Improvement of functionals in density functional theory by the inverse Kohn–Sham method and density functional perturbation theory

Abstract

We propose a way to improve energy density functionals (EDFs) in the density functional theory based on the combination of the inverse Kohn-Sham method and the density functional perturbation theory. Difference between the known EDF and the exact one is treated as the first-order perturbation. As benchmark calculations, we reproduce the theoretical exchange and correlation functionals in the local density approximation. Systems of noble-gas atoms are used for benchmark calculations, and the ground-state energies and densities, as well as the functionals, are reproduced with good accuracies.

Toward ab initio charge symmetry breaking in nuclear energy density functionals

“…To make a link to microscopic approaches of EDFs, ab initio determination of such parameters is highly motivated [2,[18][19][20][21][22][23][24][25][26][27]. To attain such a goal, novel methods using functional renormalization group [28][29][30][31][32][33][34][35][36] and inverse Kohn-Sham method [37][38][39] have also been proposed, although these attempts are still limited.…”

Insight For The Construction of R-T Phase Boundary in KNN Piezoceramics From The View of Energy Band Structure

“…The basic idea is that the physical properties of the ground state of atoms, molecules and solids can be described by the particle number density function, and the ground state of the system is the state in which the energy functional takes the minimum value under the condition of constant particle number. [11,12] This not only provides a theoretical basis for simplifying the multi-electron problem into a single electron problem but also does not need to rely on any empirical parameters. The atomic and electronic structures and related physical properties of materials can be obtained by solving the intrinsic quantum mechanical equations.…”

The complete inverse Kohn-Sham problem: from the density to the energy

“…[6][7][8][9]. This topic has recently encountered a renewed interest both in quantum chemistry [10][11][12][13][14] and in nuclear physics [15,16] (our group had undertaken preliminary steps before Ref. [15], cf.…”

“…[22] it has been shown that training a neural network EDF not only on energies, but also on potentials, greatly improves its performances, at least in a simplified one-dimensional framework. A different line of research combines density functional perturbation theory (DFPT), where an ansatz for the EDF functional form must be assumed, and IKS to improve the initial model towards the exact EDF [11,16]. Illustrative calculations have been performed in the case of covariant nuclear DFT [16].…”