Chemistry: the subtle art of character closeness

This is actually a picture of the potions classroom from the Warner Brothers Studios. Look at those self stirring cauldrons! I think J.K. Rowling said she was inspired by chemistry for the idea of potions and how they were made, and maybe her own teacher. Interestingly enough, I think she said she disliked chemistry the most and yet Snape talks about it with such descriptive and tantalizing imagery that we all want to pull up a seat in his classroom.

Chemistry, and not the one with the periodic table and moles (which are not furry little creatures that live underground). It's a word common enough that we disregard it, but what is chemistry? And how do we show it between characters?