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Mathematical methods for implicit solvation models in quantum chemistry

Abstract : This thesis is devoted to study and improve the mathematical models and methods used in implicit solvation models in quantum chemistry. The manuscript is composed of two parts. In the first part where we analyze the solute-solvent interface, we give, for the first time, a complete characterization of the so-called “smooth” molecular surface, i.e., the solvent excluded surface (SES). Based on this characterization, we develop a piecewise meshing algorithm for different molecular surfaces, especially the SES, using the advancing-front triangulation. Further, it has been pointed out in the literature that the SES-cavity (the region enclosed by the SES) is a more accurate description of the solute cavity. In the second part, we therefore construct an SES-based polarizable continuum model (PCM), in which the dielectric permittivity parameter is continuous. The electrostatic problem of this model involves solving a Poisson equation defined in R3. We then develop a particular Schwarz domain decomposition method where only local equations restricted to balls need to be solved. Finally, the Poisson-Boltzmann solvation model, another implicit solvation model, is also investigated, which takes into account both the dielectric permittivity and the ionic strength of the solvent. A similar Schwarz domain decomposition method is proposed to solve the associated Poisson-Boltzmann equation by solving local equations restricted to balls as it is for the SES-based PCM.
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  • HAL Id : tel-01919793, version 1

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Chaoyu Quan. Mathematical methods for implicit solvation models in quantum chemistry. Mathematical Physics [math-ph]. Université Pierre et Marie Curie - Paris VI; Rheinisch-westfälische technische Hochschule (Aix-la-Chapelle, Allemagne), 2017. English. ⟨NNT : 2017PA066587⟩. ⟨tel-01919793⟩

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