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.

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Presentation transcript:

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).

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.

Shape of the H 2 + molecular orbital from McQuarrie & Simon “Physical Chemistry”

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

Overlap integral from McQuarrie & Simon “Physical Chemistry”

Potential energy curves for H 2 + bonding antibonding H + from McQuarrie & Simon “Physical Chemistry”