frequently in carbon fullerenes. This double delocalization leads to increased stability and distinct chemical properties. Additionally, boron’s propensity for forming multicenter bonds contributes to the diversity in structural motifs observed in borospherenes, ranging from planar to tubular and cage-like structures, depending on the size and composition of the cluster [8,9].

Figure 1. Known borospherene structures of ${\mathrm{B}}_{28}^{-}$ [11,27], ${\mathrm{B}}_{29}^{-}$ [28], ${\mathrm{B}}_{39}^{-}$ [29], and ${\mathrm{B}}_{40}^{-}$ [6] validated by PES and quantum chemistry calculations compared with $I_h$-${\mathrm{C}}_{60}$ and $D_{5h}$-${\mathrm{C}}_{70}$. Here, ${\mathrm{B}}_{28}^{-}$ and ${\mathrm{B}}_{39}^{-}$ systems demonstrate chiral enantiomers.

Figure 1. Known borospherene structures of ${\mathrm{B}}_{28}^{-}$ [11,27], ${\mathrm{B}}_{29}^{-}$ [28], ${\mathrm{B}}_{39}^{-}$ [29], and ${\mathrm{B}}_{40}^{-}$ [6] validated by PES and quantum chemistry calculations compared with $I_h$-${\mathrm{C}}_{60}$ and $D_{5h}$-${\mathrm{C}}_{70}$. Here, ${\mathrm{B}}_{28}^{-}$ and ${\mathrm{B}}_{39}^{-}$ systems demonstrate chiral enantiomers.

The first borospherene structure experimentally and theoretically reported was neutral ${\mathrm{B}}_{40}$ [6], as shown in Figure 1. This structure consists of eight ${\mathrm{B}}_6$ quasi-planar triangle faces with two ${\mathrm{B}}_6$ rings on the top and bottom and two ${\mathrm{B}}_7$ rings on the sides in between the triangle faces. The anion counterpart, ${\mathrm{B}}_{40}^{-}$, has two coexisting degenerate isomers with planar and cage-like shapes, respectively. In the ${\mathrm{B}}_{39}^{-}$ cluster [29], two distinct chiral borospherene isomers with ${\mathrm{C}}_2$ and ${\mathrm{C}}_3$ symmetry were discovered through PES and theoretical studies, both derived from the ${\mathrm{B}}_{40}$ borospherene. The ${\mathrm{C}}_3$ isomer can be formed by replacing a ${\mathrm{B}}_7$ heptagon in the ${\mathrm{B}}_{40}$ cage with a ${\mathrm{B}}_6$ hexagon, followed by structural reorganization. The ${\mathrm{C}}_2$ ${\mathrm{B}}_{39}^{-}$ isomer, on the other hand, can be created by removing a single boron atom from the waist of the ${\mathrm{B}}_{40}$ borospherene, resulting in a narrowed boron double chain and the formation of a “defect” site. The seashell-like ${\mathrm{B}}_{28}^{-}$ has been identified as the smallest borospherene, featuring chiral enantiomers with ${\mathrm{C}}_2$ point-group symmetry [11,27], as shown in Figure 1. The PES of ${\mathrm{B}}_{29}^{-}$ [28] exhibits a complex pattern, indicating the presence of low-lying isomers. Global minimum searches and extensive theoretical calculations have revealed a complicated potential energy surface for ${\mathrm{B}}_{29}^{-}$, with multiple low-lying isomers contributing to the experimental spectrum. Among these, the global minimum is a three-dimensional seashell-like ${\mathrm{C}}_s$ ${(}^1$${\mathrm{A}}^{\prime }$) borospherene isomer, characterized by two heptagons on the waist and one octagon at the bottom. This is followed by a planar ${\mathrm{C}}_1$ ${(}^1$A) isomer with a hexagonal hole and a stingray-shaped planar ${\mathrm{C}}_s$ ${(}^1$${\mathrm{A}}^{\prime }$) isomer featuring a pentagonal hole.

Ab initio calculations suggest that ${\mathrm{B}}_{44}^{-}$ may be the next negatively charged borospherene, although extensive global minima searching has not been conducted [30]. Additionally, theoretical studies have predicted a variety of borospherene structures. The global minimum structures of several positively charged boron clusters have been identified as borospherene configurations, including ${\mathrm{B}}_{29}^{+}$, ${\mathrm{B}}_{31}^{+}$, ${\mathrm{B}}_{35}^{+}$, ${\mathrm{B}}_{38}^{+}$, ${\mathrm{B}}_{38}^{2+}$, ${\mathrm{B}}_{39}^{+}$, ${\mathrm{B}}_{40}^{+}$, ${\mathrm{B}}_{41}^{+}$, and ${\mathrm{B}}_{42}^{+}$ [26,30,31,32,33,34,35]. To date, no borospherene clusters larger than ${\mathrm{B}}_{42}$ have been identified through global minimum searches [36]. Nevertheless, numerous stable structures for large borospherenes have been predicted with high stability [36,37]. For larger clusters such as ${\mathrm{B}}_{80}$, a buckminsterfullerene template was used as the starting structure, adding one boron atom to the center of each hexagon face [38]. Subsequent studies have revealed that core–shell structures, where additional atoms are incorporated inside the cage, are more stable than their hollow counterparts [39].

3. Metallofullerene and Metalloborospherene

Metallofullerenes are formed by trapping metal atoms inside the hollow cages of fullerenes [12,13], such as ${\mathrm{C}}_{60}$ or larger fullerenes like ${\mathrm{C}}_{70}$. The encapsulation process can occur through methods like arc discharge, laser ablation, and chemical vapor deposition. Their ability to encapsulate metal atoms opens up numerous possibilities for advancements in materials science, medicine, and catalysis, making them a significant area of study in nanotechnology and materials chemistry [14,15,16]. Metalloborospherenes, unlike metallofullerenes, involve significant interactions between the metal atoms and the boron cage structures [7,17]. These interactions often result in substantial changes to the boron framework, leading to the formation of unique metalloborospherene structures through metal-boron ring chemical bonding.

