Retrospective of My Research Foundations
A look back at the ideas that got me here
- Many-body perturbation theory & approximation techniques: Studied during my undergraduate thesis to understand quantum mechanical solutions and the need for real-space methods over reciprocal-space for molecular systems.
- Molecular orbital theory & density functional theory: Learned fundamentals (including ligand-field theory) to analyze low-dimensional molecular systems and defend my thesis work.
- Molecular electronic properties & transitions: Applied in my first publication to interpret NMR chemical shifts, Landé g-factor variations, and related data.
- Charge analysis methods (Mulliken, Löwdin, ELF): Used to investigate carrier localization, its limitations, and exchange/superexchange dynamics in doped systems.
- Group theory (field splitting, Kramers degeneracy): Applied to explain orbital quenching in 3D crystals and 2D materials, and to explore how reduced dimensionality can overcome crystal field limitations.
- Noncentrosymmetric molecular behavior: Studied using finite-field density functional theory, with density-matrix–based analysis to interpret nonlinear optoelectronic responses in reduced-symmetry systems.