We present an efficient method to obtain initial state-selective cross sections for bimolecular reactions that can account for certain nuclear quantum effects by employing the ring polymer molecular dynamics approach. The method combines the well known quasiclassical trajectory (QCT) approach with the description of the system in an extended ring polymer phase space. Employing the prototypical Mu/H/D + H-2(v = 0, 1) reactions as a benchmark, we show that the presented approach does not violate zero-point energy constraints and that it can also capture the contributions of tunneling through the v = 1 vibrationally adiabatic barrier present for the Mu + H-2(v = 1) reaction. This is a significant improvement over the QCT approach with only a small increase in numerical cost.
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