NO!!!! I would strongly advise against doing this.
1.) Rain water isn't suggested for drinking and if I can't drink it, it's not going in my tank.
2.) rain water is know to contain pesticides after a dry spell, and pesticides will destroy a tank's ecosystem.
3.) It will contain pollutants, no matter where it's falling. Some areas more toxic than others.
4.) Rain water contains dissolved gases specifically, Carbon Dioxide, Nitrogen Oxide, and Sulfur Oxide. I would worry more about the sulfur than anything else.
But if your going to do this I wouls suggest setting up a cheap tank from walmart, with cheap fish, and a cheap coral, rather than risk losing your whole DT. That's a good chunk of money to dump down the drain.
I would also research filtration methods for rain water as well
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