The problem of asymptotic non-adiabatic couplings in heavy particle collisions is treated using the reprojection method. The mixing matrix
that mixes the asymptotic solutions of the coupled states to obtain appropriate boundary conditions is here derived to second order, yielding
a faster convergence of the cross section. In addition, the reprojection method is implemented in a diabatic representation and applied to
inelastic scattering of Li +Na and H +H collisions and to mutual neutralization in H+ +H− collisions.