It is not possible to differentiate the origin two antioxidant molecules having the same structure. Natural and synthetic antioxidant molecules are only different by their origin. This means that two antioxidant molecules having the same structure can both be produced in nature and by synthesis.
To explain more, being synthetic simply means that the natural molecule and its structure was studied and it was replicated in the laboratory. It is the same molecule both structurally and functionally but while one is nature made, the other one is man made.
I agree with all answers. Structurally it is imposible to distinguish between some natural or synthetic antioxidants. every time new components are being found in nature, but be carefully always with the statement that all natural is safe ;-) Everything has also their optimal concentrations ;-)