3.1. Lanthanide-Doped Fullerene and Borospherene Clusters

Endohedral metallofullerenes (EMFs) offer a unique platform for studying otherwise unstable metallic clusters due to the protective environment provided by fullerene cages. Lanthanide atoms can be encapsulated within these cages, forming various structures such as monometallofullerenes, dimetallofullerenes, carbide clusterfullerenes with an ${\mathrm{M}}_2$${\mathrm{C}}_2$ unit encapsulated inside the fullerene cages, and nitride clusterfullerenes [40,41]. The interaction between the lanthanide atoms and the coordinated carbon rings facilitates charge transfer, leading to unusual valence states and chemical bonding patterns. For example, single-electron lanthanide–lanthanide bonds can form within ${\mathrm{C}}_{80}$ fullerenes, resulting in robust redox-active molecular magnets [42,43]. Crystallographic analysis of typical carbide clusterfullerenes has revealed a relationship between the ionic radius of encapsulated metal ions and the size of the fullerene cage. Using Shannon ionic radii [44], it has been observed that larger cages accommodate larger metal ions. For example, ${\mathrm{Sc}}_2$${\mathrm{C}}_2$ is typically found within ${\mathrm{C}}_{72–88}$ cages, ${\mathrm{Er}}_2$${\mathrm{C}}_2$ within ${\mathrm{C}}_{80–92}$ cages, and ${\mathrm{La}}_2$${\mathrm{C}}_2$ within ${\mathrm{C}}_{90–104}$ cages, respectively (Figure 2) [40].

Due to the electron deficiency of boron, lanthanide elements usually form dative bonds with boron group ligands. Recent findings show that lanthanide-doped boron clusters exhibit unique structures due to charge transfer interactions and significant (d–p)$\pi$ and (d–p)$\delta$ bonding [19,20]. Unlike transition metal-doped boron clusters, which often form borometallic molecular wheels, lanthanide-doped clusters create distinct inverse-sandwich-type structures, particularly evident in ${\mathrm{Ln}}_2$${\mathrm{B}}_n^{-}$ clusters (n = 7–9) [21]. Furthermore, the latest research suggests that these inverse-sandwich configurations can extend to form lanthanide–boron nanowires. The first experimentally observed tri-metal-doped inverse triple-decker, ${\mathrm{La}}_3$${\mathrm{B}}_{14}^{-}$ with ${\mathrm{C}}_{2v}$ point group, exhibits a unique structure where three lanthanum atoms are positioned between two conjoined ${\eta }^8$-${\mathrm{B}}_8$ rings that share a B–B unit on one edge, resulting in a tilted La–${\mathrm{B}}_8$–La–${\mathrm{B}}_8$–La configuration [45]. With increasing cluster size, recent studies have identified the first perfect spherical trihedral metalloborospherenes, ${\mathrm{D}}_{3h}$ ${\mathrm{Ln}}_3$${\mathrm{B}}_{18}^{-}$ (Ln = La, Tb) [18], through joint PES and first-principles theory investigations. These metalloborospherenes are notable for their distinct geometry, featuring three deca-coordinate lanthanide centers that are integral to the cage surface. These centers are coordinated within three equivalent ${\eta }^{10}$-${\mathrm{B}}_{10}$ decagons, which share two eclipsed triangular ${\mathrm{B}}_6$ units connected by three ${\mathrm{B}}_2$ units, as shown in Figure 3. Due to the 4f electrons of lanthanides, this configuration gives these metalloborospherenes unique magnetic and catalytic properties.

Following the discovery of the first lanthanide-doped borospherene, ${\mathrm{La}}_3$${\mathrm{B}}_{18}^{-}$, a series of theoretical studies have emerged, predicting the existence of other lanthanide-doped borospherene structures with varying numbers of lanthanide atoms. Two core–shell-like metalloborospherenes, ${\mathrm{C}}_{2v}$ ${\mathrm{La}}_3$& [${\mathrm{B}}_2$@${\mathrm{B}}_{17}$${]}^{-}$ and ${\mathrm{D}}_{3h}$ ${\mathrm{La}}_3$& [${\mathrm{B}}_2$@${\mathrm{B}}_{18}$${]}^{-}$ have been identified, featuring a transition-metal-like ${\mathrm{B}}_2$ core at the center of the ${\mathrm{La}}_3$${\mathrm{B}}_{17}^{-}$ and ${\mathrm{La}}_3$${\mathrm{B}}_{18}^{-}$ cages [46]. These structures exhibit unique donor–acceptor duality within the ${\mathrm{La}}_3$&${\mathrm{B}}_n^{-}$ spherical trihedral shells (n = 17, 18). The ${\mathrm{B}}_2$ core acts as a donor–acceptor entity, contributing to the stability and electronic properties of the metalloborospherenes. Unlike the tri-lanthanide-doped metalloborospherene, which typically exhibits in-plane coordination with boron atoms, the tri-lanthanide-doped metallofullerene Ln₃@C₈₀⁺ cation features an endohedral structure [47]. In this configuration, the Ln₃ cluster is situated inside the carbon cage and interacts through a three-center two-electron (3c-2e) $\sigma$ bond. Lu et al. theoretically proposed a ${\mathrm{T}}_d$ ${\mathrm{La}}_4$${\mathrm{B}}_{24}$ cluster featuring a tetrahedral cage structure [48]. This cluster consists of four interconnected ${\mathrm{B}}_6$ triangles on the surface and four nona-coordinate lanthanum atoms embedded within four conjoined ${\eta }^9$-${\mathrm{B}}_9$ nonagonal ligands. This configuration represents a boron-based counterpart to the experimentally observed ${\mathrm{T}}_d$ ${\mathrm{C}}_{28}$ tetrahedral carbon fullerene [49].

