So far, several isomers of C₁₀₀ have been identified via chlorination followed by studies of single-crystal X-ray diffraction, including C₂-C₁₀₀(18), D_5d-C₁₀₀(1), C₁-C₁₀₀(425), and C_2v-C₁₀₀(417) [isomer numbering according to the spiral algorithm (Fowler and Manolopoulos, 1995)]. C₂-C₁₀₀(18) is the first isomer of C₁₀₀ disclosed by structure reconstruction, although theoretical calculations for all 450 IPR isomers of C₁₀₀ indicate that C₁₀₀(18) ranks second and follows the most stable D₂-C₁₀₀(449) (Zhao et al., 2004). However, C₂-C₁₀₀(18) was even excluded from the list of rather stable isomers in other theoretical calculations, whereas D₂-C₁₀₀(449) is still the most stable isomer (Cai et al., 2005; Shao et al., 2006). Interestingly, on the basis of theoretical calculations, D_5d-C₁₀₀(1), having a much higher relative formation energy, should therefore be highly unstable, but it has been captured by chlorination (Fritz et al., 2014).

Chlorination of C₁₀₀ fullerene afforded a non-classical fullerene chloride, C₉₆Cl₂₀, containing three heptagons (Yang et al., 2014a). Using structural reconstruction, C₂-C₁₀₀(18), out of 450 topologically possible IPR isomers, was established as the starting fullerene (Yang et al., 2014a). Using the same C₁₀₀(18) fullerene as the starting material, another non-classical fullerene chloride, C₉₄(NC1)Cl₂₂, containing one heptagon together with the aforementioned C₉₆(NC3)Cl₂₀ were unexpectedly obtained (Ioffe et al., 2015). The detailed structural features and transformation mechanisms are presented in Section Heptagon-containing fullerenes derived from giant fullerenes below. Fortunately, the pristine C₁₀₀(18) was directly captured by chlorination as C₁₀₀(18)Cl_28/30 (Figure 1A) without any cage shrinking; hence, the C₁₀₀(18) was reconfirmed to exist in the as-produced fullerene soot (Wang et al., 2016a). Notably, C₁₀₀(18)Cl_28/30 is produced in a relatively short reaction time of about a week, while the cage transformation needs a longer reaction time (Wang et al., 2016a). This indicates that the reaction time for chlorination plays a vital role in determining the ultimate chlorination products. As shown in the Schlegel diagrams (Figure 1A′), relatively long chains of adjacent (ortho) attachments of Cl atoms are formed in regions of two closely arranged groups of four pentagons (Wang et al., 2016a). However, due to the two additional Cl atoms attached at triple hexagon junctions (THJs), which are usually unfavorable positions for fullerenes, a longer ortho chain of Cl atoms appears in C₁₀₀(18)Cl₃₀ (Wang et al., 2016a). Two ethenylbenzene-like substructures and four isolated and nearly isolated C=C double bonds boost the stability of the structure (Wang et al., 2016a). Notably, the chlorination patterns of C₂-C₁₀₀(18)C_l28/30 are remarkably different from the assumed chlorination patterns for C₂-C₁₀₀(18)Cl₂₄, which is regarded as the pristine structure of the cage transformations to C₉₆(NC3)Cl₂₀ and C₉₄(NC1)Cl₂₂. The possible reason for this is that, in further reactions, the chlorination pattern may change to structures inclining toward skeletal transformations via a “chlorine dance.” (Wang et al., 2016a).

C_2h-C₁₀₀(1)Cl₁₂ (Figure 1B), which contains an unprecedented nanotubular carbon cage with the symmetry of highly unstable D_5d, has been reported by Troyanov (Fritz et al., 2014). The crystal of C₁₀₀(1)Cl₁₂ was distinguished from a complex mixture of chlorinated fullerenes, and similar cases were observed for the crystallization of more than one chloride from a fullerene mixture possessing different molecular shapes (Fritz et al., 2014). C_2h-C₁₀₀(1)Cl₁₂ displays a remarkable tube-like molecular shape because of a unique distribution of 12 pentagons on two poles of the D_5d-C₁₀₀(1) cage (Fritz et al., 2014). In detail, in each group formed by six pentagons on its poles, a central pentagon on the C₅ axis is surrounded by five other pentagons, which is similar to the cases of the C₆₀ and C₇₀ molecules. Therefore, according to the similarity to C₆₀, the chlorination pattern of D_5d-C₁₀₀(1)Cl₁₂ (Figure 1B′), on both poles, adopts the skew-pentagonal pyramidal (SPP) arrangement, which is identical to the addition pattern of the C_s-C₆₀Cl₆ and C_s-C₆₀(CF₃)₁₂ (Shustova et al., 2006; Omelyanyuk et al., 2007). Apparently, C₁₀₀(1) possessing fragments of the C₆₀ cage on each pole reacts easily under conditions of higher temperatures to form C₁₀₀(1)Cl₁₂; however, further chlorination may become slower because no unoccupied pentagons exist and, very likely, the chlorination product precipitates because of crystallization (Fritz et al., 2014). In fact, D_5d-C₁₀₀(1) was not expected to be present in fullerene soot on the basis of its much higher relative formation energy; that is, it should be highly unstable (Zhao et al., 2004). A plausible reason for D_5d-C₁₀₀(1) remaining in the carbon soot is that the distinctive features of the D_5d-C₁₀₀(1) cage prevent it transforming into more stable IPR isomers of C₁₀₀ during fullerene synthesis (Fritz et al., 2014).

Another chlorination experiment on the subfraction containing C₁₀₀ affords two crystalline modifications of C₁₀₀(425)Cl₂₂, while their crystal structures are different from only the packing motifs (Wang et al., 2016a). The C₁₀₀(425)Cl₂₂ molecule presents a rather spherical shape (Figure 1C) compared with C₁₀₀(18)Cl_28/30 because of the absence of coronene substructures in the cage (Wang et al., 2016a). As shown in Figure 1C′, the chlorination patterns of C₁₀₀(425)Cl₂₂ contain two sets of Cl attachments in adjacent positions (Wang et al., 2016a). As a result, three isolated C=C double bonds and two benzenoid rings contribute to the stabilization of the chlorination patterns (Wang et al., 2016a).

In addition, isomer C_2v-C₁₀₀(417) was confirmed via the chlorinated derivative C_s-C₁₀₀(417)Cl₂₈ in two crystal structures (Wang et al., 2016a). One structure is made up of symmetrical mirror molecules and C_s-C₁₀₀(417)Cl₂₈ appears observably flattened because there are two coronene substructures on opposite sides of the carbon cage (Figure 1D) (Wang et al., 2016a). Simultaneously, 26 attached Cl atoms are settled on the basis of the C_2v symmetry of the cage, whereas the symmetry of the entire chlorinated molecule is reduced to C_s because of the two attached Cl atoms, as shown in Figure 1D′ (Wang et al., 2016a). Furthermore, two butadiene-like substructures and two aromatic systems within coronene units have formed in the carbon cage of C₁₀₀(417)Cl₂₂ (Wang et al., 2016a). In the other crystal structure, C₁₀₀(417)Cl₂₈ and C₉₈(NC1)Cl₂₆ have co-crystallized in the same crystallographic site with 0.471 and 0.529 occupancies, respectively. A comparison of the Schlegel diagrams for the two molecules proved that a heptagon in the carbon cage of the chloride C₉₈ stemmed from the loss of a 5:6 C–C bond of C₁₀₀(417)Cl₂₈ (Wang et al., 2016a).

