2cm.....that's 20mm right? =) I am not good with metrics lol. Since the coin is oblong, I'd bet the 2 cm portion is the long part

. I still think it is a half-centenionalis as the full ones (Centenionalii) are anywhere from 21-26 mm in my experience (not oblonged). By the way, for terminology's sake, a half centenionalis is the same thing as an "AE3". Also, the coin is definitely Constantius II as Constantius Gallus is never portrayed on these types diademed (Gallus is always bare-headed).
There are literally thousands of variants of this coin and I would wager that it is the most common uncleaned ancient coin found in lots (coming from the Balkans these days). So, finding an "exact match" would be quite the rarity. Every single die was hand engraved (and I'm sure there were thousands of dies produced during late Roman times) so you are likely to find these variances with respect to the exact detailing of the action taking place on the coin. Good question though Montana Jim and worthy of debate! Great discussion
Gunner