What is it about?
In a recent study, the authors have proposed an integral equation for solving the inverse Kohn-Sham problem. The integral equation is numerically solved for the one-dimensional model of a He atom and an H2 molecule in the electronic ground states (T. Kato, K. Nobusada, S. Saito, J. Phys. Soc. Jpn. 2020, 89, 024301-1-15). To quantify the numerical accuracy of the calculated exchange-correlation potentials, we evaluate the exchange and correlation energies based on the virial theorem and the reproduction of the exact ground-state electronic energy.
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Why is it important?
The formulation relies on neither variational principle nor force balance equation. Our inverse Kohn-Sham integral equation is explicitly shown to be equivalent to a set of Kohn-Sham equations to reproduce an electron density. Thus, our approach is different from any previously proposed theory.
Perspectives
We notice the significance of obtaining the exact exchange-correlation energy for the ground state as a functional of the given exact electron density, because by using the electron density and the exchange-correlation energy associated with the ground state as the initial conditions, the time-dependent problem can, in principle, be solved.
Associate Professor Tsuyoshi Kato
The University of Tokyo
Read the Original
This page is a summary of: Kohn–Sham
potentials by an inverse
Kohn–Sham
equation and accuracy assessment by virial theorem, Journal of the Chinese Chemical Society, September 2022, Wiley,
DOI: 10.1002/jccs.202200355.
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