Complex energy level

Note that the approached ACF (195) may be rewritten in terms of complex energy levels, with the aid of the following equations ... 

The complex energy levels (198) and (199) characterizing the initial and final states may be considered as the eigenvalues of the effective non-Hermitean Hamiltonians characterizing the H-bond bridge ... 

The other one, the Complex Energy Levels (CEL) method, directly postulates complex energy levels. As will be seen, these two methods lead to equivalent line shapes when both the adiabatic and harmonic approximations are simultaneously removed. 

As for the special situations involved in our above adiabatic approach and dealing with the CEL method, we may write the complex energy levels as... 

The formation of the phenoxy intermediate turns to be unlikely to occur as this intermediate remains at similar energy level as observed from the cluster proach (i.e. + 150 kJ/mol), whereas protonation step and Wheland complex energy levels are around +110 kJ/mol with respect to physisorbed toluene. 

Figure 1. Complex energy levels for a model ICl-Ne system (in reduced units). Shown are the accurate results (complex scaling method, crosses), first-order diahatic (FOD, fdled squares) and first-order adiabatic (FOA. open circles).

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