Many-electron systems with fractional electron number and spin: exact properties at low and high spin values
ORAL
Abstract
It is important to accurately describe a general many-electron system, be it an atom, a molecule or a nanoparticle, even when the total number of electrons, Ntot, and the (z-projection of) the spin, Mtot, is fractional. In this talk, I address the fundamental question of what is the ensemble ground state of a general, finite, many-electron system at zero temperature, with a given Ntot and Mtot, distinguishing between low- and high-spin cases (separated by the boundary spin MB). For the low-spin case, the general form of the ensemble ground state has been rigorously derived by us in J. Phys. Chem. Lett. 15, 2337 (2024), generalizing the piecewise-linearity and the flat-plane conditions for many-electron systems. Here I discuss the ambiguity we discovered in the description of the ground state and suggest removing this ambiguity via maximization of the system’s entropy.
For the high-spin case, we recently found that the form of the ensemble ground state strongly depends on the system in question. We succeeded to prove three general properties, which characterize the ground state at high spins and narrow down the list of pure states it may consist of. Furthermore, we relate the frontier orbital energies of Kohn-Sham (KS) density functional theory (DFT) to total energy differences at high spin values, particularly the ionization potential (IP), the electron affinity and the spin flip energies. Analyzing the frontier energy levels on both sides of each boundary in the total energy profile, where the energy slope changes abruptly, we derive expressions for new derivative discontinuities, which are predicted to appear as jumps in the corresponding KS potentials. In this way, we generalize the well-known IP theorem of DFT to cases with fractional electron number and to cases with high spin. The new exact conditions for many-electron systems derived in this work are instrumental for development of advanced approximations in DFT and in other many-electron methods, both in the standard, analytical way, and by employment of Machine-Learning (ML) algorithms.
For the high-spin case, we recently found that the form of the ensemble ground state strongly depends on the system in question. We succeeded to prove three general properties, which characterize the ground state at high spins and narrow down the list of pure states it may consist of. Furthermore, we relate the frontier orbital energies of Kohn-Sham (KS) density functional theory (DFT) to total energy differences at high spin values, particularly the ionization potential (IP), the electron affinity and the spin flip energies. Analyzing the frontier energy levels on both sides of each boundary in the total energy profile, where the energy slope changes abruptly, we derive expressions for new derivative discontinuities, which are predicted to appear as jumps in the corresponding KS potentials. In this way, we generalize the well-known IP theorem of DFT to cases with fractional electron number and to cases with high spin. The new exact conditions for many-electron systems derived in this work are instrumental for development of advanced approximations in DFT and in other many-electron methods, both in the standard, analytical way, and by employment of Machine-Learning (ML) algorithms.
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Publication: [1] Yuli Goshen and Eli Kraisler, "Ensemble ground state of a many-electron system with fractional electron number and spin: Piecewise-linearity and flat-plane condition generalized", J. Phys. Chem. Lett. 15, 2337 (2024)
[2] Yuli Goshen and Eli Kraisler, "Many-electron systems with fractional electron number and spin:
exact properties above and below the equilibrium total spin value", in preparation.
Presenters
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Eli Kraisler
- Hebrew University of Jerusalem