Adaptive algorithms for computational chemistry and interactive modeling. (Algorithmes adaptatifs pour la chimie numérique et la modélisation interactive)

At the atomic scale, interactive physically-based modeling tools are more and more in demand. Unfortunately, solving the underlying physics equations at interactive rates is computationally challenging. In this dissertation, after presenting a review of theories and algorithms for interactive electronic structure computations, we propose new algorithms that allow for interactive modeling of chemical structures. • We first present a modeling tool to construct structural models of hydrocarbon systems. The physical feedbacks are based on the Brenner potential. In order to be able to interactively edit systems containing numerous atoms, we introduce a new adaptive simulation algorithm. • Then, we introduce interactive quantum chemistry simulations at the Atom Superposition and Electron Delocalization Molecular Orbital (ASED-MO) level of theory. This method is based on the divide-and-conquer (D&C) approach, which we show is accurate and efficient for this non-self-consistent semi-empirical theory. • Finally, we propose a novel Block-Adaptive Quantum Mechanics (BAQM) approach to interactive quantum chemistry. BAQM constrains some nuclei positions and some electronic degrees of freedom on the fly to simplify the simulation. We also study different applications including one study of graphane formation, education, virtual reality and virtual prototyping at the atomic scale.