For many electron molecule problems it is difficult to make the relevant measurements in the laboratory. There is thus an increasing demand for computational procedures for obtaining reliable estimated cross section and rates for key processes. These are probably three state-of-the-art ab initio methods for treating low energy electron molecule collisions including electronic excitation. These are the Kohn variational method, the Schwinger variational method and R-matrix method. (You can find out more about R-Matrix method here)
Most advanced and most widely used R-matrix codes are the UK molecular R-matrix codes. These have been developed over a period of about 30 years from a number of scientists based at Queen’s University Belfast, Daresbury Laboratory, Royal Holloway College and, most recently, University College London.
The UK R-matrix codes are very flexible. Besides the basic electron collision problem they have been adapted to find (diffuse) bound states, compute differential and momentum transfer cross sections, treat rotational and vibrational excitation, obtain resonance parameters, quantum defects and branching ratios, treat dissociative recombination both using a complete non-adiabatic method and in tandem with multichannel quantum defect theory, study photoioniosation and processes in intense laser fields, and collisions with molecules physisorbed on surfaces. The codes have recently been extended to treat higher energies, larger molecules, electronically and more challenging problems.
The codes are freely available, see this page, but can only be used successfully by experienced scientists.
Quantemol-N software system has been developed to address this problem: it both gives an expert interface for non specialists to perform ab initio electron-molecule scattering calculations and also provides training tool for those wishing to learn about such calculations.
More details on R-matrix theory can be found on publications page