A generalized gradient approximation for exchange derived from the model potential of van Leeuwen and Baerends

Self-consistent electron density with shell structure using neural network-based Pauli potential

The orbital-free density functional theory (OF-DFT) based method is a convenient tool to carry out electronic structure calculations scaling almost linearly with the number of electrons. However, the main impediment in the application of this method is the unavailability of the accurate form for the non-interacting kinetic energy functional in terms of electron density. The Pauli kinetic energy functional is the unknown part of the kinetic energy functional, and the corresponding Pauli potential appears in the governing Euler equation. In the present study, we present a feed-forward neural network (NN) approach to represent the Pauli potential of a group of atomic systems possessing spherically symmetric ground-state densities. This NN-based representation of Pauli potential combined with the Hohenberg-Kohn variational principle yields self-consistent radial densities that accurately exhibit the correct atomic shell structure. For this approach, the electron density in the form of a grid serves as the input to the NN model. In addition, we calculated the non-interacting kinetic energy by summing the Pauli kinetic energy, derived from the NN-based Pauli potential, and the von Weizsäcker kinetic energy. Our results demonstrate high accuracy for smaller atoms, while larger atoms exhibit greater deviations when compared with smaller atoms. The method presented in this paper provides an efficient way to calculate the Pauli potential and the Pauli kinetic energy without the need for functional derivatives. Our study represents a significant step forward in the application of machine learning techniques to OF-DFT, showcasing the potential of NNs in improving the accuracy and efficiency of quantum mechanical calculations in atomic systems.

Strong Correlations in Density-Functional Theory: A Model of Spin-Charge and Spin-Orbital Separations

It is known that the separation of electrons into spinons and chargons, the spin-charge separation, plays a decisive role when describing one-dimensional (1D) strongly correlated systems [ Phys. Rev. B 2012 , 86 , 075132 ]. In this paper, within the density-functional theory (DFT) formalism, we extend the investigation by considering a model for the third electron fractionalization: the separation into spinons, chargons and orbitons, the last associated with the electronic orbital degree of freedom. Specifically, we deal with two exact constraints of exchange-correlation (XC) density-functionals: (i) the constancy of the highest occupied (HO) Kohn-Sham (KS) eigenvalues upon fractional electron numbers and (ii) their discontinuities at integers. By means of 1D discrete Hubbard chains and 1D H2 molecules in the continuum, we find that spin-charge separation yields almost constant HO KS eigenvalues, whereas the spin-orbital counterpart can be decisive when describing derivative discontinuities of XC potentials at strong correlations.