Theoretically, as the number of boron atoms increases, the resulting boron cages become sufficiently large to accommodate endohedral doping. For instance, M@${\mathrm{B}}_n$ (M = Eu, Gd; n = 38, 40) clusters have been predicted to form spherically symmetric endohedral metalloborospherenes [50], which is a derivative of the ${\mathrm{B}}_{40}$ borospherene structure [6].

3.2. Transition Metal-Containing Fullerene and Borospherene

In this section, we focus on transition metal-containing EMFs to compare their structures with metalloborospherenes. Over the past two decades, rare-Earth metals, such as Group-3 elements (Sc, Y) and many lanthanides, have been successfully encapsulated within fullerene cages. The exploration of EMFs with d-block transition metals began in 1992 with the detection of Ti@${\mathrm{C}}_{28}$ [51]. The macroscopic synthesis of Ti-containing EMFs, such as ${\mathrm{Ti}}_2$${\mathrm{C}}_{80}$ and ${\mathrm{Ti}}_2$${\mathrm{C}}_{84}$, was first reported by Shinohara et al. [52,53]. In 2013, Echegoyen et al. identified ${\mathrm{Ti}}_2$S@${\mathrm{C}}_{78}$, which features a near-linear ${\mathrm{Ti}}_2$S cluster inside the fullerene cage [54]. Recently, Lu and colleagues prepared ${\mathrm{Ti}}_3$${\mathrm{C}}_3$@${\mathrm{I}}_h$(7)-${\mathrm{C}}_{80}$ [55], which displays a unique cyclopropane-like geometry. The use of Group-3 metals in mixed-metal clusters has also led to the creation of nitride and carbide clusterfullerenes [56]. Synthesizing V-only EMFs has proven to be challenging. However, inspired by the successful synthesis of the M-Ti system, researchers used Sc to facilitate the encapsulation of vanadium. This approach led to the synthesis of mixed-metal nitride and carbide cluster fullerenes, such as ${\mathrm{VSc}}_2$N@${\mathrm{I}}_h$(7)-${\mathrm{C}}_{80}$ and ${\mathrm{VSc}}_2$C@${\mathrm{I}}_h$(7)-${\mathrm{C}}_{80}$ [57]. Unlike Ti-clusterfullerenes, V-containing clusters can host one or two V atoms, highlighting their unique chemical properties. This distinction underscores the complexity and diversity of transition metal-containing EMFs, as the incorporation of different metals can lead to varied structural and electronic characteristics.

Since the isolation of the first EMFs in the early 1990s, their electronic structures have been of significant interest due to their correlation with stability. The high electron affinity of fullerenes suggests an ionic structure for EMFs, with metal cations encapsulated within negatively charged carbon cages (e.g., ${\mathrm{Y}}^{3+}$@${\mathrm{C}}_{82}^{3-}$) [58]. This was confirmed by ESR spectroscopy and molecular orbital analysis, which indicated that spin density and frontier MOs are localized on the fullerene cage. This ionic model applies to monometallofullerenes and complex species like dimetallofullerenes, nitride clusterfullerenes, and carbide clusterfullerenes, including Ti-containing EMFs such as ${\mathrm{Ti}}_2$${\mathrm{C}}_{80}$ and ${\mathrm{Ti}}_2$${\mathrm{C}}_{84}$. Various spectroscopic and computational studies [59,60,61] support this ionic nature, with XPS, UV-vis-NIR, and electrochemistry showing similar properties for isostructural EMFs. However, studies reveal a covalent contribution to metal–cage bonding, evident in smaller computed atomic charges and detailed electron density analyses [62].

Compared with metallofullerene, doping boron nanoclusters with transition metals results in significant structural transformations. As illustrated in Figure 4 and reported in our recent review paper [7], joint experimental and computational studies have observed structures including wheel-like clusters such as ${\mathrm{D}}_{8h}$ ${\mathrm{Co\copyright B}}_8^{-}$, ${\mathrm{D}}_{9h}$ ${\mathrm{M\copyright B}}_9^{-}$ (M = Rh, Ir, Re), and ${\mathrm{D}}_{10h}$ ${\mathrm{M\copyright B}}_{10}^{-}$ (M = Ta, Nb) [63,64,65], half-sandwich clusters like ${\mathrm{C}}_{3v}$ ${\mathrm{CoB}}_{12}^{-}$ and ${\mathrm{IrB}}_{12}^{-}$ [66], and tubular clusters such as ${\mathrm{D}}_{8d}$ ${\mathrm{CoB}}_{16}^{-}$ [67], ${\mathrm{MnB}}_{16}^{-}$ [68], ${\mathrm{RhB}}_{18}^{-}$ [69], ${\mathrm{C}}_s$ ${\mathrm{B}}_2$–Ta${@}_{18}^{-}$, and ${\mathrm{D}}_{10d}$ Ta@${\mathrm{B}}_{20}^{-}$, with Ta@${\mathrm{B}}_{20}^{-}$ exhibiting the highest coordination number (CN = 20) among tubular species [70]. The metal-centered tubular boron clusters exhibit multiple aromaticities due to the delocalized bonding, which results from the efficient overlap between the orbitals of the metal center and the surrounding boron group orbitals. It should be noted that no experimental evidence for the transition metal-containing metalloborospherene structures has been reported.

Table 1. Theoretically Predicted Transition Metal-Containing Borospherenes.

