Quantum Monte Carlo study of van der Waals systems

Asiri, Yassmin and Drummond, Neil (2022) Quantum Monte Carlo study of van der Waals systems. PhD thesis, Lancaster University.

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Abstract

In this thesis, we develop a new method to account for the vibrational renormalisation of electronic structure by both thermal and quantum lattice vibrational effects. Atomic configurations are randomly sampled based on quasiharmonic phonon calculations within density functional theory, and the excitation energy at each configuration is evaluated using fixed-node diffusion quantum Monte Carlo. We demonstrate that the developed technique is efficient and has the potential to be applied to a wide range of materials. We report the zero-point renormalisation of the band gap for benzene, monolayer and bulk hBN, bulk Si and C-diamond. The proposed approach within quantum Monte Carlo is found to be sufficient to capture the quantum effect of zero-point motion and improve the agreement with experiment gap results. We also investigate the temperature-dependent renormalisation of the direct band gap of benzene, bulk Si, and C-diamond arising from harmonic vibrational effects within density functional theory. We study an impurity of a single hole in ideal, dilute weakly doped 2D homogeneous electron gas modelling a van der Waals heterostructure of a MoSe2 monolayer embedded in flakes of hBN. This allows us to investigate the effect of a finite concentration of charge carriers that interact via a periodic Keldysh interaction on the formation of a negative trion. The quantum Monte Carlo results of relaxation energies and pair correlation functions at a range of low densities are reported. Our results indicate that the screening effects of the surrounding electron gas on the formation of a negative trion are weak. We perform ab initio calculations of the defect formation energy for silicon substitution and Stone–Wales defects in monolayer graphene and the atomisation energy of bulk silicon, with the aim of benchmarking the accuracy of the widely used density functional theory method in these types of calculations. Our results show that the density functional theory significantly underestimates the defect formation energy and overestimates the atomisation energy of bulk silicon.