Ensemble approach to many-electron systems: from exact relations to practical density functional approximations
Seminar
מועמד למחלקה
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Speaker
Eli Kraisler, The Hebrew University
Date
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2026-06-25 12:30:00
2026-06-25 12:30:00
Ensemble approach to many-electron systems: from exact relations to practical density functional approximations
Density functional theory (DFT) is a leading theoretical framework used to describe the electronic structure of materials. The central approximation of the theory is that of the exchange-correlation (xc) energy functional, which is responsible for all the electron-electron interactions in the system, beyond classical electrostatic repulsion. One approach to design accurate and globally applicable functionals is by satisfying exact properties of many-electron systems. An important set of properties, in which I will focus in my talk, stems from describing a many-electron system with a varying, possibly fractional, number of electrons, N, using the ensemble approach.In my talk, I first describe how the piecewise-linearity of the energy versus N results in a sharp spatial step of the effective Kohn-Sham potential in DFT, and will share with you our recent success to accurately describe this step, using the orbital-free DFT approach [1, 2, 3].Next, I will show how the piecewise-linearity condition is generalized to spin-dependent systems. Recently [4,5], we succeeded to exactly describe the ground state of a finite, many-electron system with a fractional electron number and fractional spin S, by an ensemble of pure states, and characterize the dependence of the energy and the spin-densities on both N and S. We show which pure states contribute to the ensemble, and which states do not; we find a new type of a derivative discontinuity, which manifests in the case of spin variation at constant N, as a jump in the Kohn-Sham potential. We demonstrate this property in approximate DFT calculations with hybrid xc approximations [6] and discuss deviations of common approximations from the expected exact behavior. Interestingly, for fractional N and S, we find a previously unknown ambiguity in the ground state description, where the total energy and density are unique, but e.g. 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.[1] E. Kraisler, M. J. P. Hodgson and E. K. U. Gross, From Kohn-Sham to many-electron energies via step structures in the exchange-correlation potential, J. Chem. Theory Comput. 17, 1390 (2021)[2] E. Kraisler, A. Schild, Discontinuous behavior of the Pauli potential in density functional theory as a function of the electron number, Phys. Rev. Research 2, 013159 (2020)[3] N. E. Rahat, E. Kraisler, Plateaus in the potentials of density-functional theory: analytical derivation and useful approximations, J. Chem. Theory Comput. 21, 3476 (2025)[4] Y. Goshen, E. Kraisler, Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized, J. Phys. Chem. Lett. 15, 2337 (2024)[5] Y. Goshen, E. Kraisler, Many-electron systems with fractional electron number and spin: Exact properties above and below the equilibrium total spin value, J. Chem. Phys. 164, 104109 (2026)[6] A. Hayman, N. Levy, Y. Goshen, M. Fraenkel, E. Kraisler, T. Stein, Spin migration in density functional theory: energy, potential and density perspectives, J. Chem. Phys. 162, 114301 (2025)
Resnick
המחלקה לפיזיקה
physics.dept@mail.biu.ac.il
Asia/Jerusalem
public
Place
Resnick
Abstract
Density functional theory (DFT) is a leading theoretical framework used to describe the electronic structure of materials. The central approximation of the theory is that of the exchange-correlation (xc) energy functional, which is responsible for all the electron-electron interactions in the system, beyond classical electrostatic repulsion. One approach to design accurate and globally applicable functionals is by satisfying exact properties of many-electron systems. An important set of properties, in which I will focus in my talk, stems from describing a many-electron system with a varying, possibly fractional, number of electrons, N, using the ensemble approach.
In my talk, I first describe how the piecewise-linearity of the energy versus N results in a sharp spatial step of the effective Kohn-Sham potential in DFT, and will share with you our recent success to accurately describe this step, using the orbital-free DFT approach [1, 2, 3].
Next, I will show how the piecewise-linearity condition is generalized to spin-dependent systems. Recently [4,5], we succeeded to exactly describe the ground state of a finite, many-electron system with a fractional electron number and fractional spin S, by an ensemble of pure states, and characterize the dependence of the energy and the spin-densities on both N and S. We show which pure states contribute to the ensemble, and which states do not; we find a new type of a derivative discontinuity, which manifests in the case of spin variation at constant N, as a jump in the Kohn-Sham potential. We demonstrate this property in approximate DFT calculations with hybrid xc approximations [6] and discuss deviations of common approximations from the expected exact behavior. Interestingly, for fractional N and S, we find a previously unknown ambiguity in the ground state description, where the total energy and density are unique, but e.g. 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.
[1] E. Kraisler, M. J. P. Hodgson and E. K. U. Gross, From Kohn-Sham to many-electron energies via step structures in the exchange-correlation potential, J. Chem. Theory Comput. 17, 1390 (2021)
[2] E. Kraisler, A. Schild, Discontinuous behavior of the Pauli potential in density functional theory as a function of the electron number, Phys. Rev. Research 2, 013159 (2020)
[3] N. E. Rahat, E. Kraisler, Plateaus in the potentials of density-functional theory: analytical derivation and useful approximations, J. Chem. Theory Comput. 21, 3476 (2025)
[4] Y. Goshen, E. Kraisler, Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized, J. Phys. Chem. Lett. 15, 2337 (2024)
In my talk, I first describe how the piecewise-linearity of the energy versus N results in a sharp spatial step of the effective Kohn-Sham potential in DFT, and will share with you our recent success to accurately describe this step, using the orbital-free DFT approach [1, 2, 3].
Next, I will show how the piecewise-linearity condition is generalized to spin-dependent systems. Recently [4,5], we succeeded to exactly describe the ground state of a finite, many-electron system with a fractional electron number and fractional spin S, by an ensemble of pure states, and characterize the dependence of the energy and the spin-densities on both N and S. We show which pure states contribute to the ensemble, and which states do not; we find a new type of a derivative discontinuity, which manifests in the case of spin variation at constant N, as a jump in the Kohn-Sham potential. We demonstrate this property in approximate DFT calculations with hybrid xc approximations [6] and discuss deviations of common approximations from the expected exact behavior. Interestingly, for fractional N and S, we find a previously unknown ambiguity in the ground state description, where the total energy and density are unique, but e.g. 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.
[1] E. Kraisler, M. J. P. Hodgson and E. K. U. Gross, From Kohn-Sham to many-electron energies via step structures in the exchange-correlation potential, J. Chem. Theory Comput. 17, 1390 (2021)
[2] E. Kraisler, A. Schild, Discontinuous behavior of the Pauli potential in density functional theory as a function of the electron number, Phys. Rev. Research 2, 013159 (2020)
[3] N. E. Rahat, E. Kraisler, Plateaus in the potentials of density-functional theory: analytical derivation and useful approximations, J. Chem. Theory Comput. 21, 3476 (2025)
[4] Y. Goshen, E. Kraisler, Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized, J. Phys. Chem. Lett. 15, 2337 (2024)
[5] Y. Goshen, E. Kraisler, Many-electron systems with fractional electron number and spin: Exact properties above and below the equilibrium total spin value, J. Chem. Phys. 164, 104109 (2026)
[6] A. Hayman, N. Levy, Y. Goshen, M. Fraenkel, E. Kraisler, T. Stein, Spin migration in density functional theory: energy, potential and density perspectives, J. Chem. Phys. 162, 114301 (2025)
תאריך עדכון אחרון : 18/06/2026