So far, two isomers, C₁₀₂(19) and C₁₀₂(603), among the 616 topologically possible IPR isomers of C₁₀₂ have been identified by exohedral chlorination. On the basis of theoretical calculations, C₁₀₂(603) was predicted as the most stable isomer, whereas C₁₀₂(19) has lower stability due to its relatively lower formation energy compared with those of the other giant fullerenes.

The first identified isomer of C₁₀₂ was C₁₀₂(19) in 2013, which has been confirmed by the structural reconstruction of the obtained non-IPR fullerene chloride C₁₀₂Cl₂₀ (Yang et al., 2013). There are two pairs of fused pentagons on the sharpened cage end of the cage of C₁₀₂Cl₂₀, while the other end of the cage looks rather roundish (Yang et al., 2013), as shown in Figure 2A. However, two opposite sides of the carbon cage are significantly flattened (Yang et al., 2013). The non-IPR C₁₀₂ isomer is assigned as No. 283794 [according to the spiral algorithm (Fowler and Manolopoulos, 1995)] among 341,658 topologically possible classical isomers of C₁₀₂, which contains five- and six-membered rings only (Yang et al., 2013). In ^#283794C₁₀₂Cl₂₀, five pentagons with two neighboring pairs of fused pentagons are closely located, in contrast to the seven residual pentagons situated far from them (Figure 2B) (Yang et al., 2013). In the cage area of the former, 11 Cl atoms occupy adjacent positions to the carbon atoms and form a long zigzag chain on the carbon cage (Yang et al., 2013). In the area of the seven dispersed pentagons, nine Cl atoms are primarily attached at para positions of the cage hexagons (and one ortho position), resulting in a biphenyl-like substructure formed by two pseudo-aromatic rings (Yang et al., 2013). However, the carbon cage shows a flattened shape due to two groups of fused hexagons (coronene substructures) existing in the regions between the two groups of chlorine attachments (Yang et al., 2013).

The reason for the formation of the non-IPR ^#283794C₁₀₂Cl₂₀ is Stone–Wales (SW) transformations promoted by chlorination on the basis of the assumptions that the actual pathway has a minimum number of rearrangement steps and the IPR–IPR transformations do not occur at the reaction temperature (Yang et al., 2013). The IPR C₁₀₂ fullerene No. 19, corresponding to No. 341,061 in the list of all classical C₁₀₂ cages, has been confirmed as the starting isomer by structural reconstruction, and suffered only two SW rearrangement steps to obtain the non-IPR chloride (Yang et al., 2013). As shown in Figure 2B, the skeletal transformation of chlorinated ^#341061C₁₀₂ to ^#283794C₁₀₂Cl₂₀ can be formally realized via two alternative chlorinated intermediates, ^#262246C₁₀₂Cl₂₀ or ^#258508C₁₀₂Cl₂₀, dependent on the order of SWRs of the two chlorinated C–C bonds in ^#341061C₁₀₂Cl₂₀ (Yang et al., 2013). The DFT calculations demonstrate that ^#258508C₁₀₂Cl₂₀ is the more possible intermediate on the path from the IPR ^#341061C₁₀₂ to ^#283794C₁₀₂Cl₂₀ (the SWR–SWR′ pathway), which is comparatively more stable than ^#262246C₁₀₂Cl₂₀. Fortunately, in 2018, the intermediate ^#258508C₁₀₂Cl₂₀ was captured in co-crystals with the ultimate ^#283794C₁₀₂Cl₂₀ (Mazaleva et al., 2018). Moreover, the relative energies of the two paths have been updated, which also sustains the SWR–SWR′ pathway, as shown in Figure 2B (Mazaleva et al., 2018).

The most stable IPR isomer, C₁₀₂(603), on the basis of DFT calculations, was captured by its chloride, C₁₀₂(603)Cl_18/20, in 2014, as shown in Figure 2C (Yang et al., 2014c). Furthermore, the C₁₀₂(603)Cl₁₈ and C₁₀₂(603)Cl₂₀ molecules co-crystallize in the same crystallographic site with an occupancy ratio of 63/37 (Yang et al., 2014c). As shown in Figure 2D, the attachment of Cl atoms of C₁₀₂(603)Cl₁₈ featured in para positions in cage hexagons leads to the formation of two stabilizing benzenoid rings and two isolated C=C double bonds (Yang et al., 2014c). Unusually, a carbon atom in the position of a THJ leading to more planar arrangements of C–C bonds, which is generally unfavorable for addition in fullerenes, is attached by one Cl atom. In the case of C₁₀₂(603)Cl₁₈, such an uncommon attachment site is most likely induced by the formation of an isolated quasi-aromatic substructure on the cage (Yang et al., 2014b). Furthermore, achieving C₁₀₂(603)Cl₂₀ by two additional Cl atoms attached to C₁₀₂(603)Cl₁₈ is favored because of the formation of the third (nearly isolated) benzenoid ring and two nearly isolated C=C double bonds (Yang et al., 2014b).

Four isomers of the giant fullerene C₁₀₄, named as C₁₀₄(258), C₁₀₄(812), C₁₀₄(234), and C₁₀₄(811) [according to the spiral algorithm (Fowler and Manolopoulos, 1995)], have been successively confirmed by chlorination (Yang et al., 2014b,c; Jin et al., 2017). They have different stabilities according to the DFT calculations, namely, the most stable isomer, C₁₀₄(234), a rather unstable isomer, C₁₀₄(258), a moderately stable isomer C₁₀₄(812), and much less stable isomer, C₁₀₄(811).

Isomer C₁-C₁₀₄(258) has first been captured as the chloride, C₁₀₄Cl₁₆, which displays an elongated barrel-like shape because of the distribution of pentagons on opposite sides of the cage (Figure 3A) (Yang et al., 2014c). Due to several areas of annulated hexagons (like coronene substructures) existing between the groups of pentagons, the cage appears flattened (Yang et al., 2014c). As shown in Figure 3A′, the molecule structure of C₁₀₄Cl₁₆ is distinguished by the Cl atom attachments on the opposite ends of the cage, which contains pentagons, whereas the middle parts remain without any Cl atoms attached (Yang et al., 2014c). A nearly benzenoid-like fragment on the cage is isolated by six Cl atoms, whereas an isolated C=C double bond is formed by Cl atoms in four para-positions, and a six-membered chain of adjacent Cl atom additions occurs in the area adjacent to the isolated C=C double bond (Yang et al., 2014c). In particular, the feature of the chlorination pattern in C₁-C₁₀₄(258)Cl₁₆ is that 16 Cl atoms (i.e., more than the 12 addends) occupy 10 pentagons, whereas two remaining pentagons are spare (Yang et al., 2014c). This is similar to the case of C₈₈(17)Cl₁₆, which presents a non-uniform attachment of Cl atoms, with two spare cage pentagons remaining (Yang et al., 2012b).

