6.1. Non-Born-Oppenheimer molecular Hamiltonian
Recall from Section 4.1, Born-Oppenheimer approximation, the expression of the Hamiltonian in the laboratory frame coordinates :
where in atomic units, the mass of the electron and the reduced Planck constant () are set to the value 1. The LAB Hamiltonian comprises the sum of the kinetic energy of all particles and the potential energy between all particles with the following definitions:
- and are the second derivative operator with respect to the position coordinates for electrons and nuclei, that is, and likewise for the electron.
- , , and are the distances between electrons and , electron and nucleus , and nuclei and determined by the Euclidean norm.
The list of the operators of the LAB Hamiltonian has been presented in Figure 4.3.
In the LAB Hamiltonian, the energy of the molecular system is continuous, not discrete. The center-of-mass (COM) motion does not yield any change to...