Exchange in low-energy electron-molecule scattering: Orthogonalization and free-electron-gas approximations for collisions with polar and nonpolar molecules

Three approximate treatments of the exchange interaction in low-energy electron-molecule scattering are applied to a variety of collision systems. Static-exchange calculations for $e$-${\mathrm{H}}_2$, $e$-${\mathrm{N}}_2$, $e$-CO, $e$-LiH, $e$-HCl, and $e$-LiF collisions with scattering energies from 0.01 to 1.0 Ry are discussed, and results obtained using approximate treatment of exchange are compared with those obtained in a corresponding study in which exchange is incorporated exactly via an iterative procedure. The approximate treatments considered are orthogonalized-static, free-electron-gas model potential, and orthogonalized-model-potential procedures. The latter procedure is found to be uniformly superior to other approximate methods for all systems studied, in many cases yielding results indistinguishable from those of the exact static-exchange calculation. Strengths and weaknesses of each method are discussed.