Linear algebraic approach to electronic excitation of atoms and molecules by electron impact

A linear algebraic method, based on an integral equations formulation, is applied to the excitation of atoms and molecules by electron impact. Various schemes are devised for treating the one-electron terms that sometimes cause instabilities when directly incorporated into the solution matrix. These include introducing Lagrange undetermined multipliers and correlation terms. Good agreement between the method and other computational techniques is obtained for electron scattering for hydrogenic and Li-like atomic ions and for $\mathrm{H}_2^{}{}_{}{}^{+}$ in two- to five-state close-coupling calculations.