Solvation dynamics continuum dielectric environment

The continuum dielectric theory used above is a linear response theory, as expressed by the linear relation between the perturbation T> and the response , Eq. (15.1b). Thus, our treatment of solvation dynamics was done within a linear response framework. Linear response theory of solvation dynamics may be cast in a general form that does not depend on the model used for the dielectric environment and can therefore be applied also in molecular (as opposed to continuum) level theories. Here we derive this general formalism. For simplicity we disregard the fast electronic response of the solvent and focus on the observed nuclear dielectric relaxation. 

An accurate description of the aqueous environment is essential for atom-level biomolec-ular simulations, but may become very expensive computationally. An imphcit model replaces the discrete water molecules by an infinite continuum medium with some of the dielectric and hydrophobic properties of water. The continuum implicit solvent models have several advantages over the explicit water representation, especially in molecular dynamics simulations (e.g., they are often less expensive, and generally scale better on parallel machines they correspond to instantaneous solvent dielectric response the continuum model corresponds to solvation in an infinite volume of solvent, there are no artifacts of periodic boundary conditions estimating free energies of solvated structares is much more straightforward than with explicit water models). Despite the fact that the methodology represents an approximation at a fundamental level, it has in many cases been successful in calculating various macromolecular properties (Case et al. 2005). 

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