Hamiltonian supermolecular

Obviously, the situation will be more difficult when additional approximations have to be employed, e.g., the divide-and-conquer scheme, an effective Hamiltonian or a perturbation approach. A central open question is which electronic states of the fragments have to be included so that reliable results, as compared with supermolecular calculations, can be provided. In any case, accounting for just one state per base pair will yield only semi-quantitative results. A careful analysis of this point is highly desirable for DNA-related systems. 

For the rotovibrational spectra of molecules interacting through purely isotropic forces, the Hamiltonian may be written as the sum of two independent terms. One term describes the rotational motion of the molecules, the other the translational motion of the pair. The total energy of the system is then equal to the sum of the rotovibrational and the translational energies. At the same time, the supermolecular wavefunctions are products of rotovibrational and translational functions. Let r designate the set of the rotovibrational quantum numbers and t the set of translational quantum numbers, the equation for yo may be written [314]... 

Regarding the parametrization of the Hamiltonian Eq. (7), the present approach relies on the parameters of the underlying lattice model Eq. (5). However, one could envisage an alternative approach, similar to the one described in Refs. [66-69] for small molecular systems, where a systematic diabatiza-tion is carried out based on supermolecular electronic structure calculations as described in Sec. 2.2. 

Before we define the interaction Hamiltonian, it is convenient first to define the wavefunction of the supermolecular system. We assume that the fragment wavefunctions in isolated form are known, that is,... 

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