Invariant imbedding method for multichannel Schrödinger equations with first derivative coupling

We derive and demonstrate an invariant imbedding method for calculating the S matrix for scattering problems involving a first derivative term in the Schrödinger equation for the relative motion. This method can be used directly on scattering problems derived using molecular structure calculations that determine adiabatic potential energies and their derivative coupling matrix elements. A critical discussion of the procedures that transform from an adiabatic to a diabatic representation is presented.