The Born-Oppenheimer Approximation

The molecular wave function has the electronic and nuclear coordinates as variables. In practice, it is often possible to write it as a product of an electronic wave function and a nuclear wave function. This is an approximation.

In the following, q_i refers to electronic coordinates and Q_i refers to nuclear coordinates.

The operator H_N is the sum of the nuclear kinetic energy operator and U(Q_i). E is the total energy (includes electronic and nuclear kinetic and potential energy).