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One of the essential requirements of biomolecular modeling is an accurate description of water as a solvent. The challenge is to make this description computationally facile -- reasonably fast, simple, robust and easy to incorporate into existing software packages, yet accurate. The most rigorous procedure to model the effect of aqueous solvent is to explicitly model every water molecule in the system. For many practical applications, this approach is computationally too intense, as the number of required water atoms is on an average at least one order of magnitude larger than the number of atoms of the molecule of interest. Implicit solvent models, in which solvent molecules are replaced by a continuous dielectric, have become a popular alternative to explicit solvent methods. However, implicit solvation models often lack various microscopic details which are crucial for accuracy. One such missing effect that is currently missing from popular implicit models is the so called effect of charge hydration asymmetry (CHA). The missing effect of charge hydration asymmetry -- the asymmetric response of water upon the sign of solute charge -- manifests a characteristic, strong dependence of solvation free energies on the sign of solute charge. Here, we incorporate this missing effect into the continuum solvation framework via the conceptually simplest Born equation and also in the generalized Born model. We identify the key electric multipole moments of model water molecules critical for the various degrees of CHA effect observed in studies based on molecular dynamics simulations using different rigid water models. We then use this gained insight to incorporate CHA first into the Born model, and then into the generalized Born model. The proposed framework significantly improves accuracy of the hydration free energy estimates tested on a comprehensive set of varied molecular solutes -- monovalent and divalent ions, small drug-like molecules, charged and uncharged amino acid dipeptides, and small proteins. We finally develop a methodology to resolve the issue with unacceptably large uncertainty that stems from a variety of fundamental and technical difficulties in experimental quantification of CHA from charged solutes. Using the proposed corrections in the continuum framework, we untangle the charge-asymmetric response of water from its symmetric response, and further circumvent the difficulties by extracting accurate estimate propensity of water to cause CHA from accurate experimental hydration free energies of neutral polar molecules. We show that the asymmetry in water's response is strong, about 50% of the symmetric response. / Ph. D.

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Cette thèse est consacrée à étudier et à améliorer les modèles mathématiques et les méthodes utilisées pour les modèles de solvatation implicite en chimie quantique. Ce manuscrit est composée de deux parties. Dans la première partie où nous analysons l'interface soluté-solvant, nous donnons, pour la première fois, une caractérisation complète de la surface moléculaire lisse, c'est-à-dire la surface exclue du solvant (SES). À partie de cette caractérisation, nous développons un algorithme de maillage par morceaux pour les surfaces moléculaires différentes, en particulier pour la SES, en utilisant la triangulation à front avançant. De plus, la cavité de la SES (la région entourée par la SES) est une description plus précise de la cavité de soluté. Dans la deuxième partie, nous construisons donc un modèle de continuum polarisable basé (PCM) sur la SES, dans lequel le paramètre de permittivité diélectrique est continu. Le problème électrostatique de ce modèle consiste à résoudre une équation de Poisson définie sur R3. Nous développons ensuite une méthode de Schwarz particulière, où seules les équations locales restreintes à des boules doivent être résolues. Enfin, nous étudions le modèle de solvatation de Poisson-Boltzmann, un autre modèle de solvatation implicite, qui tient compte à la fois de la permittivité diélectrique et de la force ionique du solvant. Une méthode de Schwarz similaire est proposée pour résoudre l'équation de Poisson-Boltzmann associée en résolvant des équations locales restreintes aux boules comme pour le PCM basé sur la SES. / 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.