Computation of X-ray Absorption Spectra Using a Double Cluster Model
Date
2024-09-23
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
Type
Thesis
Degree Level
Masters
Abstract
In the early 20th century, the principles of quantum mechanics revolutionized the study of materials, leading to the invention of the transistor, the key component of modern day technologies. To sustain advancements in technology, innovations in the discovery of new materials are needed. One family of elements with immense potential in creating new functional materials is the 3d transition elements, especially in \new{their perovskite oxide form}. A common method in the study of the electronic structure of such compounds is X-ray Absorption Spectroscopy (XAS). In this method, an x-ray beam is directed at a material, and the x-ray absorption of the material is recorded. This results in energy-dependent absorption spectra. If the energy of the x-ray beam is equal to the binding energy of the electrons inside the material, sharp peaks in the spectra are observed. The sharp peaks in these spectra contain detailed electronic and magnetic information about the material. Interpreting experimental spectra, however, can be challenging due to complicated lineshapes arising from quantum many-body interactions. Therefore, theoretical methods are often necessary to extract information and analyze the spectra.
This study focuses on quantum double cluster models to simulate spectra. In these models, each cluster is composed of a metal atom along with its nearest neighbor ligands. The interactions that occur within each individual cluster, as well as the interactions between the two clusters, are considered in the model to capture the complex bonding dynamics. In this study, sparse, real, and symmetric Hamiltonian matrices are constructed based on the double cluster model for 3d transition metals \new{in their perovskite oxide form} with atomic numbers 21 and 25 through 29. The resulting Hamiltonian matrices have dimensions ranging from 50 thousand to 4.6 billion. One set of these matrices represents the compounds in their initial state, before exposure to x-ray beams, and the other set represents the compounds in their excited state after exposure.
To simulate the spectra of these compounds, specific eigenpairs of the constructed Hamiltonian matrices are calculated. We employ the SLEPc library to determine the ground state eigenpairs of the initial state Hamiltonians, and utilize the Lanczos iterative method to calculate a subset of eigenpairs for the excited state Hamiltonians. The Lanczos method is powerful because it can obtain the necessary eigenpairs to plot the XAS spectra with relatively few iterations, even for large matrices.
By analyzing the covalency extracted from the calculated ground state wavefunction and comparing the double cluster XAS spectra with those from simpler single cluster models, we find that for atomic numbers 25, 28, and 29, a double cluster model is necessary to capture inter-cluster interactions. The simpler single cluster models are not able to incorporate these interactions and are inadequate to accurately represent the electronic structure and magnetic properties of the compounds. Furthermore, the double cluster spectra agree well with experimental data, confirming the effectiveness of the model.
Description
Keywords
Double Cluster Model, X-ray Absorption Spectrum
Citation
Degree
Master of Science (M.Sc.)
Department
Computer Science
Program
Computer Science