MOLPRO

52 THE COSMO MODEL 371
The COSMO output file will be written after every converged SCF calculation. The segment
charges and potentials are corrected by the outlying charge correction. For the total charges and
energies corrected and uncorrected values are given. The normal output file contains uncorrected
values only. It is recommended to use the corrected values from the output file.
Optimizations:
It is recommended to use optimizer that operates with gradients exclusively. Line search techniques
that use energies tends to fail, because of the energy discontinuities which may occur
due to a reorganization of the segments after a geometry step. For the same reasons numerical
gradients are not recommended.
52.1 BASIC THEORY
COSMO is a continuum solvation model, in which the solvent is represented as a dielectric
continuum of permittivity ε. 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
q ∗
= −A −1 Φ
where Φ is the vector of the potential due to the solute charge distribution on the segments,
and 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 (ε).
q = f (ε)q ∗ ; f (ε) = (ε − 1)/(ε + 0.5)
In every SCF step the screening charges q have to be generated from the potential Φ, and then
added to the Hamiltonian as external point charges. The total energy of the system is
E tot = E 0 + E diel ; E diel = 1 2 Φq
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),