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.

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.