Relativistic orbital-free kinetic energy density functional for one-particle nuclear systems
X. H. Wu, Z. X. Ren, H. Z. Liang, P. W. Zhao
TL;DR
This work derives an exact relativistic orbital-free kinetic energy density functional (KEDF) for a one-particle nuclear system in one dimension. From the 1D Dirac equation with vector $V(x)$ and scalar $S(x)$, it obtains $T[\rho_v,\rho_s]$ and the kinetic energy density $\tau(x)$ in terms of $\rho_+$ and $\rho_-$, specifically $\tau(x) = m\rho_s(x) + \frac{1}{2} \sqrt{\frac{\rho_-(x)}{\rho_+(x)}} |\rho'_+(x)|$. It also provides explicit functional derivatives $\delta T/\delta \rho_+$ and $\delta T/\delta \rho_-$ and handles the sign-change point via the ignition parameter $S_{\rm ign}$ to ensure finite limits. Numerical verification against Dirac solutions with Woods–Saxon–type potentials shows agreement between the wavefunction-based kinetic energy and the orbital-free functional, establishing a practical starting point for extending relativistic OF-KEDFs.
Abstract
This letter aims to derive the exact relativistic orbital-free kinetic energy density functional for one-particle nuclear systems in one-dimensional case. The kinetic energy is expressed as a functional of both vector and scalar densities. The functional derivatives of the kinetic energy density functional are also derived. Both the kinetic energy density functional and its functional derivatives are validated to be correct. This serves as a foundation for further exploration of more general relativistic orbital-free kinetic energy density functionals.