Treatment of Solvation Effects with COSMO

The **Co**nductor-like **S**creening **Mo**del [130]
(`cosmo`) is a continuum solvation model (CSM),
where the solute molecule forms a cavity within the
dielectric continuum of permittivity
that represents the solvent.
The charge distribution of the solute polarizes the dielectric medium. The
response of the medium is described by the generation of screening charges on
the cavity surface.

CSMs usually require the solution of the rather complicated boundary conditions
for a dielectric in order to obtain the screening charges. `cosmo` instead uses
the much simpler boundary condition of vanishing electrostatic potential for a
conductor,

= 0. |

This represents an electrostatically ideal solvent with = ∞. The vector of the total electrostatic potential on the cavity surface segments is determined by the solute potential , which consist of the electronic and the nuclear part, and the vector of the screening charges ,

= + = 0. |

is the Coulomb matrix of the screening charge interactions. For a conductor, the boundary condition = 0 defines the screening charges as

= | - . |

To take into account the finite permittivity of real solvents, the screening charges are scaled by a factor.

f () |
= | ||

= | f () |

The deviation between the

E_{diel} = f () |

The total free energy of the solvated molecule is the sum of the energy of the isolated system calculated with the solvated wave function and the dielectric energy

E = E(Ψ^{solv}) + E_{diel}. |

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