Use of a discrete complete set of vibrational basis functions in non-adiabatic theories of electron-molecule scattering

The non-adiabatic treatment of vibrational motion in e_-molecule scattering typically involves a sum or integral over a complete set of vibrational functions, in general including a continuum. If all functions of the vibrational coordinate are defined by interpolation on a finite point set, they can be represented as linear combinations of basis functions that are Kronecker- delta functions on this point set- Here we introduce ‘spline-delta’ basis functions with this property, providing a discrete complete set for which intermediate sums in matrix products can be closed without truncation. © 1993 IOP Publishing Ltd.