I agree with Inamdar. The optical absorption leads to an exciton (bound electron-hole pair). In order to compare the optical bandgap with the electrochemical bandgap, one needs to provide extra energy, i.e. exciton binding energy, to dissociate the bound electron hole pair into quasielectron and quasihole. Depending on dielectric constant, binding energy varies. The electrochemical bandgap can be compared with the bandgap obtained by PES and IPES since the oxidation should correspond to photoemission (ionization) while the reduction should correspond to inverse photoemission (electron injection). Only that in electrolyte, there are other effects such as solvation and electrode surface effect etc as mentioned by others in this post. Theoretically, the PES-IPES bandgap can be calculated by many-body perturbation GW theory which should be plausibly applicable to the electrochemical bandgap. On the other hand, the optical bandgap can be calculated using Bethe-Salpeter equation (BSE) on top of the GW approach.
What would be the significance of electrochemical band gap energy be less than optical band?
I assume people usually observe that optical bandgaps are smaller, as can be seen from the title of the post "why are the estimated bandgaps from electrochemical data using CV larger than the optical bandgaps". The reason should be the exciton binding energy. If you indeed observe that electrochemical band gap energy is less than optical band gap, other effects such as solvation and electrode surface may be playing a role. In this case, probably the difference between the two bandgaps is small. Just one my cent.
University of Tehran
Massachusetts Institute of Technology
Atotech Deutschland GmbH
Central Electrochemical Research Institute
Lakshman Kumar Ventrapragada
University of Ulsan
Promotion Center for Global Materials Research (PCGMR)
Singapore-MIT Alliance for Research and Technology
University of Kerala