The most stable isomer of the giant fullerene C₁₀₄, C₁₀₄(234), has been confirmed by chlorination followed by a single-crystal diffraction study, and two crystal structures of C₁₀₄(234)Cl_17.3 and C₁₀₄(234)Cl₂₂ provide information regarding the chlorination patterns of C₁₀₄(234) in the range of C₁₀₄(234)Cl₁₆₋₂₂, as shown in Figures 3B,C (Yang et al., 2014b). Three overlapping molecules of C₁₀₄(234)Cl₁₆, C₁₀₄(234)Cl₁₈, and C₁₀₄(234)Cl₂₀ co-crystallize in the same crystallographic site, while C_s-C₁₀₄(234)Cl₂₂ solely forms another crystal (Yang et al., 2014b). C₁₀₄(234)Cl₁₆₋₂₂ molecules are mirror symmetrical, which corresponds to the pristine C_s-C₁₀₄(234) cage (Yang et al., 2014b). In the C_s-C₁₀₄(234)Cl₁₆ molecule (Figure 3C′), each pentagon initially has one Cl atom, then four Cl atoms additionally attach at the 1,3-position of the four pentagons, which leads to the formation of two isolated C=C double bonds (Yang et al., 2014b). Simultaneously, the chlorination pattern is made up of four similar para-chains. However, further para-chain propagation is forbidden, because the only option is the unfavorable THJ site for para-chain propagation (Yang et al., 2014b). Therefore, ortho positions, despite the existing steric strain, are further occupied by pairs of Cl atoms, which is energetically more favorable because an extra isolated C=C double bond is formed. In the end, as shown in Figures 3B′,C′, three, four, and five C=C double bonds form in the carbon cages with 18, 20, and 22 attached Cl atoms, respectively (Yang et al., 2014b; Jin et al., 2017). Later, another chloro-derivative, C_s-C₁₀₄(234)Cl_16.78, was reported, and its structure is close to the structure of C_s-C₁₀₄(234)Cl_17.26 (Jin et al., 2017). The differences between the structures of C_s-C₁₀₄(234)Cl_16.78 and C_s-C₁₀₄(234)Cl_17.26 originate only from occupancy ratios of the molecules with 16, 18, and 20 attached Cl atoms, namely, 65/31/4 and 47/43/10, respectively (Jin et al., 2017). However, their crystallographic symmetries and packing motifs are also different (Jin et al., 2017).

The chlorination of the subfraction containing the giant fullerene D₂-C₁₀₄(812) first yields the chloride fullerene D₂-C₁₀₄(812)Cl₂₄ (Figure 4A) (Yang et al., 2014c). As shown in Figure 4A′, 24 Cl atoms symmetrically are attached to the carbon cage, although the attached pattern of Cl atoms is non-uniform (Yang et al., 2014c). Each cage pentagon is occupied by two Cl atoms, and all of the Cl atoms are situated in the para-positions of the cage hexagons (Yang et al., 2014c). Therefore, four isolated benzenoid rings and four C=C double bonds have formed on the fullerene cage (Yang et al., 2014c). Notably, in the D₂-C₁₀₄(812)Cl₂₄ molecule, there are two disordered C–C bonds formed by normal SWRs on one end of the cage, and their occupation ratio is 77:23 (Yang et al., 2014c). The alternative orientation of the disordered bonds corresponds to isomer C₁₀₄(811). Hence, the structure should be regarded as a statistical overlap of the two isomers, D₂-C₁₀₄(812)Cl₂₄ (major) and C₂-C₁₀₄(811)Cl₂₄ (minor) (Yang et al., 2014c). Later, the C₁₀₄(811) isomer has been solely captured as C₂-C₁₀₄(811)Cl₂₈, but the attachment patterns of C₂-C₁₀₄(811)Cl₂₄ and C₂-C₁₀₄(811)Cl₂₈ are significantly different (see below) (Jin et al., 2017).

In 2017, two chloro-derivatives of D₂-C₁₀₄(812) with 12 and 24 Cl atoms attached were reported, and their molecular structures demonstrate crucial features of successive chlorination (Figure 4B) (Jin et al., 2017). Chlorination of D₂-C₁₀₄(812) takes place on two poles of the carbon cage alone, which retains its molecular symmetry. In detail, six Cl atoms uniformly attached to the six pentagons of each pole lead to the formation of an S-shaped para-chain. However, further propagation of chains on the ends is forbidden due to the presence of THJs in para-positions, as shown in Figure 4B′ (Jin et al., 2017). Similar kinds of limitations are also observed in the D₂-C₈₄(22)Cl₁₂ molecule, which is quite understandable because of the close structural relationships between the D₂-C₈₄(22) and D₂-C₁₀₄(812) isomers: the inclusion of a belt of 20 carbon atoms between the two halves of D₂-C₈₄(22) produces D₂-C₁₀₄(812), both cages having the same symmetry and a very similar arrangement of six pentagons on each pole (Yang et al., 2014c). Moreover, the D₂-C₁₀₄(812)Cl₂₄ molecule inherits the attachment features of the 12 Cl atoms of D₂-C₁₀₄(812)Cl₁₂ (Jin et al., 2017). Additionally, there are 12 Cl atoms attached to the 1,3-positions of each pentagon (also to the para-position of the hexagon) in D₂-C₁₀₄(812)Cl₂₄. However, this destabilizing structure is strengthened by producing four isolated C=C double bonds and four isolated benzenoid rings on the cage (Jin et al., 2017). As expected, DFT calculations demonstrate that the relative chlorination enthalpy of C₁₀₄(812)Cl₂₄ (2.5 kJ mol⁻¹ per Cl) is much lower than that of C₁₀₄(812)Cl₁₂ (10.8 kJ mol⁻¹) (Jin et al., 2017).

The structure of C₂-C₁₀₄(811)Cl₂₈ is markedly different from that of C₂-C₁₀₄(811)Cl₂₄, as shown in Figure 4C (Jin et al., 2017). Four isolated C=C double bonds and four benzenoid rings form in the carbon cage of C₂-C₁₀₄(811)Cl₂₄, while the C₂-C₁₀₄(811)Cl₂₈ molecule contains two nearly isolated benzenoid rings and four isolated C=C double bonds, two of the latter occurring in the same positions of C₂-C₁₀₄(811)Cl₂₄ (Figure 4C′) (Jin et al., 2017). The most prominent difference observable in C₂-C₁₀₄(811)Cl₂₈ is of the many Cl atoms attached at the ortho-positions on the cage involving two six-membered ortho-chains (Jin et al., 2017). However, the formation of relatively long ortho-chains is a typical characteristic of highly chlorinated fullerenes. The changes in the chlorination patterns of C₂-C₁₀₄(811)Cl₂₄ with increasing degree of chlorination are quite similar to those of T_h-C₆₀Cl₂₄/C₁-C₆₀Cl₂₈; the chlorination pattern without any ortho-addition transforms into the structure with long ortho-chains with increasing degree of chlorination (Troyanov et al., 2005; Jin et al., 2017). Moreover, the relative chlorination enthalpy of C₁₀₄(811)Cl₂₈ (−0.1 kJ mol⁻¹) is lower than that of C₁₀₄(811)Cl₂₄ (0.5 kJ mol⁻¹) (Jin et al., 2017).

