A Quantum Monte Carlo Investigation of Weak Interactions and Sign Problems

In this work we examined weak interactions with a fixed-node quantum Monte Carlo approach. We showed that fixed-node diffusion Monte Carlo simulations of H2 bonded to transition metal centers and organic structures can be calculated to accuracies comparable with the best ab inito techniques. We proceeded to calculate H2 binding energies in a metal organic framework with Mn transition metal centers (Mn-MOF). We were able to simulate the interaction of H2 at various sites of the Mn-MOF while treating both covalent bonds and dispersion interactions to equally high levels of accuracy.;Next we worked on using exact techniques to calculate absolute energies of molecular systems with a method called release-node quantum Monte Carlo. We used this method to benchmark the first-row dimers, while determining the fermion-boson energy gaps, which are responsible for the overall efficiency of the technique. Release-node quantum Monte Carlo proved to be too expensive to generally estimate energies to accuracies higher than 10-3 [a.u.], and we therefore proceeded to develop other techniques to improve the efficiency of our calculations. These techniques improved our results for Li2, Be2, and B2 but were not efficient enough for scaling our tests to even larger systems.;Finally we considered properties of the sign problems that arise in diffusion Monte Carlo calculations. This was done with the idea of developing methods for calculating excited states and for treating non-local pseudopotentials without approximation. We anticipated these techniques would be affected by sign problems. During our analysis we showed that the sign problem for these techniques are different than the sign problem of release-node quantum Monte Carlo as they could no longer be characterized by simple fermion-boson gaps. We created a more general description of the sign problem instability, after which we demonstrated the feasibility of using such techniques.