Theoretical Investigations of Lu₂C₈₄: Unexpected Impact of Metal Electronic Configuration toward the Metal–Metal σ-Bond in Fullerene

Abstract

Recent experimental works recovered multiformity of lutetium-involved dimetallofullerenes. On the basis of density functional theory (DFT) combined with statistical thermodynamic analyses, the relative stabilities of Lu 2 C 84 dimetallofullerene were clarified. Besides the experimentally acknowledged Lu 2 @ D 2d (51591)-C 84 and Lu 2 @C 2v (51575)-C 84 , another four isomers metallofullerenes, Lu 2 @C 1 (51580)-C 84 , Lu 2 C 2 @C s (39715)-C 82 , Lu 2 C 2 @C 3v (39717)-C 82 , and Lu 2 C 2 @C 2v (39718)-C 82 , are first proposed as thermodynamically stable structures. Interestingly, the geometric relationships among the pristine cages of stable Lu 2 C 84 isomers through Stone−Wales transformation or C 2 lose/ insertion reveal important clues of the fullerene formation mechanism. The ionic interaction in the stable Lu 2 C 84 isomers is revealed, and their valence states are Lu 2 4+ @C 84 4− or (Lu 2 C 2 ) 4+ @C 82 4− . In the Lu 2 @C 84 isomers, the results of frontier molecular orbital and natural bond orbital analyses suggest that a Lu−Lu single bond is formed, which is mainly composed of the 6s and 6p orbitals of the Lu atoms. Further analyses of the M 2 @C 84 (M = Sc, Y, La, and Yb) structures disclose the importance of the electron configuration of metal element toward the formation of a single metal−metal bond in C 84 . Moreover, the covalent interaction between the Lu 2 moiety and the C 84 cages is disclosed, which is a supplement to the ionic model.

Atomically Precise Insights into Metal–Metal Bonds Using Comparable Endo-Units of Sc 2 and Sc 2 C 2

“…However, only a few cases have been found experimentally or theoretically after considerable efforts to explore endo-metal-metal bonds in fullerene cages. [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] An unexpected challenge in determining endo-metal-metal bonding in fullerene cages by X-ray crystallography is posed by severe disorder in the crystal structures, especially for metallic endo-clusters, and there can be up to tens of disordered sites when determining endo-metal atoms in a fullerene cage. Therefore, searching for an example system with less metallic disorder is the key to precisely elucidating the nature of endo-metal-metal bonds.…”

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+

“…The lowest-energy isomer of the Lu 2 C 2 @C 84 is Lu 2 C 2 @ D 2 d (51591)-C 84 with the relative energy of 18.9 kcal·mol –1 higher than that of the lowest-energy isomer of the Lu 2 @C 86 series. The D 2 d (51591)-C 84 cage is the pristine cage of the Lu 2 C 84 series . Other Lu 2 C 2 @C 84 isomers have much larger relative energies of over 28.3 kcal·mol –1 .…”

“…Previous theoretical studies have discovered geometrical relationships among the pristine cages of EMF isomers, ,− which are significant for research of the fullerene formation mechanism. Our study of Lu 2 C 84 revealed geometrical relationships among stable Lu 2 @C 84 and Lu 2 C 2 @C 82 through SWT and C 2 loss/insertion. , In fact, a larger geometrical relationship diagram among the experimentally detected and theoretically predicted Lu 2 C 2 n , including the Lu 2 C 86 series in this study, has been found. As shown in Figure , the C s (63750)-C 86 and C s (63757)-C 86 cages are related by one-step SWT.…”

“…The vibrational frequencies were also examined on the PBEPBE/6-31G­(d)∼SDD level, and all of the optimized Lu 2 C 86 isomers are free from the imaginary frequency, confirming that they localized at the local minima of the potential energy surfaces. The statistical thermodynamic analyses were performed at the same theoretical level because the component of equilibrium is closely related to both enthalpy and entropy effects at high temperature. , The formula used to illustrate the enthalpy–entropy interplay , is shown as follows where ω i is the equilibrium constant (molar fraction) of the i isomer from the selected m Lu 2 C 86 isomers; q i is the partition function; Δ H 0, i ο is the ground-state relative energy; R is the gas constant; and T is the absolute temperature in K. Statistical thermodynamic analysis is really good at describing the stabilities of EMFs, whose results have been confirmed by several experiments. ,− ,,,, …”

“…With regard to the bonding features in the Lu-based EMFs, a Lu–Lu single bond has been found in many Lu 2 @C 2 n . ,,, In our previous discussions on the Lu–Lu bond in the Lu 2 @C 84 , one determining factor, the nd 1 (n + 1)­s 2 electron configuration of the metal element, has been found . However, the bonding features among various M 2 (M = Sc, Y, La, and Lu) moieties were found to be somehow different.…”