In the context of wave packet methodology we show how to take advantage of the diffractive scattering symmetry arising when the incident beam is normal to the surface or to a surface principal axis. This may lead to a reduction in dimensionality being up to a factor of 8. The Fourier transformation is applied to evaluate the translational kinetic energy operator. Two alternative treatments are possible depending on whether the transformation is utilized to calculate the kinetic energy matrix elements in coordinate space, or whether it is applied to the wave function itself to switch between coordinate and momentum representations. The first approach is similar to the discrete variable representation treatment in the spirit of Light and co-workers whereas the second one enables the use of the fast Fourier transform (FFT) scheme of Kosloff and Kosloff. We provide a detailed comparison between the two approaches as a function of the size of the grid, with and without the presence of symmetry in the diffractive scattering.