Hamiltonian resonances

To summarize, for our model Hamiltonian, resonances appear after a bound-virtual and a virtual-virtual resonance transition. There is no method to obtain virtual energies using a square-integrable basis set, even in the complex-rotated formalism. Then, at this point we can ask if FSS is a useful method to study this kind of resonance. As we will show in the next subsection, the answer is yes FSS is a method to obtain near-threshold properties, and with FSS we can characterize the near-threshold resonances by solving the Hermitian (not complex-rotated) Hamiltonian using a real square-integrable basis-set expansion. Moreover, the critical point of the virtual resonance-resonance transition, Xr, could also be obtained using FSS. 

In the Pariser-Parr-Pople scheme, the so-called zero differential overlap approximation is used, and the u-electron system is treated as a nonpolarizable core. The interelectronic repulsions are explicitly taken into account in the total Hamiltonian. Resonance integrals, core integrals, and electronic repulsion integrals are given empirically, and Coulomb penetration integrals are neglected. ... 

The expansion of the wavefunction in (2.28) is also essentially the same basic idea as the resonating group model used in nuclear physics [77]. The different sets of Jacobi coordinates define different groups (or groupings) of atoms, and the fact that the wavefunction is a linear combination of these different terms allows for resonance (i.e. coupling, interaction) between them if there are non-zero matrix elements of the Hamiltonian ( resonance integrals ) connecting them. 

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