Time-dependent Internal DFT formalism and Kohn-Sham scheme

TL;DR

This paper extends the Internal DFT/Kohn-Sham formalism to time-dependent systems, enabling the calculation of internal properties of self-bound systems like atomic nuclei through a new scheme that accounts for center-of-mass correlations.

Contribution

It introduces a time-dependent Internal Kohn-Sham scheme and proves that internal properties depend solely on the internal density and initial state.

Findings

Formal proof of internal property dependence on internal density and initial state

Development of a practical time-dependent Internal Kohn-Sham scheme

Inclusion of center-of-mass correlations in the functional

Abstract

We generalize to the time-dependent case the stationary Internal DFT / Kohn-Sham formalism presented in Ref. [14]. We prove that, in the time-dependent case, the internal properties of a self-bound system (as an atomic nuclei) are all defined by the internal one-body density and the initial state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way to compute the internal density. The main difference with the traditional DFT / Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the functional.