I don't think so. There may be materials where you can correlate shifts of vibrational frequencies to changes in the electronic structure, but there is no simple rule for that.
It is possible to deduct information about electronic properties of materials using Raman spectra when there is coupling between for example plasmon and LO-Phonon modes, etc. Such studies are conducted more for materials with ionic bond such as III-V compounds. For example for GaAs with distinct LO-phonons and LO-phonons one can study the depletion region thickness which indicates doping concentration, which can be correlated to fermi level energy and other electronic characteristics impacted by the doping level as we studied years ago:
Raman scattering studies of reactive ion-etched MBE
B Roughani, HE Jackson, JJ Jbara… - IEEE Journal of …, 1989 - ieeexplore.ieee.org
Similar studies could be done on other systems including graphene and CNTs, such as:
Phonon linewidths and electron-phonon coupling in graphite and nanotubes
Michele Lazzeri, S. Piscanec, Francesco Mauri, A. C. Ferrari, and J. Robertson
Raman is not commonly used for that purpose but there seem to be certain cases where the Fermi level is correlated with optical processes measured by Raman. Instead, I would recommend using techniques like Kelvin Probe Force Microscopy (KPFM) or Ultraviolet Photoelectron Spectroscopy (UPS) to measure the work function.
Thank you guys. The main issue for UPS is that we are on a wet environment. I know you can do Kevin probe in liquids. Let me see if we could go further on that, Peter Schindler . I am going through your manuscript Bahram Roughani and I let you know my thoughts. Regards,