Computational Chemistry 4.3 - Born-Oppenheimer Approximation

Short lecture on the Born-Oppenheimer approximation for molecular systems.

The molecular Hamiltonian is too complex to solve the exact solutions to the Schrodinger equation. This is because of the N-body problem, where we must simultaneously solve for the interactions of all pairs of particles (a very difficult NP-complete problem). This complexity is reduced by using the Born-Oppenheimer approximation, which treats the heavy, slow-moving nuclei as fixed and stationary relative to the light, fast-moving electrons. This simplifies the molecular Hamiltonian by making the nuclear kinetic energy zero and turning the nuclear-nuclear repulsion into a simple algebraic sum for a given spatial configuration of nuclei.

Notes Slide: https://i.imgur.com/7AHv2gt.png

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