I know you're supposed to use positive associations when introducing a new cat to another. But what if your resident cat has no interest in food, treats, or playing when you open that door a crack?
My old cat, who was the resident cat, is deaf. During our long intro with my younger cat, he had no interest whatsoever in food, treats, or play, so I had little to draw on as a distraction if necessary. I found that brushing him was the best thing, since he loves to be brushed, and it would change his mood from bad to ecstatic almost in seconds.
We would also (hubby and I) sit across the room at first from each other, each of us with a cat, petting, stroking, and brushing. It seemed to calm them both and helped tremendously to have the positive association.
When we were at the door-crack stage, we just let them sniff and peek, and did not try to distract, if hissing and spitting started, we shut the door. We started off doing that for only a few minutes at a time before we progressed to the stacked baby-gate stage.