Err, there's a big difference between chloride and chlorine. Chlorine is a gas, and you can smell it. It's very dangerous in its gas form, but colloquially "chlorine" usually refers to sodium hypochlorite, which is added to water as a disinfectant.

Chloride on the other hand, is the ion form of chlorine, and you can't smell it. For instance, sodium chloride is common table salt, which you can't smell. It also doesn't evaporate. Fluoride is likewise the ion form of fluorine, and usually exists as sodium fluoride, which is added to drinking water at extremely low levels because of its beneficial effects on tooth formation. Like sodium chloride, sodium fluoride also does not evaporate.

Letting water sit will allow some of the sodium hypochlorite to turn into sodium chloride, which is less harmful to plants, but the chloride and fluoride ions will stay behind in the water.