Quantum electrodynamics Hamiltonian function

The potential energy surface used in solution, G (R), is related to an effective Hamiltonian containing a solute-solvent interaction term, Vint- In the implementation of the EH-CSD model, that will be examined in Section 6, use is made of the equilibrium solute-solvent potential. There are good reasons to do so however, when the attention is shifted to a dynamical problem, we have to be careful in the definition of Vint - This operator may be formally related to a response function TZ which depends on time. For simplicity s sake, we may replace here TZ with the polarization vector P, which actually is the most important component of TZ (another important contribution is related to Gdis) For the calculation of Gei (see eq.7), we resort to a static value, while for dynamic calculations we have to use a P(t) function quantum electrodynamics offers the theoretical framework for the calculation of P as well as of TZ. The strict quantum electrodynamical approach is not practical, hence one usually resorts to simple naive models. 

Since the spectrum of the DCB Hamiltonian is not bounded from below it is not possible to optimize the wave function by minimization of the energy. The unphysical unboundedness is due to the fact that not all possible normalizible antisymmetric wave functions of N coordinates are states of an N-electron system. The set of possible solutions also contains wavefunctions in which one or more negative energy levels are occupied and it is the mixing with such states that gives rise to unphysical arbitrarily low energies. One needs the second quantization formalism of quantum electrodynamics (QED) for a proper treatment of these states. As this is discussed in more depth elsewhere in this... 

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