Structure, stability and electron-counting rule of [B20H18]n- (n=0,2,4,6) anionic isomers

Various isomers of [B20H18](n-) (n = 0, 2, 4, 6) anions are investigated by using the DFT method at B3LYP/6-31G* level to obtain the optimized geometries and the order of stability. The optimized bond lengths are consistent with the available experimental values. The calculated vibrational frequencies are all real, so all of these isomers should be stable structures where [a(2)-B20H18](2-) (3), [a(2)-B20H18](0) (8) and [a(2)-B20H18](6-) (9) predicted in this paper were not discovered. Moreover, the analyses on counting of skeletal bonding electrons show, that isomers 1-7 obey the electronic requirement predicted by the mno rule, but isomers 8 and 9 are two exceptions.