EH-CSD

There are several versions of EH-CSD models. To make the exposition less cumbersome, in the next pages we shall only summarize one version, that was elaborated in Pisa and known with the acronym PCM (Polarizable Continuum Model) (Miertus et al., 1981 Miertus and Tomasi, 1982). We shall consider other versions later, and the differences with respect to PCM will be highlighted. Other approaches, based on effective Hamiltonians expressed in terms of discrete solvent distributions, EH-DSD, or not relying on effective Hamiltonians, will also be considered. 

In the EH-CSD approach it is not convenient to decouple electrostatic terms into rigid Coulombic and polarization contributions the effective Hamiltonian leads to compute these two terms together. Exchange repulsive terms are hardly computed when the second partner of the interaction is a liquid they may be obtained with delicate simulation procedures, and it is convenient to decouple them into two contributions, namely the work spent to form a cavity of a suitable shape and an additional repulsion contribution. Dispersion contributions may be kept we shall examine this term in more detail later. Charge-transfer contributions are damped in liquids their inclusion could introduce additional problems in the definition of Vjnt via continuous solvent distributions. It is advisable to neglect them, as it is done in the interaction potentials used in simulations with the present approach it is possible to describe the charge transfer effect by enlarging the solute M —> M-Sn. 

In principle there are no differences in applying this strategy to GfR) (eq.7) instead of E(R). On the contrary, from a practical point of view, the differences are important. All the EH-CSD methods are characterized by the presence of boundary conditions defining the portion of space where there is no solvent (in many methods it is called the cavity hosting the solute). A good model must have a cavity well tailored to the solute shape, and the evaluation of the derivatives dG(H)/dqi and d2G(R.)/dqidqj must include the calculation of partial derivatives of the boundary conditions. 

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. 

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