arXiv subjects

Yuli Goshen

Publications and source records attributed to Yuli Goshen.

3 recordsLinked to original sources

arXiv2026

Many-electron systems with fractional electron number and spin: exact properties above and below the equilibrium total spin value

In this work, we analyze the fundamental question of what is the ensemble ground state of a general, finite, many-electron system at zero temperature, with a given, possibly fractional, electron number $N_{tot}$ and a given $z$-projection of the spin, $M_{tot}$, distinguishing between low- and high-spin cases. For the low-spin case, the general form of the ensemble ground state has been rigorously derived in J. Phys. Chem. Lett. 15, 2337 (2024), finding the presence of an ambiguity in the ground state. Here we further discuss this ambiguity, and show that it can be removed via maximization of the entropy. For the high-spin case, we find that the form of the ensemble ground state strongly depends on the system in question. Furthermore, we prove three general properties which characterize the ensemble, and narrow the list of pure states it may consist of. We relate the frontier Kohn-Sham orbital energies to total energy differences, providing a generalization of the ionization potential theorem to systems with arbitrary fractional $M_{tot}$. Furthermore, we derive expressions for new derivative discontinuities, which appear as jumps in the KS potentials when crossing a boundary in the $N_{\uparrow}$-$N_{\downarrow}$ plane. Our analytical results are supported by an extensive numerical analysis of the Atomic Spectra Database of the National Institute of Standards. The new exact conditions for many-electron systems derived in this work are instrumental for development of advanced approximations in density functional theory and other many-electron methods.

cond-mat.mtrl-sci↗

arXiv2024

Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized

Description of many-electron systems with a fractional electron number $N_\textrm{tot}$ and fractional spin $M_\textrm{tot}$ is of great importance in physical chemistry, solid state physics and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system, and characterize the dependence of the energy and the spin-densities on both $N_\textrm{tot}$ and $M_\textrm{tot}$, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at constant $N_\textrm{tot}$, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

cond-mat.mtrl-sci↗

arXiv2023

Ionization Potentials and Fundamental Gaps in Atomic Systems from the Ensemble-DFT Approach

Calculations in Kohn-Sham density functional theory crucially rely on high-quality approximations for the exchange-correlation (xc) functional. Standard local and semi-local approximations fail to predict the ionization potential (IP) and the fundamental gap, departing from the Kohn-Sham orbital energies, due to the deviation of the total energy from piecewise-linearity and the absence of the derivative discontinuity. The ensemble generalization procedure introduced in Phys. Rev. Lett. 110, 126403 (2013) restores, to a large extent, these features in any approximate xc functional and improves its ability to predict the IP and the fundamental gap with negligible additional computational effort. In this work we perform an extensive study of atoms and first ions across the Periodic Table, generalizing the local spin-density and the Perdew-Burke-Ernzerhof approximations. By applying the ensemble generalization to a variety of systems, with s-, p- and d-character, we assess the accuracy of the method and identify important trends. In particular, we find that the accuracy of our approach heavily depends on the character of the frontier orbitals: when d-orbitals are involved, the performance is far less accurate. Possible sources of error are discussed and ways for further improvement are outlined.

cond-mat.mtrl-sci↗