Density functional (B3LYP) method with relativistic effective core potential (RECP) has been used to optimize the structures of Pu2 and Pu3 molecules. The results show that the ground states of Pu2 and Pu3 molecules are of D∞h and D3h symmetry, and of 13 and 19 fold, respectively. The spectral constants of Pu2, ωe=52.3845 cm-1 and ωe χe=0.0201 cm-1, and the harmonic frequencies of Pu3,ν1=56.9007 cm-1,ν2=57.1816 cm-1 and ν3=64.0785 cm-1, have also been obtained on the B3LYP/RECP level. The potential energy functions of Pu2 and Pu3 have been derived, for the first time so far as we know,from normal equation fitting and the many-body expansion theory.