Kohn-Sham potentials by an inverse Kohn-Sham equation and accuracy assessment by virial theorem

In the recent study, the authors have proposed an integral equation for solving the inverse Kohn-Sham problem. In the present paper, the integral equation is numerically solved for one-dimensional model of a He atom and an H-2 molecule in the electronic ground states. For this purpose, we propose an iterative solution algorithm avoiding the inversion of the kernel of the integral equation. To quantify the numerical accuracy of the calculated exchange-correlation potentials, we evaluate the exchange and correlation energies based on the virial theorem as well as the reproduction of the exact ground-state electronic energy. The results demonstrate that the numerical solutions of our integral equation for the inverse Kohn-Sham problem are accurate enough in reproducing the Kohn-Sham potential and in satisfying the virial theorem.

Automated summary

In this study, the authors proposed a numerical solution to the inverse Kohn-Sham problem using an integral equation. The accuracy of the calculated exchange-correlation potentials was quantified by evaluating the exchange and correlation energies based on the virial theorem and comparing with the exact ground-state electronic energy. The results showed that the numerical solutions of the integral equation were accurate in reproducing the Kohn-Sham potential and satisfying the virial theorem.