Charging free energy continuum solvation models

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Poisson-Boltzmann model The PB approximation is one of the more elaborate continuum solvation models that take into account not only the charge density of the solute but also the mobile charge density within the surrounding continuum. Continuum models of solvation are in general capable of calculating absolute free energies of solvation. 

A series of continuum solvation models (SMx, x = 1-5) has been developed by Truhlar and co-worker (Cramer and Truhlar [79]), based on the Generalized Born/Surface Area (GB/SA) model (Still et al. [86]). Recall that in the GB approach the molecular shape is taken into account as the solute charge is distributed over a set of atom-centered spheres. For this GB/SA model, the polarization free energy is given by... 

The earlier attempt to approach the electrostatic contribution to the free energy of solvation is due to Kirkwood (1934). This model is based on a multipole expansion of the charge distribution of the solute at the center of a spherical cavity surroimded by a continuum represented by the dielectric permittivity of the solvent. When this expansion is limited to rank 1 which corresponds to a pure dipole fi, one finds the Onsager model (Onsager 1936) in which the electrostatic contribution to the free energy of solvation by a solvent of dielectric constant e of a molecule having a dipole moment in a cavity of radius a takes the expression ... 

The final class of methods that we shall consider for calculating the electrostatic compone of the solvation free energy are based upon the Poisson or the Poisson-Boltzmann equatior Ihese methods have been particularly useful for investigating the electrostatic properties biological macromolecules such as proteins and DNA. The solute is treated as a body of co stant low dielectric (usually between 2 and 4), and the solvent is modelled as a continuum high dielectric. The Poisson equation relates the variation in the potential (f> within a mediu of uniform dielectric constant e to the charge density p ... 

Keeping in mind the intrinsic features associated with the definition of the cavity in the most popular QM-SCRF methods, it can be questioned what is the influence of the fine details of the cavity definition on the computed solvation free energies. This question has been investigated in a recent study by Takano and Houk [61], who have examined the dependence of the solvation free energies estimated for a series of 70 compounds, including neutral and charged species, on both the choice of the cavity and the level of theory used in computations within the framework of the conductor-like polarizable continuum model (CPCM). The mean absolute deviation (MAD) between calculated... 

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