Question

What is the Born Oppenheimer approach? b) considering it write the
Hamiltonian of the H2 molecule

Answer 1

The famous Born-Oppenheimer Approximation states that both the electronic and the nuclear motion in molecules can be separated. The electronic wavefunction depends upon the nuclear positions Rj but not upon their velocities, i.e., the nuclear motion is so much slower than electron motion that they can be considered to be fixed. The nuclear motion (e.g., rotation, vibration) sees a smeared out potential from the speedy electrons.

We can write the molecular wave function taking into consideration the electron positions ri and nuclear positions Rj.

b. Using the approximation we can write down the Hamiltonian of a Hydrogen molecule as,