Mathematical analysis and calculation of molecular surfaces

Abstract

In this article we derive a complete characterization of the Solvent Excluded Surface (SES) for molecular systems including a complete characterization of singularities of the surface. The theory is based on an implicit representation of the SES, which, in turn, is based on the signed distance function to the Solvent Accessible Surface (SAS). All proofs are constructive so that the theory allows for efficient algorithms in order to compute the area of the SES and the volume of the SES-cavity, or to visualize the surface. Further, we propose to refine the notion of SAS and SES in order to take inner holes in a solute molecule into account or not.

A domain decomposition method for the polarizable continuum model based on the solvent excluded surface

“…The solvent excluded surface (SES, see Figure 2) cavity [14,34,41] seems to be a more suitable choice, because it has a stronger physical meaning that this cavity represents the region where the solvent molecules (represented by idealized spheres) can not touch. It has been confirmed in some chemical calculation that using the SES-cavity Ω ses can yield more accurate results, such as in [44,39,40].…”

“…The region enclosed by the SES is the SES-cavity, denoted by Ω ses . See Figure 3 for a graphical illustration of the SAS and the SES of caffeine derived from our meshing algorithm [41,42]. In fact, any point on the SES has a constant distance to the SAS, equal to the solvent probe radius.…”

“…An efficient method was proposed in [41] to compute f sas analytically, which is based on finding a closest point on the SAS to an arbitrary point. This allows us to construct a continuous permittivity function based on the value of f sas .…”

Effect of the Solute Cavity on the Solvation Energy and its Derivatives within the Framework of the Gaussian Charge Scheme

“…The SES‐type cavity is, in most of the cases, generated through the GEPOL (GEnerating POLyhedra) algorithm . Other strategies to generate the SES are based on an implicit function derived from equivalence statements and Voronoi‐type diagrams . The use of solvation point charges leads, however, to discontinuities in the Coulomb potential that affect the self‐consistent field (SCF) energy and its derivatives with respect to nuclear displacements.…”

“…[11][12][13] Other strategies to generate the SES are based on an implicit function derived from equivalence statements and Voronoitype diagrams. [14] The use of solvation point charges leads, however, to discontinuities in the Coulomb potential that affect the selfconsistent field (SCF) energy and its derivatives with respect to nuclear displacements. This is firstly due to the fact that the interaction between surface elements depends on r −1 ij , r ij being the distance between charges i and j.…”