Graph neural networks (GNN) offer a potential method of bypassing the Kohn-Sham equations in density functional theory (DFT) calculations by learning both the Hohenberg-Kohn (HK) mapping of electron density to energy, allowing for calculations of much larger atomic systems and time scales and enabling large-scale MD simulations with DFT-level accuracy. In this work, we investigate the feasibility of GNNs to learn the HK map from the external potential approximated as Gaussians to the electron density 𝑛(𝑟), and the mapping from 𝑛(𝑟) to the energy density 𝑒(𝑟) using Pytorch Geometric. We develop a graph representation for densities on radial grid points and determine that a k-nearest neighbor algorithm for determining node connections is an effective approach compared to a distance cutoff model, having an average graph size of 6.31 MB and 32.0 MB for datasets with 𝑘 = 10 and 𝑘 = 50 respectively. Furthermore, we develop two GNNs in Pytorch Geometric, and demonstrate a decrease in training losses for a 𝑛(𝑟) to 𝑒(𝑟) of 8.52 · 10^14 and 3.10 · 10^14 for 𝑘 = 10 and 𝑘 = 20 datasets respectively, suggesting the model could be further trained and optimized to learn the electron density to energy functional.

Metal oxides are crucial materials that can be applied to sustainable processes for heat storage or oxygen pumping. In order to be able to apply metal oxides to industrial processes, an effective model of the metal oxide’s reduction thermodynamics is required. To do this, Wilson et al., (2023) developed a compound energy formulism (CEF) algorithm to form these models. The algorithm in its current form can effectively form model thermodynamics; however, the data set required for this model is extensive and large, leading to high costs of modeling a metal oxide. Furthermore, the algorithm faces further difficulties with uneven data densities within the set, leading to poorer fits for low density data. To assist in alleviating the cost associated with data collection, data-omitting strategies were performed to find unimportant points, or points that formed models that had good fits to the original model when removed. After conducting these tests, many points and trends were found to be crucial to keep within the data set, but due to uneven data density, no definitive conclusions could be made on how to reduce the algorithm’s data set. The tests gave evidence that points in high data density regions could be removed from the data set due to only the fact that there existed nearby points to provide essential information to closely interpolate/extrapolate the missing data. Although this project currently did not meet the goal of reducing the data set, preliminary findings of what points could be non-crucial to the data set were identified. Future testing with the proposed weighting methods will be conducted to determine what data can be safely removed from the set to form models that properly reflect the metal oxide’s properties.

Using DFT calculations and GAMESS computational software, porphine and its derivatives were analyzed for unique sites to accept the adsorbates As(III), As(V) and P(V) in order to compare resulting adsorption energies and determine if any of these molecules prefer arsenic oxyanions over phosphate. Pure porphine preferred As(III) over P(V) with a resulting adsorption energy of -0.7974 eV. Of the functionalized porphyrins tested, carboxyl porphyrin preferred As(V) over P(V) with a total adsorption energy of -0.7345 eV. Ethyl, methyl, chlorine and amino porphyrin all preferred As(III), with energies of -0.7934, -0.8239, -0.7602, and -0.8508 eV, respectively. Of the metalated porphyrins tested, copper and vanadium porphyrin preferred As(V) over P(V) with adsorption energies of -0.7645 and -2.0915 eV. Chromium, iron and magnesium porphyrin all preferred As(III) over P(V) with energies of -0.5993, -1.4539, and - 1.0790 eV, respectively.