What does the Born-Oppenheimer approximation mean for emergence?

Most philosophical debates about the emergence of molecular structure centre around the issue of irreducibility. Specifically, can the existence of structures be predicted from quantum theory without assuming their existence or invoking classical concepts? I will argue that the answer is yes, contrary to much of the philosophical literature, which relies heavily on the widespread use of the Born-Oppenheimer approximation (BOA) in quantum chemistry calculations. However, the fact that these arguments for irreducibility are weak does not mean that emergence (defined in terms of novelty) is not central to chemistry.In a previous post, I discussed recent work showing how the BOA is not necessary for quantum chemistry and that molecular structure can be defined independently of it.However, since the BOA plays a central role in the philosophical arguments, it is worth reviewing what it is and what it does and does not assume or mean.In 1927, Born and Oppenheimer introduced an approximation…