Abstract
The use of the single-particle Green’s function in quantum chemistry has become widespread as a result of its correspondence with the spectral function, allowing the study of a wide range of materials. The spectral function is a quantity central to spectroscopic investigations and characterisations, and there exists many paradigms and methods to probe it. In this thesis, an approach to finding the Green’s function will be presented. This method, based on the block Lanczos algorithm, has been investigated previously in the literature, however a new formulation that permits the access of ‘full-frequency’ dynamic Green’s functions and self-energies using only a set of static expectation values is presented. These expectation values, taking the form of the spectral moments of the particular function, are conserved through the familiar Lanczos recursion in order to physically inform the solution, and allow a systematic improvability with respect to the number of moments conserved.The reformulations of the block Lanczos algorithm will be presented, along with necessary considerations and a discussion of their application to the Dyson equation. Following this, a number of specific examples of their use for efficiently performing existing quantum chemical methods will be presented, based on many-body perturbation theory and coupled cluster theories. These discussions will include deriving and outlining the working equations, discussing any algorithmic considerations important to their implementation, and comparisons to existing solvers with respect to the existence of multiple solutions.
The performance of these methods will then be benchmarked using a number of datasets in order to quantify the change in accuracy of the methods with the number of spectral moments conserved. This data will be used to show that few spectral moments must be conserved in order to faithfully represent the spectral function within the regimes of interest, such as the frontier excitations close to the Fermi energy defining the ionisation potential and electron affinity of the particular material. Furthermore, in the case of self-consistent many-body perturbation theory, similar discussions will be used to show that an increase in the resolution of the dynamics via additional moments is actually a detriment to the accuracy of the resulting excitations, leading to an accurate and efficient approach. This approach will be applied to the important drug molecule artemisinin as an example of its applicability in elucidating physical properties, and early investigations into the suitability of the method for extended solids will be presented.
| Date of Award | 1 Jun 2023 |
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| Original language | English |
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| Supervisor | George Booth (Supervisor) |