Hamiltonian local/normal mode model

Thus, the Morse potential is the most appropriate for estimating bond energy in a molecule [4-9], The C-X and C-Y bond stretching modes in YCX3 molecules are treated as anharmonic Morse-like diatomic, non-linear coupled oscillators. The well-known [26-37] effective Hamiltonian of the local and normal mode model is used. 

The effective local and normal mode model Hamiltonian is [4-9,26-29,33] ... 

Prediction of the overtone vibrational spectra of the CX3Y methylhalides can be based on the effective local and normal mode model Hamiltonian. D parameter, differs from De parameter of the Morse potential by E0 energy of zero-point vibrations, coincides with dissociation energy of separated C-Y bond with experimental accuracy in calculations using minimal basis set, if the correlation... 

While the electronic structure calculations addressed in the preceding Section could in principle be used to construct the potential surfaces that are a prerequisite for dynamical calculations, such a procedure is in practice out of reach for large, extended systems like polymer junctions. At most, semiempirical calculations can be carried out as a function of selected relevant coordinates, see, e.g., the recent analysis of Ref. [44]. To proceed, we therefore resort to a different strategy, by constructing a suitably parametrized electron-phonon Hamiltonian model. This electron-phonon Hamiltonian underlies the two- and three-state diabatic models that are employed below (Secs. 4 and 5). The key ingredients are a lattice model formulated in the basis of localized Wannier functions and localized phonon modes (Sec. 3.1) and the construction of an associated diabatic Hamiltonian in a normal-mode representation (Sec. 3.2) [61]. 

A model atom approximation is permitted if all of the stretching vibrations of the molecule are ascribed to the local-mode limit. In the normal-mode limit, using the effective Hamiltonian of the whole molecule is preferable, as was shown in the example of CH3CI and CH3F. 

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