Inverse Kohn-Sham Equations Derived From The Density Equation Theory

We formulate the inverse Kohn-Sham equations based on the density equation theory. The present formulation relies on neither action functionals nor force balance equation. but is constructed by comparing the first-order density equation for the electron interacting real system and that for the electron non-interacting Kohn Sham system. The derived inverse Kohn-Sham integral equation requires information of an exact ground-state electron density to calculate an exact Kohn-Sham potential for a ground state and it requires an exact time-dependent electron density and a time-derivative of the exact time-dependent first-order density matrix to calculate an exact time-dependent Kohn-Sham potential. A possible algorithm to construct the Kohn-Sham potential for a ground state is suggested as well as a solution algorithm for the time-dependent inverse Kohn Sham problem without resorting to any approximations. These two solution algorithms, in combination, suggest a way to perform an exact time-dependent density functional calculation as a predictive method.