Born-Oppenheimer Approximation: The Separation of Nuclear and Electronic Motion in Molecules

1. Last hour: • Total WF: • In the BOA, the electronic WF uses R only as a parameter  separation of variables, treating degrees of freedom for nuclear and electronic motion as uncoupled. Nuclei move in “diabatic” potential energy landscapes • Terms left out in BOA: where • Adiabatic approximation: Correct zero-order energies by adding diagonal elements H’nn : • Further correction: add off-diagonal elements. They are usually small, except where two “diabatic” curves come close to one another. • For diatomic molecules, two curves corresponding to electronic states with the same symmetry cannot cross (non-crossing rule).

3. Learning Goals for Chapter 22 – The Born-Oppenheimer Approximation (BOA) • After this chapter, the related homework problems, and reading the relevant parts of the textbook, you should be able to: • explain the fundamental assumptions leading to the BOA; • explain the interpretation of the outcome of the BOA; • explain the deviations from the BOA; • qualitatively treat the region of diabatic curve crossings.

4. Shape of the H2+ molecular orbital from McQuarrie & Simon “Physical Chemistry”

5. Overlap of atomic orbitals from McQuarrie & Simon “Physical Chemistry”

6. Overlap integral from McQuarrie & Simon “Physical Chemistry”

7. Potential energy curves for H2+ antibonding H + H+ bonding from McQuarrie & Simon “Physical Chemistry”

8. from McQuarrie & Simon “Physical Chemistry”