Multiphonon-based approaches

It is thus evident that the experimental results considered in sect. 4 above are fully consistent with the interpretation based on absolute reaction rate theory. Alternatively, consistency is equally well established with the quantum mechanical treatment of Buhks et al. [117] which will be considered in Sect. 6. This treatment considers the spin-state conversion in terms of a radiationless non-adiabatic multiphonon process. Both approaches imply that the predominant geometric changes associated with the spin-state conversion involve a radial compression of the metal-ligand bonds (for the HS -> LS transformation). 

An alternative approach widely used in polyatomic molecule studies is based on the Golden Rule and a perturbative treatment of the anharmonic coupling (57,62). This approach is not much used for diatomic molecules. In the liquid O2 example cited above, the Hamiltonian must be expanded to 30th order or so to calculate the multiphonon emission rate. But for vibrations of polyatomic molecules, which can always find relatively low-order VER pathways for each VER step, perturbation theory is very useful. In the perturbation approach, the molecule s entire ladder of vibrational excitations is the system and the phonons are the bath. Only lower-order processes are ordinarily needed (57) because polyatomic molecules have many vibrations ranging from higher to lower frequencies and only a small number of phonons, usually one or two, are excited in each VER step. The usual practice is to expand the interaction Hamiltonian (qn, Q) in Equation (2) in powers of normal coordinates (57,62) ... 

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