Significant Roles of a Particularly Stable Two-Center Two-Electron Lu-Lu σ Bond in Lu2@C86: Electronic Structure of Lu and Radius of Lu2

There is still dispute over the stability of endohedral metallofullerenes (EMFs) M₂C_2n, and recently, multiform lutetium-based dimetallofullerenes have been dropped in experiments. The thermodynamic stabilities of Lu₂C₈₆ EMFs are revealed by density functional theory (DFT) in conjunction with statistical thermodynamic analyses. Inevitably, besides the experimentally reported Lu₂@C_2v(63751)-C₈₆, Lu₂@C_s(63750)-C₈₆, and Lu₂@C_s(63757)-C₈₆, other three metal carbide clusterfullerenes, Lu₂C₂@D_2d(51591)-C₈₄, Lu₂C₂@C₁(51383)-C₈₄, and Lu₂C₂@C_s(id207430)-C₈₄, rather than Lu₂@C₈₆ are first characterized as thermodynamically stable isomers of Lu₂C₈₆. Specially, the C_s(id207430)-C₈₄ is a newly non-classical fullerene containing one heptagon, which is stabilized via encaging Lu₂C₂. Another interesting phenomenon is that the outer fullerene cages of thermodynamically stable Lu₂C_82-88 molecules are geometrically connected through C₂ addition/loss and Stone-Wales (SW) transformation, suggesting a special relationship between thermodynamic stabilities and geometries of Lu₂C_82-88 EMFs. Furthermore, the electronic configurations of (Lu₂)⁴⁺@C₈₆^4- and (Lu₂C₂)⁴⁺@C₈₄^4- were confirmed. A significantly stable two-center two-electron (2c-2e) Lu-Lu σ single bond is formed in Lu₂@C₈₆. By comparing M-M bonds in M₂@C_2v(63751)-C₈₆ (M = Sc, Y, La, and Lu), two significant factors, the valence atomic orbital (ns) of metal atoms and radius of M²⁺, are found to determine the stability of the M-M bond in the C_2v(63751)-C₈₆. Additionally, the simulated UV-vis-NIR spectra of thermodynamically stable Lu₂C₈₆ isomers were simulated, which further disclose their electronic features.

Theoretical Insight into Thermodynamically Optimal U@C84: Three-Electron Transfer Rather Than Four-Electron Transfer

Four-electron transfer from U to the fullerene cage commonly exists in U@C_2n (2n < 82) so far, while four- and three-electron transfers, which depend on the cage isomers, simultaneously occur in U@C₈₂. Herein, detailed quantum-chemical methods combined with statistical thermodynamic analysis were applied to deeply probe into U@C₈₄, which is detected in the mass spectra without any further exploration. With triplet ground states, novel isomers including isolated-pentagon-rule U@C₂(51579)-C₈₄ and U@D₂(51573)-C₈₄ as well as nonisolated-pentagon-rule U@C_s(51365)-C₈₄ were identified as thermodynamically optimal. Surprisingly, there were unexpected three-electron transfers, which directly led to one unpaired electron on the cage, in all of the three isomers. Significant covalent interactions between the cage and U successively weakened for U@D₂(51573)-C₈₄, U@C₂(51579)-C₈₄, and U@C_s(51365)-C₈₄. Besides, the IR absorption spectra were simulated as a reference for further structural identification in the experiment. Last but not least, the potential reaction sites were predicted to facilitate further functionalization and thus achieve promising applications for U@C₈₄.

Stereochemistry of Simple Molecules inside Nanotubes and Fullerenes: Unusual Behavior of Usual Systems

Over the past three decades, carbon nanotubes and fullerenes have become remarkable objects for starting the implementation of new models and technologies in different branches of science. To a great extent, this is defined by the unique electronic and spatial properties of nanocavities due to the ramified π-electron systems. This provides an opportunity for the formation of endohedral complexes containing non-covalently bonded atoms or molecules inside fullerenes and nanotubes. The guest species are exposed to the force field of the nanocavity, which can be described as a combination of electronic and steric requirements. Its action significantly changes conformational properties of even relatively simple molecules, including ethane and its analogs, as well as compounds with C-O, C-S, B-B, B-O, B-N, N-N, Al-Al, Si-Si and Ge-Ge bonds. Besides that, the cavity of the host molecule dramatically alters the stereochemical characteristics of cyclic and heterocyclic systems, affects the energy of pyramidal nitrogen inversion in amines, changes the relative stability of cis and trans isomers and, in the case of chiral nanotubes, strongly influences the properties of R- and S- enantiomers. The present review aims at primary compilation of such unusual stereochemical effects and initial evaluation of the nature of the force field inside nanotubes and fullerenes.

Potential molecular semiconductor devices: cyclo-Cn (n = 10 and 14) with higher stabilities and aromaticities than acknowledged cyclo-C18

Theoretical calculations reveal that the zero-dimensional allotropes of carbon atoms, cyclo-C_n (n = 10 and 14), have higher thermodynamic, kinetic, optical, and dynamic stabilities and aromaticity than the acknowledged cyclo-C₁₈.

Oxidation states of gallium (infrequent i and common iii) tunable via medium-sized C60 and small-sized C28 fullerenes

Differently sized fullerenes are shown to be flexible tools for tuning the oxidation states of gallium, and a fluoridation strategy facilitates the further stabilization of Ga@I_h(1812)-C₆₀.

Covalent interactions depend on the distances between metals and fullerenes for thermodynamically stable M@C78 (M = La, Ce, and Sm)

Thermodynamic selectivity occurs between fullerenes and metals in M@C₇₈ (M = La, Ce, Sm), including non-IPR C₁(22 595)-C₇₈; the different number of electrons transferred from metals to C₇₈ leads to the first EMF with diradical features.