Vibrational energy relaxation perturbation expansion

The treatment of the vibrational NLO properties in the previous sections employed either the Bishop-Kirtman perturbational theory (BKPT) or the finite field-nuclear relaxation (FF-NR) approach. These approaches may fail for molecules containing large amplitude anharmonic motions, as indeed was suspected to happen in Li C6o-In such cases a more recently proposed variational method, based on analytical response theory [78, 79], would in principle be applicable, but is computationally extremely expensive, as it requires an accurate numerical description of the potential energy surface (PES), at least if the anharmonicity is so large that a power series expansion of the PES is inadequate [80]. 

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... 

---