When I went to Robinson's safety course in 2010, Tim Tucker said before they decided to put a turbine in the R66 they tried to come up with a diesel engine to run in it but the numbers were not good, in others words too heavy per HP produced!
Just comparing, a Lycoming IO360 engine is rated at 290 HP and weights about 270kg, the RR300 turbine is rated at 300 HP and weights about 90kg. Usually diesel engines are heavier than gasoline ones.