L2-basis-set theory of electron-molecule scattering with vibrational and rotational coupling

Matrix equations for electron-molecule scattering including vibrational and rotational coupling are derived in the framework of the T-matrix expansion in discrete basis sets. The basis functions employed are products of scattered-electron orbitals with vibrational or rotational functions. The matrix elements are only marginally more difficult to calculate than in the adiabatic-nuclei version. It is expected that the implementation of the formalism for vibrational or rotational coupling (though possibly not both) is quite feasible.