On the generator coordinate approximation for two-state problems

The generator coordinate approximation (GCA) is a non-adiabatic theory based on the convolution of electronic and nuclear wavefunctions. in a two-state problem there are two versions of the GCA according to which of the two electronic states is chosen. In this study we compare the quality of both approximations using a highly non-adiabatic avoided crossing in the spectrum of nitrogen. It is found that the upper state can generate quite good results for the low-energy spectrum. In the limiting case of exact crossing, both GCA versions become equal and exact.