By means of the first-principles calculations, we reveal that B 40 presents superatomic properties. It not only has superatomic 1S, 1P, 1D and 1F orbitals, but also has superatomic orbitals 2S, 2P, 2D and 2F. The superatomic 2F orbital of B 40 is partially occupied, thus adding six electrons to the cluster leads to a superatomic structure of fully occupied shells. , were also optimized at PBE0/ 6-31G* level. Frequency analyses were performed at the same level of theory to characterize the nature of the stationary points. Both B 40 and B 40 6− are true local minima, but B 40 8+ with fully occupied shell is a high order saddle point. Following the imaginary modes of B 40 8+ leads to the true local minimum without full-filled shell. The optimized geometries from different functionals are rather similar, and we only discuss the computational results from PBE0 because it has been tested extensively in previous works and found to be suitable for boron clusters [1,[20][21][22]. To investigate the electron delocalization or aromaticity of B 40 and its charged species, we calculated NICS (in ppm) [23,24] at the cage centers of the optimized geometries of the empty cage molecules using the gauge-independent atomic orbital (GIAO) method [25]. The verification of B 40 using PBE0/6-311 +G* level is shown in Table S2 in SI. All computations are carried out using the Gaussian09 package [26].Our calculations show that the ground state of B 40 fullerene (D 2d ) is non-spin-polarized singlet, with the low and high energy molecular orbitals (MOs) displayed in Figs 1, 2, respectively. Among the low-energy MOs, a double-occupied MO 7a 1 (marked by black) resembles an s-like atomic orbital, thus we call it the 1S superatomic orbital (that is, molecular orbital) for B 40 , and the specific orbital composition analyses are described in the fol-