Species	Symmetry	Doping Mechanism
${\mathrm{Ta}}_3$${\mathrm{B}}_{12}^{-}$ [75]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Zr}}_3$${\mathrm{B}}_{15}^{+}$ [77]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Zr}}_3$${\mathrm{B}}_{15}$ [77]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Zr}}_3$${\mathrm{B}}_{15}^{-}$ [77]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Hf}}_3$${\mathrm{B}}_{15}^{+}$ [77]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Hf}}_3$${\mathrm{B}}_{15}$ [77]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Hf}}_3$${\mathrm{B}}_{15}^{-}$ [77]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{V}}_3$${\mathrm{B}}_{16}^{-}$ [78]	${\mathrm{C}}_{2v}$	endohedral
${\mathrm{Cr}}_3$${\mathrm{B}}_{16}^{-}$ [78]	${\mathrm{C}}_{4v}$	endohedral
${\mathrm{Mn}}_3$${\mathrm{B}}_{16}^{-}$ [78]	${\mathrm{C}}_{4v}$	endohedral
${\mathrm{Fe}}_3$${\mathrm{B}}_{16}^{-}$ [78]	${\mathrm{D}}_{8d}$	endohedral
${\mathrm{Co}}_3$${\mathrm{B}}_{16}^{-}$ [78]	${\mathrm{D}}_{8d}$	endohedral
${\mathrm{Ni}}_3$${\mathrm{B}}_{16}^{-}$ [78]	${\mathrm{C}}_s$	endohedral
${\mathrm{Ta}}_4$${\mathrm{B}}_{18}^{-}$ [79]	${\mathrm{T}}_d$	exohedral
${\mathrm{Nb}}_4$${\mathrm{B}}_{18}^{-}$ [79]	${\mathrm{T}}_d$	exohedral
${\mathrm{Sc}}_3$${\mathrm{B}}_{20}^{-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Y}}_3$${\mathrm{B}}_{20}^{-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Ti}}_3$${\mathrm{B}}_{20}^{-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Zr}}_3$${\mathrm{B}}_{20}^{-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Hf}}_3$${\mathrm{B}}_{20}^{-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Sc}}_3$${\mathrm{B}}_{20}^{3-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Y}}_3$${\mathrm{B}}_{20}^{3-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Sc}}_4$${\mathrm{B}}_{20}^{-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{Y}}_4$${\mathrm{B}}_{20}^{-}$ [71]	${\mathrm{D}}_{3h}$	exohedral
${\mathrm{ScB}}_{24}^{-}$ [80]	${\mathrm{D}}_2$	endohedral
${\mathrm{TiB}}_{24}^{-}$ [80]	${\mathrm{D}}_{3h}$	endohedral
${\mathrm{VB}}_{24}^{-}$ [80]	${\mathrm{C}}_{2v}$	endohedral
${\mathrm{CrB}}_{24}^{-}$ [80]	${\mathrm{C}}_s$	endohedral
${\mathrm{MnB}}_{24}^{-}$ [80]	${\mathrm{C}}_s$	endohedral
${\mathrm{FeB}}_{24}^{-}$ [80]	${\mathrm{C}}_s$	endohedral
${\mathrm{CoB}}_{24}^{-}$ [80]	${\mathrm{C}}_s$	endohedral
${\mathrm{SrB}}_{40}^{-}$ [76,81]	${\mathrm{D}}_{2d}$	endohedral
${\mathrm{CaB}}_{40}^{-}$ [76,81]	${\mathrm{C}}_{2v}$	endohedral
${\mathrm{BeB}}_{40}^{-}$ [76,81]	${\mathrm{C}}_s$	exohedral
${\mathrm{MgB}}_{40}^{-}$ [76,81]	${\mathrm{C}}_s$	exohedral
${\mathrm{LiB}}_{40}$ [82]	${\mathrm{C}}_s$	exohedral
${\mathrm{NaB}}_{40}$ [82]	${\mathrm{C}}_{2v}$	endohedral
${\mathrm{KB}}_{40}$ [82]	${\mathrm{C}}_s$	exohedral
${\mathrm{BaB}}_{40}$ [82]	${\mathrm{D}}_{2d}$	endohedral
${\mathrm{TlB}}_{40}$ [82]	${\mathrm{C}}_s$	exohedral
${\mathrm{TiB}}_{40}$ [83]	${\mathrm{C}}_1$	endohedral
${\mathrm{Ti}}_2$${\mathrm{B}}_{40}$ [83]	${\mathrm{C}}_s$	endohedral

lists the predicted structures along with their corresponding doping patterns and symmetries, which await validation through experimental characterization. More recent theoretical predictions include spherical trihedral metalloborospherenes and endohedral complexes ${\mathrm{B}}_{20}$${\mathrm{TM}}_n$ (TM = Sc, Y; n = 3, 4) [71], Ta-centered metalloborospherenes such as Ta@${\mathrm{B}}_{22}^{-}$ and Ta@${\mathrm{B}}_n^q$ (n = 23–28, q = −1–3), the smallest trihedral metalloborospherene ${\mathrm{D}}_{3h}$ ${\mathrm{Ta}}_3$${\mathrm{B}}_{12}^{-}$ with $\sigma$ + $\pi$ + $\delta$ aromaticity, and the spherical tetrahedral metalloborospherene ${\mathrm{T}}_d$ ${\mathrm{Ta}}_4$${\mathrm{B}}_{18}$ with four nonacoordinate Ta centers [72,73]. For larger boron sizes, theoretical studies have previously proposed the existence of metalloborospherenes, specifically for ${\mathrm{MB}}_{40}$ (M = Be, Mg) and ${\mathrm{Ni}}_n$${\mathrm{B}}_{40}$ (n = 1–4) [74,75,76], which feature seven-coordinate metal centers on the ${\mathrm{B}}_{40}$ cage surface. These structures are related to the corresponding metalloborophenes, serving as precursors with similar coordination environments for the metal centers.

