Hf3 cluster is triply (sigma-, pi-, and delta-) aromatic in the lowest D3h, 1A1' state

The extensive search for the global minimum structure of Hf3 at the B3LYP/LANL2DZ level of theory revealed that D3h 3A2' (1a1'(2)1a2'(2)1e'(4)2a1'(2)1e'2) and D3h 1A1' (1a1'(2)2a1'(2)1e'(4)1a2'(2)3a1'2) are the lowest triplet and singlet states, respectively, with the triplet state being the lowest one. However, at the CASSCF(10,14)/Stuttgart+2f1g level of theory these two states are degenerate, indicating that at the higher level of theory the singlet state could be in fact the global minimum structure. The triplet D3h 3A2' (1a1'21a2'(2)1e'(4)2a1'(2)1e'2) structure is doubly (sigma- and pi-) aromatic and the singlet D3h 1A1' (1a1'(2)2a1'(2)1e'(4)1a2'(2)3a1'2) structure is the first reported triply (sigma-, pi-, and delta-) aromatic system.