Atomic Partitioning of Periodic Electronic-Structure Simulations

This thesis introduces a novel methodology for partitioning the total energy of periodic systems into atomic contributions through the lossless decomposition of the one-electron reduced density matrix (1-RDM). The method was implemented and validated to establish a robust and physically intuitive framework for analyzing local electronic structure in crystalline materials. Building on a molecular orbital (MO)-based approach introduced by Eriksen et al. [1, 2], the methodology is compared with an atomic orbital (AO)-based alternative by Nakai et al. [3, 4], offering deeper insights into the electronic properties of periodic systems.
The atomic partitioning of total KS-DFT energy described in this thesis was implemented in decodense [5] code, using PySCF [6, 7] as electronic structure backend, as well as in the CP2K [8] software package. The methodology was validated on various systems and shown to successfully preserve translational symmetry in periodic systems and reproduce atomic cohesive energies consistent with standard quantum chemical methods in isolated systems. Although pseudopotentials can shift the absolute cohesive energies, the relative trends and qualitative insights remained consistent across all tested systems.
Using intrinsic bond orbitals (IBO) [9] as localized MO bases and intrinsic atomic orbitals (IAO)-based weights led to smoother convergence of atomic cohesive energies, closely mirroring the convergence of total energies, both at the Γ-point and with broader k-point sampling. The scheme was also found to result in the most chemically intuitive partitionings, as well as proved to be robust to variations in computational parameters, such as the exchange-correlation (xc) functional.
Convergence of atomic cohesive energies for three-dimensional solids proved to be slower than the nearly-immediate convergence observed for the one-dimensional systems. Nevertheless, our results suggest that the MO-based IBO/IAO approach can capture subtle differences between phases with comparable total energies and stability. Although molecular cohesive energies from both implementations aligned closely, some discrepancies in atomic cohesive energies were observed. However, the relative trends confirmed the method’s qualitative agreement and robustness across the tested approaches.
The next step in the research to follow is applying the method for a model adsorption on a reaction surface, focusing on investigating adsorbant-surface interactions and analyzing energy shifts in both the adsorbant and the surface, relating these to the total change. We also propose future work, including testing and validation, to focus on improving the code’s handling of non-uniform occupations, particularly in cases such as metallic surfaces. We further propose exploring extending the method for direct energy decomposition in k-space, potentially utilizing localized Wannier orbitals [10–12]. These advancements, we hope, will provide more insights in investigations of surface reactions by focusing on local fragments instead of the entire extended system, and will contribute to future research in material design and discovery.