Question

What is the Born-Oppenheimer approximation and why is it significant? Describe how you would use the Born-Oppenheimer approximation to generate potential energy curves for the two lowest energy states of and sketch the resulting curves with properly labeled axes. How would you characterize the bonding in these states based upon these curves and why?

What is MO theory and how well does its predictions agree with the “exact” Born-Oppenheimer results for ? A sketch might help.

Answer 1

According to Born -Oppenheimer approximation motion of atomic nuclei and electron in a molecule can be treated separately .

So the total energy of an atom is due to the electronic transition and electronic spin , nuclear spin . The energy of nuclear spin is so slow that it can be neglected . for two lowest energy state hence at the distance a0 the two nuclei bind to form a molecule of lower energy .

MO theory says that each atomic orbital contributes to the molecular orbital . By taking the nuclei still and considering the wavefunction as the wavefunction of electron we do find out the molecular orbitals .