Ab initio quantum Hartree-Fock and Moller–Plesset approximations used to study cis boron hydrogen cis-(BH)n chains. The ground-state energies, binding energies, Mulliken population and the optimal geometrical configurations of cis-(BH)n are reported in terms of the chain size n. The calculated ground-state energies in terms of chain dimerization un showed two phases cis-transoid and Trans-cisoid. The energies of these two phases at MP2 fitted into the modified Su-Schrieffer-Heeger (SSH) model in order to determine the corresponding parameters. According to this model, the dimerization induces a band gap around 0.12 eV for cis-transoid phase and 0.11 eV for the trans-cisoid one.