Instead of love at first sight, why not nemesis at first sight?
No, I don’t mean hate at first sight. Nemeses don’t even have to particularly dislike each other, though it’s admittedly customary.
I mean their eyes meet from across the room, and there’s a moment of instant, mutual understanding that they will one day battle to the death on some remote, storm-lashed plain with the very fate of the world hanging on the outcome.
“Pardon me, are you Aaron Burr, sir?”
All I can think of is Perry the Platypus and Doctor Doofenshmirtz.