Tessellation, cavity surface

Cavity surface tessellation not based on atomic spheres. 29... 

The BE methods are widely used in quantum chemical calculations of solvent effects [2,3,5] with very good results. For historical reasons, the use of BE methods in molecular mechanics calculations is limited. Several versions of the BE method that differ in the cavity surface formation algorithms, evaluation of the Ese contribution, Eq. (16), and methods of solving the system of linear equations, Eq. (12), have been reported [18 22]. From a computational point of view, the BE methods are invariant to molecular rotations because the molecular surface is invariant to the rotation. The results will depend upon the method chosen for the formation and tessellation of the molecular surface. The time limiting step in BE methods is the solution of the system of linear equations (Eq. (12)). Even for relatively small proteins, the size of matrix A... 

The PCM algorithm is as follows. First, the cavity surface is determined from the van der Waals radii of the atoms. That fraction of each atom s van der Waals sphere which contributes to the cavity is then divided into a number of small surface elements of calculable surface area. The simplest way to to this is to define a local polar coordinate frame at the centre of each atom s van der Waals sphere and to use fixed increments of AO and A(p to give rectangular surface elements (Figure 11.22). The surface can also be divided using tessellation methods [Paschual-Ahuir et al. 1987] An initial value of the point charge for each surface element is then calculated from the electric field gradient due to the solute alone ... 

There are also some other ideas about possible ways to make the calculation of the gradient and of the Hessian more effective, but we limit ourselves to expose topics for which there is a working computer code. The field is in evolution but surely progresses towards computational methods with computational costs and range of applicability comparable to those used for molecules in vacuo are within reach. In our opinion the most difficult point is to find search algorithms for critical points able to treat in a more efficient way some small roughness in the PES introduced by the tessellation of the cavity surface. 

Passing directly to the computational implementation, we recall that as for the previous ASC procedures, also in the lEF we exploit a tessellation of the cavity surface into K tesserae, and approximate the charge density [Pg.10]

Figure 7 (Left) Typical configuration of particles before particle i is removed. (Right) After particle i is removed, tessellations must be reconstructed within the superpolyhedron (bold, dashed line). The volume and surface area of the cavity that once held the removed particle can then be determined. (Adapted from Ref. 71).

Formulas are given in the already quoted Cossi et al. s paper (1996a). To compute this contribution with Pierotti-Claverie s formula (eq. 80), the tessellation of the cavity portions is not compulsory. However, to exploit the subroutines used for G%is and G j, we can use the partial surface calculations via summation over the tesserae. Also the total volume is computed by using a BEM procedure, i.e. exploiting the definition of tesserae. According to the definition of the SPT cavity, there is no need of introducing GEPOL additional spheres (the Sas surface is here used). The computational cost of G av is minimal. 

In the application of the boundary element method, it is crucial to select appropriate botmdary surface for the solute cavity and to proceed as accurate as possible tessellation (triangulation) of this surface. For instance, it has been proposed that in the case of the cavity formation fi"om overlapping van-der-Waals spheres, the atomic van-der-Waals radii should be multiplied by a coefficient equal to 1.2. Other possibihties of the siuface definition include the closed envelope obtained by rolling a spherical probe of adequate diameter on the van-der-Waals surface of the solute molecule and the surface obtained ifom the positions of the center of such spherical probe aroimd the solute. 

---