Restricted Hartree-Fock calculations, with explicit non-empirical calculation of all integrals, are presented for the ground states and some low-lying excited states of eight triatomic radicals (BF2, NH2, HBF, HCO, HNF, FCO, NF2, FO2). Geometries are calculated for these species, and the results related to experiment where possible. The nature of the bonding in each species is discussed. The effect of varying the size of the Gaussian basis sets employed was examined intensively, with particular attention being paid to changes in the total calculated energy, the optimal geometry, bonding and spin density distribution. It was concluded that for reliable geometry predictions a basis of 9 s and 5 P Gaussian functions was required on each first row atom, preferably augmented by polarisation functions possessing higher orbital angular momentum quantum number. This is particularly necessary to obtain the correct bond angles for hydrides. To predict spin densities accurately a basis set of essentially Hartree-Fock quality, possessing at least 11 s functions, is required. For this latter application considerations of balancing the size of the representation on the various atoms in the molecule is particularly crucial.