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\maketitle Hydrogen-transfer reactions are probed through vibrational excitation of the HCl bond in the pre-reactive F$\cdots$HCl complex. Such open-shell species provide a challenge for quantum dynamical calculations due to the need to take into account multiple potential energy surfaces to accurately describe the system.A three-dimensional, fully-coupled potential energy surface has been constructed based on electronic energies calculated at the multireference configuration interaction+Davidson correction (MRCI+Q) level of theory with an aug-cc-pVnZ ($n=2,3,4$) basis.{ \underline{\textbf{124}}(22) 224303 (2006)}} Spin orbit calculations have also been included.{(2007)}} Here we present the results of time-dependent quantum wave packet calculations on the asymmetric hydrogen-transfer reaction of F($2$P) + HCl. In these calculations, the reaction is initiated by vibrationally exciting the HCl stretching motion in the pre-reactive F$\cdots$HCl complex. The wave packet is propagated on the coupled potential energy surfaces. Product state distributions were calculated for reactions initiated in the first three vibrationally excited states of HCl, $v=1-3$.