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Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements

Bugeanu, Monica and Di Remigio, Roberto and Mozgawa, Krzysztof and Reine, Simen Sommerfelt and Harbrecht, Helmut and Frediani, Luca. (2015) Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements. Physical Chemistry, Chemical Physics, 17 (47). pp. 31566-31581.

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Abstract

The simplicity of dielectric continuum models has made them a standard tool in almost any Quantum Chemistry package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable. Even the most advanced implementations, based on the ac{IEF} of the ac{PCM} generally lead to working equations, which do not guarantee convergence to the exact solution and/or might become numerically unstable in the limit of large refinement of the molecular cavity (small tesserae). This is because they generally make use of a surface parametrization with cusps (interlocking spheres) and employ collocation methods for the discretization (point charges). Wavelets on a smooth cavity are an attractive alternative to consider: for the operators involved, they lead to highly sparse matrices and precise error control. Moreover, by making use of a bilinear basis for the representation of operators and functions on the cavity boundary, all equations can be differentiated, to enable the computation of geometrical derivatives. In this contribution, we present our implementation of the ac{IEF}ac{PCM} with bilinear wavelets on a smooth cavity boundary. The implementation has been carried out in our module pcmsolver{} and interfaced with lsdalton{}, demonstrating the accuracy of the method both for the electrostatic solvation energy and for linear response properties. In addition, the implementation in a module makes our framework readily available to any ac{QC} software with minimal effort. The simplicity of dielectric continuum models has made them a standardtool in almost any Quantum Chemistry package. Despite being intuitive from a physical point of view, the actual electrostatic problem at the cavity boundary is challenging: the underlying boundary integral equations depend on singular, long-range operators. The parametrization of the cavity boundary should be molecular-shaped, smooth and differentiable. Even the most advanced implementations, based on the IEF of the PCM generally lead to working equations, which do not guarantee convergence to the exact solution and/or might become numerically unstable in the limit of large refinement of the molecular cavity (small tesserae). This is because they generally make use of a surface parametrization with cusps (interlocking spheres) and employ collocation methods for the discretization (point charges). Wavelets on a smooth cavity are an attractive alternative to consider: for the operators involved, they lead to highly sparse matrices and precise error control. Moreover, by making use of a bilinear basis for the representation of operators and functions on the cavity boundary, all equations can be differentiated, to enable the computation of geometrical derivatives. In this contribution, we present our implementation of the IEFPCM with bilinear wavelets on a smooth cavity boundary. The implementation has been carried out in our module PCMSolver and interfaced with LSDalton, demonstrating the accuracy of the method both for the electrostatic solvation energy and for linear response properties. In addition, the implementation in a module makes our framework readily available to any QC software with minimal effort.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Bugeanu, Monica
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Royal Society of Chemistry
ISSN:1463-9076
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:05 Dec 2016 12:14
Deposited On:15 Mar 2016 11:02

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