It is not necessary only the value of band gap  determine the type of application because there are others many parameters govern the type of application such as absorption curve,  light harvesting capacity for the materials. For example, Band gap of the TiO2 (rutile and anatase) phase is 3.2 - 3.35 eV depending on the type of preparation However, Tio2 contribute in most  photovoltaics devices due to its unique properties.

So, you can try to used chalcone compounds towards solar cell, UV sensor or photodiode applications

I attached three papers for helping you: one for chalcone compound as solar cell and other for hydroxy coumarin compound

Good Luck

Dear brother

for band gap 2.58 in organic material, it can be used as a window for solar cell applications as CdS (2.54 eV)

for 3.25 eV band gap for organic material it can be used in UV sensor and UV OLED

Band gap  is a key parameter for design the device

You might consider opto-electronic applications in colour sensing, or even optical temperature measurement. (Which uses the bandgap edge shift with temperature.)