An investigation into the nonconformity of homogeneous gas limit for kinetic energy density of atomic systems
Priya Priya, Anuvab Panda, Saswata Basu, Mainak Sadhukhan
TL;DR
The paper argues that the homogeneous electron gas limit is an improper leading term for atomic kinetic energy density in orbital-free DFT and introduces a Green's function-based Hamiltonian-partitioning framework to obtain a systematic, parameter-free expansion for KE density, with $G^{H}$ as the leading Green's function and $G^{int}$ capturing universal interelectronic effects. By applying the method to a 1D Pöschl–Teller model and comparing constant-density and nonlocal interelectronic interactions (via Suzuki–Trotter decomposition), it shows that the leading von Weizsäcker term is more physically appropriate for atoms and that HEG-based KE functionals fail to capture atomic shell structure. The work provides analytical expressions for KE contributions in weak- and nonlocal-interaction limits and demonstrates the necessity of nonuniform, nonlocal interelectronic effects. The approach lays groundwork for computing local and global KE densities for real atoms and molecules within OF-DFT, with implications for more accurate, scalable simulations of atomic systems.
Abstract
Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic approach to accurately compute the kinetic energy density in such contexts. In our recent work, we introduced an analytical Green's function-based framework to address this issue. Majority of the existing efforts to construct an approximate kinetic energy density for atomic systems uses homogeneous electron gas as the bedrock of their formalism. In this work, we have shown by using a Pöschl-Teller potential that for realistic atomic potentials such model yields improper results emphasizing the need to change the leading-order term for the quest of kinetic energy densities of atoms and molecules.