The structure of IPR C₁₀₆(1155)Cl₂₄ has been determined by chlorination of the giant fullerene C₁₀₆, followed by a study using synchrotron radiation single-crystal X-ray diffraction (Figure 5A) (Wang et al., 2016b). Surprisingly, there are two molecules in the same crystal: one is C₁₀₆(1155)Cl₂₄ and the other is C₁₀₄(NC)Cl₂₄, with an NC carbon cage (Wang et al., 2016b). The occupancies of C₂-C₁₀₆(1155)Cl₂₄ and C₁-C₁₀₄(NC)Cl₂₄ are 23 and 77%, respectively, and the molecules show the same chlorination patterns and similar shapes (Wang et al., 2016b). Their inclusion in the same crystal packing is not hindered, and it is a common phenomenon of the co-crystallization of fullerene chlorides to have similar chlorination patterns but slightly different cages, e.g., C₇₈(2,3)Cl₁₈ (Simeonov et al., 2008) and C₉₀(34,46)Cl₃₂ (Kemnitz and Troyanov, 2009). As shown in Figure 5A′, the chlorination pattern of C₂-C₁₀₆(1155)Cl₂₄ is characterized by the existing four isolated C=C double bonds and seven entirely isolated, or almost entirely isolated, benzenoid rings on the cage (Wang et al., 2016b). Furthermore, the presence of coronene and pyrene units on the poles of C₂-C₁₀₆(1155)Cl₂₄ leads to the carbon cage being somewhat flattened (Wang et al., 2016b). Another unusual characteristic of the chlorination pattern is that four Cl atoms are attached to the THJs, which are generally unfavorable addition sites for fullerenes (Wang et al., 2016b). However, each addition at a THJ leads to the formation of two, or even three, benzenoid rings; thus, it is beneficial for stabilizing the molecule (Wang et al., 2016b).

The chlorination reaction of the HPLC subfraction containing the giant fullerene C₁₀₈ affords the fullerene chloride, C₂-C₁₀₈(1771)Cl₁₂ (Figure 5B). Therefore, the presence of D₂-C₁₀₈(1771), the most stable isomer on the basis of theoretical calculations, has been confirmed in the fullerene soot (Wang et al., 2016b). As shown in Figure 5B′, the chlorination pattern of C₂-C₁₀₈(1771)Cl₁₂ is characterized by 12 chlorine attachments non-uniformly distributed on the C₁₀₈ cage. In detail, four pentagons are not occupied by Cl atoms, whereas half of the eight remaining pentagons bear two Cl atoms each (Wang et al., 2016b). This is different from the most stable addition pattern of the derivatives with 12 attached atoms or groups uniformly distributing on the carbon cage (Troyanov and Kemnitz, 2012). In general, the non-uniform attachments contribute to the formation of stabilizing substructures on the carbon cage, for example, benzenoid rings or isolated C=C double bonds (Troyanov and Kemnitz, 2012). However, there are no stabilizing substructures in C₂-C₁₀₈(1771)Cl₁₂, although two separate areas of the cage contain both para- and ortho-additions of Cl atoms, as shown in Figure 5B′ (Wang et al., 2016b). In truth, two cage regions containing six pentagons are insulated by the extended region of the coronene units, which, as a result, prevents the generation of a single-addition chain (Troyanov et al., 2005). Depending on the theoretical calculations, further chlorination may occur at the positions on the second hemisphere of the D₂-C₁₀₈(1771) cage (Wang et al., 2016b).

C₉₆(NC3)Cl₂₀ is a non-classical fullerene chloride, originating from the chlorination of C₁₀₀(18), and, according to Euler's theorem, the carbon cage of C₉₆(NC3)Cl₂₀ has three heptagons and 15 pentagons (vs. 12 pentagons in classical fullerenes), as shown in Figure 6A (Yang et al., 2014a). In detail, there are three fused pentagon pairs formed, one sequentially fused triple, one directly fused triple, and three isolated pentagons in the cage (Yang et al., 2014a). Twenty Cl atoms are non-uniformly attached to the C₉₆(NC3) cage, nine of them forming the chain of adjacent additions, the others forming shorter three- and four-membered chains (Figure 6C) (Yang et al., 2014a). As additional strain stems from the position of the fused pentagon in fullerene cages, all common edges of the fused pentagon pairs are chlorinated, which, remarkably, relieves the strain (Tan et al., 2009). In the sequentially fused triple of pentagons, three vertices of two common edges are chlorinated, which conforms to the rule drawn up previously for similar arrangements of pentagons (Tan et al., 2009). However, only three of the four vertices of fusion are chlorinated in the directly fused pentagon triple, which differs from the case of the non-IPR fullerene, C₆₄Cl₄ (Han et al., 2008), in which all four vertices of fusion are chlorinated (Yang et al., 2014a). In particular, two cage pentagons are not chlorinated, which has also been observed in higher fullerene chlorides with more than 12 attached groups, for example, C₁₀₄(258)Cl₁₆ (Yang et al., 2014a).

It is of great interest to seek the sources of the three heptagons, especially for the third heptagon. Apparently, two eliminations of 5:6 C–C bonds from the cage are responsible for the formation of the two heptagons, which is similar to the reported cases of IPR fullerene shrinkage contributing to the formation of the heptagonal rings (Troshin et al., 2005; Ioffe et al., 2010). However, the third heptagon is generated by an SWR of a 6:6 C–C bond, which joins a pentagon to a hexagon (Yang et al., 2014a). Such transformations are unprecedented for fullerenes, though an analogous rotation of a 6:6 bond in a pyrene-like fragment (four hexagons) is widely regarded as a mechanism for producing SW defects in nanotubes and graphenes (Dumitricǎ and Yakobson, 2004). Only three transformation steps (in any sequence) are necessary to reconstruct the probable pathway from C₁₀₀ to C₉₆(NC3), which involves two C₂ losses and one SW rotation with the 6:6 type, as shown in Figure 6C (Yang et al., 2014a). Therefore, a possible three-step pathway has been proposed: C₂ is lost as a chlorinated species (C₂Cl_n) occurring first, followed by the SW rotation (Yang et al., 2014a). The C₂ loss and the heptagon generations are driven by simultaneously forming chlorinated sites at pentagon–pentagon adjacencies of fused pentagon pairs and within pentagon triples (Yang et al., 2014a). Obviously, the driving force for the formation of the third heptagon (hp3) produced by the SWR of a chlorinated C–C bond originates from producing additional chlorinated pentagon–pentagon junctions, especially the directly fused pentagon triple (Yang et al., 2014a). This transformation is strongly (103 kJ mol⁻¹) exothermic on the basis of DFT calculations (Yang et al., 2014a). Moreover, one vertex of the directly fused pentagon triple remains unchlorinated due to no new chlorinated sites forming in the course of the SWR (Yang et al., 2014a).

