Designing explicit functionals for the charge density in terms of a potential
Abstract
One of the most powerful strategies to address properties of real many-body systems is to incorporate data obtained for models, for example, to use data of the homogeneous electron gas in order to build the local density approximation for the Kohn-Sham exchange-correlation potential. In the present work, we examine to what extent we can use model data to design functionals directly for observables of materials. In particular, we study different approximations for the charge density of real inhomogeneous materials expressed as a simple, explicit functional of a given Kohn-Sham potential, using as a central building block the Lindhard density-density response function of the homogeneous electron gas. Our increasingly realistic set of approximations includes a fully nearsighted expression equivalent to the Thomas-Fermi approximation, functional Taylor expansions, and different approximations to the connector theory developed by A. Aouina et al. [npj Comput. Mater. 11, 242 (2025)]. In all cases, the charge density is obtained without ever solving the Kohn-Sham Schrödinger equation. Results for cubic helium, a prototypical strongly inhomogeneous material, as well as the covalent semiconductor silicon and metallic aluminum, systematically improve with higher levels of approximation. At the present stage, the results may be used for qualitative discussions or as an optimized starting point for a self-consistent Kohn-Sham cycle. More generally, their quality indicates that this is a promising route to obtain functional expressions for observables that are relatively simple to calculate and to analyze.
Related
- Boundedness of the Density of Wiener Functionals with Low Regularity
- Explicit charge-conserving and modified energy-conserving PIC methods using the SAV approach
- Density functionals for the Pauli-Fierz Hamiltonian
- Spatially explicit capture–recapture models for relative density
- High-order Energy-stable and Charge-conservative Lagrangian FEM for 3D Incompressible Inductionless MHD equations with Variable Density
BibTeX
@article{gunes2026designing,
title = {{Designing explicit functionals for the charge density in terms of a potential}},
author = {Muhammed Güneş and Ayoub Aouina and Vitaly Gorelov and Matteo Gatti and Lucia Reining},
journal = {Physical Review B},
year = {2026},
month = oct,
doi = {10.1103/zztt-z1wj},
eprint = {2605.02492},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05734177v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Designing explicit functionals for the charge density in terms of a potential
AU - Muhammed Güneş
AU - Ayoub Aouina
AU - Vitaly Gorelov
AU - Matteo Gatti
AU - Lucia Reining
PY - 2026
DA - 2026/10/21
JO - Physical Review B
DO - 10.1103/zztt-z1wj
UR - https://hal.science/hal-05734177v1
AB - One of the most powerful strategies to address properties of real many-body systems is to incorporate data obtained for models, for example, to use data of the homogeneous electron gas in order to build the local density approximation for the Kohn-Sham exchange-correlation potential. In the present work, we examine to what extent we can use model data to design functionals directly for observables of materials. In particular, we study different approximations for the charge density of real inhomogeneous materials expressed as a simple, explicit functional of a given Kohn-Sham potential, using as a central building block the Lindhard density-density response function of the homogeneous electron gas. Our increasingly realistic set of approximations includes a fully nearsighted expression equivalent to the Thomas-Fermi approximation, functional Taylor expansions, and different approximations to the connector theory developed by A. Aouina et al. [npj Comput. Mater. 11, 242 (2025)]. In all cases, the charge density is obtained without ever solving the Kohn-Sham Schrödinger equation. Results for cubic helium, a prototypical strongly inhomogeneous material, as well as the covalent semiconductor silicon and metallic aluminum, systematically improve with higher levels of approximation. At the present stage, the results may be used for qualitative discussions or as an optimized starting point for a self-consistent Kohn-Sham cycle. More generally, their quality indicates that this is a promising route to obtain functional expressions for observables that are relatively simple to calculate and to analyze.
SN - 2469-9950
SN - 2469-9969
ER -