In an interview with Elle USA, director Catherine Hardwicke mentions Kristen and Robert Pattinson including their audition for Twilight and their immediate chemistry.
You've said that Kristen Stewart and Robert Pattinson were perfect for their roles. What did you see in them that made you cast them?
I thought Kristen was just amazing in Into the Wild. When I read the novel Twilight, I kept picturing her in that scene, where she’s sitting in the trailer, hoping to seduce Emile Hirsch. Her yearning was palpable, real, and intense. I thought, "This girl would be wonderful." So Summit flew me out to Pittsburgh, where she was shooting Adventureland. We took an actor with us and improvised a lot of scenes. To find Edward was tricky, because how he was written, he was perfect, with these cheekbones, and he was also wise beyond his years. We whittled it down from hundreds of actors to four. I'd only talked to Rob on the phone when he was much younger. He flew out on his own dime and stayed on his agent's couch. The four actors came over to my house and we workshopped all the "chemistry" scenes. With Rob and Kristen, it was apparent that those two just connected and had a magnetism for each other that was electric, right there on the spot.