In particular, non-classical C₉₄(NC1)Cl₂₂ containing one heptagon in the cage has been obtained together with the aforementioned C₉₆(NC3)Cl₂₀ having three heptagons from the same chlorination of C₂-C₁₀₀(18) (Ioffe et al., 2015). A concave region is formed in C₉₄(NC1)Cl₂₂ because the heptagons are flanked by a pair of fused pentagons and a sequential pentagon triple (Figure 6B) (Ioffe et al., 2015). As well, the C₉₄(NC1) cage has two more pairs of fused pentagons and four isolated pentagons in the other areas of the carbon cage (Ioffe et al., 2015). Similarly, the 22 attached Cl atoms on the C₉₄(NC1) cage are quite non-uniform, and several short ortho-chains dominate (Ioffe et al., 2015). Furthermore, the Cl atoms are attached mainly to the fused pentagons and the pentagon triple, and only one pentagon is unoccupied (Ioffe et al., 2015).

The shortest pathways from C₁₀₀(18) to C₉₄(NC1)Cl₂₂ and C₉₆(NC3)Cl₂₀ involve two identical C2L steps, and branches at the hypothetically common precursor, C₉₆(NC2)Cl₂₀, have been put forward and are shown in Figure 6C (Ioffe et al., 2015). Notably, the carbon cage topologies of the missing starting and intermediate structures have been clearly established depending on the structural relations between the identified compounds, whereas the hypothetical aspect is their chlorination patterns, which are likely to occur as thermodynamicallydriven rearrangements, the so-called “chlorine dance.” (Ioffe et al., 2015). A new kind of C₂ loss exclusive to non-IPR compounds has been proposed: C2L4 means removing the 5:5 C–C bond from a pentalene fragment, in other words, from a fused pair of pentagons (Ioffe et al., 2015). As a consequence, the pentalene unit transforms into a hexagon, whereas the adjacent hexagon and heptagon are reduced to a pentagon and a hexagon (Ioffe et al., 2015). Hence, C₉₄(NC1)Cl₂₂ containing only one heptagon has been achieved, as a result of C2L4 reverting a non-classical fullerene to a classical carbon cage (Ioffe et al., 2015). Additionally, both the SWR2 and C2L4 processes have been studied using DFT calculations in order to estimate which one is preferable (Ioffe et al., 2015). The process of SWR2 has a sizeable exothermic effect of 105 kJ mol⁻¹ and an activation barrier of 180 kJ mol⁻¹, which are among the lowest values previously calculated for such processes (Ioffe et al., 2015). The C2L4 elimination mechanism suggested by DFT contains complex intermediate and transient states (Ioffe et al., 2015). Finally, the calculated activation energies SWR2 and C2L4 are comparative, and the latter possesses slightly lower energy barriers (Ioffe et al., 2015). In addition, the computational results simultaneously substantiate the aforementioned shortest pathways with competitive transformations of the hypothetical common precursor, C₉₆(NC2)Cl₂₀ (Ioffe et al., 2015).

Non-classical C₉₈(NC1)Cl₂₆ with one heptagon rooted in another isomer of C₁₀₀, C₁₀₀(417), forms a co-crystal with C₁₀₀(417)Cl₂₈ at the same crystallographic site (Figure 7A), and their occupancies are 0.529 and 0.471, respectively (Wang et al., 2016a). Comparative analysis of the two structures indicates that a heptagon of the non-classical C₉₈(NC1)Cl₂₆ originates from C₁₀₀(417)Cl₂₈ via the C₂ loss of a 5:6 C–C bond (Figure 7D) (Wang et al., 2016a). In fullerenes, this type of C₂ loss is designated as C2L2 on the basis of the topological classification of skeletal transformations, which is similar to the transformation observed in isomers of C₉₆ fullerene (Yang et al., 2014d). Significantly, the stability of the resulting C₉₈(NC1)Cl₂₆ has been strengthened by Cl atom attachments to two pentagon–pentagon fusions (Wang et al., 2016a).

Both of the chlorinated derivatives, C₁-C₁₀₀(NC1)Cl₁₈ (Figure 7B) and C₁-C₁₀₀(NC1)Cl₂₂, have been confirmed in the same crystal, which contains the same non-classical C₁₀₀ cage with one heptagon (Wang et al., 2016a). In addition, 17 Cl atom attachments, including one THJ of a chlorination pattern, occur in both structures (Wang et al., 2016a). The carbon cage of C₁₀₀(NC1)Cl₁₈ contains three isolated and nearly isolated C=C double bonds and three isolated and nearly isolated benzenoid rings, whereas the corresponding numbers for C₁₀₀(NC1)Cl₂₂ are four and five, as shown in Figure 7E (Wang et al., 2016a). In particular, the most important question regarding these structures relates to the origins of the non-classical C₁₀₀(NC1) cage of the two characterized chloro-derivatives (Wang et al., 2016a). No fullerene beyond C₁₀₀ in the starting fullerenes was observed; therefore, a transformation from even higher fullerenes to targeted non-classical fullerenes by a common C₂ loss should be excluded (Wang et al., 2016a). Furthermore, C₁₀₀(NC1) can be obtained by a single SW rearrangement of the type SWR2 from the IPR isomers C₁₀₀(382) or C₁₀₀(344). However, isomer C₁₀₀(382) has been considered as the starting fullerene because of its relatively lower formation energy compared with C₁₀₀(344). But there is no obvious driving force from IPR C₁₀₀(382) or C₁₀₀(344) to C₁₀₀(NC) due to the final cage not containing fused pentagons (Wang et al., 2016a). Therefore, an alternative option is that the non-classical C₁₀₀ (NC), having a comparable low formation energy, may exist in the starting fullerene used for chlorination (Wang et al., 2016a).

