Eigenfunctions for calculating electronic vibrational intensities

For the molecular eigenfunction we may take the well-known approximate solution (discussed, for example, in Kronig’s text book) Ψ = Φ (x, r). P (r). Θ. The equation which it satisfies differs from the exact molecular equation by small terms which are conveniently treated as perturbations. Their effects are summarised in Kronig’s book. We shall assume that these effects are either negligible or that they can be calculated. Θ is a function of the angular co-ordinates which fix the direction of the internuclear axis in space. Φ is a function of all the electronic co-ordinates x, and also of the internuclear distance r; it is, in fact, the solution of the equation for the molecule with the nuclei fixed at separation r. This equation contains r as a parameter; we will write its special value as E + U(r), where U has a minimum at r0 and is there zero. E will be called the electronic energy; it is equal to the energy of the two atoms into which the molecule dissociates, minus the energy D needed to dissociate them from r = r0.