3.3. Actinide-Containing Fullerene and Borospherene

Actinide-based EMFs have recently garnered interest, compared with the extensively researched lanthanide-based EMFs [22]. Due to the diverse valence electron shells of actinide elements, actinide EMFs have revealed intricate electronic structures and novel bonding configurations not present in lanthanide counterparts [23], suggesting that the unique actinide clusters encapsulated within fullerene cages offer a valuable platform to examine the nature of actinide–ligand interactions within a controlled, inert environment, thereby unveiling new dimensions of actinide chemistry.

A defining characteristic of actinide EMFs is the substantial charge transfer from the metal to the fullerene cage, influencing both their stability and reactivity. Early actinides, such as thorium (Th), plutonium (Pu), and uranium (U), are notably redox-active and exhibit a wide range of oxidation states [84]. For instance, U can be present in various oxidation states, from U(III) to U(VI), in contrast to the limited oxidation states of lanthanides [85,86]. The high chemical activity of the 5f orbitals in actinides results in unique cage isomer preferences and novel electronic structures [85,87]. Although the radioactivity of actinides has traditionally restricted their study to theoretical calculations and limited spectroscopy, recent experimental advancements have significantly deepened our understanding, exemplified by the first crystallographic analysis of Th@${\mathrm{C}}_{3v}$(8)-${\mathrm{C}}_{82}$ and the identification of a formal ${\mathrm{U}}^{5+}$ charge state in ${\mathrm{U}}_2$C@${\mathrm{I}}_h$(7)-${\mathrm{C}}_{80}$ [49,88]. Additionally, UCU@${\mathrm{I}}_h$(7)-${\mathrm{C}}_{80}$ represents the first actinide metallic cluster EMF, showcasing unsupported U=C double bonds [89]. Recent advancements have expanded our knowledge of actinide clusterfullerene families with the synthesis and characterization of ${\mathrm{U}}_2$${\mathrm{C}}_2$@${\mathrm{I}}_h$(7)-${\mathrm{C}}_{80}$ and UCN@${\mathrm{C}}_s$(6)-${\mathrm{C}}_{82}$ [90,91,92]. ${\mathrm{U}}_2$${\mathrm{C}}_2$@${\mathrm{I}}_h$(7)-${\mathrm{C}}_{80}$ features two uranium atoms bridged by a carbon–carbon triple bond (C ≡ C), while UCN@${\mathrm{C}}_s$(6)-${\mathrm{C}}_{82}$ contains a triangular UCN cluster with ${\eta }^2$ (side-on) coordination of uranium by cyanide. These discoveries underscore the potential of fullerene cages to stabilize unconventional actinide clusters, offering profound insights into actinide bonding and paving the way for the development of advanced materials.

Although various metal-doped boron clusters have been reported, actinide (An)-doped boron clusters remain relatively unexplored due to significant challenges in both experimental and computational approaches. Similar to other metal atoms, doping boron clusters with actinides can enhance their stability and lead to diverse geometrical structures. Notable computational examples include the half-sandwich structures ${\mathrm{AnB}}_{12}$ (An = Th to Cm) [93], the double-ring tubular structures An@${\mathrm{B}}_{20}$ [94], An@${\mathrm{B}}_{24}$ (An = Th, Pu, and Am) [95], and the actinide-centered borane ${\mathrm{An}\left(\mathrm{BH}\right)}_{24}$ (An = Th to Cm) [96]. Inspired by the discovery of monovalent lanthanides in the ${{\mathrm{LnB}}_8}^{-}$ system through PES and quantum chemistry calculations [97], we investigated the ${{\mathrm{AnB}}_8}^{-}$ system and identified the potential for monovalent actinide elements in later actinides such as ${{\mathrm{BkB}}_8}^{-}$, ${{\mathrm{MdB}}_8}^{-}$, and ${{\mathrm{NoB}}_8}^{-}$ [98]. Despite significant interest in metalloborospherenes, there is limited evidence for the stabilization of boron cages by actinide metal atoms, with the notable exception of the recently theoretically reported boron cluster U@${\mathrm{B}}_{40}$. This discovery raises intriguing questions about the viability of other actinide metal-doped borospherenes. Theoretical calculations have demonstrated the existence of actinide endohedral borospherenes such as An@${\mathrm{B}}_n$ (An = U and Th; n = 36, 38, and 40) [99,100] and the chiral actinide endohedral borospherenes Ac@${\mathrm{B}}_{39}$, [Ac@${\mathrm{B}}_{39}$${]}^{2+}$, Th@${\mathrm{B}}_{39}$, and [Th@${\mathrm{B}}_{39}$${]}^{3+}$ [101]. Additionally, global searches have revealed that U@${\mathrm{B}}_{24}$ possesses a unique half-cage structure [96]. These findings highlight the potential for a broader range of actinide-doped boron clusters, suggesting new avenues for research into their stability, electronic properties, and geometric configurations. The continued exploration of these systems could provide valuable insights into the bonding characteristics and chemical behavior of actinides, further expanding the understanding of actinide chemistry in novel boron-based materials. Actinide metallofullerenes and actinide metalloborospherenes exhibit significant differences in their structural, electronic, and stability characteristics. Actinide metallofullerenes, composed of actinide atoms encapsulated within highly symmetric carbon-based fullerene cages, rely on substantial metal-to-cage charge transfer interactions for stability that are rarely observed in other systems where a single metal ion is positioned within a carbon cage, and exhibit unique redox properties influenced by the interaction of actinide 5f orbitals with the carbon $\pi$-system [22,87,88]. In contrast, actinide metalloborospherenes, consisting of actinide atoms within boron-based cages [102], present a broader range of geometrical configurations due to boron’s ability to form multicenter bonds. The study of these actinide-doped clusters provides valuable insights into the complex chemistry of actinides, with metallofullerenes offering stable environments and metalloborospherenes presenting versatile and reactive platforms for further exploration.

