A novel modification of the flux operator formalism is introduced that combines the merits of the flux operator approach with those of complex absorbing potentials. The method is used to determine initial-state selected reaction probabilities for a broad energy range from a single appropriately chosen time-dependent wave packet. The propagation may be performed solely in the coordinates of the reagents arrangement channel. State-to-state transition probabilities can also be obtained when appropriate projectors are included. In contrast to similar methods the present one does not require the calculation of derivatives with respect to the reaction coordinate. More importantly, it avoids the need to (E,t)-Fourier transform the wave packet at every grid point on a dividing surface. The proposed formula, though completely general, is especially well suited to handle multiconfiguration time-dependent Hartree wave functions. As a check of the reliability initial-state selected reaction probabilities for the collinear H+H-2-->H-2+H reaction are calculated and compared with (numerically) exact results. We also show that the initial wave packet may be placed close to the interaction region when its energy distribution is corrected for the mean potential energy.