Brominated aromatics, used extensively as flame retardants, have been studied with Br-81 nuclear quadrupole resonance (NQR) spectroscopy. NQR requires lengthy frequency searches because Br-81 NQR transition frequencies in brominated aromatics are spread over a wide (40 MHz) range. We investigate the ability of ab initio calculations to narrow this search range by predicting Br-81 NQR transition frequencies for a series of brominated aromatics, using restricted Hartree-Fock (RHF) and Becke's three-parameter Lee-Yang-Parr density functional theory hybrid method (B3LYP). Basis sets used are of double and triple-zeta quality with varying degrees of polarization included on bromine. Geometries are the isolated molecules, with coordinates optimized for lowest energy. The results of calculations for nine simple brominated aromatics are fit against experimental frequencies and the fit is subsequently used to predict frequencies of larger, two-ring brominated aromatics (one is sold commercially as a flame retardant). Comparison to experiment shows the accuracy of this approach to be approximately 5 MHz, reflecting a significant, 8-fold decrease in the spectral range to be searched by experiment.