Electronic-to-vibrational energy transfer and nonadiabatic chemical reaction from an electronically excited reagent are studied by accurate quantum dynamics calculations for Br* + H-2 --> HBr + H or Br + H-2, where an asterisk denotes electronic excitation, and the lack of an asterisk denotes the electronic ground state. We present details of the formalism for calculating the scattering matrix in a diabatic representation in which the coupling between potential energy surfaces does not vanish asymptotically. The inelastic results are discussed in terms of the translational energy gap, which is often assumed to be a dominant factor in electronic-to-vibrational-rotational energy transfer. The quenching of Br* by H-2 produces principally H-2 with one quantum of vibrational excitation; this process satisfies a near-resonance condition for electronic-to-vibrational energy transfer. Reaction to produce HBr is the next most likely branching pathway, followed by rotational translational energy transfer. Examination of the rotational distributions of each final vibrational level shows that the rotational states nearest to resonance are not the most heavily populated; i.e., the resonance condition is more important for vibration than for rotation. The reactive results are discussed in terms of the relative efficiencies of various forms of reagent energy in overcoming the endoergicity and intrinsic barrier to reaction.