## An analysis of atomic wave functions to improve density functional kinetic energy models

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Density Functional Theory (DFT) is a semi-classical computational theory devel- oped to accurately predict electron charge density, ground-state energy, band gap energies, and other electronic properties. It has applications in chemistry, semiconductor physics, material science, and other elds. A major bottleneck is the increase of resources required to calculate atomic orbitals individually when scaling to systems of many electrons. An or- bital free model that accurately predicts atomic kinetic energy densities is necessary for the largest scale problems. One approach to orbital free functionals is the work of Perdew and Constantin, who developed a model that stitches together the second order gradient expan- sion, a model that predicts kinetic energy density for a very large number of electrons well, with the von Weizsacker model, an analytical model that accurately predicts kinetic energy densities for bosons, and does well for small atoms. Our group nds the PC model to break down when predicting bonding energies, and has proposed a new class of stitching function. We are analyzing this stitching function for single atoms, studying scaling properties across the periodic table and beyond to test the validity of our model against known properties and scaling laws of atoms. We are using well known atomic electron number densities generated by a program, FHI98PP, and running them through several models including our own. We then compare kinetic energy densities, total kinetic energy densities vs nuclear charge.