Analytical continuum electrostatics approach

In a recent approach that was successfully tested for small hydrocarbons the solvation was treated semi-analytically as a statistical continuum[167]. The method treats the sum of the solvent-solvent cavity (Gcav) and the solute-solvent van der Waals (Gvdw) terms by determining the solvent accessible surface1-1681, and the solute-solvent electrostatic polarisation term (Ges) is calculated by a modified version of the generalized Bom equation[ 167,16 ]. 

Implicit solvation models developed for condensed phases represent the solvent by a continuous electric field, and are based on the Poisson equation, which is valid when a surrounding dielectric medium responds linearly to the charge distribution of the solute. The Poisson equation is actually a special case of the Poisson-Boltzmann (PB) equation PB electrostatics applies when electrolytes are present in solution, while the Poisson equation applies when no ions are present. Solving the Poisson equation for an arbitrary equation requires numerical methods, and many researchers have developed an alternative way to approximate the Poisson equation that can be solved analytically, known as the Generalized Born (GB) approach. The most common implicit models used for small molecules are the Conductor-like Screening Model (COSMO) [96,97], the Dielectric Polarized Continuum Model (DPCM) [98], the Conductor-like modification to the Polarized Continuum Model (CPCM) [99], the Integral Equation Formalism implementation of PCM (lEF-PCM) [100] PB models and the GB SMx models of Cramer and Truhlar [52,57,101,102]. The newest Miimesota solvation models are the SMD (universal Solvation Model based on solute electron Density [57]) and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [103-105] with semiempirical terms that account for local electrostatics [106]. Further details on these methods can be found in Chapter 11 of reference 52. 

There are three current approaches to continuum solvation models [25-27], according to three different approaches to the solution of the basic electrostatic problem (Poisson problem) The Generalized Born approximation, the methods based on multipolar expansions of the electrostatic potential for the analytical solution of the electrostatic problem, and the methods based on a direct numerical integration of the electrostatic problem. ... 

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