Previously, in an effective field theory formulated by us, we have carried out parameter-free calculations of a large number of low-energy two-nucleon properties. An experiment at the Institut Laue-Langevin is currently measuring spin-dependent effects in the polarized np capture process n → + p → →d+γ at threshold. Noting that spin-dependent observables for this reaction are sensitive to terms of chiral orders higher than hitherto studied, we extend our effective theory approach to this process and describe how to make parameter-free predictions on the spin-dependent observables.