The density function (B3P86) method with relativistic effective core potential has been used to optimize the structure of the ground state of BH2,BH2+ and BH2- molecules or ions,which are angular H-B-H, whose equilibrium nuclear distance and dissociation energy respectively are RBH=RBH=0.11899nm,RHH=0.21514nm，and 7.752eV; RBH=RBH=0.12896nm,RHH=0.14223nm; RBH=RBH=0.12037nm,RHH=0.21087nm. The analytic potential energy function of the ground state of BH2(2A′) has been derived by the many-body expansion theory using the equilibrium geometry structure parameters,dissociation energy and force constants,which is successfully used for describing the equilibrium geometry of BH2(2A′).