The quantum mechanical description of inelastic collisions between various types of particles is discussed and illustrated by means of some recent applications. In order to accomplish this goal it is necessary to solve the Schrödinger equation for a collection of atoms to within a satisfactory degree of accuracy. The basic theoretical procedure is to use the Born-Oppenheimer “clamped nuclei” approximation to generate potential surfaces describing the motion of the atoms in a given molecular system. The multireference configuration interaction (MR-CI) method is quite effective for this purpose, since it allows one to compute total energies and wave functions at a high level of accuracy for all types of electronic states over a wide range of nuclear conformations. It has often been employed to describe the potential curves and various coupling elements required for cross section calculations of atom-atom and atom-molecule collision processes. These results are used to solve problems in astrophysics, medicine and semiconductor design, to name a few of the most important applications. A detailed example for the Na(3s,3p)He complex will be discussed in which MR-CI results have been used in a coupled channel treatment of the corresponding inelastic collision processes [C. Y. Lin et al., Phys. Rev. A 78, 052706 (2008)].

Electron scattering requires a different theoretical approach for several reasons. First of all, electrons are too light to be described satisfactorily by the Born- Oppenheimer approximation. In addition, it is necessary to account for the typically metastable nature of the states that result from electron attachment (autoionization processes). This means that the computed energy eigenvalues
must have imaginary components that correspond to the linewidths of the resulting states. A recent example of this type will be discussed which successfully describes vibrational cross section results obtained experimentally for electron collisions with the HCl molecule [M. Honigmann et al., J. Chem. Phys. 133, 044305 (2010)]. Finally, calculations to describe molecular collisions with positrons will be presented. Such processes are also useful in medicine, such as in positron emission tomography (PET). In this case it is necessary to employ wave functions containing many electrons and a lone positron. Computations of annihilation rates and positron affinities for complexes of alkali hydrides and oxides will be used to illustrate this type of theoretical treatment [R. J. Buenker and H.-P. Liebermann, J. Chem. Phys. 131, 114107 (2009).