Non-classical C₉₈(NC2)Cl₂₆ containing two heptagons has been synthesized from C₁₀₂(19) via two C2L steps without any accompanying SWR processes (Figure 8A) (Mazaleva et al., 2018). A C2L step and an additional chlorination step take place alternately, and the so-called “chlorine dance,” equilibrium rearrangement of chlorination patterns, is also involved in the last step of the additional chlorination (Mazaleva et al., 2018). As shown in Figure 8C, the designations C2L1 and C2L3 relate to removing the pentagon–hexagon edge where the hexagon has one or three adjacent pentagons (Mazaleva et al., 2018). Remarkably, the C2L and SWR processes within the parent ^#283794C₁₀₂Cl₂₀ occur in the same area of the carbon cage, and the probable reason is that the chlorination pattern of the parent C₁₀₂(19) is characterized by a successive chain of adjacent chlorine attachments in that area (Mazaleva et al., 2018). Unexpectedly, novel non-IPR C₉₆Cl₂₈ was captured by chlorination of IPR ^#341061C₁₀₂ under the same conditions of just prolonging the reaction time (Figure 8B) (Yang et al., 2013; Mazaleva et al., 2018). As shown in Figure 8D, the formation process of the non-IPR C₉₆Cl₂₈ (or ^#185115C₉₆Cl₂₈) has three C2L steps and two pathways, as the order of the initial steps is an alternative, and one of them is the same as in the case of C₉₈(NC2)Cl₂₆ (Mazaleva et al., 2018). One of the common pentagon–pentagon edges is eliminated in the second step, which destroys the heptagon formed in the previous step, in both cases (Mazaleva et al., 2018). Dramatically, the third step represents a novel C2L5 process, which eliminates a common pentagon–pentagon edges surrounded by two hexagons, and thus neither creates nor destroys any heptagons (Mazaleva et al., 2018). The comparable activation energies of C₉₈(NC2)Cl₂₆ and non-IPR C₉₆Cl₂₈ provided by the DFT calculations lead to the concurrent formation of two derivatives under the same conditions (Mazaleva et al., 2018).

The non-classical chloride C₁-C₁₀₄(NC1)Cl₂₄ with one heptagon in the carbon cage forms a co-crystal with C₂-C₁₀₆(1155)Cl₂₄ (Figure 7C) (Wang et al., 2016b). The molecular structure of C₁-C₁₀₄(NC1)Cl₂₄ differs from that of C₂-C₁₀₆(1155)Cl₂₄ by a rotated C–C bond in one cage region along with the presence of a heptagon in another cage region (Wang et al., 2016b). As a consequence, six benzenoid rings and three isolated C=C double bonds form on the carbon cage; the former is one less than that in C₂-C₁₀₆(1155)Cl₂₄, whereas the latter is equal to that in C₂-C₁₀₆(1155)Cl₂₄ (Wang et al., 2016b). The addition positions of the 24 Cl atoms are similar to those in C₂-C₁₀₆(1155)Cl₂₄, while two Cl atoms attach in the THJs, as shown in Figure 7F (Wang et al., 2016b). C₁₀₆(1158) could be regarded as the starting fullerene, with a relative formation energy of 38 kJ mol⁻¹ (Wang et al., 2016b). However, this assumption is doubtful because no fused pentagons around the heptagon have been found, which is typically observed for the previous case of the C₂ loss from fullerene cages (Wang et al., 2016b). Alternatively, isomer C₁₀₄(NC) with one heptagon and 13 pentagons (but no fused pentagons) is also a candidate present in the fullerene soot (Wang et al., 2016b). In particular, the relative formation energy of C₁₀₄(NC) is only 40 kJ mol⁻¹ higher than that of the most stable IPR isomer C₁₀₄(234), whereas it is even lower than those of the experimentally confirmed C₁₀₄(811) and C₁₀₄(258), which have relative formation energies of 44 and 57 kJ mol⁻¹, respectively (Wang et al., 2016b).

Dy₂@C₁₀₀ was the first giant endohedral metallofullerene experimentally characterized by various spectral methods in 2006 (Yang and Dunsch, 2006). Based on the absorption spectral onset of 1,590 nm, the optical band gap is calculated to be 0.78 eV, which demonstrates that Dy₂@C₁₀₀ is a small band gap fullerene (Yang and Dunsch, 2006). Furthermore, Dy₂@C₁₀₀ exhibits instability in the solid form, which is confirmed by the existence of strong, but unresolved, absorption bands between 870 and 1,260 cm⁻¹ in the Fourier transform infrared (FTIR) spectra (Yang and Dunsch, 2006). Such broad bands are attributed to the graphitization of the dimetallofullerenes (Krause et al., 2001). Isomer 449:D₂ was calculated to be the lowest-energy isomer of C₁₀₀ (Yang and Dunsch, 2006). However, five isomers, 18:C₂, 426:C₁, 425:C₁, 442:C₂, and 148:C₁, are preferentially populated within a wide temperature interval according to the DFT calculations (Yang and Dunsch, 2006). All of the aforementioned six thermodynamically most stable isomers are regarded as the probable cage candidates for Dy₂@C₁₀₀ because fullerenes are synthesized at extremely high temperatures by arc discharges (Yang and Dunsch, 2006).

Sm₂@D_3d-C₁₀₄(822) is the first giant EMF to be unambiguously confirmed by single-crystal X-ray diffraction (Mercado et al., 2009). Three individual isomers of Sm₂@C₁₀₄ were isolated and purified, and their UV/Vis/NIR absorption spectra are presented in Figure 10A. The first eluted isomer I, with nickel octaethylporphyrin Ni(OEP) formed a black co-crystal (Mercado et al., 2009). The asymmetric unit of the crystal is made up of one molecule of Ni(OEP), one-half of the fullerene with the other half produced by a center of symmetry, and one-half of a disordered chlorobenzene molecule (Mercado et al., 2009). The crystallographic data demonstrate Sm₂@C₁₀₄(I) to be a conventional endohedral fullerene (Figure 11A) and not a carbide fullerene (Mercado et al., 2009). Sm₂@C₁₀₄(I) has a carbon cage of D_3d-C₁₀₄(822), which is the only one of the 823 isomers of C₁₀₄ obeying the IPR to possess D_3d symmetry (Mercado et al., 2009). In detail, samarium atoms show three disorder defects, and the occupancy of the major site is 0.74 and those of the two nearby sites are 0.17 and 0.09 (Mercado et al., 2009). Two primary Sm atoms are situated near the 3-fold axis of the carbon cage at a distance of 5.8322(7) Å in the molecule (Mercado et al., 2009). Each Sm atom is located beneath a canopy of three adjacent hexagonal rings, and the shortest Sm–C distance is 2.521(5) Å (Mercado et al., 2009). This cage is elongated, and its length, as measured by the distance between C1 and C1A lying on the 3-fold axis, is 10.840(9) Å, whereas its diameter is 8.264(9) Å (Mercado et al., 2009). Furthermore, the cage is closely related to a capped armchair carbon nanotube as well as to the structures of the I_h and D_5h isomers of C₈₀ (Mercado et al., 2009). Specifically, the D_3d-C₁₀₄(822) cage is generated by addition of 24 carbon atoms to fragments produced by the I_h-C₈₀ cage cutting perpendicular to the C₃ axis (Mercado et al., 2009). In addition, the electronic distribution of Sm₂@D_3d-C₁₀₄(822) is (Sm²⁺)₂@[D_3d-C₁₀₄^4-(822)] suggested by the computational data (Mercado et al., 2009).

