To my frustration, the majority of the results I found were talking about were not scholarly.
If you do look, you will find odd little relationships and hints. Maybe there's more autism among the close relatives of mathematicians and engineers. Maybe there are little hints that ADHD and schizophrenia are linked to creativity. Maybe there's more bipolar disorder among performance artists. Maybe depressed people are better writers. Maybe. These little hints and bits and bobs of evidence indicating trade-offs are rarely as straightforward as finding elevated rates in a gifted population, the way you propose.
You won't find any links between general intelligence and mental illness. It's never "intelligence", it's almost always some weird, specific, difficult to study thing. I really doubt that high IQ puts you at elevated risk of anything. Sometimes people do come up with stuff, like "existential depression" (which I'm pretty sure is just normal depression with an intellectual rationalization), but it's pretty sparse.
There's supposed to be a body of literature (mostly pre-2000) with "gifted children" which I haven't really looked into demonstrating frustrations arising from atypical development, but I haven't seen any really good evidence for trade-offs or especially difficulties on that front either. It's been mostly collections of case studies. (That said, I haven't read that area much.)
For a site extremely focused on fixing bad thinking patterns, I've noticed a bizarre lack of discussion here. Considering the high correlation between intelligence and mental illness, you'd think it would be a bigger topic.
I personally suffer from Generalized Anxiety Disorder and a very tame panic disorder. Most of this is focused on financial and academic things, but I will also get panicky about social interaction, responsibilities, and things that happened in the past that seriously shouldn't bother me. I have an almost amusing response to anxiety that is basically my brain panicking and telling me to go hide under my desk.
I know lukeprog and Alicorn managed to fight off a good deal of their issues in this area and wrote up how, but I don't think enough has been done. They mostly dealt with depression. What about rational schizophrenics and phobics and bipolar people? It's difficult to find anxiety advice that goes beyond "do yoga while watching the sunrise!" Pop psych isn't very helpful. I think LessWrong could be. What's mental illness but a wrongness in the head?
Mental illness seems to be worse to intelligent people than your typical biases, honestly. Hiding under my desk is even less useful than, say, appealing to authority during an argument. At least the latter has the potential to be useful. I know it's limiting me, and starting cycles of avoidance, and so much more. And my mental illness isn't even that bad! Trying to be rational and successful when schizophrenic sounds like a Sisyphusian nightmare.
I'm not fighting my difficulties nearly well enough to feel qualified to author my own posts. Hearing from people who are managing is more likely to help. If nothing else, maybe a Rational Support Group would be a lot of fun.