4. Theoretical and Computational Methods

Theoretical and computational methods are crucial for studying metalloborospherene, as they enable the prediction of stable geometries and electronic structures that are challenging to investigate experimentally. Additionally, simulating spectroscopy and comparing it to experimental observations can provide evidence of the true global minimum structures. These methods offer detailed insights into the bonding patterns and aromaticity of metalloborospherene. We recently proposed the novel concept of “cluster-assembly materials” [98], wherein highly symmetric stable clusters serve as the foundational building blocks for derivative materials. This approach guides experimental efforts and enhances our understanding of these advanced materials.

4.1. Global Minimum Search

Global minimum searching can be performed using several different algorithms. One of the earliest methods for this purpose is the Basin Hopping (BH) algorithm [103]. This method randomly perturbs the current structure, performs a geometry optimization, and then accepts the new structure if the energy is lowered, or based on a probability determined from the ratio of the population of the previous structure to that of the new structure as determined by the canonical ensemble partition function (Equation (1)). This strategy was implemented in the TGMin package, which allows acceptance of higher energy structures, enabling the BH algorithm to avoid becoming trapped in local minima that are not the global minimum [103,104,105,106]. The pure BH algorithm has been successfully used to identify the structures of ${\mathrm{B}}_{40}^{-}$ [6], ${\mathrm{MnB}}_{16}^{-}$ [68], etc.

$$p<e^{{\displaystyle \frac{E\left(X_0\right)-E\left(X_{new}\right)}{k_{B}T}}}$$

(1)

A modified version of the BH method was developed in TGMin 2.0 [107], enhancing efficiency through several modifications: checking displaced structures for low-coordination numbers, freezing some atoms to reduce search dimensions, adjusting unreasonable structures before ab-initio calculations, and preventing the revisiting of prior structures. TGMin 2.0 has successfully identified the global minimum structures of ${\mathrm{La}}_3$${\mathrm{B}}_{18}^{-}$, ${\mathrm{Tb}}_3$${\mathrm{B}}_{18}^{-}$, ${\mathrm{MnB}}_{16}^{-}$, and ${\mathrm{La}}_3$${\mathrm{B}}_{14}^{-}$ [45,68,77].

In addition to the BH method, the Stochastic Surface Walking (SSW) method [108,109] enhances global minimum searching by adding random displacements to the current local minima structure and performing a biased dimer rotation to incorporate information about transition states between isomers, followed by geometry optimization [110]. This method has been successfully used to determine the global minimum structure of ${\mathrm{B}}_{40}^{-}$ [6]. Similarly, the Coalescence Kick algorithm [111,112,113], which was employed to find the global minimum structure of ${\mathrm{MnB}}_{16}^{-}$, involves displacing each atom within a spherical radius R of its prior position, akin to the displacement strategies used in BH, TGMin, and SSW.

Another advanced technique is the CALYPSO (Crystal Structure Analysis by Particle Swarm Optimization) package [114], which predicts structures by generating random structures with symmetry constraints followed by geometry optimization. Each structure is assigned a geometric parameter similar to a genetic code, and position adjustments are made through particle swarm optimization [115,116]. This method was used to predict the structures of ${\mathrm{AnB}}_{36}$ (An = Pa, Np, Pu, Am, Cm, Bk, and Cf) clusters [102].

For the energy calculation, ab initio methods need to be employed using quantum chemistry software such as Gaussian (16) [117] and ADF (2024.1) [118,119]. These calculations are essential for accurately determining the electronic structure and properties of the systems under investigation. However, as the number of atoms in a system increases, the computational cost of ab initio calculations becomes a significant bottleneck. This necessitates the use of faster, less accurate basis sets and functionals for initial global minimum searches, followed by more precise calculations at higher levels of theory for the most promising structures.

To address these computational challenges, the development of machine learning (ML) potentials is becoming increasingly important. ML potentials can significantly accelerate energy and geometry optimizations by learning from a subset of high-quality ab initio calculations and then predicting the properties of new configurations with high accuracy. This approach has been successfully applied in various fields, demonstrating its potential to handle large systems efficiently [120,121,122,123]. For example, Behler–Parrinello neural networks [120] and Gaussian approximation potentials [124] are among the techniques that have been developed to create accurate and transferable potential energy surfaces based on machine learning.

Furthermore, integrating ML potentials with traditional quantum chemistry methods can create hybrid approaches that balance accuracy and computational efficiency. This integration allows for initial rapid screening of large configurational spaces using ML models, followed by detailed ab initio calculations on a select number of configurations. This hybrid strategy has shown promise in materials science and chemistry, making it a valuable tool for studying complex systems such as metalloborospherenes and other large clusters [125,126,127]. By leveraging the strengths of both ab initio methods and machine learning, researchers can more effectively explore the vast configurational landscapes of complex molecular systems, leading to a deeper understanding and more accurate predictions of their properties.

