The Nonelectronic States of Diatomic Molecules

We assume that the Born-Oppenheimer Schrodinger equation for the electrons of a diatomic molecule has been solved repeatedly for different intemuclear distances, giving the electronic energy, E, as a function of the intemuclear distance, tab- The Born-Oppenheimer energy is the sum of the electronic energy and the nuclear-nuclear repulsion energy, %a.  

For a diatomic molecule, the nuclear-nuclear repulsion energy is given by 

Because bo depends only on nuclear position, it acts like a potential energy for nuclear motion, and we denote it as 

Since %xt depends only on the center-of-mass coordinates, Hnuc can be separated into a center-of-mass term and a relative term in the same way as is discussed in 

22 Translational, Rotational, and Vibrational States of Atoms and Molecules 

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