Cavity Construction:

In order to ensure a sufficiently accurate and efficient segmentation of the molecular shaped cavity the COSMO implementation uses a double grid approach and segments of hexagonal, pentagonal, and triangular shape. The cavity construction starts with a union of spheres of radii $R_{i}+RSOLV$ for all atoms $i$. In order to avoid problems with symmetric species, the cavity construction uses de-symmetrized coordinates. The coordinates are slightly distorted with a co-sinus function of amplitude AMPRAN and a phase shift PHSRAN. Initially a basis grid with NPPA segments per atom is projected onto atomic spheres of radii $R_{i}+RSOLV$. In order to avoid the generation of points in the problematic intersections, all remaining points, which are not in the interior of another sphere, are projected downwards onto the radius $R_{i}$. In the next step a segment grid of NSPH segments per H atom and NSPA segments for the other atoms is projected onto the surface defined by $R_{i}$. The basis grid points are associated to the nearest segment grid centers and the segment coordinates are re-defined as the center of area of their associated basis grid points, while the segment area is the sum of the basis grid areas. Segments without basis grid points are discarded. In order to ensure nearest neighbor association for the new centers, this procedure is repeated once. At the end of the cavity construction the intersection seams of the spheres are paved with individual segments, which do not hold associated basis grid points.