I have a tank that collects rainwater. The water has a nasty smell. What can I add to improve the smell but hurt my plants.

Somewhere in the back of my brain, the words 'potassium permanganate' came into my consciousness! Just looked it up and found:
"Potassium permanganate - This is another cheap and easy way to purify water. Potassium permanganate crystals can be bought from any chemist and you need add only about 3 or 4 crystals per litre of water (or until the water stains a light pink) and leave for 30 minutes. Potassium permanganate can also be used as a disinfectant for cleaning wounds, add crystals one by one until water turns purple (approx. 0.01% solution). "
(Travel Health Zone website.)
If it is ok to drink it should be ok on plants. Worth trying, though the stink in the rainwater is only from natural algae and stuff, so is probably better for plants.

you can use it very weak for a tonic for an ill pond or fish tank to

There is also an organic product called 'Re-fresh' which makes rainwater as clear and sweet as spring water, although I still wouldn't be tempted to drink it :-0) It is also a good idea to keep your tank, water-butt, barrel w.h.y. covered. This will prevent thing like leaves and creepy
crawlies falling in and rotting at the bottom.

i thaught the manky stuff was good for your plants .i water my plants with my tank and pond water then top them up works a treat.

We used to collect rainwater in an open barrel but it became really offensive to the point where we had to completely empty it. We've since 'installed' a rain butt with a close fitting lid & there's no smell at all.
One thing you can use to 'clean' rain water is Milton (it's the stuff to sterilise babies bottles) - we use a small amount in our fountain & it cleans the water - v. useful if you've got mozzie lavae in fairly still water.
Our cats, the fox, birds etc., don't drink from this particular water as it's right next to the patio door so I'm not sure I'd use it otherwise.