4.2. Photoelectron Spectroscopy Simulation

The PES can be simulated using the $\Delta$SCF-TDDFT method [128]. In this approach, the adiabatic detachment energy (ADE), which also refers to the electron affinity of the neutral species, is calculated as the energy difference between the neutral molecule at its optimized geometry and the anion at its optimized geometry, defining the onset of the first band in the PES. The peak of the first band, known as the first vertical detachment energy (VDE1), is determined as the energy difference between the neutral molecule and the anion, both at the anion geometry [129]. Higher VDEs are obtained by simulating the excitations of the neutral molecule at the anion geometry using time-dependent DFT (TDDFT) methods for systems without strong electron correlations, while for systems with strong electron correlation or spin–orbit (SO) coupling effects, single-electron VDEs from the anion ground state to the corresponding ground and excited states of the neutral cluster are calculated using the CASSCF/CCSD(T)/SO approach [130], where CCSD(T) energy values replace the diagonal elements of the CASSCF matrix with SO effects treated as a perturbation. Excitations with the electron detached from occupied molecular orbitals to the corresponding molecular orbital of the anion are selected, and the first VDE energy is added to these excitations to produce higher VDEs, corresponding to the peaks of subsequent bands in the PES.

The method of statistical average of different orbital model potentials (SAOP) [131] is typically preferred for the calculation of the excitation energies in metalloborophenes due to its accurate long-range behavior, which is essential for calculating charge transfer excitations in systems with significant charge separation in excited states, such as between metal fragments and boron clusters [18]. In pure boron fullerenes, such as ${\mathrm{B}}_{40}^{-}$, the time-dependent DFT formalism [6,129] is used at the PBE0 level to achieve similar accuracy.

4.3. Molecular Orbitals and Chemical Bonding Analysis

The analysis of molecular orbitals (MOs) in metalloborophenes is vital for understanding their structural stability and the interactions between the metal atoms and the borospherene framework [132]. Moreover, determining the oxidation states of the encapsulated metals is crucial, which can be achieved through appropriate fragment analysis. As illustrated in Figure 5, the MO plot for ${\mathrm{La}}_3$${\mathrm{B}}_{18}^{-}$ reveals that the 6${\mathrm{e}}^{″}$, 12${\mathrm{e}}^{\prime }$, and 2${\mathrm{a}}_1^{″}$ irreducible representations associated with the ${\mathrm{La}}_3$ moiety exhibit La 5d character, whereas the 4${\mathrm{e}}^{″}$, 6${\mathrm{e}}^{\prime }$, and 1${\mathrm{a}}_1^{″}$ irreducible representations associated with the ${\mathrm{B}}_{18}$ framework exhibit B 2p character. Consequently, the 5${\mathrm{e}}^{″}$, 9${\mathrm{e}}^{\prime }$, and 1${\mathrm{a}}_1^{″}$ MOs demonstrate significant bonding interactions between La 5d and ${\mathrm{B}}_{18}$ 2p orbitals. This bonding pattern indicates that the La atoms are in their favored +III oxidation state in ${\mathrm{La}}_3$${\mathrm{B}}_{18}^{-}$, which can be approximately represented as (${\mathrm{La}}^{3+}$${)}_3$ [${\mathrm{B}}_{18}^{10-}$].

To further understand the charge and energy distribution between metal and borophene fragments, the EDA-NOCV (Energy Decomposition Analysis–Natural Orbital for Chemical Valence) method [133,134,135] can be applied by decomposing the internal energy into several distinct contributions: steric repulsion, orbital interactions, and preparation energy. Steric repulsion encompasses both Pauli repulsion, which arises from the overlap of electron densities, and electrostatic repulsion, which results from the Coulombic interactions between charged particles. Orbital energy, on the other hand, reflects the interactions between occupied and unoccupied molecular orbitals, capturing the essence of bonding and antibonding interactions within the system. Preparation energy accounts for the energy required to distort the fragments from their equilibrium geometries to the configurations they adopt within the complete molecule. This energy component is crucial for understanding the structural adjustments necessary for bonding. By applying the EDA-NOCV method, one can detect the flow of electrons between different fragments and quantify the contribution of each orbital to the total orbital interaction energy [135]. This detailed analysis allows for a deeper insight into the nature of the interactions, providing a comprehensive understanding of the electronic structure and bonding characteristics in metalloborophenes.

For instance, in the case of the ${\mathrm{Be}}_2$${\mathrm{B}}_{24}^{+}$ metalloborospherene cluster, as shown in Figure 6 [136], EDA-NOCV reveals that the ${\mathrm{Be}}_2$–${\mathrm{B}}_{24}$ interaction is significantly covalent in nature, with notable contributions from highly polarized covalent bonds formed between Be and the boron atoms. The analysis shows how these interactions stabilize the unique four-ring tubular structure of the boron framework, which consists of two ${\mathrm{B}}_{12}$ tubular subunits connected by ${\mathrm{B}}_6$ rings and capped by beryllium atoms. This method also illustrates the charge transfer and orbital mixing between the fragments, highlighting the role of Be to form strong covalent bonds, which is crucial for the stability and unusual geometry of the metalloborospherene.

Bader’s Quantum Theory of Atoms in Molecules (QTAIM) [137] provides a refined method for analyzing electron density and thereby understanding metal–cage interactions in EMFs [62]. Instead of focusing on individual molecular orbitals, QTAIM assesses the overall electron density, identifying natural boundaries between atoms via surfaces with zero flux in the gradient vector field. These boundaries, or atomic basins, allow for the integration of scalar properties, such as electron density, to specific atoms. Critical points (CPs) where the density gradient vanishes are classified by their rank (number of nonzero Hessian eigenvalues) and signature (sum of Hessian eigenvalue signs). Different types of CPs (nuclear, bond, ring, and cage) provide insights into bonding characteristics. Bond critical points (BCPs) are particularly crucial, as their presence between atoms signifies bonding. The electron density at BCPs (${\rho }_{bcp}$) and its Laplacian (${\nabla }^2{\rho }_{bcp}$) help distinguish between covalent (high ${\rho }_{bcp}$, negative ${\nabla }^2{\rho }_{bcp}$) and noncovalent (low ${\rho }_{bcp}$, positive ${\nabla }^2{\rho }_{bcp}$) interactions. Studies on EMFs using QTAIM, such as those by Kobayashi and Nagase [138,139], reveal the ionic character of metal–cage bonds through small ${\rho }_{bcp}$ values and positive ${\nabla }^2{\rho }_{bcp}$, alongside high bond ellipticity, indicating delocalized metal–cage interactions. Despite QTAIM’s robustness, its application in EMF studies has been limited, primarily focusing on atomic charges rather than a comprehensive analysis of bonding indicators. This approach can provide a more detailed understanding of bonding in various EMF classes, including mono- and dimetallofullerenes, nitride cluster fullerenes, and carbide cluster fullerenes (Figure 7).

