The suppression of Raman scattering is of high interest for the achievement of sub-diffraction-limited resolution in Raman scattering spectroscopy and microscopy. We present density matrix calculations of the suppression of spontaneous Raman scattering via ground state depletion in a level system based on the molecule tris(bipyridine)ruthenium(ii). This particular molecule has been earlier used for an experimental demonstration of the suppression of spontaneous Raman scattering, allowing us to successfully verify the validity of our numerical calculations by a comparison to the experimental results. We investigate the required level of detail of the molecule model as well as the influence of certain molecule and pulse parameters on the Raman scattering suppression. It was found that pulses with a duration longer than the lifetime of the electronic states allow for a high suppression of the Raman scattering. Pulses shorter than the coherence lifetime between the ground state and electronic states lead to a similarly high suppression but also accomplish the suppression with more than one order of magnitude lower pulse energy fluence. Additionally, using a laser wavelength that is in resonance with one of the electronic transitions of the sample should allow suppressing the Raman scattering with four to six orders of magnitude lower pulse energy fluence.