Hole and Cusp Formalism in Electron-Positron Density Functional Theory

We investigate the hole formalism and positron screening within the framework of Den sity Functional Theory (DFT). This study revisits the Local Density Approximation (LDA) and its extensions - such as semilocal functionals and the Weighted Density Approximation (WDA), show ing their importance in modeling exchange and correlation potentials. We further examine the two-component density functional approach to describe electron-positron interactions, with particular em phasis on the formation of the electron screening cloud around the positron site. The performance of various computational techniques in describing charge inhomogeneities and positron surface states is critically assessed. Moreover, we identify the limitations of conventional models in low-dimensional systems and propose a novel method based on the electronic dielectric response to improve the accu racy of positron screening predictions.