Corporate Captain reported #1 engine propeller blade was damaged during taxi.

Narrative

Our day started in ZZZ1 at XA:00; where we departed ZZZ1 for ZZZ to pick up passengers. We continued on to ZZZ2 before having a long sit at ZZZ2 and returning to ZZZ to drop them off. After dropping the passengers off at the FBO; we started the engines back up at approximately XP:00. Before taxiing from the FBO at ZZZ; I briefed our taxi to Runway XX via Taxiway 1-Taxiway 2-Taxiway 3-Taxiway 4. When making coming to the intersection of Taxiway 2/Taxiway 3; it appeared that there was a gate closing off most of the ramp connecting Taxiway 3/Taxiway 4. Unsure if I would be able to fit through the gate or make a 180 degree turn after turning right onto Taxiway 3; I briefed my SIC that we would make a left on Taxiway 3; taxi via Runway XY to back taxi XX and depart. When making the left turn from the Taxiway 2/Taxiway 3 intersection onto Taxiway 3; I felt as if the left main dipped but could not see the surface directly below the area of my left wing/engine. After taking Taxiway 3 to XY; I proceeded to taxi Runway XY to Runway XX and conducted a high speed taxi to check the function of the left main wheel. After no notice of any abnormalities; I continued to the end of XX before departing the runway. Upon arriving in ZZZ1 and securing the aircraft; I conducted my post-flight inspection and noted damage to the #1 Engine's propeller blades.