La₂@D₅-C₁₀₀(450) was isolated by extensive chromatographic separations, though a series of giant endohedral metallofullerenes from La₂C₉₀ to La₂C₁₃₈ were confirmed by MS (Beavers et al., 2011). The UV/Vis/NIR spectra of La₂@D₅-C₁₀₀(450) shown in Figure 10B are different from those of Dy₂C₁₀₀ having a low-energy absorption band at ~1,060 nm (Yang and Dunsch, 2006; Beavers et al., 2011). It is possible that different cages for the two compounds or paramagnetic dysprosium (Dy) may lead to this discrepancy (Beavers et al., 2011). In the co-crystal, La₂@D₅-C₁₀₀(450) is immobilized by two Ni(OEP) molecules, one at each end (Figure 11B) (Beavers et al., 2011). The carbon cage is chiral but occupies a centrosymmetric site in the crystal (Beavers et al., 2011). Both the carbon cage and the lanthanum ions suffer from disorders, specifically, four nearly populated sites for the carbon cage, two for each enantiomer, and four sites for the La ions. The occupancies of the La ions are 0.6891(13), 0.1242(16), 0.1072(10), and 0.0794(14), respectively (Beavers et al., 2011). La₂@D₅-C₁₀₀(450) is a conventional dimetallofullerene and not a carbide fullerene, as is the Sm₂@D_3d-C₁₀₄(822) (Beavers et al., 2011). The nanotubular shape of La₂@D₅-C₁₀₀(450) resembles those of Sm₂@D_3d-C₁₀₄(822) (Mercado et al., 2009) and D_5h-C₉₀(1) (Yang et al., 2010). The centroid-to-centroid distance between pentagons on the major axis is 10.083 Å, while five perpendicular 2-fold axes bisecting the 6:6 ring junctions are being, and their average centroid-to-centroid distance is 8.024 Å (Beavers et al., 2011). The cage structure is D₅-C₁₀₀(450) according to theoretical predictions, which is most appropriate for encapsulating the (M³⁺)₂ unit (Beavers et al., 2011). This cage also satisfies the maximal pentagon separation rule: the physics of fullerene stabilization by requiring maximal separation between the 12 pentagons (Rodríguez-Fortea et al., 2010). The La ions can be observed to reside in the curved poles of the cage located by the pentagons (Beavers et al., 2011). Simultaneously, two La ions diverge slightly from the fivefold axis of the carbon cage and are widely separated by a distance of 5.7441(4) due to the repulsion of the two cations, which is similar to the cases of other La-containing endohedrals (Beavers et al., 2011). Additionally, in the crystal, the long axis of the La₂@D₅-C₁₀₀(450) molecule is perpendicular to the planes of the two porphyrins (Beavers et al., 2011). Hence, the most curved part of the carbon cage is close to the planar Ni(OEP) molecules. In contrast, the less-curved interior portions of Sm₂@D_3d-C₁₀₄(822) are adjacent to the two neighboring Ni(OEP) molecules (Beavers et al., 2011). As a result, in La₂@D₅-C₁₀₀(450)·2Ni(OEP)·2(toluene), the Ni1—Ni1A separation of 15.8785(6) Å across the carbon cage is longer than the corresponding Ni—Ni separation of 14.3850(13) in the centrosymmetric Sm₂@D_3d-C₁₀₄(822)·2Ni(OEP) C₆H₅Cl (Beavers et al., 2011).

La₂C₂@D₅-C₁₀₀(450) was unambiguously confirmed as a carbide fullerene by single-crystal X-ray diffraction (Figure 12A) (Cai et al., 2015). The cage isomer, D₅-C₁₀₀(450), is the same as that of La₂@D₅-C₁₀₀(450). However, the Vis-NIR spectrum is significantly different from those of La₂@D₅-C₁₀₀(450) and Dy₂@C₁₀₀ (Figure 10B), which indicates that their electronic configurations differ (Cai et al., 2015). Unexpectedly, in the co-crystal, the Ni(OEP) added as a co-crystallization host is absent, leaving only the fullerene and the intercalated CS₂ molecules (Cai et al., 2015). Both the carbon cage and the embedded La₂C₂ cluster show several disorder defects, and the chiral fullerene cage has two disordered enantiomers with almost equal occupancy (0.52:0.48) (Cai et al., 2015). There are 19 sites for two La ions, and the major two sites are over a respective [6,6]-bond junction near a pole of the cage passing the fivefold axis of the cage (Figure 12A′) (Cai et al., 2015). The inner C₂ unit possesses four disordered sites with C–C bond distances of 1.00–1.21 Å (Cai et al., 2015). Furthermore, numerous disordered sites with La ions and C₂ units demonstrate the free movement of metal atoms and the flexible swing of the C₂ unit within the carbon cage (Cai et al., 2015). The La–La separation distance of the major sites is 4.83 Å, which is obviously shorter than that of La₂@D₅-C₁₀₀(450) (Cai et al., 2015). The La₂C₂ cluster shows a bent configuration, with a dihedral angle of 141.3° between the two LaC₂ portions (Cai et al., 2015). Moreover, the C₂ unit is considered to be rotating in the cluster plane, which confirms the computed prediction of the possibility of the linear M₂C₂ cluster structures in the giant fullerene (Cai et al., 2015).

Most notably, the anomalous axial compression of D₅-C₁₀₀(450) is clearly observed when the structures of La₂C₂@D₅-C₁₀₀(450) and La₂@D₅-C₁₀₀(450) are compared (Figure 13) (Cai et al., 2015). The length of the cage in La₂@D₅-C₁₀₀(450) is 10.083 Å, and the width of the cage is 8.024 Å. In contrast, the long axis of La₂C₂@D₅-C₁₀₀(450) reduces to 9.585 Å, but the width of the cage is 8.332 Å, that is, slightly expanded (Cai et al., 2015). This result clearly reveals the larger cluster La₂C₂ obviously contracts the carbon cage, rather than expanding it (Cai et al., 2015). Moreover, the La–La separation distance of the two major La atoms in La₂C₂@D₅-C₁₀₀(450) (4.830 Å) is apparently shorter than that in La₂@D₅-C₁₀₀(450) (5.744 Å), while the La–cage distances are nearly equal in the two molecules (Cai et al., 2015). The reason for the shortened La–La distance is that the positive charge is partly neutralized by the electronegative C₂ unit and the Coulombic repulsion between the two La ions is weakened (Cai et al., 2015). Hence, the axial compression of the carbon cage may result from the stronger bonding interactions between the La ions and the C₂ unit (Cai et al., 2015). Based on the calculated X-ray results for La₂C₂@D₅-C₁₀₀(450) and La₂@D₅-C₁₀₀(450), the whole axial strain of this small capped zigzag (10,0) nanotube, D₅-C₁₀₀(450), is 5% (Cai et al., 2015). Detailed analyses reveal that the [10] cyclacene sidewall segment containing purely [6,6]-bonds is responsible for the structural deformation, but that the pentagon-dominating corannulene caps are very rigid (Cai et al., 2015).

