A few bricks shy of an outhouse, yea. Psychopath, I don't think so.
If anything I pity him. Imagine waking up to a world where you pushed the shiny red button and destroyed everything. You are all alone, cut off from the life you knew. All around you, the world is lifeless and void of what you knew. Slowly you begin to find signs of life where you didn't expect it, but life so unbelievably primitive that it doesn't feel real. I imagine this is some of what he's experiencing when first awakened. He compounds his mistake giving his orb to Corypheus. Then takes responsibility and tries to fix the error. He doesn't like making anyone suffer for his mistakes and gains approval whenever the Inquisitor helps people around him, slowly realizing that they are people. He frees you of the mark as much because it's killing you as to get his power back.
Now this is 'friended' Solas. I am unsure what changes exist for romanced or 'enemy' Solas.
To me these are not the acts of a psychopath. I would imagine a psychopath to be someone more delusional or lacking in empathy (like Norman Bates or Hannibal Lector).
Even if he does want to restore his world (and send the modern one crashing around everyone's ears), he wants the Inquisitor to prove him wrong. Even "I hate you" Solas has a moment when confronted where you can see it on his face, he wants you to prove him wrong. Of course, I've not played Trespasser yet, I and I can't antagonize him enough to reach that point, so I had to see it online, but even the clip I saw showed his remorse/regret if only for a moment. Then a distancing for himself as in that version he says 'it might' not that 'it will' destroy the current world. He still wants be talked out of it, but the inquisitor in question wouldn't even listen/talk to him.
I don't hate him or want him dead, I'd like the chance to redeem him and turn him from his path, show him another way. But if push came to shove, and the only option to change his mind involves a few not so gentle raps to the noggin, I'll go that path too.