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

Abstract

In this paper, an efficient solver for the polarizable continuum model in quantum chemistry is developed which takes the solvent excluded surface (the smooth molecular surface) as the solute–solvent boundary. This model requires to solve a generalized Poisson (GP) equation defined in [Formula: see text] with a space-dependent dielectric permittivity function. First, the original GP-equation is transformed into a system of two coupled equations defined in a bounded domain. Then, this domain is decomposed into overlapping balls and the Schwarz domain decomposition method is used. This method involves a direct Laplace solver and an efficient GP-solver to solve the local sub-equations in balls. For each solver, the spherical harmonics are used as basis functions in the angular direction of the spherical coordinate system. A series of numerical experiments are presented to test the performance of this method.

On the Scalability of the Schwarz Method

“…, N . Notice that ( 19) is exactly given in [5, Theorem 7, formula (24)]. Following the same arguments as in [5], we notice that ess sup…”

“…It is important to note however that we must make a choice for the value of the radius of each atomic cavity. While this is a non-trivial question in general (see, e.g., the references in [24]), the most basic convention (see, e.g., [2]) Hydrogen, green denotes Nitrogen, blue denotes Oxygen and magenta denotes Sulphur. The atomic cavities were constructed using 1.1 times the radii obtained from the Universal Force Field (UFF) [25].…”

“…In the computational chemistry community, it is generally argued that using scaled van der Waals radii to construct atomic cavities leads to a sub-optimal definition of the molecular cavity that is unable to accurately capture the physical behaviour of the molecule in a polarisable medium. A more elaborate definition of the molecular cavity is given by the so-called Surface Accessible Surface (SAS) (see, e.g., [24]). According to this definition, each atomic cavity is constructed using the sum of two radii: the atomic van der Waals radius and a so-called 'probe radius', which can generally be taken to be 1.4 Angstrom, i.e., the approximate radius of a water molecule.…”

A Domain Decomposition Method for the Poisson--Boltzmann Solvation Models

“…Both the ddCOSMO and the ddPCM work for the solute cavity constituted by overlapping balls, such as the van der Waals (VDW) cavity and the solvent accessible surface (SAS) cavity [47,48]. In the case of the PCM based on the "smooth" molecular surface, i.e., based on the solvent excluded surface (SES) [49,50], another domain decomposition method has been proposed in [51], which is called the ddPCM-SES.…”

“…Developing a Laplace solver in a ball is not difficult and has already been presented in our previous work including the ddCOSMO [38], the ddPCM [45] and the ddPCM-SES [51]. For the sake of completeness, we recall briefly the Laplace solver in the following content.…”