I've found that caffeine actually puts me to sleep. Initially, it is a stimulant; but if I get too much, about an hour later (much less than the half life mentioned above), I'll be unable to keep awake. About a year after I discovered why I couldn't keep awake after lunch, I actually read a study that said that caffeine has some other side effects, such as reducing the brain's ability to use sugar. I don't know if this is relevant to me or not, but I suppose being hypoglycemic doesn't help here.

Also, some stimulants are known to act as calmatives to people with ADD.