Multiplet computation methods for core level X-ray spectroscopy of transition metal and rare earth elements

QC 2023-05-23

Abstract

With the development of new generation synchrotron facilities, the performances of various X-ray spectroscopies have become more advanced. In order to interpret the X-ray spectrum experiments of various novel materials related to transition metal and rare earth elements, new advanced theoretical methods are required. The present thesis incorporates four modus operandi based on the classic multiplet theory to study the core level X-ray spectroscopy of transition metal and rare earth element. The four approaches consist of new methods developed from classic multiplet approach to high level first-principles method assisted multiplet calculation. Some methods are selected from previous researches and some are invented by original researches. These methods are integrated together to form a complete set of multiplet computational methods. This set of multiplet computational methods can perform calculations on various X-ray spectroscopies such as XAS, XPS, XES and RIXS related to the core-level electron. These wide range of spectroscopic methods coupled to different multiplet theory approaches serve as efficient tools to understand the electronic structure of metal sites and their unique contribution to the physical/chemical properties of the materials.

The thesis creatively improves the classic multiplet theory on several aspects: (1) the relation between crystal field parameters and local structure factors; (2) the difficulty of processing point group symmetry branching chain in low symmetric structure; (3) the first-principles calculation of semi-empirical parameters. Four modus operandi are presented in this thesis: the first is the classic multiplet theory consisting of the multiplet effect, crystal field effect and charge transfer effect via several semi-empirical parameters as description for these effects. The second level multiplet theoretical approach analyze the crystal field potential matrix in various symmetries according to the point group symmetry branching rules. Then the crystal field effect parameters used in classic multiplet theory are linked analytically to the specific structural factors such as bond length and angles. This approach is a good tool to study the structural distortion from higher to lower order symmetry with analysis of X-ray spectral feature changes in experiment. The third modus operandi adopts large cluster model consisting of point charges at equivalent atoms position to simulate the crystal field effect on the center metal site. This approach handles low order symmetric crystal field with long range effect in multiplet calculation in an easier way than the classic multiplet theory. The fourth modus operandi initially studies the system of interest in first-principles calculation for the electronic wavefunctions. Then the electronic wavefunctions are used to derive the maximally localized Wannier functions at metal/ligand sites. The analysis of these Wannier functions provide a lot of semi-empirical parameters required in the classic multiplet calculation approach in a first-principles way. This modus operandi has substantially resolved the problem of finding the best set of semi-empirical parameters to fit the calculated X-ray spectrum with experimental data.

In order to study the core electrons of the light elements (such as C/N/O) around center metal ions, a theoretical calculation method used to study the core electrons' vibrationally-resolved X-ray spectroscopy is also introduced as a complementary research and applied to C1s core ionized XPS calculation as an example.

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