A Semi-Empirical Orbital-Free DFT Approach for Modeling Partial Charges and Interaction Energies

Accurate functionals for the kinetic energy and exchange-correlation potential energy remain a critical challenge within Orbital-Free Density Functional Theory (OFDFT). The Thomas-Fermi model, one of the earliest and most significant approaches in this domain, provides a computationally efficient framework for modeling very large systems where Kohn-Sham DFT (KSDFT) is computationally prohibitive. In this work, we extend our previous OFDFT methodology [J. Phys. Chem. A (2024), 128, 6, 1163–1172 and J. Chem. Phys. 160 (2024) 235101] by introducing several key enhancements: a more rigorous theoretical formulation that solely relies on variational calculus, fictitious atomic kinetic energy terms that use the Thomas-Fermi and von Weizsäcker functionals, and empirically fitted coefficients that only depend on the atomic numbers of the pair of interacting atoms. The parameters of the model are optimized by fitting to reference data generated using KSDFT calculations on the B3LYP/aug-cc-pVTZ level of theory, allowing us to evaluate the ability of our model to capture complex chemical environments.