Treatment of Solvation Effects with COSMO

The **Co**nductor-like **S**creening **Mo**del [169]
(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

= + = 0. |

is the Coulomb matrix of the screening charge interactions. For a conductor, the boundary condition

= | - . |

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

f () |
= | ||

= | f () |

The deviation between the COSMO approximation and the exact solution is rather small. For strong dielectrics like water it is less than 1%, while for non-polar solvents with

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}. |

A COSMO energy calculation starts with the construction of the cavity surface grid. Within the SCF procedure, the screening charges are calculated in every cycle and the potential generated by these charges is included into the Hamiltonian. This ensures a variational optimization of both the molecular orbitals and the screening charges and allows for the evaluation of analytic gradients.