Based on the Gaussian03 calculation software, QCISD method is used to optimize the possible ground-state structures of XF2(X=B,N) molecules with the different basis sets. On this basis, the resonant frequencies and force constants are calculated with the D95(df, pd) and D95+(df, pd) basis sets respectively. The potential energy functions of XF2(X=B,N) are derived from the many-body expansion theory. At the same time, according to the potential energy functions, three equivalent potential energy diagrams for the XF2(X=B,N) ground states are drawn. The potential energy surface is verified to be consistent with the three atomic molecular geometry. The structures and the features of XF2(X=B,N) can correctly reappear on the potential surface.