Five different pure density functional theory (DFT) and hybrid Hartree-Fock/DFT methods have been used to search for the molecular structures, thermochemistry, and electron affinities of the bromine hydrogen fluorides HBrF(n)/HBrF(n)(-) (n = 2, 4). The basis sets used in this work are of double-zeta plus polarization quality in conjunction with s- and p-type diffuse functions, labeled as DZP++. Structures with Br-F and Br-H normal bonds, that is, HBrF(2)/HBrF(2)(-) with C(2v) or C(s) symmetry and HBrF(4)/HBrF(4)(-) with C(4v) or C(s) symmetry, are genuine minima. However, unlike the original BrF(3) and BrF(5) molecules, the global minima for HBrF(n)/HBrF(n)(-) (n = 2, 4) species are predicted to be complexes, some of which contain hydrogen bonds. The demise of the hypervalent structures is due to the availability of favorable dissociation products involving HF, which has a much larger dissociation energy than F(2). Similar reasoning suggests that PF(4)H, SF(3)H, SF(5)H, ClF(2)H, ClF(4)H, AsF(4)H, SeF(3)H, and SeF(5)H will all be hydrogen bond structures incorporating diatomic HF. The most reasonable theoretical values of the adiabatic electron affinities (EA(ad)) are 3.69 (HBrF(2)) and 4.38 eV (HBrF(4)) with the BHLYP method. These electron affinities are comparable to those of the analogous molecules: Br(2)F(n), ClBrF(n), and BrF(n)(+1) systems. The first F-atom dissociation energies for the neutral global minima are 60 (HBrF(2)) and 49 kcal/mol (HBrF(4)) with the B3LYP method. The first H-atom dissociation energies for the same systems are 109 (HBrF(2)) and 116 kcal/mol (HBrF(4)). The large Br-H bond energies are not sufficient to render the hypervalent structures energetically tenable. The dissociation energies for the complexes to their fragments are relatively small.