  We analyze how to obtain non-resonant and resonant Raman spectra within the
Placzek as well as the Albrecht approximation. Both approximations are derived
from the matrix element for light scattering by application of the Kramers,
Heisenberg and Dirac formula. It is shown that the Placzek expression results
from a semi-classical approximation of the combined electronic and vibrational
transition energies. Molecular hydrogen, water and butadiene are studied as
test cases. It turns out that the Placzek approximation agrees qualitatively
with the more accurate Albrecht formulation even in the resonant regime for the
excitations of single vibrational quanta. However, multiple vibrational
excitations are absent in Placzek, but can be of similar intensities as single
excitations under resonance conditions. The Albrecht approximation takes
multiple vibrational excitations into account and the resulting simulated
spectra exhibit good agreement with experimental Raman spectra in the resonance
region as well.
