Electronic states Born-Huang expansion

In the two-electronic-state Born-Huang expansion, the full-Hilbert space of adiabatic electronic states is approximated by the lowest two states and furnishes for the corresponding electronic wave functions the approximate closure relation... 

II. n-ELECTRONIC STATE ADIABATIC REPRESENTATION A. Born-Huang Expansion... 

The energies and are associated with the initial and final vibronic states, respectively ( (r R)i/ Fermi distribution which ensures that the initial (final) electronic state is occupied (free) at a given temperature. Note that here, in contrast with the traditional Born-Huang expansion, eqn (5), the vibrational and electronic indices are separated, since the vibronic states within a band are treated as separable. In the spirit of first-order perturbation theory, the non-adiabatic contribution of each nuclear degree of freedom is treated as an independent relaxation channel... 

---