If you only have rainwater, which is fairly pure, the plants won't have nutrients with which to grow.
In any sort of cultivation, the plants need (a lot of) water as well as nutrients.
In soil cultivation, the nutrients and a lot of water are in the soil.
In hydroponics, the nutrients are added as a solution to the water.
In aquaponics, the nutrients are provided by the fish.
You can use rain-water catchment to do lots of stuff. If you're set on hydroponics, you'll need to add those nutrient solutions periodically. Personally, I'm aquaponically-biased, so I'd recommend going that route with your rain-water.
