Experimental studies have shown that the dissociative attachment of electrons to HBr monomer; viz., HBr + e(-) --> H-. + Br- is an endothermic process, which requires electrons of energy near the endothermicity (Delta E = +38 kJ/mol). In contrast the attachment to the dimer via the reaction: HBr . HBr + e(-) reversible arrow HBr . HBr.- --> H-. + BrHBr-proceeds readily with electrons of thermal (i.e., near zero) energy. The energetics of the reactions with both the monomer and the dimer have been studied by ab initio methods. In each case the structure of the neutral and anion species have been computed using large basis sets and diffuse orbitals at the MP2 level. Energies have been obtained at this level and at the CCSD(T) level. The initial interaction of the free electron with the molecule produces a dipole continuum state (DCS) of the anion. The DCS subsequently undergoes a transition to a bound state via an avoided crossing. On the basis of the CCSD(T) energies, the H-Br.-.. HBr interaction lowers the energy for dissociation of the H-Br.- bond to the thermal energy range. Also the decomposition of HBr . HBr.- to H-. and BrHBr- is 47 kJ/mol exergonic and the BrHBr- fragment is expected to be in a vibrationally excited state. In both the monomer and dimer anions the transition from DCS to the bound valence state is very sudden, and is marked by enormous (10-fold) changes in the dimensions of the orbitals occupied by the electron.