We present a method for obtaining the thermal rate constant directly (i.e., without first solving the state-to-state reactive scattering problem) from the time integral of the Aux-flux autocorrelation function, C-ff(t). The quantum mechanical trace involved in calculating C-ff(t) is efficiently evaluated by taking advantage of the low rank of the Boltzmannized flux operator. The time propagation is carried out with a Hamiltonian which includes imaginary absorbing potentials in the reactant and product exit channels. These potentials eliminate reflection from the edge of the finite basis and ensure that C-ff(t) goes to zero at long times. In addition, the basis can then be contracted to represent a smaller area around the interaction region. We present results of this method applied to the O + HCl reaction using the J-shifting and helicity conserving approximations to include nonzero total angular momentum. The calculated rate constants are compared to experimental and previous theoretical results. Finally, the effect of deuteration (the O + DCl reaction) on the rate constant is examined.