The equilibrium geometries, total electronic energies, and vibrational frequencies for singlet, triplet, and quinted states of three all-metal X 3 -(X ϭ Sc, Y, and La) anions and nine relevant neutral singlet MX 3 (M ϭ Li, Na, K, X ϭ Sc, Y, La) clusters are investigated with four density functional theory (DFT) and correlated ab initio methods B3LYP, B3PW91, MP2, and CCSD(T). To our knowledge, the theoretical study on these clusters composed of the transition metal Sc, Y, La is first reported here. The calculated results show that for the X 3 clusters the singlet states with trigonal D 3h structures are the lowest energetically, while the neutral singlet MX 3 clusters each have two stable isomers: one trigonal pyramidal C 3v and one bidentate C 2v structures with the pyramidal C 3v isomer being ground state. In addition, we calculate the resonance energies (RE) and nucleusindependent chemical shift (NICS) for the singlet trigonal X 3 rings and show that these singlet trigonal X 3 rings exhibit higher degree of aromaticity. The detailed molecular orbital (MO) analyses reveal that the singlet trigonal X 3 anions have one delocalized -type and one delocalized -type MOs, which follow the 4n ϩ 2 electron counting rule, respectively and play an important role in rendering these species two-fold aromaticity. Here, an explicit theoretical evidence is given to prove that the contribution to the two-fold aromaticity of the singlet trigonal X 3 -(X ϭ Sc, Y, and La) rings originates primarily from the d-orbital bonding interactions of these component transition metal X atoms.

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