QTAIM has also been widely used to analyze the chemical bonding in metalloborospherenes. For example, in Th@${\mathrm{B}}_{36}$ metalloborospherene as shown in Figure 8 [140], QTAIM provides a detailed topological analysis of the electron density, highlighting critical points that reveal the nature of boron–boron (B-B) and metal–boron (Th-B) interactions. The analysis identifies BCPs for B-B bonds, indicating a significant covalent character due to high ${\rho }_{bcp}$ and negative ${\nabla }^2{\rho }_{bcp}$. Additionally, ring critical points (RCPs) and cage critical points (CCPs) indicate the presence of multicenter bonding, a characteristic feature of boron clusters. For Th-B interactions, QTAIM reveals smaller electron density and positive Laplacian values at the BCPs, suggesting a closed-shell interaction with partial covalent character, further supported by negative values of the energy density (H(r)) at these points.

The Adaptive Natural Density Partitioning (AdNDP) [141] analysis, which integrates Lewis theory with canonical molecular orbital theory, provides a powerful approach for describing the bonding in complex molecular systems. This method assigns each molecular orbital as an n-center (1,2)–electron bond, where n can range from 1 to the total number of atoms in the molecule, indicating a spectrum of bonding scenarios from localized to fully delocalized electrons.

AdNDP analysis is particularly effective in visualizing bonding patterns that are not easily represented by traditional two-center, two-electron bonds. For instance, in systems with delocalized bonding, such as the ${\mathrm{La}}_3$${\mathrm{B}}_{18}^{-}$ system as shown in Figure 9, AdNDP can reveal multicenter bonds that involve three or more atoms sharing electron pairs. This capability is essential for understanding the electronic structure of such molecules, where conventional bonding models fall short.

Moreover, AdNDP analysis can also provide insights into the aromaticity of certain compounds by demonstrating the presence of delocalized electron clouds that contribute to the stability and reactivity of the molecule. All these advanced computational techniques collectively provide a comprehensive understanding of the electronic structure, bonding, and stability of metalloborophenes, facilitating the design and synthesis of new materials with tailored properties.

5. Conclusions and Perspectives

In summary, metalloborospherenes represent a fascinating and rapidly evolving class of materials that parallel the well-studied metallofullerenes. The unique electron-deficient nature of boron leads to diverse and complex bonding patterns, enabling the formation of stable boron cages when doped with various metals. These metalloborospherenes exhibit a range of intriguing structural motifs and electronic properties that differ significantly from their carbon-based counterparts.

Recent advancements have demonstrated the ability of metalloborospherenes to stabilize novel metal clusters, particularly those involving transition metals, lanthanides, and actinides. These studies have provided deep insights into the electronic structure, bonding characteristics, and potential applications of these materials. For instance, the stabilization of actinide clusters within borospherenes and fullerenes has revealed complex electronic configurations and bonding interactions not observed in lanthanide-doped systems.

The potential applications of metalloborospherenes are vast, spanning catalysis, materials science, and nanotechnology. The unique bonding and structural properties of these clusters offer opportunities for designing new materials with tailored electronic and catalytic properties. Moreover, the ability to encapsulate and stabilize actinide elements opens up new avenues for research in actinide chemistry, with implications for nuclear science and advanced materials.

Future research should continue to explore the synthesis, characterization, and theoretical modeling of metalloborospherenes. Advanced computational methods, such as global minimum searches and machine learning potentials, will play a crucial role in predicting and understanding the properties of these complex systems. Additionally, experimental techniques such as photoelectron spectroscopy and crystallography will be essential for validating theoretical predictions and uncovering new structural motifs. The practical application of metalloborospherenes relies heavily on the feasibility of their macroscale synthesis. Current research in this area is predominantly theoretical and experimental at the nanoscale. However, advancements in synthetic techniques for boron-based nanostructures and metallofullerenes provide a promising foundation for scaling up production. One potential method for macroscale synthesis involves chemical vapor deposition (CVD), which has been successfully employed for producing other boron-rich nanomaterials [142,143]. By optimizing the parameters of CVD, such as temperature, pressure, and precursor composition, it may be possible to achieve controlled synthesis of metalloborospherenes on a larger scale. Another promising approach is the use of solution-based synthesis methods, including solvothermal and hydrothermal processes [144,145]. These methods can facilitate the formation of boron cages and their subsequent doping with metal atoms in a controlled environment. The development of suitable solvents and reaction conditions will be crucial for this approach. Additionally, template-assisted synthesis [146], where preformed templates guide the assembly of boron and metal atoms into the desired structures, could provide a pathway for producing metalloborospherenes at scale. This method has been used successfully for other complex nanostructures and could be adapted for metalloborospherenes. Overall, while the macro-scale synthesis of metalloborospherenes presents challenges, ongoing advancements in nanomaterial synthesis techniques hold promise for overcoming these obstacles, making the large-scale production of these materials feasible in the near future.

Overall, the study of metalloborospherenes is a dynamic and promising field that bridges the gap between boron chemistry and nanomaterials science. The insights gained from this research will not only advance our understanding of boron-based clusters but also pave the way for the development of innovative materials with unique properties and wide-ranging applications.