Universität Stuttgart
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Item Open Access Accurate force- and Hessian predictions from neural network potentials(2020) Cooper, April Mae; Kästner, Johannes (Prof. Dr.)Item Open Access Development of full configuration interaction quantum Monte Carlo methods for strongly correlated electron systems(2019) Dobrautz, Werner; Alavi, Ali (Prof. Dr.)Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a prominent method to calculate the exact solution of the Schrödinger equation in a finite antisymmetric basis and gives access to physical observables through an efficient stochastic sampling of the wavefunction that describes a quantum mechanical system. Although system-agnostic (black-box-like) and numerically exact, its effectiveness depends crucially on the compactness of the wavefunction: a property that gradually decreases as correlation effects become stronger. In this work, we present two -conceptually distinct- approaches to extend the applicability of FCIQMC towards larger and more strongly correlated systems. In the first part, we investigate a spin-adapted formulation of the FCIQMC algorithm, based on the Unitary Group Approach. Exploiting the inherent symmetries of the nonrelativistic molecular Hamiltonian results in a dramatic reduction of the effective Hilbert space size of the problem. The use of a spin-pure basis explicitly resolves the different spin-sectors, even when degenerate, and the absence of spin-contamination ensures the sampled wavefunction is an eigenfunction of the total spin operator. Moreover, targeting specific many-body states with conserved total spin allows an accurate description of chemical processes governed by the intricate interplay of them. We apply the above methodology to obtain results, not otherwise attainable with conventional approaches, for the spin-gap of the high-spin cobalt atom ground- and low-spin excited state and the electron affinity of scandium within chemical accuracy to experiment. Furthermore we establish the ordering of the scandium anion bound states, which has until now not been experimentally determined. In the second part, we investigate a methodology to explicitly incorporate electron correlation into the initial Ansatz of the ground state wavefunction. Such an Ansatz induces a compact description of the wavefunction, which ameliorates the sampling of the configuration space of a system with FCIQMC. Within this approach, we investigate the two-dimensional Hubbard model near half-filling in the intermediate interaction regime, where such an Ansatz can be exactly incorporated by a nonunitary similarity transformation of the Hamiltonian based on a Gutzwiller correlator. This transformation generates novel three-body interactions, tractable due to the stochastic nature of FCIQMC, and leads to a non-Hermitian effective Hamiltonian with extremely compact right eigenvectors. The latter fact allows application of FCIQMC to larger lattice sizes, well beyond the reach of the method applied to the original Hubbard Hamiltonian.Item Open Access Calculation of reaction rate constants via instanton theory in the canonical and microcanonical ensemble(2018) Löhle, Andreas; Kästner, Johannes (Prof. Dr.)Item Open Access Machine-learning techniques for geometry optimization(2023) Born, Daniel; Kästner, Johannes (Prof. Dr.)Geometry optimization in computational chemistry is still a challenging task. The bottleneck is the computationally expensive ab initio calculations. Thus reducing the total amount of these calculations to accelerate minimization and transition state search is essential. In recent years machine-learning techniques, like Gaussian process regression or neural networks, became popular among scientists. These can be used to calculate the surrogate surface of the potential energy surface and perform geometry optimization there. Another important aspect of geometry optimization is the choice of coordinate system. While Cartesian coordinates describe uniquely a molecule, they are highly coupled. To reduce the coupling between the coordinates, the so-called internal coordinates were developed a long time ago. In addition, these coordinates are non-redundant. With these types of coordinates, a speedup of geometry optimization was obtained. Combining internal coordinates with machine-learning technique has thus the potential to significantly improve geometry optimization. In this thesis, the improvement is demonstrated.Item Open Access Theoretical investigations of atom tunneling in the interstellar medium(2018) Meisner, Jan; Kästner, Johannes (Prof. Dr.)