46.1 BASIC THEORY

COSMO is a continuum solvation model, in which the solvent is represented as a dielectric continuum of permittivity $\epsilon$. The solute molecule is placed in a cavity inside the continuum. The response of the continuum due to the charge distribution of the solute is described by the generation of a screening charge distribution on the cavity surface. This charge distribution can be calculated by solving the boundary equation of vanishing electrostatic potential on the surface of a conductor. After a discretization of the cavity surface into sufficiently small segments, the vector of the screening charges on the surface segments is

$${\bf q^{*}} = -{\bf A^{-1}} \Phi$$

where $\Phi$ is the vector of the potential due to the solute charge distribution on the segments, and $\bf A$ is the interaction matrix of the screening charges on the segments. This solution is exact for an electric conductor. For finite dielectrics the true dielectric screening charges can be approximated very well by scaling the charge density of a conductor with $f(\epsilon)$.

$${\bf q} = f(\epsilon) {\bf q^{*}} ; \quad f(\epsilon) = (\epsilon - 1)/(\epsilon + 0.5)$$

In every SCF step the screening charges $\bf q$ have to be generated from the potential $\Phi$, and then added to the Hamiltonian as external point charges. The total energy of the system is

$$E_{tot} = E_{0} + E_{diel}; \quad E_{diel} = \frac{1}{2} \Phi {\bf q}$$

where $E_{0}$ is the bare self-energy of the system and $E_{diel}$ the dielectric energy.

Cavity construction:
First a surface of mutually excluding spheres of radius $R_i+rsolv$ is constructed, where the $R_i$ are the radii of the atoms, defined as element specific radii and $rsolv$ is some radius representing a typical maximum curvature of a solvent molecular surface. $rsolv$ should not be misinterpreted as a mean solvent radius, nor modified for different solvents. Every atomic sphere is represented by an underlying basis grid of nppa points per full atom. Basis grid points which intersect a sphere of a different atom are neglected. In a second step the remainder of the basis grid points are projected to the surface defined by the radii $R_i$. As a third step of the cavity construction the remaining basis grid points are gathered to segments, which are the areas of constant screening charges in the numerical solution. Finally, the intersection seams between the atoms are filled with additional segments.
Now the A-matrix can be set up. The matrix elements will be calculated from the basis grid points of the segments for close and medium segment distances (governed by the disex value), or using the segment centres for large segment distances.

Outlying charge correction:
The non vanishing electron density outside the cavity causes an error that can be corrected by the outlying charge correction. This correction uses the potential on the so called outer surface (defined by the radii $R_i+\mbox{rsolv} \times \mbox{routf}$) to estimate a correction term for the screening charges and the energies (A. Klamt and V. Jonas, J. Chem. Phys., 105, 9972-9981(1996)). The correction will be performed once at the end of a converged SCF calculation. All corrected values can be found in the COSMO output file.