A general penalty method for density‐to‐potential inversion. Issue 22 (6th August 2020) - Kumar, Ashish; Harbola, Manoj K.
Abstract: A general penalty method is presented for the construction of the Kohn‐Sham system for a given density through Levy's constrained search. The method uses a functional S [ ρ ] of one's choice. Different forms of S [ ρ ] are used to calculate the kinetic energy and exchange‐correlation potential of atoms, jellium spheres, and the Hookium, and consistency among results obtained from them is shown for each system. Abstract : Inversion algorithms for construction of exact exchange‐correlation potential for a given density either use Lieb's maximization or the Levy's constrained search approach. While there are many methods based on Lieb's maximization, there is only one widely used method (developed by Zhao, Morisson and Parr) that utilizes Levy's constrained‐search. In the present work we develop a general penalty method to show that Levy's constrained‐search can also be applied in many different ways. This then gives several methods of obtaining the exchange‐correlation potential for a given density by employing the constrained search approach.