The Born-Oppenheimer Approximation

• first of several approximations made to try to solve Schrodinger's equation for more complex systems than one or two particles

  • -separates electrons and nuclear motions, based on the idea that nuclear mass is so much larger than electron mass that the nuclei are basically "fixed" particles. Electrons react instanteously to changes in the position of the nuclei.

  • -the full Hamiltonian for a molecular system is written as:
    

  • -an "electronic" Hamiltonian (one that neglects the kinetic energy for the nuclei) can be written: