Crossing or Diabatic Curves

It will be shown later that exact solutions of the electronic Schrodinger equation can give rise to double minimum potential curves. Such potentials can be inconvenient for treating some perturbation situations. It is often more convenient to start from approximate solutions of Hel where potential curves, which would have avoided crossing for the exact Hel, actually cross. In such a case, 

VeN (r. R) is the Coulomb electron-nuclear attraction energy operator, 

Note that the negative sign of VeN implies that it contributes to energy stabilization. Crossing curves are obtained by excluding parts of the spin-orbit term, Hso, and of the interelectronic term, Vee, from the Hel operator/ The effect of Vee, discussed in Section 3.3.2, is extremely important as it compromises the validity of the single electronic configuration picture which is often taken as synonymous with the diabatic potential curve picture. 

In both crossing and noncrossing curve approaches, perturbations between levels of the same symmetry can occur. In the diabatic picture, these are usually called electrostatic perturbations because they arise from Vee. In the adiabatic picture, they arise from TN, the nuclear kinetic energy operator, but are often misleadingly called electrostatic perturbations. 

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