I wouldn't say that high intelligence has something to do with suicide, but I would argue that it is correlated to depression, which can lead to suicide.
At the social level, I believe that people with high intelligence tend to overanalyze, and over rationalize, certain social situations. I believe this is because they are skeptical of other humans. They can see the fault of humankind, and therefore, chose not to get involved in the disarray of human interaction, ultimately leading to their isolation.
In the intuitive self, intelligent people are often more critical of their skills and capabilities. They hold high standards for themselves, and when they cannot perform, they end up criticizing and demeaning themselves over the smallest details.
At the most rudimentary level, intelligent people are not normal. They find it difficult to hold intellectual conversations with other people, and fit in with the rest of society. They are outcasts, only because they see the world differently from regular members of society. This self-rejection ultimately leads to depression, which can trigger suicidal ideations.
