We apply the absorbing boundary condition (ABC discrete variable representation (DVR) theory of quantum reactive scattering to the initial state selected D + H-2(v = 1, j) --> DH + H reaction. The ABC-DVR Green’s function is efficiently computed by a Newton polynomial I expansion. We compute accurate reaction probabilities for the total energies and angular momenta required to obtain the thermal rate constants k(v=1,j)(T). At T = 310 K, a thermal average over j = (0,1,2,3), is performed to yield the final result k(v=1)(310 K) = 1.87 X 10(-13) cm(3) molecule(-1) s(-1). in quantitative agreement with the most recent experimental value (1.9 +/- 0.2) X 10(-13) cm(3) :molecule(-1) s(-1). The J-shifting approximation using accurate J = 0 reaction probabilities is tested against the exact results. It reliably predicts k,,I(,T) for temperatures up to 700 K, but individual (v = 1, j) selected rate constants are in error by as much as 41%.