20-electron exohedral alkaline-earth metallofullerenes M(C₆₀)₃ (M = Ca, Sr, and Ba)

Electron-counting rules are promising for determination of chemically stable complexes for various elemental groups. While the 18-electron rule has been established for transition metals, recent experiments have discovered that alkaline-earth metals may follow a 20-electron rule when coordinated with CO or benzene. Herein, by employing first-principles calculations at the level of the generalized gradient approximation functional combined with the def2-SVP basis set, we theoretically predict a series of stable 20-electron exohedral alkaline-earth metallofullerenes, in which each alkaline-earth metal is η⁶-coordinated with three C₆₀s, leading to stable trigonal pyramidal structures. Molecular orbital calculation and energy decomposition analysis indicate that not only (n)s orbitals but also (n - 1)d(n)p orbitals of the alkaline-earth metal atoms participate in bonding interactions with the fullerenes. Energy decomposition analysis reveals that the bonding between metal atoms and C₆₀ can be divided into weak donation from C₆₀ to metal d orbitals and strong back-donation from the metal d orbitals to C₆₀, consistent with 20-electron metal complexes. Based on stable trigonal pyramidal building blocks, we designed a series of two-dimensional assembled materials with fullerenes forming a Kagome sublattice and metals forming a honeycomb sublattice, possessing topologically nontrivial flat bands with exotic quantum properties.