The equations that govern molecular structure are well known, but their solutions are not. Exact analytical solutions to the Schrödinger equation don’t exist for systems of more than two interacting particles, and exact numerical solutions are prohibitively time-consuming for systems with more than a few particles. Researchers need to make approximations, and one of the most basic of those is the Born–Oppenheimer approximation. Put one way, it says that the molecular wavefunction can be written as the product of a nuclear wavefunction and an electronic wavefunction, and that the nuclear kinetic-energy operator acting on the electronic wavefunction is negligible. Put another way, it says that when the heavy nuclei move around, the light electrons adjust so quickly that the response might as well be instantaneous.
The Born–Oppenheimer approximation allows computational chemists to split the Schrödinger equation into separate equations for the electronic and nuclear wavefunctions and solve them one at...
