Interactive Control of Quantum Mechanical Calculations in Chemistry

The increasing computing power and the algorithmic improvements in quantum chemistry have been accelerating first-principles calculations for many years. Nowadays, single-point calculations for molecular systems of moderate size are feasible on a second timescale, even on personal computers. Accordingly, the possibility of quasi-instantaneous calculations gave rise to interactive approaches in quantum chemistry. One such approach, real-time quantum chemistry, focuses on the interactive exploration of potential energy surfaces to study reaction mechanisms. In real-time quantum chemistry, chemists can simulate a molecular system and interact with it using a computer mouse or specialized hardware such as force-feedback haptic devices. The fast quantum chemical calculations deliver an immediate visual and haptic feedback with which chemists can instantaneously experience the effect of their manipulations. For a reliable description of potential energy surfaces, self-consistent field methods are necessary. Single-point calculations based on self-consistent field methods involve an iterative procedure that stops when the electronic density is converged. In addition to the challenge to do so in as few iterations as possible, there is a chance that the calculation does not converge at all. Furthermore, the equations underlying self-consistent field methods can be solved by different electronic densities, of which only one delivers the desired properties. While such issues are ubiquitous in quantum chemistry, they are especially problematic in interactive applications. To accelerate self-consistent field calculations, we present a density propagation algorithm for sequences of structures. It delivers improved initial density matrices for single-point calculations and hence reduces the number of necessary iterations. In interactive approaches, visual and haptic feedback must also be available in case of calculations converging slowly or not at all. In order to guarantee reliable real-time feedback, we introduce a mediator strategy. The mediator creates surrogate potentials that approximate the potential energy surface and enable high-frequency feedback. In addition, the mediator restricts the exploration to regions of configuration space for which the available orbitals are reliable, which is important when calculations do not converge. To ensure that real-time reactivity explorations rely on correctly converged quantum chemical calculations, we design an orbital perturbation scheme that detects incorrect self-consistent field convergence. This scheme continuously tests in the background whether different solutions can be obtained with randomly perturbed initial electronic densities. The perturbation approach can also be applied to independent single-point calculations in non-interactive environments. With real-time quantum chemistry, new areas of quantum chemistry can be explored. We introduce the concept of molecular propensity with which multiple states of a molecular system are explored simultaneously. It offers chemists the possibility to discover the inclination of the system under study to undergo transformations such as reduction, oxidation, photoexcitation, or protonation, without the necessity to consider such processes explicitly in the simulation setup. In this thesis, we also present an algorithm to process the results of real-time explorations of reactivity. We convert sequences of structures recorded during an exploration to B-spline curves, from which we extract candidates for stable structures and elementary reactions. The candidates are then optimized and stored in a reaction network. For the optimization of reaction paths and the determination of transition states, we develop a new double-ended method called ReaDuct that describes reaction paths by parametrized curves. To determine minimum energy paths and transition states, it optimizes the parameters of the curve rather than discrete structures along the reaction path