Applications of the Schwinger multichannel method to electron-molecule collisions

We discuss some recent developments in the implementation of the Schwinger multichannel method for electron-molecule collision calculations. The evaluation of matrix elements involving the operator ${\mathrm{VG}}_P^{\mathrm{}(+)\mathrm{}}$V, previously accomplished by insertion of a Gaussian basis on either side of $G_P^{\mathrm{}(+)\mathrm{}}$, is now done by direct numerical quadrature. This approach avoids the necessity of very large Gaussian basis sets, allowing the size of the basis to reflect only the dynamical requirements of the scattering wave function. We find that the reduction in the required basis size results in improved efficiency, in spite of the additional numerical effort of performing the quadrature. Trial applications to electron-${\mathrm{CH}}_4$ scattering in the static-exchange approximation and to electronic excitation of ${\mathrm{H}}_2$ illustrate the excellent convergence characteristics of the procedure.