La₂C₂@C_s-C₁₀₂(574) was also isolated and characterized by HPLC, Vis-NIR spectra, and single-crystal X-ray diffraction, as shown in Figure 12B (Cai et al., 2016). Its Vis-NIR spectrum shown in Figure 10C indicates that it has a small HOMO-LUMO gap due to the spectral onset at around 1,300 nm, which is similar to those reported for the giant endohedral metallofullerenes (Cai et al., 2016). Similarly, the crystal units contain merely one La₂C₂@C_s-C₁₀₂(574) molecule and two CS2 molecules, whereas the co-crystallization host Ni (OEP) used, as well as other solvent molecules, are absent (Cai et al., 2016). There are two bands of 10 contiguous hexagons encircling the cage, which is similar to the previously reported tubular D_3d-C₁₀₄(822), D₅-C₁₀₀(450) and D_5h-C₉₀(1). Within the cage, the carbide cluster shows several disordered positions, and there are 18 La positions for the two La atoms, which display as an umbrella shape relative to the three disordered sites of the C₂ unit (Cai et al., 2016). Furthermore, the two major La ions in La₂C₂@C_s-C₁₀₂(574) are detached and the line connecting them is a little displaced from the long axis of the carbon cage (Cai et al., 2016). One of them is situated under a hexagon, while the other is located over a [5,6]-bond on the opposite side (Figure 12B′) (Cai et al., 2016). The La₂C₂ unit shows a stretched and nearly planar configuration, which differs from the bent butterfly-like configuration dominating in the Sc₂C₂ cluster fullerene (Kurihara et al., 2012). Moreover, the disordered C₂ unit is no more perpendicular to the line crossing the two major La ions (Cai et al., 2016). The La–C–C–La dihedral angle (173.6°) in La₂C₂@C_s-C₁₀₂(574) is much larger than that in La₂C₂@D₅-C₁₀₀(450) (141.3°) (Cai et al., 2016). This demonstrates that the carbide cluster transforms from a slightly bent structure into a nearly planar configuration as the cage length increases, which is consistent with the theoretical predictions that the M₂C₂ cluster may prefer a linear geometry in large cages (Zhang et al., 2012).

La₂C₂@C₂-C₁₀₄(816) is also unambiguously confirmed as a carbide by single-crystal X-ray diffraction, as shown in Figure 12C (Cai et al., 2016). The spectral onset of the Vis-NIR spectrum occurs at ~1,300 nm (Figure 10C), resulting in a small HOMO-LUMO gap (Cai et al., 2016). The analogous crystallization behavior as described above is also present, where the co-crystallization host Ni(OEP) used is absent from the co-crystal (Cai et al., 2016). The cage of La₂C₂@C₂-C₁₀₄(816) shows a “defective” tubular structure resulting from the insertion of a pyracylene unit into the two bands of hexagons on the waist of the cage and leading to a reduction in the symmetry of the cage (Cai et al., 2016). Inside the cage, the carbide cluster shows some degree of disorder: six existing La sites for the two La atoms and two disordered positions for the C₂ unit (Cai et al., 2016). It appears that the defective C₂-C₁₀₄(816) cage appreciably hinders the free movement of the metal atoms when compared with the locations of La₂C₂@D₅-C₁₀₀(450) and La₂C₂@C_s-C₁₀₂(574) possessing ideal tubular cages (Cai et al., 2016). The pyracylene unit existing in the [10]cyclacene framework is responsible for this phenomenon (Cai et al., 2016). In addition, the predominant La ions in La₂C₂@C₂-C₁₀₄(816) are detached, and the line across them is slightly misaligned along the long axis of the carbon cage (Cai et al., 2016). As shown in Figure 12C′, the two major La ions in La₂C₂@C₂-C₁₀₄(816) depart from the pyracylene region, with one situated around a [6,6]-bond and the other located over a [5,6]-bond on the opposite side. Similarly, the La₂C₂ unit shows a stretched and nearly planar geometry, and the disordered C₂ unit is no longer perpendicular to the line across the two major La ions (Cai et al., 2016). The La–C–C–La dihedral angle (157.5°) is much larger than that in La₂C₂@D₅-C₁₀₀(450) (141.3°), whereas and is less than that in La₂C₂@C_s-C₁₀₂(574) (173.6°) (Cai et al., 2016). The abnormally small value of the La–C–C–La dihedral angle in La₂C₂@C₂-C₁₀₄(816) may be attributed to the presence of the pyracylene “defect” destroying the ideal tubular structure (Cai et al., 2016).

So far, Y₂C₂@C₁-C₁₀₈(1660) has been the largest metallofullerene, with the linear configuration of the encapsulated carbide cluster characterized by crystallography, as shown in Figure 12D (Pan et al., 2018). The Vis-NIR absorption spectrum of Y₂C₁₁₀ showing absorption bands at 533, 654, 852, and 1,037 nm, with an onset at around 1,400 nm (Figure 10D), indicates that it has a small optical gap (0.89 eV) (Pan et al., 2018). Fortunately, the molecular structure of Y₂C₁₁₀ has been definitely confirmed by the crystallographic study of co-crystals of Y₂C₂@C₁-C₁₀₈(1660)·2Ni(OEP) (Pan et al., 2018). There are some degrees of disorder with respect to the metal atoms, showing 12 positions in all, with occupancies ranging from 0.080 to 0.204 (Pan et al., 2018). This endohedral fullerene is obliquely surrounded by two Ni(OEP) molecules, and the Ni–cage distances are 2.895 and 3.054 Å, which equal those for La₂@D₅-C₁₀₀(450) and Sm₂@D_3d-C₁₀₄(822) (Mercado et al., 2009; Beavers et al., 2011). Y₂C₁₁₀ is unambiguously assigned to a carbide cluster EMF, Y₂C₂@C₁-C₁₀₈(1660), utilizing an asymmetric chiral cage, which is one of the 1799 IPR isomers of C₁₀₈ (Pan et al., 2018). Surprisingly, this cage has a relatively round shape as a result of the absence of a band of contiguous hexagons and more evenly distributed pentagons, which differs from the reported tubular giant EMF (Mercado et al., 2009; Beavers et al., 2011; Cai et al., 2016). Hence, Y₂C₂@C₁-C₁₀₈(1660) has a relatively short length (10.04 Å) compared with the other smaller giant cages (Pan et al., 2018). In particular, as shown in Figure 12D′, the Y₂C₂ cluster shows a linear configuration along the long axis of the carbon cage due to its ample inner space. This is the first experimental evidence of a linear M₂C₂ cluster that is coincident with the theoretical predictions of Dorn et al. (Zhang et al., 2012). The Y–C–C–Y dihedral angle is 173.1°, which indicates a linear configuration, while the C–C bond (1.08 Å) is shorter than a typical C≡C triple bond. The Y–Y distance of 5.85 Å is nearly equal to that of the free Y₂C₂ cluster (5.83 Å) suggested by theoretical calculations, but is obviously longer than the theoretical values for Y₂C₂ in Y₂C₂@C_3v-C₈₂(8) (3.74 Å), Y₂C₂@D₃-C₉₂(85) (4.92 Å), and Y₂C₂@D₅-C₁₀₀(450) (5.51 Å) (Zhang et al., 2012). This confirms experimentally that the compression of the encapsulated cluster induced by the fullerene cage can be ignored in Y₂C₂@C₁-C₁₀₈(1660) (Pan et al., 2018).